目录

牛津通识课：黑洞

牛津通识课：光

牛津通识课：行星

牛津通识课：引力

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Black Holes: A Very Short Introduction

Copyright:© Katherine Blundell 2015

Black Holes: A Very Short Introduction was originally published in English in 2015. This

translation is published by arrangement with Oxford University Press. Dook Media Group Limited

is solely responsible for this translation from the original work and Oxford University Press shall

have no liability for any errors, omissions or inaccuracies or ambiguities in such translation or for

any losses caused by reliance thereon

中文版权：©2020 读客文化股份有限公司

经授权，读客文化股份有限公司拥有本书的中文（简体）版权

版权所有，不得翻印

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图书在版编目（C I P）数据

牛津通识课. 黑洞 / [英] 凯瑟琳·玛丽·布伦德尔

著 ; 张建东译. -- 海口 : 海南出版社，2020.4

书名原文：Black Holes: A Very Short

Introduction

ISBN 978-7-5443-9273-0

Ⅰ. ①牛… Ⅱ. ①凯… ②张… Ⅲ. ①科学知识 - 普

及读物 ② 黑洞 - 普及读物 Ⅳ. ① Z228 ② P145.8-49

中国版本图书馆CIP数据核字 (2020) 第061524号

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牛津通识课：黑洞、光、行星、引力

作 者 [英] 凯瑟琳·玛丽·布伦德尔 [英] 伊恩·沃尔姆斯利

作 者 [英] 戴维·罗瑟里 [英] 蒂莫西·克利夫顿

译 者 张建东 叶昊扬 周应秋 刘 悦 颜子昂

责任编辑 杨 艳 陈 波

执行编辑 徐雁晖

封面设计 读客文化 021-33608311

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版 次 2020年4月第1版

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定 价 120.00元（全四册）

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版权所有，侵权必究

献给蒂姆和路易斯·桑德斯，我深爱着你们。

致谢

菲利普·欧科克、罗素·欧科克、史蒂文·巴尔拜斯、罗杰·布兰德福特、史蒂芬·布伦德尔、史蒂芬·贾斯姆、汤姆·兰开斯特、拉莎·梅农、约翰·米勒和保罗·托德为本书的草稿提供了很多有用的意见。史蒂芬·布伦德尔为本书制作了图表。斯蒂文·李协助进行了光学观测。我对他们表示衷心的感谢。

凯瑟琳·玛丽·布伦德尔

KMB

牛津大学

2015年4月

目录

01 黑洞是什么 What Is a Black Hole？

02 游览时空 Navigating Through Spacetime

03 黑洞的特征 Characterizing Black Holes

04 落入黑洞…… Falling Into a Black Hole

05 黑洞的熵和热力学 Entropy and Thermodynamics of Black Holes

06 你怎样给黑洞称重 How Do You Weigh a Black Hole?

07 吃得更多，长得更大 Eating More and Growing Bigger

08 黑洞和副产品 Black Holes and Spin-offs

索引

Acknowledgements

Chapter 1 What is a black hole?

Chapter 2 Navigating through spacetime

Chapter 3 Characterizing black holes

Chapter 4 Falling into a black hole . . .

Chapter 5 Entropy and thermodynamics of black holes

Chapter 6 How do you weigh a black hole?

Chapter 7 Eating more and growing bigger

Chapter 8 Black holes and spin-offs

Further reading

Index

01 黑洞是什么 What Is a Black Hole？

黑洞就是一个引力很强的空间区域。任何东西——甚至连光——都因为不够快，不能从其内部逃离。虽然这一概念最初是在理论物理学家丰富的想象中被构思出来的，但现在我们已经在宇宙中发现了数百个黑洞，并且它们以百万计。尽管这些黑洞是不可见的，但它们以一种很容易被探测到的方式与周围环境相互作用，并对其产生影响。确切地说，这种相互作用的性质取决于相对黑洞的距离：太近的话是不能逃脱的，但更远的地方就会出现一些戏剧性的壮观现象。

1964年，安·尤因(Ann Ewing)在一篇报道1963年于得克萨斯州举办的一个研讨会的文章中首次提到了“黑洞”一词，然而她从未说明是谁发明了这个词。1967年，美国物理学家约翰·惠勒(John Wheeler)需要一个词作为“引力坍缩彻底的恒星”的简写，于是开始推广这个术语——不过坍缩的恒星这一概念早在1939年就由他的美国同事罗伯特·奥本海默(Robert Oppenheimer)和哈特兰·斯奈德(Hartland Snyder)提出来了。事实上，关于现代黑洞概念的数学基础在1915年就已经诞生了。德国物理学家卡尔·史瓦西(Karl Schwarzschild)在空间中有孤立无转动的质量的条件下解出了爱因斯坦的重要方程(在他的广义相对论中被称为场方程)。

在此之后过了20年，印度物理学家苏布拉马尼扬·钱德拉塞卡(Subrahmanyan Chandrasekhar)研究了恒星死亡时会发生什么。以此为基础，英国的亚瑟·爱丁顿爵士(Sir Arthur Eddington)解决了一些相关的数学问题——比奥本海默和斯奈德的工作稍早一点。爱丁顿的计算表明，当大质量恒星耗尽所有燃料时会坍缩形成黑洞，不过爱丁顿自己在1935年向皇家天文学会宣称其物理含义是“荒谬的”。尽管这个概念看起来荒谬，但黑洞无疑是我们的银河系乃至整个宇宙物理现实的重要组成部分。1958年，美国的大卫·芬克尔斯坦(David Finkelstein)取得了更进一步的进展，他明确了黑洞周围存在一个单向表面。这对于我们将在下一章中讨论的内容具有重要的意义。这个表面的存在不允许光从黑洞内部强大的引力中脱离，而这也是黑洞是黑色的原因。要理解这种现象是如何产生的，我们首先要理解物理世界的一个深刻的特性：任何运动的粒子或物体都存在一个最大速度。

快是有多快

丛林法则之一是：不想死得快，就得跑得快。除非你异常狡猾或者善于伪装，否则只有足够敏捷才能存活下来。哺乳动物摆脱劣势的最大速度取决于其质量、肌肉力量和新陈代谢之间复杂的生化关系。宇宙中运动最快的实体所能达到的最大速度是由完全没有质量的粒子所呈现的，例如光的粒子(被称为光子
)。这个最大速度被精确地定为每秒299 792 458米，相当于每秒186 282英里，几乎比空气中的音速快100万倍。如果能以光速旅行，我将能够在十四分之一秒内从我在英国的家中到达澳大利亚，就是一瞬间的事情。从离我们最近的恒星，也就是太阳出发的光只需要8分钟就可以到达我们这里。而从太阳系最外层的行星海王星出发，光子到地球的行程时间也只有几个小时。我们说太阳离地球有8光分，而海王星离我们有几光时。这会导致一个有趣的后果，如果太阳停止发光或海王星突然变成紫色，地球上的任何人发现这些重要信息都分别需要花上8分钟或几小时。

现在让我们来考虑光线从太空中更加遥远的地方传回地球的时间有多长。我们的太阳系所在的银河系是一个长达几十万光年
的星系。这意味着光从银河系的一侧行进到另一侧需要几十万年。离本星系群(银河系是其中的重要成员)最近的星系团，

也就是天炉座星系团，离我们有几亿光年。因此，

在围绕天炉座星系团中的某颗恒星运行的行星上如果有一位观察者，手头配备了恰当的仪器回看地球，可能会看到恐龙在地球上徘徊。不过这只是由于宇宙浩瀚得令人难以置信，才使得光的运动看起来迟缓且费时。但当我们开始考虑如何将火箭发射到太空时，宇宙规定光速是上限这一点就会带来一种有趣的效应。

逃逸速度

如果我们希望将火箭送到太空但发射速度太慢，那么火箭将没有足够的动能
来挣脱地球的引力场。反之，如果火箭的速度恰好足以逃离地球引力的拉扯，我们就说它已达到了逃逸速度
。火箭从诸如行星之类的大质量物体上逃离时，行星质量越大，火箭距行星的质心
越近，逃逸速度也就越大。逃逸速度Vesc
可以写成
，其中M是行星的质量，R是火箭与行星质心的距离，而G是被称为牛顿引力常数的自然常数。重力作用总是将火箭拉向行星或恒星的中心，朝向被称为质心
的点。不过，逃逸速度的取值与火箭的质量完全无关。因此，不论其内部载荷是几根羽毛还是几台三角钢琴，从距离地球质心约6400千米的卡纳维拉尔角发射的火箭都具有相同的逃逸速度，也就是11千米/秒多一点或约为声速的34倍(可以写为34马赫)。现在假设我们可以压缩地球的全部质量，使它占据更小的体积，假定它的半径变为其当前的四分之一。如果火箭发射处距离质心6400千米，其逃逸速度将保持不变。然而，如果它重新放到距质心1600千米的压缩后的地球的新表面，那么逃逸速度将会是原始值的两倍。

现在假设某些灾难的发生导致地球的全部质量都收缩到了一个点，我们把这样的物体称为奇点
。它现在已经成了一个“质点”，一个占据空间体积为零的有质量物体。在距这个奇点只有1米左右的地方，逃逸速度将远大于在1600千米处的取值(实际上将约为光速的10％)。离奇点更近，略小于1厘米的地方，逃逸速度将等于光速。在这个距离上，光本身没有足够的速度来逃离引力的拉扯。这是理解黑洞性质的关键思想。

对“奇点”一词的用法值得明确。我们不相信在持续的引力坍缩的终点，物质会变成某个几何点；正相反，我们会发现经典引力理论失效并进入量子体系。从这里开始，我们将使用术语奇点来指代这种极其致密的状态。

事件视界

现在想象你是一名驾驶宇宙飞船的宇航员，并且正在接近这个奇点。当距离它还有一段距离时，你可以随时将发动机反转并逃之夭夭。但是距离越近，就越难体面地撤离。最终你会到达一个无论装载的发动机有多强大都无法逃脱的距离。这是因为你已经到达了事件视界
，这是一个用数学方式来定义的球面，它也被定义为内部逃逸速度超过光速的边界。对于我们关于地球坍缩到一个点的思想实验而言，这个表面将是一个以奇点为中心，半径只有1厘米的球面，这对我们的太空船来说可能很容易避开。然而当黑洞由恒星而不是行星坍缩形成时，事件视界会变得更大。事件视界有一个重要的物理效应：如果你在那个表面之上或者里面的话，物理定律根本不允许你逃离，因为这样做你需要打破普适的速度限制。事件视界是一个强制性的标界：在它之外你有决定你命运的自由，而在它之内你的未来将被锁在里面，不可改变。

这个球面半径被称为史瓦西半径，是为了纪念前面提到的卡尔·史瓦西。作为第一次世界大战中的一名士兵，史瓦西得到了广义相对论中著名的爱因斯坦场方程的第一个精确解。史瓦西半径写为Rs
=2GM/c^2
，其中M是黑洞的质量，G是牛顿引力常数，c是光速。根据这个公式，地球的史瓦西半径还不到1厘米。以此类推，太阳的史瓦西半径为3公里，这意味着如果我们的太阳被压缩成奇点，那么距这一点仅3公里之处的逃逸速度就将等于光速。一个质量是太阳质量10亿倍的黑洞(具有10^9
太阳质量)将使史瓦西半径扩大10亿倍(一个无旋转的点质量的史瓦西半径与其质量成正比)。正如我将在第6章中所描述的那样，这些巨大的黑洞被认为存在于很多星系的中心。

在牛顿物理学中，这种对事件视界的描述是合理的。事实上，在爱因斯坦和其他我们提到的人之前几个世纪，类似黑洞的物理实体是被想象出来的，而它们深刻地改变了我们对空间和时间的理解。最早想象出类似黑洞的“暗星
”的人是18世纪的约翰·米歇尔(John Michell)和皮埃尔·西蒙·拉普拉斯(Pierre Simon Laplace)，而现在我将解释他们做了什么。

天文学的一个非凡之处在于，即使你被困在地球上也能发现关于宇宙的很多事情。例如，没有人曾经游览过太阳，然而在19世纪后期通过分析太阳光谱探测到了太阳中存在的氦。需要特别注意的是，这也是氦元素本身被第一次发现；它在太阳上被发现的时间要比在地球上被探测到早得多。在更早的18世纪，关于黑洞背后的一些想法就开始形成了，特别是关于所谓的暗星的概念。人在很大程度上是他那个时代的产物，那些饱含奇思妙想、迈出第一步的人都是这样。

约翰·米歇尔

英格兰的乔治王时代是一个相对和平的年代。英国内战是过去很久的事情了，英格兰已经成为一个内部相对安宁的国度(距拿破仑在法国的崛起还有一段时间)。约翰·米歇尔(图1)和他的父亲一样，作为牧师接受了大学教育并加入了英格兰教会。作为西约克郡桑希尔的教区长，米歇尔能够继续他的科学研究，把他对地质学、磁学、重力学、光学和天文学的兴趣贯彻下去。与当时在英国工作的其他科学家同样——比如天文学家威廉·赫歇尔(William Herschel)和物理学家亨利·卡文迪许(Henry Cavendish)(米歇尔的密友)——米歇尔能够顺应新的牛顿式思想的潮流。艾萨克·牛顿爵士(Sir Isaac Newton)通过构想出他的引力定律，彻底改变了人们对宇宙的理解。这个定律解释了太阳系中行星的轨道与他那颗从树上掉落的著名苹果，是受到了相同的力的作用。

图1　约翰·米歇尔，博学家

牛顿的思想允许用数学来研究宇宙，而新一代的科学家们也能够将这种新颖的世界观运用到不同的领域。米歇尔特别关注的是利用牛顿的思想，通过测量邻近恒星发出的光来估计地球与它们之间的距离。为此，他想出了各种方案来做到这一点，比如将恒星的亮度与其颜色联系起来；此外他还考虑了双星
(一对处于对方引力束缚中的恒星)以及它们的轨道运动如何给出有用的动力学信息。米歇尔研究了恒星在天空中特定区域的聚集情况，他将此与随机分布进行对比、检验并推断出聚集的原因是引力成团。这些想法没有一个在当时是切实可行的：人们知道的双星很少(虽然赫歇尔正在制作令人印象深刻的关于许多双星和新天体的目录)，而且恒星的亮度和颜色之间的关系也并非尽如米歇尔所认为的那样。不过米歇尔尽力对更广阔的宇宙做了牛顿对太阳系所做的事情：对观测进行科学、合理和动态的分析，以此提供关于天体的性质、质量和距离的新信息。

米歇尔一个洞若观火的观点来自这样一个思想实验：用他的话说，就是光的粒子以“与我们熟悉的所有物体相同的方式被吸引；也就是说，受到与它们的惯性(他的意思是质量)成正比的力。据我们所知，目前还没有任何理由怀疑或相信，万有引力是一个普适的自然定律”。他推断，这些由大恒星发出的光粒子会受恒星引力的吸引而减速。因此到达地球的星光会更慢。牛顿已经证明了光在玻璃中会减速，而这解释了折射的原理。米歇尔推论出如果星光确实也会减速，那么用棱镜来探测星光就可能会观测到这种减速效应。实验是由皇家天文学家牧师内维尔·马斯基林(Nevil Maskelyne)博士而不是米歇尔做的，他希望观察到星光折射能力的减弱。卡文迪许写信告诉米歇尔这并没有什么效果，而且“几乎不太可能找到光线被显著减弱的恒星”。米歇尔感到沮丧，但是这种天文学推断很大程度上需要对不可估量的事情的猜测：星光会受到发射出它的恒星的引力影响吗？米歇尔无法确定。但他大胆地作出了一个有趣的预测。

如果一颗恒星的质量足够大，并且引力确实会影响到星光，那么引力就足以完全控制住光粒子并防止它们逃逸。这样的物体将是一颗暗星
。这样，这个在约克郡的教区中写作的鲜为人知的牧师就成了第一个构想出黑洞的人。然而在那时，米歇尔自己测量到恒星距离的程序还不完善。更重要的是，他此前一直对自己的健康漠不关心，这令他无法继续使用望远镜。卡文迪许给他写了一封信安慰他：“如果你的健康状况不允许你继续使用(望远镜)，我希望它至少可以让你更轻松省力地权衡(称量)这个世界。”卡文迪许这唯一的笑话(他以沉默寡言而闻名)指的是米歇尔得到的另一个思想实验。“称量世界”是让扭秤横梁两端的两个大铅球被两个固定的铅球所吸引。人们可以用测量引力强度的方法，推断出地球的重量。从来没有人这样做过。米歇尔的想法非常棒，但他生前并没有完成这个实验。米歇尔的实验后来由卡文迪许代劳，而且现在被称为卡文迪许实验。这一荣誉被转嫁给卡文迪许，但他也付出了更多的代价。卡文迪许没有发表自己许多具有突破性的研究，更多突破归功于后来的研究者(包括“欧姆定律”和“库仑定律”的提出)。

皮埃尔·西蒙·拉普拉斯

在英吉利海峡的另一边，皮埃尔·西蒙·拉普拉斯没享受到英国启蒙运动和平时期的宁静田园风光。拉普拉斯经历了法国大革命，不过他的职业生涯因为影响了新成立的法兰西学院和综合理工大学而蓬勃发展。有一段时间，他甚至担任过拿破仑统治下的内政部长，这是一次短暂的任命，因为皇帝后悔了。拿破仑意识到拉普拉斯是一流的数学家，但作为管理者还达不到平均水平。拿破仑后来在写到拉普拉斯时说，“他到处寻求微妙之处，只考虑问题本身，最终把‘无穷小’的精神带进了政府”。拿破仑有其他管理人员可以征召，但世界上几乎没有像拉普拉斯那样高产且富有洞察力的数学家。他在几何学、概率学、数学、天体力学、天文学和物理学方面都作出了重要贡献。他研究的主题包括毛细作用、彗星、归纳法、太阳系的稳定性、声速、微分方程和球谐函数等形形色色的方面。他考虑过的一个想法就是暗星。

1796年，拉普拉斯出版了他的《宇宙体系论
》(Exposition du système du monde)。这本书是为受过教育的知识分子撰写的，书中描述了天文学所依据的物理原理，万有引力定律和行星在太阳系中的运动方式，以及运动和力学定律。这些概念被应用于各种现象，包括潮汐和岁差，书中还包含了拉普拉斯对太阳系起源的推测。书中有那么一段与我们的故事密切相关。拉普拉斯计算出类似地球大小的物体需要多大才能使其逃逸速度等于光速。他的计算很对：当一个天体密度和地球相当但半径是太阳的250倍时，它的表面引力会让光都无法逃离。因此，他推断宇宙中最大的物体是看不见的。它们是否仍然潜伏在黑暗的夜空中无法被探测，而我们幻想“外面”只有我们能看到的那些明亮发光体？匈牙利天文学家弗兰茨·萨韦尔·冯·扎克(Franz Xaver von Zach)请求拉普拉斯提供导出这一结论的计算方法，拉普拉斯还帮忙将其(用德语)写出来并发表在冯·扎克担任编辑的一本期刊上。

后来，拉普拉斯慢慢了解到了光的波动说。米歇尔和拉普拉斯的想法都部分基于光的粒子说。如果光由微小的粒子组成，那么这些粒子会受到引力场的影响，并且将永远被束缚在质量大小足够的恒星上，这一结论似乎是合理的。但是在19世纪早期，人们看到了许多实验，这些实验似乎更能证明光的波动理论。如果光其实是波，那么就会更加难以观察到引力对它的影响。拉普拉斯对于暗星的预测在《宇宙体系论
》后来的版本中被悄然省略了。毕竟米歇尔和拉普拉斯一直在对理论进行推测和探索，而不是致力于解释观测结果，因此这个想法被遗忘了一段时间。米歇尔和拉普拉斯所想象的物体就是“暗星”，这种宇宙中的庞然大物可以凭借其质量维持行星系统，但同样凭借其压倒性的体积也使其无法通过光的辐射被观测到。从米歇尔和拉普拉斯认为的暗星表面发出的星光太过缓慢，无法克服强大的表面引力。米歇尔和拉普拉斯无法猜到的是，这种庞大的质量累积将会不稳定并坍缩。而且在它们坍缩的过程中，它们会刺穿空间和时间的结构并产生奇点。因此“黑洞”不是“暗星”，而要继续讨论下去并接触关于黑洞的天文发现，我们首先需要了解时空的本质。

时空

我们的日常经验让我们对有形宇宙可以通过一个时间坐标t和三个空间坐标[例如沿着三个相互垂直的轴x、y和z。这是由勒内·笛卡尔(RenéDescartes)发明的概念，并被称为笛卡尔坐标]。1905年，爱因斯坦发表了他关于狭义相对论的革命性论文，阐述了运动和静止的相对性。1907年，赫尔曼·闵可夫斯基(Hermann Minkowski)阐述了如何借助四维时空来更深入地理解这些结果。四维时空中由四维坐标(t、x、y、z)所确定的点对应着“事件”。这个事件是在特定时间(t)和特定地点(x、y、z)所发生的事情。所谓的闵可夫斯基时空的这种四维坐标，精确地指明了事件会在什么时间什么地点发生。爱因斯坦的狭义相对论可以用闵可夫斯基时空来表述，并为相对运动的不同参照系中的物理过程提供了一种方便的描述方法。“参考系”仅仅是某个特定观察者所拥有的视角。爱因斯坦称这种理论为“狭义”，是因为它只涉及一个特定的情况，也就是无加速的参考系(称为惯性坐标系或参照系)。狭义理论只能应用于匀速运动的非加速参考系。如果你扔下一块石头，它会加速落向地面。附在石头上的参考系是一个加速的参考系，因而不能用爱因斯坦的狭义理论来处理。你在有引力的地方就会有加速度。

这个缺点促使爱因斯坦在他的狭义理论发表10年后提出了一个广义相对论。他发现，虽然笛卡尔空间和闵可夫斯基时空是物体“生活、移动和存在”于其中的刚性框架，但时空实际上是一个敏感的实体：它可能会因质量的存在而弯曲或变形。一旦质量存在于物理情境中，描述了现实的行为就会不可分割地互相联系起来。这被约翰·惠勒(John Wheeler)简练地总结为：

·物质作用于时空，告诉它如何弯曲。

·时空作用于物质，告诉它如何移动。

这种特性是由广义
相对论中的爱因斯坦场方程所量化的，该方程将时空曲率与引力场联系了起来。

物理学家谈论大质量物体周围的引力势阱
。图2所示的漫画显示了时空在一对黑洞附近是如何变形的，其中每个区域的弯曲方式都可以被认为是与其质量也就是与引力本身直接相关。时空中的奇点可以被认为是时空中的曲率变得非常高，而使你超越了经典引力体系，进入了量子体系的地方。奇点周围的事件视界起到了单向膜的作用：粒子和光子可以从外部宇宙进入黑洞，但没有任何东西可以从黑洞的视界内逃逸到外部宇宙。事实上，质量并不是黑洞可能拥有以及被测量的唯一属性。如果黑洞在旋转，也就是说它具有自旋，那么就会出现更极端的行为。在研究这个问题之前，我们将稍微绕一下，学习一下如何用示意图来表示时空本身。

图2　时空由于物质的存在而产生的变形，也就是弯曲

02 游览时空 Navigating Through Spacetime

数学是一种精致而完美的语言，它可以用于描述相对论是如何适用于物理宇宙和整个时空的，而这种描述包括了在黑洞附近所发生的奇怪行为。虽然数学的描述强大而准确，但对于那些没有经过适当的专业培训的人来说，也可能是一门令人生畏的外语。描述性的言辞无论多么雄辩，都缺乏数学方程式的严谨和强大，并且是不精确且局限的。然而图像(据说是)胜过千言万语，它不仅是一种有效的折中方案，也是一种非常有用的将发生的事情可视化的方法。因此花一些精力来理解这种被称为时空图的图画是非常值得的，这将有助理解黑洞周围时空的性质。

时空图

图3展示了一个简单的时空图。依照传统，“类时”轴是在页面中垂直的那一根，而“类空”轴则被画成垂直相交于它。当然，我们实际需要四根轴来描述时空，因为有三根类空的轴(通常表示为x、y和z)和一个类时的轴。不过两根轴就足以实现我们的意图了(而且四根相互垂直的轴也画不出来)。这两根轴相交的地方被称为原点，可以被视为构造其时空图的观察者“此时此刻”所在的点。一个理想化的瞬时事件，例如按下相机快门，发生在特定的时刻和特定的空间位置。这样的一个瞬时事件由时空图上的一个点表示，对应于所讨论的时间和空间位置。图3中有两个点，它们在空间上是分开的(它们不发生在空间轴上的同一点)，但它们又是同时的(它们在时间轴上具有相同的坐标)。你可以想象这两个点对应于两个间隔一段距离的摄影师同时按下快门，拍摄同一个的景象。如果点代表事件，那么时空图中的线代表什么？一条线只是显示出一个物体在时空中通过的路径。当我们过着我们的生活时，我们穿越时空，并在身后留下路径(有点像蜗牛在它后面留下一条闪闪发光的黏液痕迹)，它是时空中的一条线，有一个专业术语叫世界线
。如果你整天待在家里，你的世界线就是一个通过时空的垂直路径(例如，空间坐标=“金合欢大道22号”)。你在时间上向前，但是在空间中不动。另一方面，如果你进行了一次漫长的旅行，你的世界线会因为你的距离随着时间改变而倾斜，因为你在空间和时间上都进行了移动。

图3　一个简单的时空

例如，考虑图3所示的世界线，这条线的一部分是垂直的，然后就变成了倾斜的。这对应于某个实体的世界线，在垂直的线所对应的时间范围内，这个实体是静止的。一个例子是一位摄影师丢在椅子上的相机(它的世界线由于位置没有变化，所以是垂直的)，然后它被偷走了(当空间位置连续变化时)。这条线倾斜的部分就是它的空间位置随时间变化的部分。这条线的斜率会告诉你距离随时间的变化率，而这通常被称为速度。在这种情况下，这是窃贼带着赃物逃跑的速度。小偷逃走的速度越快，或者说他在给定的时间内经过的距离越远，这条线这一部分的夹角就越大。当然，小偷带着赃物逃离的速度有一个固定的上限，就是光速，正如第1章所讨论的那样。光束的轨迹将由最大限度倾斜的线(通常通过巧妙设计的单位，最大倾斜时间线在时空图中与时间轴成45度)来表示。因为没有物体可以比这个速度更快，所以没有世界线可以与时间轴形成更大的夹角。

时空图上的世界线具有一个最大倾斜角度，对应于光速这个最大速度，引出了被称为光锥的重要概念。这个概念非常简单：你只能通过一些前因对宇宙产生影响，并且因果关系的传播速度不能快于光速。因此，你此刻的“影响范围”被包含在一个有限的时空区域内，即如图4所示的与正时间轴成45度角以内的部分。此外，你只能受到传播速度不比光速更快的事件的因果链的影响。这就是说，只有位于与负时间轴成45度角以内的事件才会在当下影响你。如果我们现在画一个具有两个类空轴和一个类时轴的时空图，那么图4中的三角会变成如图5所示的圆锥，而这就是我们所说的光锥
。图5中的光锥描绘一个观察者(视作他此时此刻位于原点)原则上不需要借助破坏宇宙速度的限制，即超光速行进，就可以到达(或在过去已经到达)的空间区域。以正时间轴(未来的时间)为中心的区域被称为未来光锥，而以负时间轴(过去的时间)为中心的圆锥被称为过去光锥。

图4　一个简单的光锥图

因此，公元前44年暗杀尤利乌斯·恺撒(Julius Caesar)是你过去的一部分，因为这个事件与你之间存在着可以想象的因果联系(如果你必须在学校学习它，这就表明存在因果关系)。因为来自仙女星系的光可以到达地球上的望远镜，所以它也是你过去的一部分。然而，光需要600万年才能照到我们，所以600万年前的仙女星系是你过去的一部分并坐落在你的光锥上。今天的仙女星系，甚至是公元前44年的仙女星系都在你的光锥之外，都不能在此刻影响你，否则因果联系的传播就必须比光速更快。

图5　一个表现了某个特定观测者的光锥的时空图

到目前为止，我们在本章中看到的三个时空图，它们的轴被标记为时间和空间。事实上，专业人士通常不会在时空图中画上轴的标签，甚至连轴也不画。时间垂直空间水平是常规操作，但这并不会导致专业天体物理学家都变得草率马虎(虽然这倒不是稀罕事)，实际上是因为所有观察者都无法就时空中的确切位置达成共识。在狭义相对论的世界中，同时性的概念被打破了：一个观察者看到两个事件同时发生，但并不完全意味着它们对其他观察者来说也是同时发生的。

因此，两个摄影师“同时”按下他们的相机快门，在一个相对相机快速行进的飞船上的观测者的视角来看，这件事并不是同时发生的。这个观察者推断出的结论将是一个相机在另一个之前被按下。在图3中，我画了垂直高度相同的两个点(之前我断言两个事件同时发生)，但出现在快速行进的观测者的时空图上时，它们将出现在高度不同的位置。爱因斯坦的相对论强调说这位宇航员的时空图和我的一样有效。因此，如果时空图上的点位取决于观测者的视角，即他们的参照系，那何必把它们画出来呢？

关注一个运动中粒子的世界线有助我们理解这一点；我们现在将画一个新的时空图，粒子带着它的光锥一起在时空中运动(这个技巧被称为使用共动参照系)。要注意在图6中，粒子的路径即其世界线始终保持在光锥内部，因为它的运动不能比光速更快。

爱因斯坦的狭义相对论是他的广义相对论的一个子集，适用于一组有限的物理情境。 在时空不断扩张的前提下，我们需要一个超越狭义相对论的概念框架，一个突出的例子就是不断膨胀的宇宙。在这种情况下，因果关系的表象即为：你无法运动得比你身边局部空间里的光速更快。

物体怎么知道要去哪里

虽然光子没有质量，但事实证明它们仍然受到引力的影响。不过最好不要把这看成是某种力的作用，我们应该认为它是由时空的曲率导致的。通常人们认为光子沿着直线行进，这让我们得到了“光线”的概念。然而在弯曲的时空中，光子的行进路径被称为测地线
。尽管测地线(其名称来自测地学，即测量我们的行星表面陆地的位置)的含义是基于地球的，但它也是描述整个宇宙中时空性质的重要概念。如果空间没有弯曲[就是完全等同于我们可能在学校从欧几里得(Euclid)或他的继承者之一那里学到的日常几何学]，那么测地线将是光线会走过的“直线路径”。但两点之间的最短距离，即光线“想要”走的路线，术语是“零测地线”。在弯曲的空间中，两点之间的最短距离并不是我们所预想的直线，但“测地线是弯曲空间中的直线”。直线也可以被描述为，你保持在相同的方向上移动时的路径。通过比较球面上的经线，可以看出曲面上的几何学有多么不同。如图7所示，两条相邻的经线(在赤道处彼此平行)将在极点处相遇于一点。然而在平直空间中，平行线只有在无穷远处才会相遇(依据欧几里得的最后一个公理)。

图6　沿其世界线运动的粒子的时空图。该粒子总会被包含在其未来光锥的内部

图7　球体上的经线在赤道处是平行的，并且在极点处相遇于一点

打个比方，在存在质量的这种时空被弯曲的地方，不受任何外力影响而自由运动的光线或 “测试粒子”(物理学家使用的一种假想中的装置)在两个事件之间移动时，这种曲率实际上会在移动的路径上体现出来。两个事件应该被视为四维时空中的两个点，每个事件以x、y、z、t的形式表示。

被称为度规
的制度规定了我们如何用时钟和尺子测量空间和时间中事件的间隔，它还为解决几何学的问题提供了基础。一个简单的例子是毕达哥拉斯定理，它告诉我们如何计算平面上两个点的距离。爱因斯坦场方程的解则告诉我们如何在物质的分布已知的情况下计算时空的度规。我们用这种方法来构造真实宇宙的测地线。例如，广义相对论的第一批观测证据之一就是在日食期间测量太阳导致的星光弯曲(日食是测量靠近日面的恒星表观位置的好时机，因为来自日面的光被月亮挡住了。1919年，亚瑟·爱丁顿爵士抓住了一个机会)。太阳的质量会弯曲时空。因此，从遥远的恒星到地球上的望远镜的最短路径(测地线)并不是一条直线——如图8所示，它被太阳的引力场弯曲了。

图8　诸如太阳之类的质量会在时空中引起变形或弯

星光的弯曲表明空间是弯曲的，但爱因斯坦的广义相对论告诉我们实际上弯曲的是时空。因此，我们可以预期质量对时间也有一些奇怪的影响。实际上，即使是地球的引力场也足以使地球上的时钟比在外太空中的更慢，尽管变化很小但可以测量(大约十亿分之一)。黑洞事件视界附近的引力效应要强得多。因此，即使对于最简单的非自旋黑洞，它附近的时间流逝也与离黑洞很远的时间流逝相差甚远。这是一个真实的属性，并不会随着测量方式不同而变化(例如用原子钟或是电子表)。时间流速的改变直接来自由质量引起的时空曲率，这种效应会使光锥向有质量的物体倾斜。图9显示了这种情况的大体效应。

图9　黑洞周围的时空图。显示了事件视界上物体的未来光锥是怎样位于事件视界内的

黑洞会显著影响光锥的倾斜方向。粒子越接近黑洞，它的未来光锥越向黑洞倾斜，因此黑洞会越来越不可避免地成为其未来的一部分。当粒子穿过事件视界时，其未来所有可能的轨迹都在黑洞内终结。而粒子刚好位于事件视界上时，光锥会大幅倾斜，以至于其一侧与事件视界平行并且其未来完全位于事件视界以内，并且不可能逃出黑洞。图9本质上是“局域时空图”的代表，因为这些光锥可以让你知道处于不同位置的测试粒子所经历的局域条件。在这个图中，时间沿着页面向上增加，所以这个图也表现出了黑洞是如何形成并因坠入的物质而增长的。

第1章中，我们讨论了米歇尔和拉普拉斯的暗星，它们可能在周围的轨道上维持行星系统，像我们的太阳系一样，实际上我们说的是黑洞。我们只能通过它的引力拉扯而知道附近有一个黑洞。这可能会让你以为表征黑洞的唯一属性就是它的质量。事实上，黑洞是否在旋转会对其性质产生巨大影响，而我将在第3章中解释这种影响是如何产生的。

03 黑洞的特征 Characterizing Black Holes

我们在第1章中介绍了质量奇点的概念，它由引力坍缩形成，并被一个叫事件视界的界面所包围。这种类星体中不自转的被称为史瓦西黑洞
，这个名词专门表示不转的黑洞：用术语来说就是它们没有自旋
。简单地说，除了位置以外，能够将两个史瓦西黑洞区分开的唯一特征就是其质量有多大。我们将会在第7章了解黑洞是如何生长的，但目前只要知道引力作用下的坍缩是关键因素就够了。如果坍缩前的物质在旋转，那么无论它转得多慢，在发生坍缩时转速都将增加(除非发生某些意外阻止旋转的发生)。这是由一种被称为角动量守恒
的重要物理定律导致的。这个定律可以通过一个正在做单脚旋转的滑冰者来说明：当收回手臂时她就会转得更快。同样，如果产生黑洞的恒星在缓慢旋转，那么它最终形成的黑洞旋转将会非常显著，这种黑洞被称为克尔黑洞
。实际上大多数恒星都是在旋转的，因为它们原本是由缓慢旋转的大质量气体云引力坍缩形成的。如果最初的气体云有哪怕很小的净旋转，坍缩成的云都将具有非零的角动量，而随着其体积越来越小，坍缩成的物体的最终旋转也越来越快。因此我们可以看到，对于新生的黑洞，常有被称为自旋的转动，这即便不是普适的性质也是广泛存在的。我们现在相信，在天体物理中的真实的自旋是不可避免的，就像在当今政治中的倾向性描述一样(尽管在后一种情况下，它并非来自角动量守恒
[1]

)。

我们现在已经阐明了黑洞的第二个物理参数，即自旋或角动量。自旋和质量一样，可以用来区分不同的黑洞。因此，当我们研究黑洞的行为时，这两个性质是很重要的：质量和旋转。理论上，黑洞还可能存在与它们的行为有关的第三个特性：电荷。这也是物理学中的守恒量，而电荷之间被称为静电力的力与引力有许多相似之处。两者关键的相似之处在于，在大尺度上它们都是平方反比定律的例证。就是说有两个大型物体，当它们彼此的距离增加到原来的两倍时，它们受到的引力将减小到原始值的四分之一。引力和静电力的关键区别是，虽然引力总是吸力，但静电荷只在有些时候是吸力(当两个物体电荷相反时，即一个带正电而另一个带负电)，而在其他时候则是斥力(当两个物体电荷相同时，无论是都带正电还是都带负电都会互相排斥)。如果两个带电物体带有同种电荷，那么虽然引力倾向于吸引，但静电斥力将倾向于阻止它们聚集。因此，虽然电荷原理上可能是黑洞的第三个属性，人们希望能以之测量黑洞，但实际上黑洞携带的电荷会迅速被周围的物质所中和。因此，一个很好的假设是黑洞只有两个可以明确区分的特性：质量和自旋。就这样!

现在，你可能想知道是否可以通过不同黑洞的成分来区分它们。比如一个黑洞可能是由氢气云形成的，另一个则是由氦气云形成的。为什么坍缩产生黑洞的物质并没有在随后形成的黑洞的可测量性质中体现呢？那是因为信息无法逃出事件视界!光是信息传递的手段，但我们已经在第1章中看到它无法从黑洞的事件视界里面逃脱出来。因此从外界看来，落入黑洞的物质的化学成分对黑洞的性质没有影响。将引力看成需要“逃离”黑洞的东西是不正确的。黑洞外部的引力场是随着黑洞形成过程中的时空弯曲而产生的。事件视界形成后，黑洞内部的情况不会影响到外界。

黑洞无毛

当要求我们描述一个人时，经常涉及的一个显著特征就是他们的发色(例如金红色、银灰色、巧克力棕色)。有时人们的头发会含有关于他们年龄或国籍的线索。其他有关身体特征的信息如“体重指数”，可能会提供有关其饮食健康的信息。与人类相反，黑洞这个实体除了质量和自旋以外，绝对没有明显特征(基于前文所述的原因，这里忽略了电荷)。为了强调黑洞没有保留任何关于其前身天体性质的这一特征，约翰·惠勒创造了短语“黑洞无毛”。这里指黑洞不含有原来的形状、原来的团块结构、原来的地形、原来的磁性、原来的化学成分，什么都不包含。白俄罗斯物理学家雅可夫·泽尔多维奇带领团队进行了计算，结果表明，如果一个表面起伏不平的非球形恒星坍缩成一个黑洞，其事件视界最终会稳定成没有任何团块或起伏的平滑均衡的形状。所以，一个黑洞从来不会有不愉快的一天
[2]

!你唯一可以知道的关于黑洞的事情就是它的质量和自旋。

自旋改变现实

引力场会将物体拉到旋转黑洞的旋转轴周围，而不仅仅是朝向它的中心，也许这就是旋转黑洞最引人注目的特征。这种效果被称为参考系拖曳
。在黑洞的引力场中自由落下时，径向落往克尔黑洞的粒子将获得非径向的运动分量(转动)。

对于具有自旋的测试粒子(例如一个小陀螺)来说，这意味着如果它向着旋转的大质量物体(例如克尔黑洞)自由下落，它的自转轴将会发生变化。就好像中央大质量物体的旋转拖拽了自旋测试粒子的局部参考系一样。这种现象在1918年被发现，并被称为伦泽-蒂林效应，实际上它不仅发生在黑洞的周围，在任何旋转物体的周围，都会有一定程度的影响。如果你把一个非常精确的陀螺仪放在环绕地球的轨道上，那么参考系拖曳会导致陀螺仪的进动
[3]

。

爱因斯坦场方程对黑洞进行了数学描述，如第1章所述，在稳态(无转动)黑洞的情形下，卡尔·史瓦西解出了这些方程。鉴于史瓦西解出方程是在1915年，也就是爱因斯坦引入广义相对论的同一年，可以说这是一项了不起的成就。在很久之后的1965年，新西兰人罗伊·克尔(Roy Kerr)才解决了旋转黑洞的情形。几年之后，澳大利亚人布兰登·卡特(Brandon Carter)进一步探索了克尔的解。卡特深入研究了克尔度规
[4]

的效应，他证实了由于参考系拖曳，旋转黑洞会在周围的时空中产生巨大的旋涡。旋风属于一种旋涡，靠近旋风中心的空气旋转很快，会带动沿途的任何东西，无论是干草地里的干草还是沙漠中的沙子。在离旋风远一点的地方，空气(以及干草或沙子)会旋转得更慢。旋转黑洞周围的时空也是如此：远离事件视界的地方，时空旋转的速度很慢，但在视界处，时空的旋转速度与视界自旋的速度相同。

旋转(克尔)黑洞的事件视界与非旋转(史瓦西)黑洞的事件视界非常相似，只是黑洞旋转越快，引力势阱就越深：相同质量的克尔黑洞和史瓦西黑洞，前者形成的引力势阱比后者形成的更深，因此克尔黑洞会是比非旋转黑洞更强大的能量源。我们会在第7章中重新介绍这一点。同时为了帮助理解这种现象总结出的一个结论是：史瓦西黑洞的事件视界仅取决于质量，但克尔黑洞的事件视界取决于质量和自旋。

有一个特别的问题：即使只在理论层面上，是否存在未被包裹在事件视界中的时空奇点，也就是所谓的“裸奇点”。根据定义，爱因斯坦场方程的所有黑洞解都有事件视界，而正如第1章所示，光无法逃离这种视界，因此信息也不行。我们认为所有的黑洞奇点都封闭在事件视界之中，也就是说不是“裸”的，所以宇宙的其余部分无法获得有关奇点的直接信息——这就是英国数学家罗杰·彭罗斯所表述的所谓的宇宙监督猜想。他提出所有通过正常的初始条件形成的时空奇点都被事件视界所隐藏，并且在空间中没有裸奇点。

太大的自旋有多大

黑洞所能拥有的角动量大小是有限制的。这个极限取决于黑洞的质量，因此质量大的黑洞比质量小的黑洞旋转得更快。接近它最大极限的旋转黑洞被称为极端克尔黑洞。如果你试图加速一个黑洞的旋转来制造一个极端克尔黑洞，方法是朝它射入高速旋转的物质(也就是搅拌一下)，最后旋转黑洞产生的离心力甚至会阻止物质进入事件视界。

离旋转黑洞的事件视界稍微远一点的地方是另一个重要的数学界面，被称为稳态极限面
。如果某个大质量物体的自旋不为零，那么在其稳态极限面内就不存在静止的观察者，这叫作对惯性参考系的拖曳：稳态极限面以内的每个可实现的参考系都必须旋转。在这个界面内，空间旋转得非常快，以至于光本身也必须与黑洞一起旋转，而不能保持静止。稳态极限面和事件视界之间的这个区域被称为能层
，但很令人困惑的是能层并不是球形的
[5]

，如图10所示。在赤道方向上，能层要比事件视界大得多，但在两极方向上能层与事件视界的半径相同。这导致了能层的形状是扁球形的，类似没有梗的加拉戴尔南瓜。能层的前两个音节来自希腊语中的名词érgon，它与“工作”或“能量”有关[比如“人体工程学(ergonomics)”一词]，旧的能量单位尔格(erg)也来源于此。值得注意的是，希腊语中还有一个表示围绕和远离的动词ergo，也很符合能层的性质。也许这就是在给这个旋转黑洞周围的区域起名并推广开来时，罗杰·彭罗斯(Roger Penrose)和季米特里奥斯·赫里斯托祖卢(Demetrios Christodoulou)脑海中的依据。能层的重要之处在于在这个区域里能够从黑洞中提取能量。

图10　史瓦西(静止)黑洞和克尔(旋转)黑洞周围不同的界面[在常用的“博耶-林德奎斯特(Boyer-Lindquist)”坐标中表示]

由于在能层内的空间在旋转，这部分空间内的物质粒子也被迫转动。因此，在这个空间旋转中存储了可观的转动能，这是一件非常重要的事情，而我们将在第8章中重新讨论它。

白洞和虫洞

广义相对论的爱因斯坦场方程非常丰富多彩，可选择不同的解来描述各种弯曲时空的版本。这是几乎取之不尽的平行宇宙的来源，可以提供给宇宙学家描述和思考。我们实际居住的宇宙是哪种类型只能通过观察决定(如果可行的话)。但这并不能阻止理论物理学家利用爱因斯坦场方程找到各种有趣的解。

数学物理学家梦寐以求的有趣物体之一就是所谓的白洞
。白洞表现得就像一个黑洞，但时间是倒流的(可以想象一部倒放的电影)。物质并非被吸入，而是被喷出。事件视界不再是你永远无法逃脱的区域，恰恰相反，它标志着任何东西都无法进入的区域。一旦物质从白洞中出来，它就永远不能再返回那里了——它的整个未来都在外面。正如我们在第6章中看到的那样，黑洞是由坍缩的恒星形成的，并且依据量子力学理论最终会形成霍金辐射(见第5章)。另一方面，白洞只能源自于因某种原因自发聚集成的黑洞的辐射。我们很难理解这在现实中是如何发生的，而且道格拉斯·厄德利(Douglas Eardley)已经证明了白洞本质上是不稳定的。

当爱因斯坦和他的学生内森·罗森(Nathan Rosen)在20世纪30年代研究爱因斯坦场方程时，他们发现了一个有趣的解。如果一个时空区域弯曲得足够厉害，也就是说它折叠得足够厉害，时空中两个之前被分开很远的部分就可以如图11所示，通过一座小桥或者说虫洞连接起来。对于那些希望让人类在宇宙舞台上大展拳脚的作家来说，恒星和星系之间的遥远距离一直是件烦心事，而虫洞(也称为爱因斯坦-罗森桥)则为作家提供了一个完美的推动情节的工具，让他们可以把英雄和反派传送到不同的地方。这个数学上的发明对于科幻小说作家来说绝对是一个福音，因为它为穿越太空中遥远的距离提供了一种便捷的手段，从理论上支持了各种高度虚构的和难以置信的飞行器。但回过头来，我们还没有观测到任何表明我们的宇宙中存在虫洞的证据。此外，有相当多的理论证据表明，虫洞形成后不会长时间保持稳定。为了让虫洞持续开放，我们可能需要大量的具有负能量的物质，而所有常规物质都具有正能量(这与引力通常总是吸引这一事实有关)。穿过虫洞的常规物质就足以使虫洞不稳定，然后破坏它，使其变成一个黑洞奇点。

图11　一个连接两个独立的时空区域的虫

如果虫洞确实存在，并且可以维持一段合理的时间长度，那么它们将具有一些令人惊讶且匪夷所思的特性。虫洞不仅可以提供一种在广阔的空间中任意穿梭的捷径，而且可以让旅行者及时返回。于是人们就可以构造在时空中循环的闭合的类时曲线，曲线上的光锥会形成一个环(参见图12)。这就像在电影《土拨鼠之日
》中那样，沿着闭合类时曲线行进的人将会简单地一遍又一遍地重复同样的经历。

图12　一个封闭的类时循环，你的未来将成为你的过

事实上除了虫洞之外，还有许多爱因斯坦场方程的解具有这种令人担忧且违反直觉的性质。1949年，数学家库尔特·哥德尔(Kurt Gödel)发现了一种描述旋转宇宙的解，其中包含的闭合类时曲线与《土拨鼠之日》的循环完全相同，这些曲线在无尽循环中反复穿过同一个事件(显然“自由意志”不是场方程的一部分)。克尔解中有描述事件视界之外的时空的部分，我们认为这在现实世界中是具有真正物理意义的。与此同时，克尔解在数学上关于事件视界内的部分是合理的，但目前还不清楚其是否具有任何物理上的相关性。在克尔解的这一部分中，奇点不是一个点(在非旋转黑洞中是一个点)，而是快速转动的环的形状(不过其现实有效性还仅限于推测)。这种环状奇点被闭合类时曲线所包围。在这样的曲线上，你的未来也是你的过去，理论上你有可能在你的父母出生之前谋杀你的祖父母!因此，闭合类时曲线的存在让与时间旅行相关的各种悖论成为可能。对此一种可能的解决方案是承认我们没有将量子力学(描述非常小的物体)和广义相对论(描述非常重的物体)联系起来的理论，也就是我们没有量子引力理论。我们不知道极重却极小的物体的物理特性。大多数物理学家认为我们需要这种理论，才能充分理解非常接近奇点的地方的时空特性。因此，或许爱因斯坦场方程的这些奇怪的解并不真正存在于宇宙中，因为它们被基本的量子力学性质所禁止。例如，量子效应可能会使虫洞不稳定。斯蒂芬·霍金(Stephen Hawking)认为情况确实如此，并将这一原则称为“时序保护猜想”。他讽刺道：这是可以保证宇宙免于历史学家侵害的基本原则。

旋转黑洞的内部有许多事情都在我们对基础物理的理解极限之外，因此我们很多描述都是高度依赖推测的。相比之下，黑洞的旋转及其对周围环境的影响，对于理解我们用望远镜所看到的东西具有巨大的现实意义。因此，接下来我们将更加详细地考虑当物质落入黑洞时会发生什么。

[1]
原文为“spin is as inevitable in real astrophysical black holes as it is in current-day politics”。此处spin一词有“自旋”和“倾向性报道”两个意思。

[2]
此处为a bad hair day的双关，hair可以指黑洞的参数，而a bad hair day是指不愉快的一天。

[3]
进动是指旋转物体在外力的作用下，自转轴绕某一中心旋转。

[4]
即克尔得到的旋转黑洞的度规。

[5]
能层英文为ergosphere，其中sphere的意思是球面。

04 落入黑洞…… Falling Into a Black Hole

太近是有多近

如果你或者你的东西不幸落入黑洞会发生什么？在我们详细考虑这个问题之前，了解特定观测者的特定视角或参考系的影响是很重要的。这意味着不同的观测者会看到非常不同的事情。你如何看待落入黑洞的物体完全取决于你离这个物体有多远(以及你是否就是那个物体)。在黑洞的事件视界之外的一个光子，因为它在视界之外，所以理论上可以逃离。而在事件视界内，故事将会不同了——光子无法逃离黑洞的引力场。但即使在事件视界之外，离开黑洞的光子也不会毫发无损地逃脱。光子会由于要克服引力做功而损失能量。这是一个引力势阱的例子，就像你将自己从深井中拉出来需要能量一样，光子也需要消耗能量以使自己远离大质量天体附近的区域；甚至从在地球引力中移动的光子当中，人们也已经测量到了这种效应。光子的能量与其波长成反比：高能光子波长短，而低能光子波长长。光子在从黑洞逃离时会失去能量，因此其波长会增加。这会改变光的颜色，使其在光谱上从蓝色端(短波)向红色端(长波)移动。这种移动被称为引力红移
，产生于时空本身的延展，或由于黑洞之类的大质量物体作用而弯曲的地方。要注意的是约翰·米歇尔虽然在暗星问题上给出了重要的原创想法，却错误地认为当光从势阱中爬出时速度会降低。我们现在知道了受大质量恒星所影响的是光的波长(也就是频率)。

黑洞附近的时间会受到什么影响

在第1章和第2章中，我描述了时空是如何因质量(也就是自身会产生引力场的事物)的存在而变形的，而这意味着在黑洞附近不仅是空间，时间也会受到影响。

想象一下，你想与史瓦西黑洞保持安全的距离，但是你又想了解在其附近时间是如何表现的。因此，你安排了26名固定的观察者安全驻扎在黑洞外靠近事件视界的地方。这些观察者按照从A到Z的顺序命名，并且排成一条直线，其中A最接近事件视界，而Z最接近安全地待在远处的你。从A到Z的每个观察者都有一个精确的时钟，来测量他们所在的特定位置的时间。为说服A到Z参与这个实验，你还为他们每个人额外提供了一个不同寻常的时钟作为礼物。这些时钟经过调整，与你所在的安全位置的时钟读数相同。最接近你的参与者Z会发现他所拥有的两个时钟所读取的时间略有不同，因为他自己的时钟测量的是当地时间(术语叫作“固有时
”)，其运行会比与你在更远更安全的距离所测量到的时间相同的礼物时钟更慢一点。参与者Z到A所整理出的结果将显示出一个显著效应：与他们特别调整过的礼物时钟上所显示的远处的时间相比，越接近黑洞测时的时钟“运行得越慢”。爱因斯坦的广义相对论所描述的这种效应被称为时间膨胀
。对于更加靠近黑洞的字母表开头的观察者来说，效应会越来越明显。与远处观测者使用的时钟相比，本地时钟(不管是原子钟还是生化钟)越靠近黑洞，运行速度就会越慢。

假设让另一组26个观测者处在一个不同的黑洞的相同情况下，进行你实验的另一项任务。他们的排列方式与第一个黑洞附近的同名观测者相同。不过在第二种情况下，黑洞的质量是第一次实验中黑洞的两倍。相比第一个实验，你为第二组观察者所准备的作为礼物的特别时钟需要进行彻底的调整，直到每个特别时钟所需调整到的速率恰好是第一组实验中对应的时钟的两倍。因为它们到黑洞中心的距离与第一组完全相同，而第一个黑洞的质量仅有第二个黑洞的一半。黑洞质量越大，时间膨胀效应也会越大，而且越接近事件视界这种效应会变得越极端。

请注意，这种时间膨胀不是因为时钟离黑洞更近，而离你这个远处的安全观测者更远造成的。光有额外的传播时间，对于远离黑洞的观察者来说，仅仅补偿传播时间是不够的。无论你用哪种可靠的方法，当时钟越接近黑洞时，所测得的时间流逝的速率就越慢。时间本身被拉长了(或者实际上是膨胀了)。

黑洞附近时间膨胀的必然结果是什么？在黑洞附近的观测者的参考系与离黑洞非常遥远的观测者的参考系中，其效应产生的结果截然不同，实际上可以说是天差地别。

现在让我们考虑一下，在你的第一个实验中，如果观察者A变得有点粗心并且弄掉了他的第一个时钟(就是他可以测量他所在位置固有时的那个)并使它落向黑洞会发生什么。尽管发生了这场灾难，他仍然可以紧紧抓住你吸引他参与实验的礼物时钟。你和A都会看到他的第一个时钟向洞口移动。时钟会发现自己越来越快地进入黑洞。你和A会注意到在下落的时钟上读到的时间与A的另一个时钟(被调整为比本地时钟运行得更快，与你的时间相同的时钟)上的时间差异更大了。过了一会儿，你和A又会注意到下落的时钟的读数停止了。从事件视界向远处的观测者发出的光子似乎无限期地停在了那里。任何落入黑洞的物体在穿过事件视界的临界半径之后所发生的事情，对外部的观测者来说都是不可知的。因此，事件视界可能会被当成时空中的一个洞。正如我们在第1章中看到的那样，光无法从事件视界中逃出，这就是为什么事件视界是黑色的。然而，在通过事件视界直线下落的时钟的参考系中，生活远非一成不变的。从时钟的角度来看，假设黑洞的质量是我们太阳的10倍，那么它将在仅仅十万分之一秒内落到奇点。如果时钟不幸落入一个质量是我们太阳的10亿倍的超大质量黑洞(例如我们在第8章讨论类星体时将遇到的那个)，那么它在极大的事件视界和奇点之间的旅程将会是悠闲的几个小时。

黑洞附近的潮汐力

假设A一时心软希望与他掉落的时钟重新团聚，并想知道脚朝下跳进黑洞会发生什么。接下来的事可以证明这种跳跃将是一个严重的错误，因为他最后生存的概率将为零。作用在他脚上和头上的引力之间的差异将会变得非常大，诸如大质量物体的引力场之类都有这种特征，它们都是平方反比例场。地球与月球的距离很远，但即使这样，地球两侧受到的月球引力的微小差异(也就是所谓的潮汐力)，也会导致每天两次的涨潮落潮。一般来说，由不同位置的引力差异所导致的力都被称为潮汐力。还有其他因素可以丰富潮汐涨落的细节，例如由于月球的相对角度产生的引力以及大陆板块的具体形状。但即使地球表面完全被海洋覆盖而没有陆地，仍然会有潮汐，其导致的海平面每天两次的变化幅度约20厘米，这仅仅是因为地球上的点到太阳距离不同，所受到的引力也有差别。

现在让我们来考虑一下比我和地球中心之间更小的距离。当我坐着写下这一章的时候，我的头比我在书房地板上的脚要高出1米多一点。因此，我的脚比我的头更靠近地球的中心。因为引力遵循平方反比定律，所以会表现得好像地球的所有质量都集中在地球的正中心；而因为我的脚比我的头到这个中心的距离更小，所以我的脚会感受到更大的引力。但实际上，这个差异是相当微弱的：每相隔1米，重力的差异是千万分之三。这种差异这么小是因为我距离地球中心大约6400千米。接近黑洞这样的点质量时，径向相隔1米的两个点所受到的引力差异将更加极端。在接近奇点时，A的脚所受到的拉力将会超过他的肌腱和肌肉的承受范围，从而将它们从A身上撕扯下来，而他本人会被拉长成类似长意大利面一样的东西。所以最好不要跳向黑洞。

动态时空

黑洞的旋转不仅对围绕它运行的物质的轨道有着重要影响，还可以影响从黑洞中提取能量的多少。根据罗伊·克尔的工作和他的爱因斯坦场方程解，我们知道了粒子绕着黑洞转的最小轨道只取决于黑洞的旋转速度。如图13所示，黑洞旋转的速度越快，物质在被黑洞吞没之前就能靠得越近。尽管黑洞外面除了虚空什么都没有，但如果你让某个东西直直落向一个旋转的黑洞，它将开始绕着这个黑洞转。在能层之外，还有可能靠火箭克服这种参考系拖曳，但在它的内部则不能这么做。在旋转黑洞能层内部也就是事件视界之外的区域，没有任何东西可以停滞不前。旋转黑洞实际上拖动了时空，以及周围时空中的物体。这种参考系拖曳的另一个效应是，即使光正朝着黑洞旋转的反方向行进，它也将被带动以相同的方向绕着黑洞转。

图13　气体绕着旋转黑洞的轨道会比绕着无旋转黑洞的轨道更靠近黑洞

绕着黑洞运行

思考诸如我们的太阳在此刻突然变成一个黑洞会发生哪些事情，是非常有意思的。你或我注意到的第一件事将会发生在8分钟后，我写作时所沐浴的美丽的春日阳光会突然消失。虽然与第8章将会讨论的类星体和微类星体相比，我们称之为太阳的这颗孤单的恒星的光度很小，但它离地球的距离近到可以为我们的星球提供平均每平方米一千瓦的能量。值得注意的是，这足以供养地球上的所有生命，植物得以生长，然后被动物吃掉，再然后动物又被其他动物吃掉。太阳一直是这一切背后的推手。但如果太阳内部的聚变停止并且(与所有人的预期相反)坍缩成黑洞，那么它将变得非常黑暗，而我们最终都会死亡(这是一个有些令人沮丧的前景，但我希望读者坚持看到第7章，在那里我们将了解到我们的太阳不是那种能形成黑洞的恒星——它的质量太轻了)。但从动力学角度而言，对于地球这颗行星和我们所考虑的整个太阳系的行星、矮行星和小行星来说，什么都不会改变。绕着太阳运行的所有大质量物体将在几乎相同的轨道上继续运行。引力的作用方式是，无论太阳是否具有与现在相同的大小，或者是否坍缩成直径3公里的事件视界以内的奇点，其外面的引力都将保持不变。在引力作用下，球对称坍缩成的黑洞并不会改变绕转物体的角动量，因此太阳系内的规律、演化和潮汐都将完全不变，只是缺少了阳光。

但是在之前充斥着太阳等离子体的地方，会存在一些更接近太阳形成的黑洞的新轨道。不过这些轨道不能离事件视界太近。质量奇点使时空弯曲的一些细节意味着在刚刚超出事件视界之外的地方绕转是不可能的。试图沿着圆形轨道绕转就需要用火箭进行修正以维持轨道。实际上，数学计算表明，对于我们或任何有质量的粒子来说，可能存在于静态黑洞附近的稳定圆形轨道的最小半径是史瓦西半径的3倍。正如前面我提醒过你的。

实际上，不稳定的圆形轨道距史瓦西(无旋转)黑洞的距离可能会达到这个距离的一半。这个距离定义了一个有时被称为光子球
的球面。但即使对于光子来说，这些轨道也是不稳定的，并且在不久之后，绕转的光子将要么向黑洞偏离再也回不来，要么就跑到太空中去了。

对于存在自旋的克尔黑洞而言，黑洞附近的轨道会有所不同。特别是与静态的史瓦西黑洞周围只有一个光子球不同，这里会存在两个光子球。最外层的球面上是与黑洞旋转方向相反(也就我们所说的在逆
行轨道
上)的光子。在其内部的光子球上则是与黑洞旋转方向相同(在顺行轨道
上)的光子。对于那种与史瓦西黑洞并没有太大不同的自转非常缓慢的黑洞，这两个光子球在空间距离上非常接近。随着黑洞的自旋越来越快，两个球面间也将越来越远。

离旋转黑洞更近的地方，还有着另一个重要的界面(在第3章中讨论过)，被称为稳态极限面
。在一个遥远的观测者看来，没有任何东西可以在这个表面上保持静止——就算你装备的火箭无比强大，都不可能在离旋转黑洞这么近的地方保持不动。在这个界面上，即使是反向(转动)的光线也会被拖成顺着旋转方向转动。虽然仍然可以借助足够的推力从如此靠近旋转黑洞的地方逃离，但是在这里任何东西都不可能保持静止不转。继续向内前进，下一个重要的表面就是我们在第1章中讨论的事件视界，这也是我们最初在史瓦西黑洞情况下遇到的单向膜。和静态黑洞的情况一样，向外穿越事件视界是不可能的，而向内穿越它所面临的命运则不可避免地和向内穿越无旋转黑洞一样。

克尔黑洞周围的轨道一般不会被限制在某个平面上。只有那些落在赤道面上的轨道才是被限制在平面上的轨道(与旋转黑洞的镜像对称的平面)。这个赤道面外的轨道会在三维空间中移动。这些轨道被限制在由最大和最小半径以及被赤道平面的最大角度所限制的范围内。

黑洞自旋这一细节对粒子能离黑洞多近有着显著影响，并且取决于粒子相对于自旋的行进方向。对于极限自旋的黑洞，轨道与黑洞自旋同向(正旋)的光线对应的光子球的半径是史瓦西半径的一半。对于逆行轨道上的光线，其光子球的半径是史瓦西半径的两倍。对于顺行轨道上的有质量粒子，它们可以绕转的最内稳定圆轨道也是史瓦西半径的一半。对于逆行轨道上的那些粒子，这么近的距离将是不稳定的，它们的最小稳定圆形轨道是史瓦西半径的4.5倍。因此，相比无转动的黑洞，旋转的黑洞可以让顺行轨道上的粒子在更靠近黑洞的轨道上运转，只要还没到事件视界粒子就有回头的余地，否则将变得无法返回。在第7章中，我们会考虑这两件事的重要性：物质在落入黑洞之前能绕着多靠近黑洞的轨道运转，以及可以从中提取多少能量。

05 黑洞的熵和热力学 Entropy and Thermodynamics of Black Holes

人如其食

人们常说人如其食。因此，如果你的饮食纯粹是垃圾食品和巧克力，那么你的气色和身心健康都将与你食用以沙拉和地中海式饮食为主的健康食品时大不相同。但是，黑洞似乎并不挑食。无论是吸收广阔的星际尘埃还是吸收一整个立方光年的煎蛋，它们的质量都会无可避免地增加。实际上，在黑洞吃完丰盛的食物后，你无法分辨它吃了什么，只能知道它吃了多少(不过你可以分辨它吃的东西是否带有电荷或角动量)。你只知道饮食的数量，而不是饮食的品质。第2章中描述的“无毛定理”说，黑洞仅有很少的参数(质量、电荷和角动量)表征，因此我们无法去讨论黑洞是由什么构成的。

缺乏对黑洞所吸入的物质性质的了解，看起来似乎是个微不足道的事情，但实际却有深远影响。有关黑洞午餐菜单的信息从根本上丢失了。落入黑洞的任何事物都已放弃了自己的特性，我们无法对它进行探测，也无法了解关于它的任何细节。

黑洞与引擎

对于那些研究过热力学这门美丽的学科的人来说，以下情况再熟悉不过了。在该领域，理解信息是如何通过物理过程丢失或耗散掉是很容易的。热力学有着悠久而有趣的历史。关于热力学的现代理论始于工业革命，当时人们试图研究如何提高蒸汽机的效率。在对“能量”进行定义时，应要求其始终保持守恒，并且可以在不同形式之间进行转换，这被称为热力学第一定律。尽管你可以让能量在不同类型之间进行一些转换，有些特殊的转换却是不被允许的。例如，尽管你可以将机械功完全转换为热(每当你踩刹车令汽车完全停住时都在这样做)，但你无法将热量完全转化为机械功；不幸的是，这正是我们想用蒸汽机做到的事情。因此，火车中的蒸汽机只能将炉子中的热量部分地转化为使车轮转动的机械功。人们最终意识到，热是一种涉及原子随机运动的能量，而机械功则涉及一些诸如轮子或者活塞这种大块物质的协同运动。因此，热的本质中的一个重要部分就是随机性：由于热的物体内原子的振动，你将无法跟踪单个原子的运动轨迹。这种随机运动不可能在没有任何额外代价的情况下被非随机化。在任何孤立系统的各种物理过程中，专业名称为熵
的这种随机性都不会减少，且必须始终保持不变或增加——这就是热力学第二定律。对这种现象的一个解释是，由于无法跟踪大型系统中所有原子的运动，我们所知的关于世界的信息总是在减少。随着能量从宏观尺度转移到微观尺度，也就是从简单的活塞运动转化为大量原子的随机运动，对于我们来说信息就丢失了。热力学使我们能够将这个模糊的概念完全定量化。事实证明，这种信息的丢失与我们所描述的物质落入黑洞是完全类似的。

尽管热力学是为蒸汽机服务发展出来的，但这些原理被认为适用于宇宙中的所有过程。最早认为这与黑洞有关的人之一是牛津物理学家罗杰·彭罗斯(Roger Penrose)。他认为由于黑洞有自旋，我们有可能从中提取能量并将其用作某种引擎。他提出了一个巧妙的方案，将物质投向一个旋转的黑洞，使该物质的一部分带着比被扔进去时更多的能量跑出来。能量是从事件视界之外的区域提取的(实际上就是从第3章中讨论过的能层提取的)。彭罗斯过程减慢了黑洞的转速。原则上，可以通过这种方式从黑洞中提取大量的能量，但这当然还只是个思想实验，因此目前似乎还不能用它来解决地球这颗行星上迫在眉睫的能源危机!在彭罗斯的工作完成几年之后，詹姆斯·巴丁(James Bardeen)、布兰登·卡特(Brandon Carter)和斯蒂芬·霍金(Stephen Hawking)取得了划时代的进步，并用公式表示出了所谓的黑洞动力学三定律，而这为霍金后来对黑洞热力学的思考奠定了基础。这一思考需要用到由黑洞的质量和自旋所决定的黑洞的温度这一概念。

黑洞和熵

彭罗斯的洞察力是促使其他人思考黑洞热力学的一个重要因素。他与R.M.弗洛伊德(R. M. Floyd)一起，表明了在他所想象的过程中，黑洞事件视界的面积将趋于增加。斯蒂芬·霍金开始研究彭罗斯的巧计。这个面积以一种相当复杂的方式依赖于质量和自旋(和电荷)，但是霍金能够证明，在任何物理过程中，这个面积始终会增加或保持不变。一个有趣的效应是，如果两个黑洞合并，则合并后的黑洞的事件视界的面积大于之前的两个黑洞的事件视界面积之和(直观地看这是可靠的，因为事件视界的半径正比于质量，而众所周知表面积依赖于半径)。这与我们在热力学中所看到的熵的情况相同，因此人们开始怀疑是否黑洞的熵和它的面积有着某种联系。这不仅仅是一个有趣的类比，不是吗？约翰·惠勒的一个学生雅各布·贝肯斯坦(Jacob Bekenstein)走在了前面，他在自己的博士学位论文中提出了一个直接的联系。贝肯斯坦运用热力学中信息论的观点论证了黑洞事件视界的面积与它的熵成正比(这一选择意味着你要将事件视界的面积除以普朗克面积，并在乘以一个数值因子后得到熵。普朗克面积是一个物理学基本常数，是10~70平方米。这种单位的选择会使黑洞的熵特别大)。

最初，霍金并不相信贝肯斯坦的研究结果。但在进一步的验算中，他不仅证实了这个结果，而且加深了我们对黑洞热力学的原理的理解。或许我们应该去了解如何进行这些分析，这样我们既可以理解它的优势，也可以理解它的局限性。研究该领域的理想方法，是使用结合了量子力学和广义相对论的、被称为量子引力的方法，用它来研究类似黑洞中的奇点这种非常小但引力在其中有着重要作用的系统。不幸的是，我们目前还没有一个很好的量子引力理论。一个还不错的方法是使用广义相对论来计算时空如何弯曲，然后将其与量子力学一起使用，以理解粒子在弯曲时空中的行为。这就是霍金试图理解黑洞热力学的方法。

真空是空的吗

真空(也就是什么都“没有”的区域)这一概念有着悠久而曲折的历史。大多数古希腊哲学家都出于在今天看来似乎非常神秘的理由而讨厌这个想法，但还是有一小部分原子论者将真空纳入了对世界的描述。因此在科学复兴之前，真空的想法已经非常过时了。但随着1650年人们发明了空气泵，真空变得可以通过实验被证实。尽管按照现代的标准，在17世纪从容器能够抽出的空气量所提供给你的真空度仍然很差，但虚无的观念已变得更可信了。随着人们在20世纪初期证明了原子的存在毋庸置疑，验证某个空间区域中有没有原子，不仅变得无可争议，而且是不可避免的。

原子的存在被证明后不久，就出现了新的物理学理论——量子力学。这种新理论的一个令人惊讶的结论是：在短暂的瞬间内能量似乎不需要守恒。热力学第一定律是物理学中最重要，而且看上去牢不可破的原理，它坚称无论何时何地，在能量的借方和贷方之间都必须进行严格的核算。“能量必须始终保持平衡!”宇宙的会计大声疾呼。实际上，宇宙间的会计规则似乎更加宽松，并且有可能获得信贷。在短时间内借用能量是完全可以接受的，只要你随后迅速偿还即可。你所能借到的金额取决于贷款的期限，而这个量则由海森堡不确定性原理所描述。例如，即使在所谓空无一物的真空中，也可以借用足够的能量来产生粒子和反粒子对。这两个物体可能在一瞬间产生，并在持续极短时间后湮灭，而后在所允许的最长时间限内偿还能量(时间间隔越短，所能借入的能量就越多)。这样的过程每时每刻都在进行。我们甚至可以测出这个过程!现在，我们知道了真空实际上不是空的，而是由这些成对产生并消失的所谓虚粒子构成的场。因此，真空不是空无一物的不毛之地，而是充斥着量子层面的活动。

黑洞蒸发和霍金辐射

霍金使用现代关于真空的理论，也就是量子场论来研究粒子在黑洞事件视界附近的行为。他的分析是数学化的，但我们可以用一种非常简单的方式来描述它。实际上，在黑洞的事件视界附近产生的一对“虚”粒子，也就是一个粒子及其反粒子(电荷相反，质量相同)最后可能被拆散。如果这对正反粒子中的一个落入事件视界，它将陷入奇点，并且永远无法恢复。但是，其伙伴可能仍留在黑洞之外。这个粒子失去了它的虚拟伙伴，但现在是一个真实的粒子，并有逃逸的可能。如果粒子确实逃了出来而不是掉了回去，那么它就成了所谓霍金辐射
的一部分。在远处的观察者看来，黑洞已经因为发射粒子而损失了质量。人们已经认识到，在考虑量子场论的情况下，黑洞并不是完全黑的，它可以辐射出粒子。这个论证也适用于光子。所以，如果霍金的论点是正确的，黑洞就会发出非常弱的光(也被称为电磁辐射)。

所有非零温的物体都会以光子的形式发出热辐射。你本人也会这样，这就是为什么即使在黑暗中你也会出现在红外摄像机上(这也正是警察和军方使用该类摄像机的原因)。物体越热，辐射的频率就越高。我们会发出红外辐射，但红热的火钳可以热到发出可见光。因为黑洞会发出霍金辐射，所以如前所述，它会具有一个温度(被称为霍金温度)，然而通常这一温度非常低。质量为太阳的100倍的黑洞，它的霍金温度比绝对零度(比水的冰点低273摄氏度)只高不到十亿分之一摄氏度!这就是霍金辐射尚未被检测到的原因之一：它太弱了。但是，人们相信它确实是存在的。

然而，霍金辐射确实对黑洞的演化有一个有趣的影响：它是导致黑洞最终死亡的罪魁祸首。再想想这两个虚粒子。从黑洞中逃出的实粒子的能量必须为正，但由于虚粒子对是从真空中自发出现的，吸入黑洞中的虚粒子必须具有负能量作为补偿。因为能量和质量是相关联的，所以这个过程的效果是黑洞净增加了负质量。因此，由于发出霍金辐射，

黑洞的质量将会降低。

由此，霍金发现了一种可以令黑洞蒸发的机制。随着时间的流逝，黑洞会慢慢发出辐射并损失质量。最初，这个过程非常缓慢。事实证明，黑洞越大，其“表面引力
”越小。这是因为尽管表面引力取决于质量，但仍遵循平方反比定律。对于更大的黑洞来说，质量会更大，体积也更大。因此最终结果是，大黑洞的表面引力会很小，而这相当于温度非常低。因此，大的黑洞比小的黑洞发出的霍金辐射更少。

但是，随着黑洞蒸发并损失质量，霍金辐射的量会随着表面引力的增加而上升，因此温度也会升高。假设黑洞没有吸收任何其他的能量，这种效应将使质量损失的速度越来越快，直到黑洞在寿命尽头突然消失。因此，黑洞的寿命结束时并不会发出一声巨响，而是更加安静，发出“砰”的一声。这种蒸发过程仅适用于温度高于其周围环境温度的黑洞。在宇宙历史的当前阶段，从宇宙微波背景辐射的光谱形状测得的宇宙温度比绝对零度高2.7摄氏度，因此质量超过100万亿千克的黑洞现在不会蒸发，因为它们的温度低于其周围环境的温度。但是，当宇宙随着进一步膨胀而变得更冷时，这些质量比太阳小得多的黑洞就能蒸发了。到目前为止，宇宙中所有比这个微不足道的质量的百分之一还要小的黑洞都应该已经消失了。

黑洞信息悖论

这一切会引发的一个问题是：落入黑洞的物质中所储存的信息会怎么样？一种观点认为，即使黑洞在物质落入后马上就蒸发掉，这些信息也会永远丢失。另一种观点则认为那些信息不会丢失。后者的论证过程是，因为黑洞蒸发了，所以落入黑洞的原始物质中所包含的信息必须以某种方式存储在黑洞的辐射中。因此，如果你可以分析来自黑洞的所有霍金辐射并完全理解这些辐射的意义，你就能重建最初掉入黑洞中的所有物质的细节。关于这件事，在斯蒂芬·霍金、基普·索恩和约翰·普雷斯基尔(John Preskill)之间有一个著名的赌注。索恩和霍金支持前一种观点，而普雷斯基尔支持后一种观点。他们的赌注是，败者将输给胜者一套他所选择的百科全书。2004年，霍金被“信息可以被编码在黑洞的辐射中”的想法彻底说服了，于是他认输并给了普雷斯基尔一套关于棒球的百科全书。不过，这件事现在仍然有争议。

尽管这些理论推测都很巧妙，但值得再次说明的是，人们连黑洞发出的最普通的霍金辐射都还没有观察到。物理学的历史上充斥着古老精巧但最终被证明是谬误的理论的残骸。实验和观测经常会产生出乎意料的结果。确实如此，从我们对宏伟的天文现象的观测可知，或许根本没人预测出黑洞的基本原理。未能观测到这些微弱的霍金辐射的原因之一，是我们所知道的许多黑洞都位于宇宙中某些最亮的物体的中心。而这些黑洞实在太大了，也就是说它们都太冷不能通过霍金辐射蒸发。这些物体由于完全不同的原因而异常明亮，我们将在第6章和第8章中对此进行探讨。

06 你怎样给黑洞称重 How Do You Weigh a Black Hole?

太阳以及围绕它运行的行星、矮行星(其中冥王星是最著名的例子)、小行星和彗星共同组成了太阳系。太阳系本身在银盘上绕着在银心
的质心转动。我们的太阳系在银盘中的圆轨道上绕转的速度大约是7千米/秒，绕着银心转完一整圈需要几亿年。除了这种轨道运动之外，整个太阳系还垂直于银道面
运动。它所表现出的这种运动是物理学家所熟知的简谐运动，而把我们的太阳系拉回到位于银道面上的平衡位置的回复力，则来自构成银盘的恒星和气体的引力。目前我们在这个平衡点上方约45光年的地方。从现在起大约2100万年后，太阳系将到达银盘上方320光年处的极值点；在此之后再过4300万年，太阳系将重新回到银河系的中心平面。当太阳系位于银道面的中心时，地球将最大限度地暴露在宇宙射线中。这些宇宙射线会在银道面上呼啸着转圈，它们被磁力线所俘获，以介于完全杂乱无章和完全有序之间的某种方式运动—— 一边沿着磁力线前进，一边绕着磁力线旋转。有人猜测可能是由于太阳穿过银道面的运动导致了恐龙灭绝。但是这种推测很难被证实或反驳，因为这种轨道运动的时标对于寿命通常不会超过一个世纪的人类观测者来说显然是难以观察的。人们采用足够精确和彻底的手段进行天文学观测也只有几个世纪。因此，在观测天文学中，当我们想要关注某种以比这还长得多的时标变化的过程时，这是一个很常见的问题。

然而，至少在相关的时标与人类及其望远镜所关注的时间尺度差不多的情况下，银河系中的轨道运动非常容易测量。既然我们在讨论黑洞，那么最令人感兴趣的显然是银河系最内部区域中恒星的轨道运动，这一区域位于天空中被称为人马座A*的那一部分。当我们观察这个在南半球最容易看到的区域时，也是在看向距我们27 000光年远的银河系的正中心。这是一个天体特别稠密的空间区域，而当我们想研究银心时，会导致两个问题。首先是恒星的空间密度较高，其次是尘埃很多。

第一个问题意味着你需要使用一种能够实现高分辨率成像的测量技术，也就是精细的细节可以被区分开，就像在给定的相机上长焦镜头提供的细节比广角镜头提供的细节更精细一样。仅仅使用更大的望远镜肯定不足以解决这个问题，因为除非我们把望远镜放在大气层外的卫星上，否则我们将不可避免地通过具有湍流的大气来观察所有的天体。不过，人们已经开发出了各种各样的技术来消除地球大气中湍流的影响。最为重要的是一种被称为自适应光学
的技术。这种技术的工作原理是观察明亮恒星(被称为导星)模糊的图像，通过使望远镜的主镜变形以抵消这种变化着的使图像模糊的效应，从而校正大气变化的影响。当所感兴趣的天空中没有明亮的恒星时，则可以向上发出高功率的准直激光束，以激发大气中的原子，并由此进行大气校正。

第二个问题是朝着银心的方向存在着大量的星际尘埃，这所导致的问题是：很难透过尘埃看到可见光，就像来自太阳的紫外线很难透过不透明的遮阳帽一样。解决这个问题的方法是：我们需要在红外波段而不是可见光波段进行观测。

如何测量银河中心的黑洞的质量

这种红外观测得到了两个小组的支持，一个小组由加利福尼亚的安德烈·盖齐(Andrea Ghez)领导，另一个小组由德国的莱因哈特·甘泽尔(Reinhard Genzel)领导。两支团队的工作均独立提供了对银河系中心质量的非常精确的测量结果。图14展示了安德烈·盖齐和她的团队的数据。在过去的几年中，他们对银心的中心区域进行了多次观测，并看到了每次观测中恒星相对上一次观测是如何运动的。因为这些恒星的光谱类型是已知的，因此它们的质量也是已知的。年复一年，随着每颗恒星的轨道路径变得清晰，盖齐及其团队能够根据动力学方程(开普勒定律，也是主导了我们太阳周围行星运动的定律)独立求解每个轨道，并推算出这些轨道共同的焦点所在的“黑暗”区域的质量。这些独立的解很好地确定了该暗区的质量。现在人们知道，暗区在半径不超过6个光时的区域内，具有的质量刚好是我们太阳质量的400万倍。因为这个物体虽然不可见，但质量非常大，所以唯一的结论就是我们银河系的中心存在一个巨大的黑洞。

图14　该图显示了绕我们银河系中心黑洞运动的恒星的连续位置

没有理由认为我们所在的星系——银河系——是唯一的中心存在一个黑洞的星系。与此相反，人们强烈怀疑所有星系，至少在更大的星系的中心，都可能存在一个黑洞。这是由于当时在杜伦大学的约翰·马格里安(John Magorrian)和同事发现了一对看起来非常基本的关系，也就是星系中心的黑洞质量与星系质量的关系。当然，不论测量黑洞的质量还是星系的质量都非常困难。在我们银河系中心表现得如此出色的技术无法应用于外面的星系，因为它们太远了。

椭圆星系中心的黑洞质量超过了太阳质量的100万倍，实际上可能达到甚至超过太阳质量的10亿倍。因此，它们通常被称为超大质量黑洞
。

尽管在测量黑洞质量和星系质量方面存在着困难，但是人们已经发现，在各种不同的星系中，中心黑洞的质量与其宿主星系的质量成比例。人们认为这暗示着中心黑洞和星系本身在整个宇宙的时间尺度上是协同生长和演化的。

银盘上遍布着许多黑洞

除了位于银河系中心的唯一中心超大质量黑洞之外，人们认为在每个星系的范围内还散布着几百万个黑洞，并相信这些黑洞与星系中心的黑洞的形成方式非常不同。星系中心的黑洞是通过逐渐吸收下落的物质增长，而这些恒星质量黑洞
以前则是大质量恒星，曾经发出非常明亮的光芒，其内部的聚变产生了能量并使之保持高温高压，而最重要的一点在于这些能量可以抵抗引力坍缩。当它们的核燃料全部耗尽时，就不再存在可以支撑恒星的辐射压 ，因而就没有任何东西可以平衡向内的引力。对于质量与我们的太阳相似的恒星，在引力作用下的坍缩最终会形成一个被称为白矮星的致密物体。致密一词在天体物理学中具有特殊的含义，表示该物质的密度与普通物质完全不同。按照普通物质密度的标准，白矮星中的物质已经被极度压缩，所以它是致密的。这些物质的所有电子都与其原子核相分离，也就是被电离了，但是又很冷(通常物质仅在高温下才会被电离)。电子产生抵抗持续向内引力的压力，是因为它拒绝被压缩到过于狭窄的区域(这是海森堡不确定性原理的结果)，这种效应的学名是电子简并压力。如果在用尽所有燃料后坍缩
中的恒星的质量更大一些，那么使物质收缩的引力也会更大，使得电子和对应的质子会融合形成中子。这样就可以形成比白矮星更加致密的天体——中子星。

如果我们对黑洞感兴趣，那么我们必须转向比将会生成白矮星甚至中子星的恒星的质量更大的恒星。质量更大的恒星在其燃料持续存在且核聚变能够维持的期间将会非常亮。一旦所有燃料都被用完，恒星的寿命就结束了，发出的光也会熄灭。如果这颗恒星现在已经足够重，以至于引力甚至可以压垮强大的“中子简并压力”，那么因此导致的坍缩会强到连中子简并压力也无法平衡，于是坍缩就会不可避免地导致黑洞的产生。大质量恒星的坍缩通常伴随着壮观的超新星残骸的爆发，而在原来恒星的位置上只会留下一个黑洞。在这样的爆炸中，许多元素，尤其是比铁重的元素，都被合成了出来。

第一个通过测定双星系统中两颗星的质量而认证的黑洞叫V404 Cyg。豪尔赫·卡萨雷斯(Jorge Casares)与菲尔·查尔斯(Phil Charles)和他们的同事非常仔细地观测了两颗星的轨道，并从分析中推断出这对双星包含一颗质量至少是太阳6倍的致密星，因此它就是一个黑洞(后来发现它的质量其实是太阳的12倍)。

对银河系中的恒星数量及其质量进行合理估算是可行的。之后通过考虑有多少大质量恒星在足够早的历史时期就已经形成，并且到现在已经通过聚变用掉了所有的核燃料，我们就可以估算银河系中“恒星质量”黑洞的数量。即使我们银河系中只有极少比例的恒星会演化成黑洞，但因为银河系中有超过10^11
个星体，所以我们仍然会有许多黑洞。

我们如何测量这些遍布星系的黑洞质量？实际上，对于某些恒星所残留的黑洞，需要用到的技术在动力学上面与测量银河系中心的黑洞时所使用的技术非常相似。原因是我们银河系以及其他星系中很大一部分恒星，都形成了成对的双星系统。我们很容易猜测到这是怎么发生的：引力使得物体互相吸引，而很多两体轨道都是稳定的，因此一旦两颗恒星相遇并被引力束缚在一起，它们就很可能会保持这种状态。对于双星系统，如果我们可以测量恒星彼此绕转完整的一圈所花费的时间——也就是轨道周期的时长，并且如果我们知道它们之间的距离，那么就可以知道它们的质量。如果致密星绕着光谱类型与质量都已知的正常恒星(正在发生聚变)的轨道运动，那么致密星的质量就很容易测出。如果类似黑洞这样的致密星是孤立的，没有处于双星系统中，那么缺少其动力学信息就意味着没有办法推断出它的质量或确定它确实是黑洞。我们可以测量的最小的黑洞质量是太阳的几倍，但是最重的恒星质量的黑洞可能比我们的太阳重100倍。

在当前的技术条件下，测量黑洞质量非常容易，不过这仍然需要良好的耐心和韧性。鉴于质量本质上只是黑洞两个基本的物理特性之一，因此这些研究只能让我们了解它一半的特性。不过，测量黑洞自旋的难度要更大，而在第7章中，我会描述尝试并做到这一点所需的英勇努力。

07 吃得更多，长得更大 Eating More and Growing Bigger

它们吃得有多快

黑洞会“吞噬一切其周围物质”的流行观点，只在事件视界附近成立，并且坠入物质的角动量还不能太大。在远离黑洞的地方，外部的引力场与质量相同的任何其他球形物体的引力场相同。因此，一个粒子可以按照牛顿动力学，像绕着其他恒星一样，绕着黑洞公转。是什么打破了粒子绕着圆圈(实际上是椭圆)不停转下去的模式，而按照更奇特的轨迹运行呢？答案是，总是有不止一个粒子在绕着黑洞转。我们观察到的天体物理学现象之所以丰富多彩，是因为有许多物质在黑洞周围绕转，这些物质之间可以发生相互作用。此外，引力并不是唯一的必须遵守的物理定律：角动量守恒定律也必须成立。将这些定律应用于可能被黑洞吸引的大量物质，会引发显著的可观测现象，被称为类星体的奇异天体就是一个很好的例子。类星体
就是核心有一个超大质量黑洞的星系中心的天体，它对自身附近物质有影响，这种影响，使它在整个电磁波谱发出的光甚至比某些星系中所有恒星还要亮。我们将在第8章中讨论类星体和其他类型的“活动星系”，还有缩小版的微类星体——它们的黑洞要比类星体内的黑洞质量小几个量级。现在，让我们回过头来继续探究黑洞周围的物质。

正如我们所看到的，你没有办法直接观测一个孤立的黑洞，因为它根本不会发光，你只能通过黑洞与其他物质的相互作用来探测它。任何落入黑洞的物质都将获得动能，并且与其他下落物质一起形成旋涡。这个旋涡被称为湍流
，通过湍流的物质会被加热，而这种加热会使原子电离，发出电磁辐射。因此，黑洞对附近物质的作用会导致黑洞周围发出辐射，而黑洞本身不会辐射。

黑洞不是在太空中孤立的、没有相互作用的实体。它们的引力场会将所有物质吸过去，无论是附近的气体还是恒星。由于引力随着距离的缩短而急剧增加，如果恒星不幸与黑洞发生了近距离接触，它们就会被撕裂。图15就是一个例子。被吸过去的物质中有一部分将被黑洞完全吞噬或吸收
。物质不会只是加速冲向黑洞，并飞快地穿过事件视界。相反，在引力吸引物质并使其靠近黑洞时，会有一些精心设计的“求爱仪式”。人们发现，吸积物质会具有特殊的几何形状——通常是盘状。如果引力场是成球状对称的，黑洞将无法决定气体沉积到哪个平面上形成吸积盘——吸积盘的平面位置将由远离黑洞的气体流的性质决定。但是，如果黑洞具有自转，那么无论在半径较大的地方气体如何流动，物质最终都会沉积到垂直于其自转轴的平面上。如果被吸引的物质根本没有旋转，那么就必须考虑在第3章中当我们讨论最终会坍缩成黑洞的物质的转动时所提到的角动量守恒。旋转意味着物质在失去能量时将沿着非常圆但实际上是螺旋状的轨道向内运动。在黑洞附近，我们在第3章中提到的伦泽-蒂林效应则意味着，在半径较小的地方，吸积盘可能会与旋转黑洞的赤道面一致(这个论点中，此效应称为巴丁-彼得森效应)。

图15　艺术家关于吸积盘(从中可以看到射出的喷流——见第8章)和施主星的艺术效果图。其中施主星正被吸积盘中心的黑洞的潮汐力所撕裂

如果气体是坍缩物质的重要组分，那么气体原子就可以与位于其所在轨道上的其他气体原子发生碰撞，而这些碰撞会导致那些原子中的电子被激发到更高的能级。当这些电子回落更低的能级时，它们所释放的光子能量恰好是电子所在的较高能级与较低能级间的能量之差。释放出光子就产生了辐射能，这意味着坍缩中的气体云损失了能量。尽管能量被释放了出来，但整体的角动量保持不变。因为角动量依然留存在系统中，所以坍缩中的物质仍然会在某个平面上保持初始净角动量的方向旋转。因此，被吸引的物质将总会形成一个吸积盘—— 一种可以维持很长时间的物质绕着黑洞运转的结构。由于绕转的物质可以离黑洞非常近，物质实际的热度可能达到令吸积盘所发出的辐射包含X射线光子，温度几乎等于1000万度(温度这么高的时候，使用开氏温标还是摄氏温标并没有太大关系)。

对牛顿物理学中一些熟悉的方程的简单分析表明，给定质量的下落物质所释放出的引力能，取决于其质量与它旋转落入的黑洞质量的乘积，以及下落物质最终距离黑洞的远近。如图16所示，对于给定质量的，类似黑洞这样产生引力的物体，下落的物质离它越近，释放出的引力势能就越大。可辐射出的能量是下落物质在加速之前位于远处时的能量(使用爱因斯坦著名的公式E=mc^2
计算，其中E是能量，m是质量，c是光速)与它在最内稳定圆轨道上的能量之差。

尽管聚变是地球未来能源的巨大希望，但它最多只能产生可用能量(由E=mc^2
计算出)的0.7％。相比之下，可用的静止质量的更多部分，则可以通过电磁辐射或其他辐射从吸积物质中以能量的形式释放出来。如第4章中所述，吸积物质能够到达离黑洞多近的地方，取决于黑洞的旋转速度。如果黑洞旋转很快，则物质就可以维持在更小(或者说距离黑洞更近的)轨道上绕转的模式。事实上，将物质吸积到旋转的黑洞上，是用质量换取能量的最有效方法。人们认为正是这个过程为类星体提供了燃料。类星体是宇宙中最强大的持续释放能量的场所，我们将在第8章中进一步讨论这个问题。

图16　该图显示质量(测试粒子)的势能如何随着到黑洞的距离减小而减小

我已经提到过质量和能量之间是等效的，并且对于史瓦西(无旋转)黑洞来说，原则上可以释放相当于其初始质量6％的能量。罗伊·克尔找出的爱因斯坦场方程的解表明：旋转黑洞的最内稳定圆轨道的半径比相同质量的无旋转黑洞小得多。原则上可以从克尔黑洞中提取更多的转动能，但前提是下落的物质按照与黑洞本身相同的方向转动。如果物质按照与黑洞自转方向相反的方向转动，也就是说它处于逆行轨道上，那么就只有不到4％的静止能量会以电磁辐射的形式被释放出来。假如物质坠入一个以最大限度自转的黑洞，并且自转方向与黑洞自转的方向相同，那么原则上如果该物质能够损失足够多的角动量，并且能够在顺行的最内稳定圆轨道上绕转，将有多达42％的静止能量能以辐射形式被释放出来。

它们吃得有多快？

我们在第6章提到过，位于人马座A*
的银河中心黑洞的吸积率是每年亿分之一的太阳质量。听起来似乎不多，但要知道，这相当于每年吞噬300个地球。典型类星体的巨大光度所需要的物质落入量，是每年几倍的太阳质量。而我们将在第8章中讨论的更小规模的微类星体的典型光度，所需的物质落入量可能是典型类星体的百万分之一。

另一种类似的能量提取过程可能发生在伽马射线暴
中，通常也被称为GRBs。它是指突然闪烁的强烈的伽马射线束，与遥远星系中的剧烈爆炸有关。20世纪60年代后期，美国卫星首次观测到这些射线束，它们一开始发出的信号被怀疑是来自苏联的核武器。

考虑到物质通过圆盘螺旋落入黑洞的情况是普遍存在的，物理学家们认为对一些重要物理量的大小进行简单而有启发性的计算是非常有帮助的。如果我们考虑的是球面几何而不是圆盘几何，那么某些有趣的限制就会出现：一个特别有说服力的例子来自恒星世界，与吸积盘相比，将它们视为等离子体球要好得多。亚瑟·爱丁顿爵士指出，被激发的电子与恒星热气体中的其他离子碰撞，所释放的辐射将对随后被其拦截的任何物质施加辐射压力。光子可以“散射”(这就意味着“给予能量和动量”)恒星内部被热电离的等离子体中的电子。向外的压力通过静电力(由电荷相互作用产生的与引力类似的力)传递到带正电的离子上：例如氢原子核(也被称为质子)、氦，还有其他更重的元素的原子核。

以恒星为例，净辐射沿着径向射出，由此产生的辐射压也与将物质向内拉向中心的引力作用方向相反。对于类球形的恒星而言，在向外的辐射压力超过向内的引力并使恒星自己炸开之前，其辐射压有一个最大限制。这个辐射压的最大值被称为爱丁顿极限
。更高的辐射压力必然来自能产生更高辐射光度，如果我们知道到物体的距离，就可以根据其亮度估算它的光度。因此，通过一些简化假设——比如将吸积盘视为球体，就可以推断出物体内部的辐射压力大小。这种简单的方法有时被用于粗略估计黑洞的质量：通过观测周围等离子体所发出的辐射的光度，并假设这就是达到最大极限值的“爱丁顿光度”(超过这个阈值的光度所施加的辐射压力，会高到足以超过内部质量产生的引力，从而将自身撑爆)，就可以估算出它的质量。

在对物质吸积率作出合理假定的情况下，爱丁顿光度可以看成是物质所能达到的最大吸积率。这给出了一个被称为爱丁顿比率(在假定的效率下)的最大值。有多种方法可以打破这个最大值的限制，其中之一就是拒绝球对称假设(对于恒星来说还好，但显然不适用于我们为理解黑洞如何生长所需要考虑的圆盘几何)。

如何测量吸积盘内的旋转速度

由于天文学技术的进步，现在，至少在离地球比较近的情况下，可以测量物质绕黑洞运行的速度。最大的挑战之一是：要获得在足够精确的角度范围内的信息非常难。其所需的空间分辨率比通常的光学望远镜高出至少100倍，有时甚至是1000倍。原则上，用望远镜获得更高分辨率的方法是在更短的波长下观测，或者建造更大的望远镜，尤其注意要减小观测波长与所用望远镜口径的比值。不幸的是，后一种方法非常昂贵，前一种方法则会将通常的可见光观测带到紫外区域，而紫外线是很难穿过地球大气的。与直觉相悖，要实现更小的观测波长与望远镜口径之比，需要在无线电波段(比可见光或紫外线的波长长得多)观察，因为无线电波可以穿过大气层，但这样一来望远镜的口径几乎要等于地球直径。

这个方法存在的一些技术问题，需要在此稍作讨论：事实证明，多亏法国数学家让·巴普蒂斯·约瑟夫·傅里叶(Jean Baptiste Joseph Fourier)在数学发展中作出的贡献，即使实际采集区域只是理想状况下完整孔径的稀疏子集，对于望远镜完整孔径所观察到的信号，我们还是能将其中大部分恢复出来。如果将分立天线(每个天线看起来像一个单独的望远镜，请参见图17所示被称为VLBA的甚长基线阵列)的信号相互关联在一起，就可以重构天空中某个区域内的图像，这些图像的精细程度与一个完整地球大小的望远镜所能观察到的图像的精细程度相当。为了表明这个分辨率有多惊人，假设我站在纽约帝国大厦的顶上，而你在旧金山，在这个距离下，你仍然能看清我的小拇指指甲(我忽略了地球是一个球体，实际上旧金山和帝国大厦之间并没有直接的视线，但你应该能明白我想说什么)。这意味着使用VLBA，我们可以分辨其他星系中尺度小于一个光月的图像。

图17　艺术家关于甚长基线阵列(V L B A)的艺术效果图些天线可以共同给出分辨率与孔径几乎等于地球半径的望远镜相同的图像

同时具有空间意义上的高分辨率和光谱意义上的高分辨率(意味着我们可以非常精确地识别光谱中某个特定的波长)，是一种非常强大的结合。哈佛大学的吉姆·莫兰(Jim Moran)所领导的研究小组，利用多普勒效应对附近一个名为NGC 4258的星系中心黑洞周围的吸积盘使用VLBA进行了观测。他们测量了在整个旋转的吸积盘上波长变化的特定光谱信号(被称为“水脉泽
”)，并利用随着发出脉泽的物质靠近和远离地球时导致的红移和蓝移，来探测物质在黑洞周围给定距离的轨道上运动速度的变化。这些精确的数据证实了物质绕着黑洞转动的轨道正如开普勒定律所描述的那样，这些轨道如图18所示。

图18　VLBA测量了星系NGC 4258(也被称为梅西耶106的吸积盘上绕中心黑洞转动的分立脉泽的分布。这个黑洞的质量是太阳质量的4000万倍

旋转的物质

在质量是我们太阳质量1亿倍的黑洞的最内稳定轨道中，角动量是典型星系中绕转的物质的角动量的万分之一。显然，要让物质被黑洞所吸积，就需要除去绝大部分的角动量，而这正是通过吸积盘实现的。吸积盘中的轨道可以被近似地看成圆形，尽管实际上它们是两侧略微收缩成螺旋状的。开普勒定律表明，在半径较小的轨道上的物质将比在半径稍大的轨道上的物质运动得更快。这种较差转动使得黑洞能够吸收构成吸积盘的等离子体：快速旋转的更加靠内的轨道上的物质，会与半径稍大的相邻轨道上旋转较慢的物质发生摩擦，从而产生热量。这种速度上的差异意味着，由于黏性湍流效应，稍大的轨道上的物质将被拖快一些；相应地，更靠内的轨道上的物质将被拖慢一些。因此，由于轨道运动进一步增加，角动量会从内部物质传递到外部物质，同时将物质加热。

总体而言角动量是守恒的，内部物质可以逐步失去角动量，因而更容易被黑洞吞噬。请注意，如果轨道上的一团物质角动量太大，那么它将远离所绕转的质心——它将因移动得太快而无法靠近。什么样的黏性效应可能与吸积盘内的等离子体有关呢？在这种情况下，原子间的黏度会很小，构成吸积盘的气态等离子体稠度与糖浆相差甚远。实际上，磁场对于将角动量转移出来可能非常重要。磁场从何而来？吸积盘中的等离子体非常热，因此原子被部分电离为电子和带正电的核子。如同詹姆斯·克拉克·麦克斯韦(James Clerk Maxwell)的方程所描述，带电粒子流和移动的电荷会产生磁场。只要存在非常微弱的磁场，它们就可以被较差自转
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拉伸和放大，并被等离子体的湍流所修正，直至达到所需的黏度。这就是所谓“磁旋转不稳定性”的基础。20世纪90年代初，在弗吉尼亚大学工作的史蒂夫·拜尔巴斯(Steve Balbus)和约翰·霍利(John Hawley)最早意识到了这种机制的重要性。

通过黏性湍流和其他可能的方式，等离子体最终会失去角动量，并在更靠近黑洞的、比其半径更小的轨道上绕转。一旦气态等离子体到达最内稳定轨道，不再需要任何摩擦力就可以落入黑洞，此后就再也看不到它了，但它会增加黑洞的质量和自旋。

吸积盘看起来是什么样的，它们有多热

我们已经看到，黏性和湍流效应在去除轨道物质的角动量方面起着重要作用，因为它们，物质大可以在更近的地方绕黑洞运动，并被黑洞吞噬。不过，黏性作用会导致的一个后果是，整体的轨道螺旋运动被转换为随机的热运动，物质变热了。物质的随机热运动越剧烈，其所拥有的热能就越多，温度也越高。如第5章所述，有热量的地方就会有热电磁辐射。除非处于绝对零度，每个物体都会发出热辐射。

这个加热过程是我们能从吸积盘上观测到高光度辐射的原因。对于环绕位于类星体中心的超大质量黑洞的吸积盘，其特征尺度有10亿千里，并且这些吸积盘发出的辐射在光谱上主要分布在可见光和紫外区域。对于在所谓微类星体(会在第8章中进行讨论)中质量更小的黑洞的吸积盘，其大小要比类星体小100万倍，并且辐射以X射线为主。黑洞质量越大，最内稳定圆轨道就越大，因此周围的吸积盘也就会越冷。

质量是太阳100倍的超大质量黑洞周围的吸积盘，最高温度可达100万开尔文；而恒星质量黑洞周围的吸积盘的最高温度，比这还要高100倍。

如何测量黑洞自旋有多快

实际上，你无法直接看到黑洞，因此你也看不到它们在旋转。但仍然有两种主流的方法可以测量黑洞的自旋有多快。如第4章所述，当黑洞的自旋非常快时，黑洞周围稳定轨道上的物质就可能比没有自旋的情况下靠得更近。事实证明，在离黑洞非常近的轨道上的物质，螺旋下落时会由于强烈的湍流和黏性效应被加热，巨大的热量使它辐射出X射线，这种辐射同时取决于物质被黑洞吞噬前与黑洞有多近。广义相对论预言，谱线形状呈现的某种特征是受辐射物质与黑洞的距离影响。这种特征来自于物质中铁原子的荧光辐射，这一从X射线光中提取信息的方法由剑桥大学的安德鲁·法比安(Andrew Fabian)率先提出。

这种测量非常具有挑战性，因为存在许多不可控的因素，比如吸积盘相对于地球的倾斜度，以及实际上来自吸积盘表面的风和外流物质的性质。在吸积盘内缘的附近(沿着我们的视线方向)有着可以揭示黑洞信息的特征，关于黑洞的信息通过其他方式是看不到的。测量恒星质量黑洞自转的其他方法包括测量较大范围的X射线谱，用于解释吸积盘的内部区域(更热)和较远区域(逐渐变冷)的不同温度。我们可以根据X射线光谱的形状得到吸积盘的倾角，并根据最高温度(假设你知道黑洞的质量及其与地球的距离)得到最内的物质在离黑洞多远的地方绕转。杜伦大学的克里斯汀·多恩(Christine Done)正在开发一种类似的方法，以便测量类星体中心的超大质量黑洞的自旋。物质能够在多近的轨道(在被黑洞吞没之前)上绕转，会告诉你黑洞的自旋有多快。

狼吞虎咽的黑洞

事实证明，只有一小部分(估计有10％，尽管实际上可能比这要高得多)被吸向黑洞的物质能到达事件视界并被吞噬。第8章将讨论那些落向黑洞却没有被吞没到事件视界内的物质发生了什么。在穿过吸积盘时，物质可以像风一样被吹走；而从吸积盘的最内半径里会喷出速度非常接近光速的快速等离子体喷流。如第8章所述，没有被黑洞吞噬的东西会旋转而出，形成相当壮观的喷射。

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又名“差动自转”，指天体自转时不同部位的角速度互不相同的现象

08 黑洞和副产品 Black Holes and Spin-offs

黑洞不只是吸收

如果我们的眼睛可以在射电或者X射线波段观察天空，就会看到一些星系被巨大的气球或等离子体波瓣包裹。这些等离子体中含有运动速度接近光速的带电粒子，发出一定波长范围内的辐射。其中一些星系(比如“活动星系”)所表现出的等离子波瓣是由喷流所产生的，它们是从黑洞事件视界周围喷出来的，运动速度快到可以与光速相提并论。罗杰·彭罗斯概括性地指出：理论上，从黑洞的能层中提取自转能量是可能的。罗杰·布兰福德(Roger Blandford)和罗曼·扎纳克(Roman Znajek)明确提出了将旋转黑洞中存储的能量转移到电场和磁场中的方法，从而为产生相对论性等离子体喷流提供动力。从黑洞附近发出喷流的机制也有其他解释，这些解释中哪个才是正确的，正是当前活跃且令人兴奋的研究主题。

最终无论哪种机制被证实，这些喷流都是从黑洞附近(当然是在事件视界外)喷出的高度聚焦且准直的射流。实际上，星系之间的区域并不是真空。与此相反，其中弥散着非常稀薄的被称为星际介质
的气体。当喷流撞击星际介质时会形成激波，其内部会发生壮观的粒子加速，而被黑洞附近喷流所激发的等离子体，其内部也会发生极其剧烈的运动，从而流出当前的激流区域。随着等离子体膨胀，它会向星际介质传输大量能量。这些等离子喷流中，有许多会延伸至数百万光年外。因此，黑洞对超过事件视界很多光年的宇宙依然有着巨大影响。在本章中，我将描述黑洞对其周围环境的影响以及与周围环境的相互作用。

如第6章所述，在大多数星系的中心(可能)有一个黑洞，物质会被其吸积，从而产生电磁辐射。这样的星系被称为活动星系。它们其中一些的吸积过程非常有效，产生的辐射光度极高。这样的星系被称为类星体(这个词源于它们最初被识别为“类似恒星的射电源”，因为它们是遥远的亮度很高的射电点光源)。我们现在知道，类星体是宇宙中已知的最强大的持续能量释放场所。类星体辐射的能量跨越整个电磁频谱，从长波射电波到光学(可见光)波段，再到X射线并继续向后。上面提到的射电瓣之所以特别引人注目，是因为它们跨越了数十万光年(见图19)。射电波段辐射的能量来自那些巨大的波瓣——也就是存有超热的磁化等离子体的地方，其能量是由空间上长距离传输能量的喷流所提供的。高能电子(此处高能是指其传播速度非常接近光速)在行经等离子体波瓣时会受到来自遍布其中的磁场所施加的垂直于运动方向的力。这种加速使它们发出被称为同步辐射的光子(可能是射电的，也可能是红外的；或者在极短的波长下高能的情况，也可能是X射线)。

图19　一个巨大类星体的射电图像。它的范围超过100光年

要了解类星体产生的功率的规模，我们来考虑以下几个典型情况。我用于工作的LED灯，输出功率是10瓦。它们由输出功率高达数十亿瓦的本地发电站提供的电能所点亮(10亿瓦等于10^9
瓦或1吉瓦)。太阳的输出功率约为4×10^26
瓦，是这个发电站功率的10亿亿倍。我们所在的星系，也就是银河系包含超过1000亿颗恒星，其输出功率接近10^37
瓦。但是类星体产生的功率甚至可以比银河系的输出功率高100倍以上。请记住，这个功率不是由一个星系或1000亿颗恒星发出的，而是由单个黑洞周围的能量所产生的。这样的辐射可能会对地球上生物的健康造成极大损害，因此可以说我们非常幸运，因为在距离银河系很近的地方没有这样强大的类星体!

人们认为类星体中的喷流可以持续10亿年或更短时间，这个判断来自对这些物体喷流的成长速度的估计，以及对它们长大后的尺寸的测量。因此根据距离、时间和速度之间的简单关系，可以为整个宇宙中类星体中可能观测到的喷流活动的持续时间提供参考。

随着这些射电波瓣的扩张，它们的磁场会减弱，波瓣中各个电子的“内部”能量也随之减弱。这两种效应会让辐射强度随着时间的推移和到黑洞距离的增加而减小，强度下降的幅度取决于其中高能电子与低能电子的相对数量。同步辐射的一个特性是，磁场强度越弱，所需的产生射电望远镜可接收长波的辐射的电子能量就越高。所以当等离子体波瓣扩展到外部空间时，同步辐射也随之减弱。不仅电子会随着等离子体的膨胀损失能量，随着磁场强度的减弱，与被望远镜观测到的现象有关的，只有那些和高能量电子相关的现象，而且通常情况下，这些电子的数量要远少于低能电子。就类星体的射电波瓣而言，光可以在很短时间内就熄灭。

不过，这场表演还远没有结束，只是奇观转移到了另一个波段。一些非比寻常的事情正在发生：波瓣会在X射线波段上亮起来。这是通过被称为“逆康普顿散射
”的过程发生的。当存在足够大的磁场时，电子会发出同步辐射，从而失去能量。而我们在此处讨论的另一种能量损失机制，则是通过这些电子与构成宇宙微波背景辐射(CMB)的光子相互作用发生的，这些光子源于大爆炸残留的辐射，宇宙目前正沐浴在这种凉爽的微波辉光中。这些电子可能会与CMB中的光子发生碰撞，光子从中获得比碰撞前高得多的能量，电子则相反(要记住整体的能量是守恒的)。特别令人感兴趣的是，当快速运动的电子能量减少到静止电子能量的1000倍时(此前是静止电子能量的成百上千倍)，恰好可以将CMB光子散射为X射线光子。高能电子与低能光子通过相互作用产生高能光子。这在某种程度上类似斯诺克中的情况，白色母球(想象这是一个电子)与某个红色的斯诺克球发生碰撞(为了便于说明，请忽略球并没有以光速运动)，而红色的球从母球那里获得了大量能量。尽管(希望如此)红球最终会落在台球桌上的一个球袋中，但光子(原本的波长约为1毫米)获得的能量是碰撞前的100万倍，因此它的波长也缩短了100万倍。

NASA于1999年发射的钱德拉
(Chandra)卫星对X射线波段很敏感，并且能够在X射线波段探测到一对哑铃形的波瓣，就像射电望远镜可以在厘米波段探测到这些双瓣结构一样。图20和21显示了在射电波段观察到的双瓣结构的等高线图和在X射线波段探测到的双瓣结构的灰度图。

图20　这个巨大的类星体的范围达到了50万光年，并且在电(以等高线显示)和X射线(以灰度显示)波段都具有双瓣结构

图21　该类星体在射电波段(等高线图)上观测到的双瓣结构显示出近期的活动与在X射线能量(灰度，CMB光子的逆康普顿散射所揭示的遗迹的辐射)下观测到的双瓣结构的方向不同，这表明喷流轴可能像微型类星体的喷流轴一样发生进动

实际上，如果我们能够监测这些类星体在整个演化阶段的生命周期(这与生物学家观察青蛙的生命周期类似，从蛙卵到蝌蚪，再到带有很小的腿的蝌蚪，到尾巴粗短的小青蛙，最后到大青蛙和死青蛙)，我们将观察到双重结构辐射从射电波段逐渐变为X射线波段。首先，射电结构会逐渐消失，直到无法探测到，然后X射线结构也将逐渐消失，直至无法探测到。当然，如果喷流重新开始——例如黑洞获得了更多的燃料，那么喷流将为新的发射射电波的双瓣提供燃料，然后再为发射X射线的波瓣提供燃料。如图20和21所示，在某些类星体中，我们可以同时看到射电和X射线的双重结构，而在另一些类星体中，只能看到射电或X射线其中之一(图22)。在一些不同寻常的情况下，我们看到了X射线的双重结构，这与先前的喷流活动相对应，但也有一些角度不同的新射电活动，这是因为反向喷射的喷流方向发生了转动，也就是产生了进动。这种现象的一个例子如图21所示。

图22　这张X射线图像，显示了横跨这个星系的双瓣结构它只能在X射线波段被探测到

许多类星体和射电星系喷流轴的稳定性，揭示了超大质量黑洞自旋的稳定性，这就像陀螺仪一样。为什么某些喷流轴会发生进动而另一些则不会，这个问题将在我们发现黑洞附近发射点处控制喷流角动量的因素是什么时得到解答。究竟是与黑洞本身的自转轴，还是由分别在第3章和第7章中提到的伦泽-蒂林或巴丁-彼得森效应所决定的吸积盘内部区域的角动量矢量有关，目前尚不清楚。我们需要更多数据才能彻底阐明已观测到的现象。但是，有一些来自更靠近我们的较小天体的线索可能表明，喷流轴的进动与吸积盘的角动量有关。

微类星体

到目前为止，我们一直讨论的类星体都是位于活动星系中心的超大质量黑洞。事实证明，还有另一类天体的行为与它们非常相似，但规模小得多。这些质量较小的黑洞可以在离我们更近的地方被观测到。实际上，它们就位于我们自己的银河系中，被称为“微类星体”。尽管大小悬殊，但我们银河系中的微类星体和其他星系中心的系外类星体一样，都是具有类似物理性质的等离子喷流源。人们认为两者都是由受引力作用落向黑洞的物质所驱动。在微类星体中，黑洞的质量与太阳相当。对于强大的系外类星体而言，其黑洞质量可能比我们的太阳的质量大1亿倍。就天体物理学家所关心的事情来说，本地事例的一个重要优势在于其质量较小，因此演化的速度要快得多。它们的演化时标是几天，而不像类星体那样要几百万年。不过，与类星体一样，从所有活动中心附近喷出的喷流都是源于事件视界之外的，而且很可能是从吸积盘的最内缘发出的。

作用于微类星体间的机制非常复杂，而且喷流的发射速度和与其相关的黑洞质量的关系也并不简单。在监测被称为天鹅座X-3的黑洞微类星体中的喷流过程时，有时会发现离开黑洞喷流等离子体的速度发生了变化。这是利用延时天文测量法得到的，就是在一段时间进行连续观测使我们能够确定等离子体喷流从黑洞附近跑出来时速度有多快。测量结果显示，某一次喷流的速度是光速的81％，而4年后则是67％。没有迹象表明喷流速度只会随着时间推移降低，自从发现这个微类星体以来，快速和慢速的喷流都已经被观测到很多次。喷流速度的变化似乎也是我们银河系中另一个著名微类星体SS433的特征，我将在下面对它进行详细介绍。这个微类星体中的喷流速度忽快忽慢，实际上，几天之内它的速度可能是光速的20％~30％之间的任意值。

对称之美

图23显示了银河系中的微类星体SS433的射电图像，它距离我们只有18 000光年。等离子体喷流的结构投影到我们的天空平面上时，会呈现出醒目的之字形或螺旋形图案。组成喷流的各个等离子体火球，正分别以某个介于光速20％~30％之间的惊人速度运动。火球运动的方向按照一个固定的周期变化。实际上，喷流的发射轴的进动方式与在皮划艇参考系下看到的运动员划桨方式大致相同，只不过这一过程的时标是6个月而不是几秒钟。显然，至少在某些类星体中(见图21)也发生了相同的情况，不过如前文所述，它们的速度慢到我们无法对发生的变化进行恰当的时间采样。

喷流在天空中呈现之字形还是螺旋形直接取决于火球的物理运动方式，以及进行观测的具体时间。喷流的一个显著特征就是它们的对称性：东侧喷流部分的物理运动与西侧喷流部分等大且反向：当一个等离子体火球速度达到光速的28％时，在反向喷流中与之对应的部分速度也是这么大；而对于以22％的光速运动的另一个等离子火球，其反向喷流中与之对应的部分速度也会和它一样。实际上，如果一个喷流看起来具有之字形结构，而另一个喷射流看上去则是完全不同的螺旋形结构，这是由于喷流等离子体始终以与光速相当的速度运动，此种情况下会发生相对论性畸变。微类星体的辐射功率相对于系外类星体而言是很小的，但是与太阳微不足道的功率相比仍然非常巨大。太阳的总光度只有4×10^26
瓦，还不到图23中的微类星体辐射功率的十万分之一。

图23　微型类星体SS433在射电波段呈现

喷流的发射

室女座星系团是由1000多个星系构成的，距银河系只有5000万光年。它的中心是一个被称为M87[梅西耶87的缩写，列在法国天文学家查尔斯·梅西耶(Charles Messier)制作的星表中]的巨大星系。该星系的核心是一个质量是太阳30亿倍的超大质量黑洞。从其中发出的是如图24所示的非常强的直线喷流。

图24　从M 87星系中心的超大质量黑洞，以接近光速喷出等离子体喷流

这个喷流在光学波段、射电波段和X射线波段都很容易被看到。据认为，落入物质以每年2~3倍太阳质量的吸积率，到达第6章中描述的那种吸积盘正在发挥作用的核心区。这个喷流的发射点可能在吸积盘的最内部，其从发射点向外传播的速度非常接近光速，因此我们称之为相对论性喷流。利用我在第7章中介绍过的VLBA仪器进行连续监测，可知喷流速度非常接近光速，而位于地球大气层之外的哈勃空间望远镜和钱德拉X射线卫星，都比其位于地面上时具有更高的灵敏度。在距地球5000万光年的位置上，以光速运动的物体每年会在天空中移动4毫弧秒。如果我们考虑到一弧只有一度的1/3600弧度，那么它的四千分之一听起来会是一个小到几乎无法测量的角度，但是VLBA仪器能很容易分辨这么小的间隔。VLBA已经对这个喷流底部不到其超大质量黑洞30倍史瓦西半径的范围进行了成像。

图25显示了源于M87中超大质量黑洞的相对论性喷流的等离子体射电辐射的波瓣和羽流的示例。

图25　源于M87星系中心的超大质量黑洞所发出的相对论喷流的射电辐射波瓣

为了进一步说明膨胀的波瓣与相对论性喷流有关，图26展示了一个在天空中延伸了6度的示例，并呈现出了用于观测的望远镜阵列，以便让人能够感受其尺度。依拉娜·费恩(Ilana Feain)和她的同事使用的望远镜是澳大利亚望远镜致密阵列。

图26　月亮和澳大利亚望远镜致密阵列的光学照片与半人马座A的无线电图像的合成照片

相对论性喷流从黑洞附近发射的机制目前还只是推测，还不具有普适性。不过，来自世界各地的不同团队进行的各项独立研究中，绝大多数证据表明该理论的基本细节是正确的。除了宽泛的图像以外，这些机制及其详细功能还属于推测，只是在光子不足且具有选择效应的情况下被耐心检验过。证明不属于科学，但证据属于科学。我们之所以受到阻碍，是因为即使当今已部署的最先进的成像技术，也无法区分并识别释放了大部分能量的最小区域，不过，利用功能强大的计算机进行数值模拟，就可以突破当前技术的限制。最新发表的模拟结果表明，吸积盘发出的喷流完全可以由广义相对论效应进行解释。这些模拟将组分和公理作为已知输入，允许喷流和吸积盘演化到其特性可以与最新观测结果相匹配的尺度。

那么，我们现在对宇宙中黑洞的质量有哪些了解呢？看起来它们分为两个主要的类别。首先是那些质量与恒星类似的黑洞。这些恒星质量黑洞的质量是太阳质量的3~30倍，它们来自烧光了全部燃料的恒星。

然后就是超大质量黑洞，它们能达到约100亿太阳质量。正如我们已经讨论过的，它们存在于包括我们自己的银河系在内的星系中心，并且与活跃星系和类星体的种种奇特现象有关。

我们已经讨论过物体掉入黑洞，但当一个黑洞掉入另一个黑洞时会发生什么？这不是一个抽象的问题，因为人们已经知道可能存在双黑洞。在这样的天体中，两个黑洞会互相绕转。人们认为由于发出了引力辐射，双星中的黑洞将失去能量并以螺旋形向内互相绕转。在这种螺旋运动的最后阶段，广义相对论会达到临界点，两个黑洞突然合并为具有常规事件视界的单个黑洞。在一个双星系统中，两个超大质量黑洞合并所产生的能量是惊人的，有可能超过可见宇宙中所有恒星的所有光。它的大部分能量都被注入引力波，这些时空曲率的涟漪会以光速在整个宇宙中传播。对这种波存在证据的搜寻尚在进行。人们设想，当引力波经过像长杆一样的物质时，其波长会在时空曲率的涟漪穿过时随之上下波动。如果可以使用诸如激光干涉之类的技术来测量这些微小的波长变化，就能得到一种可以探测宇宙中其他地方产生的引力波的方法。目前已经建成，以及更多还在计划中的地基和天基引力波探测器，都可能探测到来自黑洞合并的信号。实际上，引力波非常难检测，需要非常强力的能量源才有机会进行此类实验，而在这些强力源的候选名单中，黑洞并合居于首位。在撰写本文时，尚未直接检测到引力波，但实验仍在进行
[1]

。

自1915年爱因斯坦提出广义相对论以来，我们最好的引力论已接受了无数次考验。事实证明，与被其替代的牛顿经典理论相比，广义相对论的实验具有更好的一致性。但如果要对广义相对论在极限状况下进行检验，那么你可以期待黑洞会成为现代物理学这一基石的终极测试地。此种情况下，引力在最小的空间区域中表现得最强，因此量子效应会很重要，而这正是广义相对论可能会崩溃的地方。不过，广义相对论也可能在宇宙中的大尺度上失效。当然，目前最热门的话题是广义相对论在解释宇宙最大尺度上的加速膨胀时的完备性。讨论广义相对论的偏差，可能会与加速膨胀和暗能量有关。如果探测到源自黑洞并合的引力波，或观测结果拓展了我们对发生在这些引人入胜的物体附近的基本物理学的理解，那我们就有机会见证爱因斯坦的理论是能够经受住检验的，还是需要用某些新理论来代替的。

我们为什么研究黑洞

研究黑洞的原因有很多，第一个原因是：它开启了对物理参数空间的探索，即使是国际财团的预算也无法独立胜任这一工作。黑洞系统代表了我们所能探索的极端环境，我们能借此研究极端情况下的物理学。它们将广义相对论和量子力学结合起来，但统一尚未实现，并且仍是物理学的前沿问题。第二个原因是，试图理解黑洞现象引起了科学家和许多有思想的外行人的兴趣，提供许多人被科学所激发的途径，鼓动人们去了解我们周围宇宙的伟大之处。第三个原因也许会令人惊讶，研究黑洞给了尘世一些副产品。对黑洞的研究怎么可能改变我们的生活？答案是这种事情已经发生了。当我将这本小书的最后几句话输入笔记本电脑时，它会同时通过802.11Wi-Fi协议将我的工作备份到我大学的服务器上。这项复杂而巧妙的技术源于在射电波段寻找爆发黑洞的某个特定特征时的研究。这项研究由罗恩·埃克斯(Ron Ekers)所领导的团队完成。他们想要检验马丁·里斯(Martin Rees)(现在是皇家天文学家)提出的模型。在约翰·奥沙利文(John O'Sullivan)的带领下，来自澳大利亚心灵手巧的无线电工程师发明了一种干扰抑制算法，本来是想将它用于探测来自遥远空间的微弱信号这一棘手的工作，但他们随即意识到，这项技术还可以应用于地球上的通信传输。因此，黑洞有能力改写物理学，重新激发我们的想象力，甚至革新我们的技术。黑洞有许多副产品，它们都远远超出了其事件视界。

全书完

[1]
2016年2月11日激光干涉引力波天文台(LIGO）、处女座干涉仪(Virgo)研究团队共同发布结果：于2015年9月14日首次探测到引力波现象。

索引

A

absolute zero 绝对零度

accretion disc 吸积盘

active galaxies 活动星系

Australia Telescope CompactArray
澳大利亚望远镜致密阵列

B

Balbus, Steve 史蒂夫·拜尔巴斯

Bardeen, James 詹姆斯·巴丁

Bardeen-Petterson 巴丁- 彼得森

Bekenstein, Jacob 雅各布·贝肯斯坦

binary star 双星

Blandford, Roger 罗杰·布兰福德

C

Cape Canavaral 卡纳维拉尔角

Carter, Brandon 布兰登·卡特

Casares, Jorge 豪尔赫·卡萨雷斯

Cavendish, Henry 亨利·卡文迪许

centre of mass 质心

Chandra satellite 钱德拉卫星

Chandrasekhar, Subrahmanyan 苏布拉马尼扬·钱德拉塞卡

Charles, Phil 菲尔·查尔斯

Christodoulou, Demetrios 季米特里奥斯·赫里斯托祖卢

chronology protection conjecture 时序保护猜想

conservation of angular momentum 角动量守恒

cosmic censorship conjecture 宇宙监督猜想

Cosmic Microwave Background 宇宙微波背景（CMB）

D

dark star 暗星

Descartes, René 勒内·笛卡尔

Done, Christine 克里斯汀·多恩

E

Eardley, Douglas 道格拉斯·厄德利

Eddington limit 爱丁顿极限

Eddington luminosity 爱丁顿光度

Eddington rate 爱丁顿比率

Eddington, Sir Arthur 亚瑟·爱丁顿爵士

Einstein–Rosen bridge 爱因斯坦- 罗森桥

Ekers, Ron 罗恩·埃克斯

electron degeneracy pressure 电子简并压

energy, kinetic 动能

entropy 熵

ergosphere 能层

escape velocity 逃逸速度

event horizon 事件视界

Ewing, Ann 安·尤因

extreme Kerr black hole 极端克尔黑洞

F

Fabian, Andrew 安德鲁·法比安

Feain, Ilana 依拉娜·费恩

Finkelstein, David 大卫·芬克尔斯坦

first law of thermodynamics 热力学第一定律

Floyd, R. M. R. M. 弗洛伊德

Fornax cluster 天炉座星系团

Fourier, Jean Baptiste Joseph 让·巴普蒂斯·约瑟夫·傅里叶

frame dragging 参考系拖曳

frame of reference 参考系

fusion 聚变

G

Galactic centre 银心

Galactic plane 银道面

gamma-ray bursts 伽马射线暴

general relativity 广义相对论

Genzel, Reinhard 莱因哈特·甘泽尔

geodesic 测地线

Ghez, Andrea 安德烈·盖齐

Gödel, Kurt 库尔特·哥德尔

gravitational potential well 引力势阱

gravitational redshift 引力红移

guide star 导星

H

Hawking radiation 霍金辐射

Hawking temperature 霍金温度

Hawking, Stephen 斯蒂芬·霍金

Hawley, John 约翰·霍利

Heisenberg uncertainty principle 海森堡不确定性原理

helium 氦

Herschel, William 威廉·赫歇尔

Hubble Space Telescope 哈勃空间望远镜

I

inertial frame of reference 惯性坐标系

information paradox 信息悖论

information theory 信息论

intergalactic medium 星际介质

inverse Compton scattering 逆康普顿散射

K

Kepler's laws 开普勒定律

Kerr black hole 克尔黑洞

Kerr, Roy 罗伊·克尔

kinetic energy 动能

L

Laplace, Pierre-Simon 皮埃尔·西蒙·拉普拉斯

Lense-Thirring 伦泽- 蒂林

light cone 光锥

M

Magorrian, John 约翰·马格里安

Maskelyne, Nevil 内维尔·马斯基林

Messier 梅西耶

metric 度规

Michell, John 约翰·米歇尔

microquasars 微类星体

Minkowski spacetime 闵可夫斯基时空

Minkowski, Hermann 赫尔曼·闵可夫斯基

Moran, Jim 吉姆·莫兰

N

naked singularity 裸奇点

Neptune 海王星

neutron degeneracy pressure 中子简并压力

neutron star 中子星

Newton, Sir Isaac 伊萨克·牛顿爵士

Newton's gravitational constant 牛顿引力常数

null geodesic 零测地线

O

Oppenheimer, Robert 罗伯特·奥本海默

O'Sullivan, John 约翰·奥沙利文

P

Penrose, Roger 罗杰·彭罗斯

photon 光子

photon sphere 光子球

Planck area 普朗克面积

plasma lobes 等离子体波瓣

point mass 质点

Preskill, John 约翰·普雷斯基尔

prograde orbits 顺行轨道

Q

quasars 类星体

R

radio lobes 射电波瓣

redshift 红移

Rees, Martin 马丁·里斯

relativistic jet 相对论性喷流

retrograde orbits 逆行轨道

Rosen, Nathan 内森·罗森

Royal Astronomical Society 皇家天文学会

S

Schwarzschild black hole 史瓦西黑洞

Schwarzschild radius 史瓦西半径

Schwarzschild, Karl 卡尔·史瓦西

second law of thermodynamics 热力学第二定律

simple harmonic motion 简谐运动

Snyder, Hartland 哈特兰·斯奈德

solar eclipse 日食

Solar System 太阳系

spacetime 时空

spacetime diagrams 时空图

spacetime, curvature of 时空曲率

special relativity 狭义相对论

speed of light 光速

spin 自旋

static limit 稳态极限面

steam engine 蒸汽机

stellar mass black holes 恒星质量黑洞

supermassive black holes 超大质量黑洞

surface gravity 表面引力

synchrotron radiation 同步辐射

T

thermal radiation 热辐射

Thorne, Kip 基普·索恩

tidal forces 潮汐力

time dilation 时间膨胀

turbulence 湍流

V

vacuum 真空

Very Long Baseline Array 甚长基线阵列(VLBA)

virtual particles 虚粒子

W

water maser 水脉泽

Wheeler, John 约翰·惠勒

white dwarf 白矮星

white hole 白洞

worldline 世界线

wormhole 虫洞

Z

Zach, Franz Xaver von 弗兰茨·萨韦尔·冯·扎克

Znajek, Roman 罗曼·扎纳克

Contents

Acknowledgements xv

List of illustrations xvii

1 What is a black hole?

2 Navigating through spacetime

3 Characterizing black holes

4 Falling into a black hole . . .

5 Entropy and thermodynamics of black holes

6 How do you weigh a black hole?

7 Eating more and growing bigger

8 Black holes and spin-offs

Further reading

Index

Acknowledgements

I should like to recordmywarmthanks to PhillipAllcock, Russell Allcock, Steven Balbus, Roger Blandford, Stephen Blundell,Stephen Justham, Tom Lancaster, LathaMenon, John Miller, and Paul Tod for many helpful comments on drafts of this book, to Stephen Blundell for preparing the diagrams, and to Steven Lee for assistance with the optical observations.

KMB

Oxford,

April 2015

Chapter 1 What is a black hole?

A black hole is a region of spacewhere the force of gravity is so strong that nothing, not even light, can travel fast enough to escape from its interior. Although they were first conceived in the fertile imaginations of theoretical physicists, black holes have now been identified in the Universe in their hundreds and accounted for in their millions. Although invisible, these objects interact with, and can thus influence, their surroundings in a way that can be highly detectable. Exactly what the nature of that interaction is depends on proximity relative to the black hole: too close and there is no escape, but further afield some dramatic and spectacular phenomena will play out.

The term `black hole' was first mentioned in print in an article by Ann Ewing in 1964, reporting on a symposium held in Texas in1963, although she never mentioned who coined the expression.In 1967, American physicist JohnWheeler needed a shorthand for`gravitationally completely collapsed star' and began to popularize the term, though the concept of a collapsed star was developed by fellow Americans Robert Oppenheimer and Hartland Snyder back in 1939. In fact, the mathematical foundations of the modern picture of black holes began rather earlier in 1915, with German physicist Karl Schwarzschild solving some important equations of Einstein's (known as the field equations in his General Theory of Relativity) for the case of an isolated non-rotatingmass in space.

Two decades later in the UK, a little before Oppenheimer and Snyder's work, Sir Arthur Eddington had worked out some of the relevant mathematics in the context of investigating work by the Indian physicist Subrahmanyan Chandrasekhar on what happens to stars when they die. The physical implications of Eddington's calculations, namely the collapse of massive stars when they have used up all their fuel to form black holes, Eddington himself pronounced to the Royal Astronomical Society in 1935 as being‘absurd'. Despite the apparent absurdity of the notion, black holes are very much part of physical reality throughout our Galaxy and across the Universe. Further advances were made in the United States by David Finkelstein in 1958, who established the existence of a one-way surface surrounding a black hole whose significance for what we shall study in the coming chapters is immense. The existence of this surface doesn't allow light itself to break free from the powerful gravitational attraction within and is the reason why a black hole is black. To begin to understand howthis behaviour might arise we need to first understand a profound feature of the physical world: there is a maximum speed at which any particle or any object can travel.

How fast is fast?

A lawof the jungle is that if youwant to escape a predator you need to run fast. Unless you have exceptional cunning or camouflage, you will only survive if you are swift. The maximum speed with which a mammal can escape an unpleasant situation depends on complex biochemical relationships between mass,muscle strength, and metabolism. The maximum speed with which the most rapidly travelling entity in the Universe can travel is that exhibited by particles that have no mass at all, such as particles of light (known as photons). This maximum speed can be given very precisely as 299,792,458 metres per second, equivalent to 186,282 miles per second, which is almost approaching a million times faster than the speed of sound in air. If I could travel at the speed of light, I would be able to travel

from my home in the UK to Australia in one fourteenth of a second, barely time to blink. Light travelling from our nearest star,the Sun, takes just eight minutes to travel to us. From our outermost planet, Neptune, it's a journey time of just a few hours for a photon.We say that the Sun is eight light-minutes away from Earth and that Neptune is a few light-hours away from us. This has the interesting consequence that if the Sun stopped shining or if Neptune suddenly turned purple, no one on Earth could find out about such important information for eight minutes or a few hours respectively.

Let's now consider how fast light can travel from even more immensely distant points in space back to Earth. The Milky Way,the Galaxy in which our Solar System resides, is a few hundred thousand light-years across. This means that light takes a few hundred thousand years to travel from one side of the Galaxy to the other. The Fornax cluster is the nearest cluster of galaxies to the local group of galaxies (of which the Milky Way is a significant member) and is hundreds of millions of light-years away from us.Thus, an observer on a planet orbiting a star in a galaxy within the Fornax cluster looking back to Earth right now might, if equipped with appropriate instrumentation, see dinosaurs lumbering around on Earth. However, it is only the mind-boggling vastness of the Universe thatmakes the motion of light look sluggish and time-consuming. The role of the speed of light as a mandatory upper limit has an intriguing effect when we start to consider how to launch rockets into space.

Escape velocity

If we wish to launch a rocket into space but its launch speed is too slow then the rocket will have insufficient kinetic energy to break free from the Earth's gravitational field. However, if the rocket has just enough speed to escape the gravitational pull of the Earth, we say it has reached its escape velocity. The escape velocity of a rocket from a massive object such as a planet is larger the more massive the planet is and larger the closer the rocket is to the centre of mass of the planet. The escape velocity vesc
is written as vesc
=
where Mis the mass of the planet and R is the separation of the rocket from the planet's centre of mass and G is a constant ofNature known asNewton's gravitational constant.Gravity always acts so that it pulls the rocket towards the centre of the planet or star in question, towards a point known as the centre of mass. However, the value of the escape velocity is completely independent of the mass of the rocket. Thus, the escape velocity of a rocket at Cape Canavaral, some 6,400 kmaway from the centre of mass of Planet Earth, takes the same value, just over 11 km/s or approximately 34 times the speed of sound (which may be written as Mach 34), irrespective of whether its internal payload is a few feathers or several grand pianos. Now, suppose we could shrink the entire mass of Planet Earth so that it occupies a much smaller volume. Let's say that its radius becomes one quarter of its current value. If the rocket was launched at a distance of 6,400 km away from the centre of mass, its escape velocity would remain the same. However, if it relocated to the new surface of the shrunken Earth 1,600 km from its centre, then the escape velocity would be double the original value.

Now suppose some disaster occurs with the result that the entire mass of the Earth were shrunk to a point, having no spatial extent whatsoever.We call such an object a singularity. Ithasnowbecome a `pointmass', amassive object that occupies zero volume of space.At a very small distance of only onemetre away fromthis singularity,the escape velocity would be much larger than it was at 1,600 km(and in fact would be about 10% of the speed of light). Closer to the singularity still, just under one centimetre away the escape velocity would be equal to the speed of light. At this distance, light itself would not have sufficient speed to escape this gravitational pull.This is the key idea to understand how black holes work.

It is worth clarifying use of the word `singularity'.We do not believe that at the end point of a continuing gravitational collapse the matter goes down to a geometric point but rather that our classical theory of gravity breaks down and we enter a quantum regime. From here on, we will use the term singularity to refer to this ultra-dense state.

The event horizon

Now imagine you are an astronaut flying a spacecraft and that you are approaching this singularity.While still at some distance from it, you could always throw your engines into reverse and retreat from it. But the closer you get, the harder a dignified retreat becomes. Eventually you reach a distance from which it is impossible to escape, no matter how powerful your onboard engines are. This is because you have reached the event horizon, a mathematically-defined spherical surface, which is defined as being the boundary inside of which the escape velocity would exceed the speed of light. For our thought-experiment about Earth collapsed to a point, this surface would be a sphere of radius only one centimetre with the singularity at its centre, easy enough perhaps for our spacecraft to avoid. However, the event horizon becomes much larger when the black hole is formed from a collapsed star rather than a collapsed planet. The event horizon has an important physical consequence: if you are on that surface or inside it, the laws of physics simply won't allow you to escape because to do so you would need to break the universal speed limit. The event horizon is a mandatory level of demarcation:outside it you have freedom to determine your destiny; inside it,and your future remains unalterably locked within.

The radius of this spherical surface is named in honour of Karl Schwarzschild, who was mentioned earlier. While a soldier in WorldWar I, Schwarzschild provided the first exact solutions of Einstein's famous field equations that underpin general relativity.The Schwarzschild radius is written as RS
=2GM/c^2
where Mis the mass of the black hole, G is Newton's gravitational constant,and c is the speed of light. Using this formula, the Schwarzschild radius of the Earth comes out to be just under one centimetre.Similarly, the Schwarzschild radius of the Sun is found to be 3 km,meaning that if the mass of our Sun could all be squashed into a singularity, then at just 3 km away from this point the escape velocity would be equal to the speed of light. A black hole one billion times more massive than the Sun (i.e. having a mass of 109solar masses) would have a Schwarzschild radius one billion times larger (the Schwarzschild radius of a point mass that is not rotating simply scales directly with its mass). As I describe in Chapter 6, such mammoth black holes are believed to be at the centres of many galaxies.

This description of the event horizon can be reasonably thought of within Newtonian physics. Indeed, physical entities resembling black holes were imagined centuries before Einstein and others profoundly changed our understanding of space and time. The principal thinkers who imagined `dark stars' that resemble black holes were JohnMichell and Pierre-Simon Laplace, starting back in the 18th century, and I will now explain what they did.

One of the remarkable things about astronomy is how much you can discover about the Universe even when you are stuck on planet Earth. For example, no human being has ever visited the Sun, and yet the presence of helium in the Sun was detected in the late19th century by analysing the spectrum of sunlight. This is particularly remarkable as this constituted the discovery of the element helium itself; it was found on the Sun long before being detected on Earth. Even earlier, in the 18th century, some of the ideas behind black holes were beginning to be formulated, and in particular the idea of what is called a dark star. The person who made the first imaginative leap was verymuch a product of his time.

John Michell

The Georgian era was, in England, a time of relative peace. The English CivilWar was long in the past, and England had become a land of relative domestic tranquillity (the rise of Napoleonic France was still some way off ). Like his father before him, the Reverend JohnMichell (Figure 1) received a university education and entered the Church of England. As a rector in Thornhill,West Yorkshire, Michell was able to continue his scientific research,following up his interests in geology, magnetism, gravity, light, and astronomy. In common with other scientists working in England at the time, such as the astronomer WilliamHerschel and the physicist Henry Cavendish (who was a personal friend),Michell was able to ride the wave of the new Newtonian thinking. Sir Isaac Newton had revolutionized the way in which the Universe was perceived, formulating his law of gravitation which explained the orbits of the planets in the Solar System as being due to the same force that caused his famous apple to drop from the tree.

1. John Michell, polymath.

Newtonian ideas allowed the Universe to be studied using mathematics, and this fresh breed of scientists was able to deploy this novel world-view into different fields. Michell was particularly concerned to use Newtonian thinking to estimate the distance to nearby stars by using measurements of the light they emitted.He came up with various schemes to do this, by relating a star's brightness to its colour; he also considered binary stars (pairs of stars gravitationally bound to one another) and how their orbital motions could give useful dynamical information.Michell also investigated how stars tend to cluster in particular areas of the sky, testing this against a random distribution and inferring gravitational clustering. None of these ideas was practicable at the time: few binary stars were known (though Herschel was producing some impressive catalogues of various double stars and new objects) and the relationship between a star's brightness and its colour turned out to be not quite asMichell had thought it was.Nevertheless, Michell was straining to do for the wider Universe what Newton had done for the Solar System: allow a scientific,rational, and dynamical analysis of observations to provide new information about the properties, masses, and distances of the heavenly bodies.

One particular insight that came toMichell followed from the idea that particles of light are, inMichell's words, `attracted in the same manner as all other bodies with which we are acquainted; that is,by forces bearing the same proportion to their vis inertiae [by which he meant mass], of which there can be no reasonable doubt,gravitation being, as far as we know, or have any reason to believe,an universal law of nature'. Such particles emitted from a large star would, he reasoned, be slowed down by the gravitational attraction of the star. Thus the starlight reaching Earth would be slower. Newton had shown that light slows down in glass, and this explained the principle of refraction. If starlight was indeed similarly slowed, Michell argued that it might be possible to detect this slowing by examining starlight through a prism. The experiment was tried, not by Michell, but by the Astronomer Royal, the Reverend Dr NevilMaskelyne, who looked for the diminishing of the refractability of starlight. Cavendish wrote to Michell to tell him that it hadn't worked and that `there is not much likelyhood [sic] of finding any stars whose light is sensibly diminished'.Michell was dismayed, but such astronomical speculations required much guessing of imponderables: was starlight affected by the gravitational attraction of the star from which it is emitted? Michell couldn't be sure. But he was bold enough to make an interesting prediction.

If a star was sufficiently massive, and gravity really did affect starlight, then the gravitational force could be sufficient to hold back the particles of light completely and prevent them from leaving. Such an object would be a dark star. This little-known cleric writing in his rectory in Yorkshire had thus been the first person to conceive of a black hole. However, so farMichell's own programme of measuring the distances to stars lay in tatters.What was more, his health had been indifferent and this had stopped him using his telescope. Cavendish wrote to him a consoling letter: `if your health does not allow you to go on with[the telescope] I hope it may at least permit the easier and less laborious employment of weighing the world.' This singular example of a joke from Cavendish (who was notoriously buttoned up) refers to another idea thatMichell had conceived. `Weighing the world' meant an experiment in which two large lead spheres at either end of the beam of a torsion balance are attracted by two stationary lead spheres. This allows one to measure the strength of the gravitational force, and thereby infer the weight of the Earth.No one had ever done this before. Michell's idea was brilliant,but he didn't live to complete the project. Instead,Michell's experiment was performed by Cavendish and is now known as Cavendish's experiment. This transfer of credit to Cavendish is more than compensated for by the numerous breakthroughs made by Cavendish which he neglected to publish and were later attributed to subsequent researchers (including `Ohm's' law and`Coulomb's' law).

Pierre-Simon Laplace

On the other side of the English Channel, Pierre-Simon Laplace did not enjoy the tranquil idyll afforded by the peaceful period of the English Enlightenment. Laplace lived through the French Revolution, though his career prospered as he influenced the newly founded Institut de France and the 恈ole Polytechnique. He even spent a period asMinister for the Interior under Napoleon, a short-lived appointment the Emperor came to regret. Napoleon realized that Laplace was a first-rate mathematician but as an administrator he was worse than average. Napoleon later wrote of Laplace that `he sought subtleties everywhere, conceived only problems, and finally carried the spirit of "infinitesimals" into the administration'. Napoleon had other administrators to call upon,but the world has had few mathematicians as productive and insightful as Laplace. He made pivotal contributions to geometry,probability, mathematics, celestial mechanics, astronomy, and physics. He worked on topics as diverse as capillary action,comets, inductive reasoning, solar system stability, the speed of sound, differential equations, and spherical harmonics. One of the ideas he considered was dark stars.

In 1796 Laplace published his Exposition du système du monde.Written for an educated public, this book describes the physical principles on which astronomy is based, the law of gravity and the motion of the planets in the Solar System, and the laws of motion and mechanics. These ideas are applied to various phenomena,including the tides and the precession of the equinoxes, and the book also contains Laplace's speculations on the origin of the Solar System. One particular passage is of special relevance to our story.Laplacemade a calculation of how large an Earth-like body would need to be so that its escape velocity was equal to that of light.He showed, quite correctly, that the gravitational strength on the surface of a star, with density comparable to that of Earth but with a diameter of about 250 times that of the Sun, would be so intense that not even light would be able to escape. Thus, he reasoned, the largest bodies in the Universe would therefore be invisible.Could they still be lurking, undetectable in the dark night sky,while we imagined that the only things `out there' were the bright luminous objects that we can see? The Hungarian astronomer Franz Xaver von Zach requested that Laplace provide the calculations that led to this conclusion, and Laplace obliged,writing this up (in German) for one of the journals that von Zach edited.

However, Laplace was becoming aware of the wave theory of light.Both Michell's and Laplace's ideas were based in part on the corpuscular theory of light. If light were to consist of tiny particles,then it seemed reasonable that these particles would be affected by a gravitational field and would be bound forever to a star of sufficient size. But the early 19th century saw a number of experiments which seemed to give greater credence to the wave theory of light. If light were instead a wave, then it was harder to see that it should be affected by gravity. Laplace's dark star prediction was quietly omitted from later editions of Exposition du système du monde. After all,Michell and Laplace had been conjecturing and exploring theory, rather than being driven by the need to explain observations and thus, this idea was forgotten for a while. The objects imagined by Michell and Laplace were thus`dark stars', enormous objects in the Universe which by virtue of their mass could sustain planetary systems but by virtue of this same overwhelming bulk could not be observed via the radiation of light. Starlight emitted from the surfaces of Michell's and Laplace's dark stars would be too sluggish to overcome the intense surface gravity.WhatMichell and Laplace could not have guessed was that such gargantuan accumulations of mass would be unstable to collapse. Moreover, in their collapse they would puncture the very fabric of space and time and give rise to a singularity. Thus `black holes' are not `dark stars' and to take the argument forward and begin to meet up with the astronomical discovery of black holes we will first need to understand the nature of spacetime.

Spacetime

Our everyday experience leaves us comfortable with the notion that the tangible Universe may be described by one temporal (or time) coordinate t and three spatial coordinates (for example x, y, and z along three mutually perpendicular axes, a construct invented by René Descartes and known as Cartesian coordinates).In 1905, Einstein published his revolutionary paper on Special Relativity, the relativity of motion and stationarity. In 1907,Hermann Minkowski showed how these results could be understood more deeply by considering a four-dimensional spacetime whose points, specified now by the 4-D coordinate (t, x,y, z), correspond to ‘events'. An event is something that happens at a particular time (t) and at a particular place (x, y, z). Such 4-D coordinates in what is known asMinkowski spacetime specify exactly where and when an event occurs. Einstein's special theory of relativity could be formulated in terms of Minkowski's spacetime and provides a convenient description of physical processes in different frames of reference that move relative to one another. A `frame of reference' is simply the perspective possessed by a particular observer. Einstein called this theory `special' because it deals only with a particular case, namely reference frames that are non-accelerating (called inertial frames of reference). The special theory can only be applied to uniformly moving, non-accelerated, frames of reference. If you drop a stone,it accelerates towards the ground. The frame of reference attached to the stone is an accelerating frame of reference and cannot be treated by Einstein's special theory.Where you have gravity, you have acceleration.

This drawback prompted Einstein to formulate a general theory of relativity, which he published a decade after his special theory.What he found was that whereas Cartesian space and Minkowski spacetime were rigid frameworks in which objects `live,move and have their being', spacetime was actually a more responsive entity:it could be curved and otherwise deformed by the presence of mass. Once mass is present in a physical situation then the following inextricably linked behaviour describes reality, neatly summarized by JohnWheeler:

·mass acts on spacetime, telling it how to curve！

·spacetime acts on mass, telling it how to move

This behaviour is quantified by Einstein's field equations within General Relativity, which relate the curvature of spacetime to the gravitational field.

Physicists talk about a gravitational potential well as surrounding a massive object. The cartoon shown in Figure 2 encapsulates how the spacetime is distorted in the vicinity of a couple of black holes,where each region can be regarded as curved in a way which is directly related to its mass and hence to the gravitational force itself. The singularity in spacetime may be regarded as where the curvature in spacetime becomes very high and you go beyond the classical theory of gravity, into the quantum regime. The event horizon surrounding the singularity functions as a one-way

2. The distortion, i.e. curvature, in spacetime due to the presenceofmasses.

membrane: particles and photons can enter the black hole from outside but nothing can escape from within the horizon of the black hole out to the external Universe. In fact mass is not the only property that a black hole may possess and be measured by. If the black hole is rotating, that is to say it possesses some spin, then even more extreme behaviour emerges. Before we examine this,we will take a little detour to learn a littlemore about how we may schematically represent spacetime itself.

Chapter 2 Navigating through spacetime

Mathematics is the exquisitely perfect language needed for describing how the theory of relativity applies to the physical Universe and all of spacetime, and that description includes the strange behaviour that occurs near black holes. A mathematical description, while powerful and exact, even so can be something of a foreign and forbidding language for those without the appropriate technical training. Descriptive words, however eloquent, lack the rigour and power of a mathematical equation and can be imprecise and limiting. Pictures however, being(it is said) worth a thousand words, can be not only a useful compromise but a very helpful way to visualize what is going on. For this reason, it is well worth spending a little effort to understand a particular type of picture, called a spacetime diagram. This will help in understanding the nature of spacetime around black holes.

Spacetime diagrams

The cartoon in Figure 3 shows a simple spacetime diagram.Following tradition, the `time-like' axis is the one that is vertical on the page and the `space-like' axis is drawn perpendicular to this.Of course, we really need four axes to describe spacetime because there are three space-like axes (usually denoted x, y, and z) and one time-like axis. However, two axes will suffice for our purpose(and of course four mutually perpendicular axes are impossible to draw!).Where these two axes intersect is called the origin, and this may be regarded as the point of `here and now' for the observer who has constructed their spacetime diagram. An idealized instantaneous event, say the click of a camera shutter,occurs at a particular moment in time and at a particular location in space. Such an instantaneous event is represented by a dot on a spacetime diagram, appropriate to the time and spatial location in question. There are two dots in Figure 3, which are spatially separated (they do not occur at the same point on the space axis)but they are simultaneous (they have the identical coordinate on the time axis). You could imagine these two dots correspond to the simultaneous shutter presses of two photographers who are standing some distance apart from one another, photographing the same spectacle. If points represent events, what do lines in a spacetime diagram represent? A line simply shows a path of an object through spacetime. As we live our lives, we journey through spacetime and the path we leave behind us (somewhat as a snail leaves a glistening trail of slime behind it) is a line in spacetime,and in the jargon this is called a worldline. If you stay at home all day, your worldline is a vertical path through spacetime (with space coordinate = `22 Acacia Avenue', for example). You move forward in time but are fixed in space. If on the other hand you made a long journey, your worldline slants over because your distance changes with time, because you move in space as well as time.

3. Asimplespacetime diagram.

For example, look at the worldline shown in Figure 3, the line which is part vertical, then further up becomes slanting. This corresponds to the worldline of some other entity, which is stationary for the time indicated by the vertical extent of the line. An example might be a camera belonging to one of the photographers, left on a chair (so that its worldline is vertical because its position isn't changing), before it was stolen and whisked away (when the spatial location changes continuously).Where this line becomes slanting is where its spatial location is changing with time. The slope of this line tells you about the rate of change of distance with time, which is more commonly called the speed. In this case this is the speed at which the thief is whisking away the stolen camera. The faster the thief is making off with the camera, in other words the more ground he is covering in a given time, the less vertical and themore slanting this part of the line will be. There is of course a robust upper limit to the speed at which the thief can run off with his illegally gotten gains and this,as discussed in Chapter 1, is the speed of light. The trajectory of a beam of light would be represented by a maximally slanting line(commonly represented in spacetime diagrams as being at45 degrees to the time axis by using cleverly crafted units).Because nothing can go faster than that speed, no worldline can be at a greater angle to the time axis than this.

Worldlines on a spacetime diagram having this maximally slanting angle, corresponding to this maximal speed, the speed of light,give rise to an important concept called a light cone. The idea of this is very simple: you can only have an effect on the Universe in the future by some prior cause and that causal sequence cannot propagate faster than the speed of light. Therefore your `sphere of influence' right now is contained in a restricted range of spacetime, namely that part which is within a 45-degree angle to the positive time axis as shown in Figure 4.Moreover, you can only have been influenced by a causal chain of events that could not have propagated faster than the speed of light. Therefore only events within a 45-degree angle to the backwards time axis can influence you now. If we now draw a spacetime diagram with two space-like axes and one time-like axis, then the triangles in Figure 4 become cones and these are what we mean by light cones,as shown in Figure 5. The light cone in Figure 5 delineates regions of space within which an observer (deemed to be located at the origin, their `here and now') could in principle reach (or have reached in the past) without having to invoke breaking the cosmic speed limit and travelling faster than the speed of light. The region centred on the positive (future) time axis is known as the future light cone while the cone centred on the negative time axis (i.e.past times) is known as the past light cone.

4. Asimplelightconediagram.

Thus the assassination of Julius Caesar in 44 BC is part of your past, because there is a conceivable causal link between that event and you. (If you had to learn about it at school, that demonstrates the existence of a causal link!) Because light from the Andromeda Galaxy can reach a telescope on Earth, it too is part of your past.However, the light takes 6 million years to get to us, so it is the

5. A spacetime diagramshowing the light cone of a particular observer.

Andromeda Galaxy of 6 million years ago that is part of your past and sits on your light cone. The Andromeda Galaxy of today, or even the Andromeda Galaxy of 44 BC, is outside your light cone.Events happening on Andromeda, either now or even back in44 BC, cannot influence you right nowbecause any causal link would have had to travel faster than the speed of light.

The three spacetime diagrams that we have seen in this chapter so far have their axes labelled as time and space. In fact, professionals wouldn't normally include axis labels or even the axes in spacetime diagrams. This isn't simply that it is so routine that time goes up and space goes across that professional astrophysicists get sloppy (though that's not an unknown phenomenon) but it is because the exact positions in spacetime cannot be agreed upon by all observers. In the world of special relativity, the notion of simultaneity breaks down. Just because two events are seen to be simultaneous for one observer doesn't at all mean that they are simultaneous for other observers.

Thus the two photographers pressing the shutters of their cameras‘simultaneously' will not be what an observer travelling in a spacecraft very fast relative to the cameras sees. That observer will deduce one camera click occurring substantially before the other.The two points in Figure 3 which I drew at the same vertical height (since I claimed the events occurred at the same time)would appear at different vertical positions on the spacetime diagram of the rapidly travelling observer. Einstein's relativity insists her diagram is just as valid as mine. So if the points on a spacetime diagram depend on an observer's point of view, i.e. their frame of reference, what's the reason for drawing them?

To understand this, it is helpful to focus on the worldline of a moving particle and so we will now draw a new spacetime diagram in which a particle moves through spacetime, taking its light cone with it (this trick is known as working within the co-moving frame). Notice that in Figure 6 the particle's path (i.e.its worldline) always stays within the light cone as it cannot travel faster than the speed of light.

Einstein's Special Theory of Relativity, which is a subset of his General Theory, pertains to a restricted set of physical situations.A different conceptual framework beyond Special Relativity is needed in the context of spacetime which is expanding, the pre-eminent example of which is the expanding Universe. In this context, themanifestation of causality is such that you cannotmove faster than the speed of light with respect to your local bit of space.

How do objects know where to go?

Although photons have no mass, it turns out that they are still influenced by gravity. It is best not to think of this as due to a force, but rather that this comes about because of the curvature of spacetime. A photon is usually thought to travel in a straight line,which is where we get the notion of a `light ray'. However, through a curved spacetime itwill follow a path known as a geodesic.

6. Aspacetimediagramofaparticlemovingalongitsworldline,thatis always containedwithinits futurelight cone.

Despite its Earth-based connotations, a geodesic (whose name comes from geodesy, i.e. measuring the lie of the land of our planet's surface) is an important concept describing the nature of spacetime throughout the Universe. If space were not curved(meaning entirely consistent with everyday geometry that we may have learned at school from Euclid or one of his successors), then a geodesic would be the `straight line path' that a light ray would travel. But the shortest distance between two points, which is the route that a light ray `wants' to take, is known by the term `null geodesic'. In curved space the shortest distance between two points isn't what we think of as straight, but `geodesics are straight lines in curved spaces'. A straight line can also be characterized as the path you follow by keeping moving in the same direction. An example of how geometry is seriously different on a curved surface comes from considering lines of longitude on a sphere. Two adjacent lines of longitude (which are parallel to one another at the equator) will meet at a point at the pole, as shown in Figure 7.However, in flat space parallel lines will meet only at infinity (as per Euclid's last axiom).

Actually, where spacetime is curved, for example because of the presence of mass, that curvature is manifested in the path that a light ray or (a mental device used by physicists) a `test particle' freely able to move with no influence of any external force, would move along between two events. Two events should be regarded as two points in 4-D space time, each denoted in the form (t, x, y, z).

7. Lines oflongitudeon asphere areparallel atthe equator, andmeetat a point at the poles.

A rule called a metric tells us how clocks and rulers measure the separations between events in space and time and provide the basis for working out problems in geometry. A very simple example of a metric is Pythagoras' theorem, which tells us how to compute the distance between two points that lie in a plane. The solutions to Einstein's field equations tell us how to calculate the metric of spacetime when the distribution of matter is known.We use this to construct the geodesics for the real Universe. For example, one of the first pieces of observational evidence for General Relativity was the bending of starlight by the Sun,measured during a solar eclipse (a good time to examine the apparent positions of stars close to the Sun's disc because light from the disc is blocked out by theMoon, an opportunity seized upon by Sir Arthur Eddington in 1919). The Sun's mass curves spacetime. Thus the shortest path (the geodesic) from a distant star to a telescope on Earth is not quite a straight line: it is bent round by the Sun's gravitational field, as shown in Figure 8.

The bending of starlight demonstrates that space is curved, but Einstein's General Theory tells us it is actually spacetime that is curved. Therefore we might expect that mass also has some strange effects on time. In fact, even the Earth's gravitational field is sufficient to make Earth-bound clocks tick a bit slower than they would do in deep space, although the effect is small (roughly one part in a billion) but measurable. The gravitational effects near the event horizon of a black hole are much stronger. Thus, even for the simplest case of a non-spinning black hole, time runs differently close to the black hole compared to how it runs at a huge distance from the black hole. This is a real effect and does not depend on how the time is measured (for example by an atomic clock, or by a digital watch). It follows directly from the curvature of spacetime induced by the mass which tips the light cones towards the mass.Figure 9 indicates the general effect.

8. Amass suchasthe Suncausesdistortion, or curvature, inspacetime.

Black holes profoundly affect the orientations of the light cones.As a particle approaches a black hole, its future light cone tilts more and more towards the black hole, so that the black hole becomes more and more a part of its inevitable future. When the particle crosses the event horizon, all of its possible future trajectories end inside the black hole. Just within the event horizon, the light cone tilting is so great that one side becomes parallel with the event horizon and the future lies entirely within the event horizon; escape from the black hole is not possible.Figure 9 also illustrates this point: it is essentially a representation of `local spacetime diagrams', because the assembly of light cones allows you to understand the local conditions experienced by a test particle located at different positions. In this figure, time increases up the page and so this diagram also gives a sense of how a black hole forms and grows due to infalling matter.

9. Diagramofthe spacetimesurroundingablackhole showinghowthefuturelight conesforobjects onthe eventhorizonlie insidetheeventhorizon.

Just as for the dark stars of Michell and Laplace discussed in Chapter 1 which could have sustained planetary systems in orbit around them much like our Solar System, so it is that we only know that a black hole is nearby due to its gravitational pull. This might lead you to think that the only property that characterizes a black hole is itsmass. In fact,whether or not a black hole is rotating has a dramatic effect on its properties, and I will explain how this comes about in Chapter 3.

Chapter 3 Characterizing black holes

In Chapter 1, we introduced the concept of a mass singularity,forming in gravitational collapse, and surrounded by an event horizon. Examples of such objects that are not spinning are called Schwarzschild black holes and this term specifically denotes black holes that are not rotating: in the jargon, they have no spin.Simply put, the only characteristic that distinguishes one Schwarzschild black hole from another (other than location) is how massive it is. In Chapter 7 we will learn how black holes grow but for now, it will suffice to know that collapse under gravity is the key ingredient. If there is any rotation whatsoever in the pre-collapsed matter, however gentle, then as the collapse occurs the rotation rate will increase (unless something acts to stop that happening). This arises due to a remarkable physical law known as the conservation of angular momentum. This law is illustrated by a pirouetting skater: as she pulls her arms in she spins faster. In the same way, if the star that gives rise to the black hole is gently rotating then the black hole that it ultimately forms will be spinning significantly and is termed a Kerr black hole. Most stars are in fact rotating, because they themselves are formed from the gravitational collapse of slowly rotating massive gas clouds. (If such a gas cloud had even a minute amount of net rotation then the collapsing cloud will have non-zero angular momentum, and as the matter occupies an increasingly smaller volume the final rotation of the collapsed object may well be rather rapid.) Thus we see that rotation, more commonly called spin, is likely to be a prevalent, if not actually a ubiquitous, characteristic for black holes that have just formed from the collapse of matter.We now believe that spin is as inevitable in real astrophysical black holes as it is in current-day politics (though in the latter case it arises from something other than the conservation of angular momentum!).

We have now stated that a second physical parameter, that of spin or angular momentum, is a characteristic that distinguishes one black hole from another just as mass does. Thus, there are two properties of black holes that are important to keep in mind as we study the behaviour of black holes: mass and spin. In principle,there is a third characteristic of black holes that might be relevant to their behaviour: electrical charge. This is also a conserved quantity in physics, and the forces between electric charges,known as electrostatic forces, have a number of resemblances to gravitational force. A key similarity is that both are (on large scales) examples of inverse-square laws meaning that, in the case of two massive objects, as you double the distance that separates them from one another the gravitational force they experience reduces to a quarter of the original value. A key difference is that while gravity is always attractive, electrostatic charges are only sometimes attractive (when the two bodies are oppositely charged,i.e. one is positive and the other is negative). They are at other times repulsive (when the bodies have charge of the same sign,either both positive or both negative, they repel each other). If two charged bodies have the same type of charge, then electrostatic repulsion will tend to prevent them coalescing, even if gravity is tending to attract them. So while charge could in principle be a third property of black holes that one might hope to measure,in reality a charged black hole would be rapidly neutralized by the surrounding matter. It is therefore a good operational assumption that there are only two relevant properties of black holes that distinguish one from another: mass and spin.That's all!

Now, you might wonder whether black holes could be distinguished by their composition. One might have been formed from a hydrogen gas cloud, another from a helium gas cloud.Why should it be that the provenance of the collapsed matter that gave rise to the black hole isn't manifested in the measurable properties of the black hole subsequently formed? That's because information can't get out of the event horizon! Light is the means by which information might be transmitted, but we have already seen in Chapter 1 that it cannot escape from inside the event horizon of a black hole. Thus the chemical composition of the matter that fell into the black hole can have no effect on the properties of the black hole as determined from the outside. It would not be correct to think of gravity as something that needs to `get out of ' the black hole. The continued existence of a gravitational field external to the black hole is something that is laid down in the formation of the black hole as spacetime becomes distorted. No influence from inside the black hole could change the external field after the event horizon has formed.

Black holes have no hair

When we are asked to describe another person, a distinguishing characteristic that is often included is their hair (for example,strawberry blonde, or silver grey or chocolate brown). There are sometimes clues in the nature of people's hair as to their age or their nationality. Information about further physical characteristics such as `Body Mass Index' might provide information on their diet. In contrast to humans, black holes are entities that have absolutely no distinguishing characteristics other than their mass and their spin (neglecting charge for the reasons noted above). This is captured in the breviloquent phrase`Black holes have no hair', coined by JohnWheeler to emphasize that there is nothing about a black hole that bears any evidence of the nature of its progenitor star. Not its shape, not its lumpiness,not its landscape, not its magnetism, not its chemical composition.Nothing. Calculations done by, amongst others, the Belarusian physicist Yakov Zel'dovich demonstrated that if a non-spherical star with a lumpy surface collapsed to form a black hole, its event horizon would ultimately settle down to a smooth equilibrium shape having no lumps or bumps of any kind. So, a black hole never has a bad hair day! The only things you can know about it are its mass and spin.

Spin changes reality

Perhaps the most remarkable feature of a spinning black hole is that the gravitational field pulls objects around the black hole's axis of rotation, not merely in towards its centre. This effect is called frame dragging. A particle dropped radially onto aKerr black hole will acquire non-radial (i.e. rotating) components of motion as it falls freely in the black hole's gravitational field.

What this means for a test particle having spin (such as a small gyroscope) is that if it falls freely towards a rotating massive body,such as a Kerr black hole, it will acquire a change to its spin axis.It is as though its local frame of reference was dragged by the rotation of the central massive body. This phenomenon,discovered in 1918, called the Lense-Thirring effect actually occurs not just around black holes, but to some extent around any spinning object. If you put a very precise gyroscope in orbit around the Earth, the frame dragging causes the gyroscope to precess.

It is Einstein's field equations that describe the mathematics of black holes and, as also mentioned in Chapter 1, Karl Schwarzschild solved these equations for the case of the stationary(non-rotating) black hole, a remarkable achievement given that he did this in 1915, the same year that Einstein introduced his general theory of relativity. The case of the spinning black hole was treated much later by New Zealander Roy Kerr in 1965. A few years after this, the Australian Brandon Carter explored Kerr's solution further still. Carter carried out an in-depth investigation into the consequences of the Kerr metric. He established that a spinning black hole causes a dramatic swirling vortex in the spacetime that surrounds it which arises because of the dragging of the reference frame. An example of a vortex is a whirlwind-close to the centre of the whirlwind the air swirls rapidly, carrying with it anything in its path, be it hay in a hay field or sand in a desert. Further from the whirlwind the air (and hence hay or sand) rotates much more slowly. So it is too, with spacetime surrounding a spinning black hole: far away from the event horizon, the speed at which spacetime itself rotates is slow, but at the horizon, spacetime itself spins with the same speed that the horizon spins.

The event horizon for the spinning (Kerr) black hole is much the same as for a non-spinning (Schwarzschild) black hole, except that the faster the black hole is spinning, the deeper the gravitational potential well: a Kerr black hole forms a deeper gravitational potential well than a Schwarzschild black hole of the same mass,and therefore a Kerr black hole can be a more powerful energy source than a non-spinning one, a point to which we return in Chapter 7. In the meantime, it is helpful to summarize this behaviour by saying the event horizon of a Schwarzschild black hole depends only on mass, but that of a Kerr black hole depends on both mass and spin.

An outstanding question is whether there could be, even in principle, any spacetime singularities that are not enclosed within and hidden by event horizons-a so-called `naked singularity'. By definition, all black hole solutions to the Einstein field equations do have event horizons and, as shown in Chapter 1, no light and therefore no information can escape from within such horizons.All black hole singularities are believed to be enclosed within event horizons and therefore not `naked', so that direct information about the singularity is inaccessible from the rest of the Universe. The so-called cosmic censorship conjecture was formulated by the British mathematician Roger Penrose and states that all spacetime singularities formed from regular initial conditions are hidden by event horizons and that there are no naked singularities out in space.

How much spin is too much?

There is a limit to how much angular momentum a black hole can have. This limit depends on the mass of the black hole, so that a more massive black hole can spin faster than a less massive black hole. A black hole that is rotating close to this maximum limit is known as an extreme Kerr black hole. It is possible to show that if you try to spin up a black hole, to make an extreme Kerr black hole, by firing rapidly rotating matter into it (i.e. giving it a stir)then centrifugal forces prevent the matter from even entering the event horizon.

Somewhat further out from the event horizon of a rotating black hole is another significantmathematical surface which is known as the static limit. The dragging of inertial framesmeans that if the spin of the massive body is non-zero then there are no stationary observers inside of this surface: every physically realizable reference frame inside the static limit must rotate.Within this surface, space is spinning so fast that light itself has to rotate with the black hole, i.e. it is impossible to remain motionless. The region between the static limit and the event horizon is known as the ergosphere, which rather confusingly is not spherical, as shown in Figure 10. In equatorial directions the ergosphere is much larger than the event horizon, but in the polar directions the radius of the ergosphere is the same as the radius of the event horizon. The resulting shape of the ergosphere is an oblate spheroid, resembling the shape of a Jarrahdale pumpkin(without the stalk). The first two syllables of ergosphere, however,come from the Greek noun 俽gon relating to `work' or `energy' (as in `ergonomics') from which the old unit of energy, the erg, is also derived. It is intriguing to note that in addition there is a Greek verb ergo which means to enclose and keep away, appropriately for the nature of the ergosphere. Perhaps this may have been in the minds of Roger Penrose and Demetrios Christodoulou who coined and championed the name of this region around a spinning black hole. The importance of the ergosphere is that it is the region within which energy can be extracted away from the black hole.

10. The different surfaces around a Schwarzschild (stationary)black hole and around a Kerr (spinning) black hole (in the frequentlyused representation of `Boyer-Lindquist' coordinates).

Since inside the ergosphere space is spinning, particles of matter within that space also get swept up into a rotational motion.Considerable rotational energy is therefore stored in this rotation of space, a very important point to which we return in Chapter 8.

White holes and wormholes

Einstein's equations of General Relativity are particularly rich and allow many different solutions describing alternative versions of curved spacetime. This provides an almost inexhaustible source of possible universes for cosmologists to describe and think about.Which type of universe we actually live in is a matter that can only be decided by observation (if at all!). But that doesn't stop mathematical physicists playing around with Einstein's equations to find all kinds of interesting solutions.

One intriguing object that can be dreamt up by mathematical physicists is what is called a white hole. A white hole behaves just like a black hole but with the direction of time reversed (imagine a movie played backwards). Instead of matter being sucked in, it is spewed out. Instead of the event horizon marking out the region from which you can never escape, it stakes out the region into which nothing could ever enter. Once matter exits from a white hole, it can never return there; its entire future is outside. As we see in Chapter 6, a black hole is formed from a collapsing star and must eventually evaporate by the laws of quantum mechanics into Hawking radiation (see Chapter 5). A white hole, on the other hand, could only result from radiation that for some reason spontaneously assembles into a black hole. It is not easy to understand how this could happen in practice, and moreover Douglas Eardley has demonstrated that white holes are inherently unstable.

When Einstein and his student Nathan Rosen were playing around with Einstein's equations in the 1930s, they found an interesting solution. If a region of spacetime could be strongly curved, it might be possible for it to become sufficiently folded that two parts of spacetime which had previously been separated by a large distance could become connected by a small bridge,or wormhole, as shown in Figure 11. The enormous distances between the stars and galaxies have always been unfavourable for those writers who wish to set human dramas on a cosmic stage,and wormholes (also known as Einstein-Rosen bridges) have provided the perfect plotting device for writers to transport their heroes and villains about. This mathematical invention has been an absolute boon to the writers of science fiction, because it provides a ready means for traversing enormous distances through space and thereby to sustain various highly artificial and unbelievable plot devices. Yet again, we have no observational evidence that wormholes actually exist in our Universe. In addition, there is considerable theoretical evidence that a wormhole, once formed, would not be stable for very long. It seems that to keep a wormhole propped open, one needs a large amount of negative energy matter, and all normal matter has positive energy (this is connected with the fact that gravity is normally always attractive). Normal matter passing through a wormhole may be enough to destabilize and destroy it, causing it to turn into a black hole singularity.

11. A wormhole connecting two otherwise separate regions ofspacetime.

If wormholes did exist, and could be maintained for any reasonable length of time, they would have some surprising and bizarre properties. Not only would they provide a means for taking an enormous shortcut across a vast expanse of space, but they would also allow a traveller to journey back in time. One would then be able to construct closed time-like curves, loops in spacetime in which the light cones form a ring (see Figure 12) so that, like in the movie Groundhog Day, a person travelling along a closed time-like curve would simply repeat their same experiences over and over again.

In fact, there are a number of solutions to Einstein's equations in addition to wormholes which have this alarming and counterintuitive property. In 1949, the mathematician Kurt Göel found a solution that described a spinning universe, and this contains exactly the same sort of closed time-like curves which pass through events again and again in an endless Groundhog Day cycle. (Evidently `free will' is not part of the field equations!)The part of the Kerr solution thought to have genuine physical significance in the real world is that which describes the spacetime outside of the event horizon. However, it is unclear whether the part of the Kerr solution inside the event horizon, while mathematically sound, has any physical relevance. In this part of the Kerr solution, the singularity is not a point (as it is for the non-rotating black hole) but has the form of a rapidly rotating ring(however, the physical validity is very speculative). This ring-like singularity is surrounded by closed time-like curves. On such a curve, your future is also in your past and you have the theoretical possibility of murdering one of your own grandparents before they had produced your parents! Thus the existence of closed time-like curves seems to create the possibility of all kinds of paradoxes relating to time travel. One possible solution to this is to admit that we do not have a theory that links quantum mechanics (which describes the very small) and general relativity (which describes the very massive), in other words a theory of quantum gravity.We don't know the physics of extremely massive but very small objects.Most physicists think we need this to fully understand the behaviour of spacetime very close to singularities. Thus it may be that these strange solutions to Einstein's equations do not actually occur in the Universe because they are prohibited by its fundamental quantum mechanical nature. Quantum effects may,for example, destabilize wormholes. Stephen Hawking believes this to be the case and has called this principle the `Chronology Protection Conjecture'. He has quipped that this is the underlying principle that keeps the Universe safe for historians.

12. A closed time-like loop, on which your future becomes your past.

There is much about the interior of rotating black holes that pushes our understanding of fundamental physics to the limits and therefore to where much of our description is highly speculative. By contrast, the rotation of black holes and their effect on their surroundings is something that has enormous practical significance for understanding what we can see with our telescopes. Thus our next step is to consider in more detail what happens to matter when it falls into a black hole.

Chapter 4 Falling into a black hole . . .

How close is too close?

Before we can consider in detail what would happen if you or your belongings had the misfortune to fall into a black hole, it is important to understand the effect of an observer's particular perspective, or frame of reference. This means that different observers see very different things. Exactly what your perspective is on an object falling into a black hole depends on how far away you are from that object (and indeed whether you are that object!). Consider a particle of light, a photon, that is outside the event horizon of a black hole: since it is outside the horizon, it can in principle escape. Inside the event horizon it would be a different story-the photon could not escape the gravitational field of the black hole. But even outside the event horizon, a photon that is travelling away from the black hole will not escape completely unscathed. The photon suffers a loss in its energy due to the work it has to do against gravity. This is an example of a gravitational potential well; just as energy would be needed to haul yourself upwards out of a deep well, so the photon needs to expend energy to pull itself away from the region near a massive object. The effect has even been measured for photons moving in the Earth's gravity.The energy of a photon is inversely related to its wavelength: a high-energy photon has a short wavelength whereas a low-energy photon has a long wavelength. The photon loses energy as it retreats away from the black hole, so its wavelength increases.This changes the colour of the light, moving from the blue (short wavelength) towards the red (long wavelength) end of the spectrum (this effect is called redshift). This sort of redshift,known as gravitational redshift, arises where spacetime itself stretches out, or is curved, for example by the effect of a massive body such as a black hole. Note that John Michell, despite having significant original thoughts about dark stars, was incorrect in thinking that the velocity of light decreases as it climbs out of the potential well.We now know that it is the wavelength(hence frequency) of light that is affected by the presence of a massive star.

What happens to time near a black hole?

In Chapters 1 and 2 I described how spacetime is distorted by the presence of a mass (i.e. something which produces its own gravitational field) and this means that not just space, but also time is affected close to a black hole.

Imagine you want to keep a safe distance from a Schwarzschild black hole but you want to learn more about how time behaves nearby. Thus you have arranged for twenty-six fixed observers to be stationed close to the black hole's event horizon but definitely safely outside it. These observers are named A to Z, and are arranged in a line with A closest to the event horizon and with Z being nearest to you, safely far away. Each observer from A to Z has a good clock with which to measure their local time, at their particular location. As part of the deal to persuade A to Z to participate in this experiment, you had offered them each an inducement in the form of a gift of an additional, unusual clock that had been adjusted so that the time on it would read the same as the time on your clock at your safe distance. Participant Z,closest to you, would find that the two clocks in his possession read slightly different times because his own clock, which measures local time (`proper time' in the jargon),would be running slightly more slowly than the gift clock which matches the time you measure at your rather safer and more remote distance.The collated results of participants Z to A would display a remarkable effect: closer to a black hole, a clock measuring time`runs more slowly' compared with the distant time as reported on the participants' specially adjusted gift clocks. This effect,described by Einstein's theory of general relativity, is known as time dilation. The effectwould be greater and greater for the observers nearer the start of the alphabet who are nearer to the black hole. The greater the proximity to a black hole, the more slowly a local clock (of any kind: atomic, biochemical) will run compared to a clock used by a distant observer.

Suppose you were multi-tasking your experiments with a different set of twenty-six observers at the same distances from a different black hole. They are arranged in just the same way as their namesakes near the first black hole. However, in this second case,the black hole has twice the mass of the black hole in your first experiment. The unusual clocks you had prepared as gifts for this second set of observers would need to be radically altered as for your original experiment, but the rate at which each unusual clock has to be adjusted is exactly double that of the rate needed for the corresponding clock in the first set of gift clocks at the exact same distance from the centre of the first black hole which has half the mass of the second. These time dilation effects are larger if the black hole mass is larger, and also become more extreme the closer you get to the event horizon.

Note that this time dilation is not a consequence of some additional light-travel time for a clock closer to the black hole and hence further from you, the safely-distant observer: there is not merely a time offset for an observer further away from the black hole. The closer a clock is to a black hole, the slower is the rate at which time is measured to flow on that clock, no matter what reputable means you use to measure that flow of time. Time itself is stretched (or, indeed, dilated).

What is the corollary of time dilation near a black hole? This causes effects that happen in the frame of an observer very local to the black hole to be measured to be very different from those in the frame of an observer who is very distant, worlds apart in fact.

Let's now consider what happens if in your first experiment,observer A became a little careless and dropped his first clock(the one with which he could measure proper time at his location)so that it fell towards the black hole. Despite this disaster, he would be nonetheless safely gripping onto the gift clock with which you had enticed him to participate in the experiment. Both you and A would see his first clock move towards the hole. The clock would find itself moving into the black hole, more and more rapidly. You and A would gradually notice that the time you read on the plummeting clock becomes even more discrepant with the time on A's other clock (namely the clock that was adjusted to run faster than the local clock in order that it would read the same time as the one corresponding to your time). After a while both you and A would begin to notice that time stops for the plummeting clock. A photon emitted at the event horizon towards a distant observer appears to stay there indefinitely.What happens to anything that falls into a black hole after it has passed within the critical radius of the event horizon is unknowable to an external observer. So the event horizon may be regarded as a hole in spacetime. No light will emerge from within the event horizon,as we saw in Chapter 1. That is why it is black. However, in the reference frame of the dropped clock plummeting through the event horizon, life is very far from unchanging. From the clock's perspective, it would travel to the singularity in a mere one ten-thousandth of a second, assuming that the black hole had a mass of ten times that of our Sun. If the clock had the misfortune to fall into a supermassive black hole with a mass one billion times that of our Sun (such as we meet when we study quasars in Chapter 8), its journey time inwards between the vastly larger event horizon and the singularity would be a more leisurely few hours.

Tidal forces near a black hole

Suppose in a weak moment, person A wonders about jumping,feet first towards the black hole, in hopes of being reunited with the clock he dropped. What would happen? Such a leap would prove to be a big mistake, as the survival outcome would be zero.The difference between the gravitational force on his feet and the force on his head would become extreme. This is a feature of any inverse-square force field, such as gravity from a massive body.The Earth is rather a long way from the moon, yet even the small differences in gravitational force due to the moon experienced on opposite sides of the Earth, known as tidal forces, are at the root of why the tides come and go about twice per day. In general, these forces resulting from differences in gravity in different places are called tidal forces. There are additional factors that enrich the details of the rising and falling of tides such as the gravitational force due to the relative angle of the moon, and the detailed shapes of continental masses. But even if the surface of Earth were entirely covered by ocean without land, there would still be tides with the amplitude of the sea level varying by about 20 cm twice per day, simply because of the differential gravitational force experienced by points on the planet at different distances from the Sun.

Let's now consider the smaller distance between me and the centre of the Earth. As I sit typing this chapter, my head is somewhat over a metre higher than my feet which are on the floor of my study. My feet are thus closer to the centre of the Earth than my head is. Because the gravitational force follows an inverse-square law behaviour as though all the mass of the Earth were located at the very centre of the Earth, and because my feet have a smaller distance to this centre they feel a stronger force, or pull, to the centre of the Earth than my head does. But actually,the difference is rather slender: for a height difference of one metre the difference in gravitational force is three parts in ten million. This is such a slight difference because I am about6,400 km from the centre of the Earth. Much closer to a point mass such as a black hole, the difference in gravitational force experienced at points just a metre apart in the direction towards the black hole would be vastly more extreme. So extreme that close to the singularity A's feet would be stretched away from his knees and the rest of his body beyond what his tendons and muscles could hold together, and he would be elongated into something resembling long spaghetti. Best not to jump.

Dynamic spacetime

The rotation of a black hole makes an important difference regarding how close matter can orbit around it, and this relates to how much energy can be extracted from it. From the work of Roy Kerr and his solution to the Einstein field equations, we know that the smallest orbit that a particle can have around a black hole without falling in depends on just how fast the hole is spinning.The faster a black hole is spinning, the closer the matter can get before the hole swallows it, as illustrated in Figure 13. If you drop something straight down into a spinning black hole, it will start orbiting the hole even though there is nothing but empty spacetime outside the hole. Outside the ergosphere, it is possible to overcome this frame dragging using rockets, but not inside it. In the region inside the rotating black hole's ergosphere, just outside its event horizon, nothing can stand still. The spinning hole actually drags the spacetime and hence its contents around with it.A further aspect of this frame-dragging is that even if light itself is going against the direction the black hole is rotating, it will be carried in the reverse direction around the hole.

13. Gas can orbit closer to a spinning black hole than to a non-rotatingone.

Orbiting around a black hole

It is interesting to ponder what would be the sequence of events if our Sun were to spontaneously metamorphose into a black hole right now. The first that you or I could know about it would be eight minutes later; the beautiful Spring sunlight by which I am writing would come to an abrupt halt. Although the luminosity of the single star we call our Sun is tiny by comparison with the quasars and microquasars discussed in Chapter 8, it is sufficiently close to the Earth that it provides on average about a kilowatt per square metre of power to our planet. Remarkably, this has been enough to sustain all life on the planet, allowing plants to grow and then be eaten by animals that are then eaten by other animals.The Sun has been the engine behind it all. But if fusion ceased in the Sun and it were (contrary to all expectation) to collapse into a black hole, then it would go very dark and we would all eventually die. (This is a bit of a gloomy outlook, but I encourage the reader to hold fast until Chapter 7, where we learn that our Sun is not the kind of star to form a black hole-it's too lightweight for that.)However, dynamically speaking, as far as planet Earth and the whole Solar System of planets, dwarf planets, and asteroids are concerned, nothing will change at all. All massive bodies in orbit around the Sun will continue in pretty much the same orbits. The way that gravity works is that whether the Sun has the same extent that it has now, or whether it collapses to a singularity within an event horizon of 3 km, the gravitational attraction outside the Sun would remain unchanged. The spherical collapse under gravity to a black hole would not change the angularmomentumof the orbiting bodies at all, so the patterns and progressions and tides within the Solar System would continue utterly unaltered by the lack of sunshine.

Some new orbits would be possible however, much closer to the black-hole Sun than were possible previously when the solar plasma was in the way. However, these orbits could not get too close to the event horizon. The details of the warping of spacetime by a mass singularity mean that it is not possible to orbit just outside the event horizon itself. Attempting a circular orbit there would require corrective action by rockets in order to maintain the orbit. In fact, the mathematics shows that the closest that we or any other mass particle could exist on a stable circular orbit near a stationary black hole would be at a distance three times that of the Schwarzschild radius away. You have been warned.

Actually, unstable circular orbits are possible up to half this distance away from a Schwarzschild (non-spinning) black hole.This distance defines a spherical surface that is sometimes called the photon sphere. Even for a photon, these orbits are unstable,and before too long an orbiting photon would either slither in towards the black hole, never to return, or indeed away into space.

For a Kerr black hole though, one that has spin, the situation is different for the orbits near the black hole. In particular, there are two photon spheres, in contrast with the one photon sphere around a stationary Schwarzschild black hole. The outermost sphere is for photons that are orbiting oppositely to the direction of rotation of the black hole (the ones we say are on retrograde orbits). Inside this is the photon sphere for photons travelling in the same sense around the black hole as it is rotating (on prograde orbits). For a very slowly rotating black hole that isn't so very different from a Schwarzschild black hole, these two photon spheres are very nearly co-spatial. For black holes of increasing spin, these surfaces are increasingly further apart.

Moving closer in towards a rotating black hole, there is another important surface (discussed in Chapter 3), called the static limit.This is the surface at which nothing can remain static with respect to a distant observer: it is just impossible to sit still this close to a rotating black hole, no matter how powerful the rockets you might be equipped with. At this surface, even retrograde light rays are dragged along in the direction of rotation. It is still possible to escape from this close to a rotating black hole, with sufficient propulsion, but it's just not possible for anything to remain stationary and non-rotating here. Moving inwards still further,the next surface of significance is the event horizon we met in Chapter 1, the one-way membrane that we met originally in the context of Schwarzschild black holes. Crossing this outwards isn't possible and crossing it inwards has an ineluctable destiny, just as for the static black hole.

An orbit around a Kerr black hole is not generally confined to a plane. The only orbits confined to a plane are those in the plane that contains the equator (i.e. the plane of mirror symmetry of the spinning black hole). Orbits out of this equatorial plane move in three dimensions. These orbits are confined to a volume that is limited by a maximum and minimum radius and by a maximum angle away from the equatorial plane.

The details of the spin of a black hole have a dramatic effect on how close particles may encounter the black hole, which itself depends on their direction of travel relative to the spin. For a maximally spinning black hole, the photon sphere for light rays orbiting in the same sense (prograde) as the black hole spin has a radius that is half of what the Schwarzschild radius would be. For light rays on retrograde orbits, the radius of their photon sphere is twice the Schwarzschild radius. For particles with mass that are on prograde orbits, the innermost stable circular orbit on which they can move is again at half of the Schwarzschild radius. For those on retrograde orbits, such a close distance would be unstable: their innermost stable circular orbit is at 4.5 times the Schwarzschild radius. Thus, a rotating black hole enables particles on prograde orbits to orbit more closely without reaching the point of no return at the event horizon, more closely than if the black hole were non-rotating. In Chapter 7, we consider the importance of just how close matter can orbit before falling onto a black hole and how much energy may be consequently leveraged.

Chapter 5 Entropy and thermodynamics of black holes

You are what you eat

It is often said that you are what you eat. Thus if your diet is purely junk food and chocolate, then your complexion, not to mention your physical and mental well-being, will be rather different than if you subsist on a healthy diet of salad andMediterranean food.However, it seems that black holes are not fussy eaters. Whether they are hoovering up a vast expanse of interstellar dust or a cubic light-year of fried eggs, their mass will similarly increase inexorably. In fact, after a black hole has finished its sumptuous meal, you have no way of telling what it was eating, only how much it has consumed (although you could tell if what it ate had charge or angular momentum). You only know the quantity of its diet, not about the quality. The `no-hair theorem' described in Chapter 2 says that the black hole is only characterized by a very few parameters (mass, charge, and angular momentum), and thus we cannot talk about what the black hole is made of.

This lack of knowledge about the nature of what has been sucked in by a black hole may seem like a trivial observation, but it is actually rather profound. Information about a black hole's lunch menu has been fundamentally lost. Any matter which has fallen into the black hole has surrendered its identity.We can't perform measurements on that matter, or discern any details about it.

Black holes and engines

This situation is eerily familiar to those who have studied the beautiful subject of thermodynamics. In that field it is quite common to understand how information can become lost or dissipated through physical processes. Thermodynamics has a long and interesting history. The modern theory began during the industrial revolution when people were trying to work out how to make steam engines more efficient. `Energy' could be defined in such a way that it was always conserved and could be converted between different forms. This is known as the first law of thermodynamics. However, although you can make some conversions between different types of energy, there are particular conversions you are not permitted to make. For example, although you are allowed to convert mechanical work completely into heat(you do that every time you use the brakes to bring your car to a complete stop), you cannot convert heat completely into mechanical work, which unfortunately is precisely what we would like to do with a steam engine. Therefore a steam engine in a train only succeeds in making a partial conversion of heat from the furnace into mechanical work which turns the wheels. It was ultimately realized that heat is a type of energy involving the random motion of atoms, while mechanical work involves the coordinated motion of some large bit of matter, like a wheel or a piston. Therefore, a crucial component of the nature of heat is randomness: because of the jiggling of atoms in a hot body, you lose track of the motion of the individual atoms. This random motion cannot simply be unrandomized without additional cost.The randomness, or to give it the technical name, entropy, in any isolated system never decreases but must always either stay the same or increase in every physical process. (This is the second law of thermodynamics.) One way of looking at this is to say that our information about the world always decreases because we cannot keep track of the motion of all the atoms in a large system. As energy moves from macroscopic scales to microscopic scales, from a simplemoving piston to the randommotion of huge numbers of atoms, then information is lost to us. Thermodynamics allows us to make this vague-sounding notion completely quantitative.This information loss turns out to be exactly analogous to what we've been describing for matter falling into a black hole.

Although thermodynamics was developed for steam engines, the principles are thought to apply to all processes in the Universe.One of the first people to think about this in connection with black holes was the Oxford physicist Roger Penrose. He reasoned that because a black hole has spin, it might be possible to extract energy from it and thus to use it as some kind of engine. He came up with an ingenious scheme in which matter is thrown towards a spinning black hole in such a way that some of it emerges with more energy than was thrown in. Energy is extracted from the region just outside the event horizon (in fact from the ergosphere discussed in Chapter 3). Penrose's process slows the rotation of the black hole. In principle, an enormous amount of energy can be extracted from a black hole in this way, but of course this is just a thought experiment and so doesn't seemto be at present a practical solution to planet Earth's looming energy crisis!Within a few years of Penrose's work, James Bardeen, Brandon Carter, and Stephen Hawking made a landmark advance and formulated what they called the three laws of black hole dynamics which laid the foundations for Hawking's later thinking on the thermodynamics of black holes, which required the concept of temperature for a black hole which is determined by its mass and spin.

Black holes and entropy

Penrose's insight was a significant impetus and got others thinking about the thermodynamics of black holes. Together with R. M.Floyd, he showed that in his imagined process the area of the black hole's event horizon would tend to increase. Stephen Hawking started working on Penrose's clever scheme. The area depends on the mass and spin (and charge) in a rather complicated way, but Hawking was able to prove that in any physical process this area always increases or remains the same.One of the consequences of this intriguing result is that if two black holes coalesce then the area of the black hole event horizon of the merged black holes is larger than the sum of the areas of the two original black hole event horizons. (This is intuitively reassuring because the radius of the event horizon scales with mass, and surface area has a well-known dependence on radius.)This is the same sort of behaviour that we see with entropy in thermodynamics and therefore people began to wonder whether the entropy of a black hole and its area were somehow connected.Is this more than just an interesting analogy? One of John Wheeler's students, Jacob Bekenstein, went ahead and proposed a direct connection in his PhD thesis. Bekenstein used the ideas from the information theory of thermodynamics to argue that the area of a black hole event horizon is proportional to its entropy.(The choice he made means that you take the area of the event horizon and divide by one of physicists' fundamental constants,the Planck area, which is roughly 10-70
square metres, and within a numerical factor you get the entropy. This choice of unitsmakes the entropy of a black hole absolutely enormous.)

Initially Hawking didn't believe Bekenstein's results, but on further examination he was able not only to confirm the approach but deepen our understanding of how black hole thermodynamics works. It is perhaps worth understanding how these analyses are done so one can appreciate both their power but also their limitations. The ideal way forward in this field would be to use a combination of quantum mechanics and general relativity, called quantum gravity, to study systems which are both very small, like a singularity in a black hole, but in which gravity plays a big role.Unfortunately we do not have a good theory of quantum gravity at present. A good approach is to use general relativity to model how spacetime curves and then use this together with quantum mechanics to understand the behaviour of particles in the curved spacetime. This was the approach that Hawking took to attempt to understand the thermodynamics of black holes.

Is empty space empty?

The concept of the vacuum (a region where there is `nothing' there) has had a long and tortuous history.Most of the ancient Greek philosophers hated the idea, on grounds that today seem extraordinarily arcane, but there were a small band of atomists who included the vacuum in their description of the world. Until the scientific renaissance, the idea of the vacuum was therefore very much out of fashion. However, following the invention of the air pump in 1650, the vacuum was something that you could experimentally demonstrate. Even though the amount of air that you could pump out of a vessel in the seventeenth century still gave you a rather poor vacuum by modern standards, the idea of nothingness had become substantially more believable. Once the existence of atoms had been demonstrated beyond all reasonable doubt in the early 20th century, the idea of a region of space with no atoms in it became not only uncontroversial, but inevitable.

No sooner had atoms been demonstrated than a new theory of physics arose: quantum mechanics. One of the surprising consequences of this new theory was that there were fleeting moments when it seems like energy needn't be conserved. The first law of thermodynamics, the grand and seemingly unbreakable principle of physics, insisted that at every moment and at every place there had to be a strict accountancy between energy debits and energy credits. `Energy must always balance!' thunders the Cosmic Accountant. In fact, it seems that the Universal accountancy rules are more lenient and it is possible to obtain credit. It is perfectly acceptable to borrow energy for a short period of time as long as you pay it back quickly afterwards. The amount you can borrow depends on the duration of the loan, by an amount described by the Heisenberg Uncertainty principle. For example, even in the supposedly-empty vacuum it is possible to borrow enough energy to make a particle and anti-particle pair.These two objects can wink into existence and then after an extremely short period annihilate each other, thereby paying the energy back within the maximum allowed time limit (a time interval which is shorter the more energy is borrowed). Such a process goes on everywhere, all the time. It can even be measured!We now understand that the vacuum is actually not empty, but is a soup of these pairs of so-called virtual particles winking in and out of existence. Thus, the vacuum is not sterile and unoccupied, but is teeming with quantum activity.

Black hole evaporation and Hawking radiation

Hawking used the modern theory of the vacuum, quantum field theory, to study its behaviour close to the event horizon of a black hole. His analysis was mathematical but we can picture it in quite a simpleway. The essence is that a pair of `virtual' particles, a particle and its antiparticle (opposite in charge, identical in mass),created close to the event horizon of a black hole may end up becoming torn apart from one another. If one of that pair, either the particle or the anti-particle, falls into the event horizon it will plunge into the singularity and can be never recovered. However,its partner may remain outside the black hole. This particle has lost its virtual partner but it is now nonetheless a real particle and has the possibility of escape. If the particle does escape, rather than falling back in, it forms part of something called Hawking radiation. As far as a distant observer is concerned, the black hole has lost mass because a particle has been emitted.What had been realized is that, taking account of quantum field theory, black holes are not completely black, but they can actually emit particles. This argument also applies to photons, and so very weak light (also known as electromagnetic radiation) emerges from a black hole if Hawking's argument is correct.

All bodies at non-zero temperature emit thermal radiation as photons. You do this yourself, which is why you would show up on an infra-red camera even in the dark (and this is why the police and the military use such cameras). The hotter the body, the higher the frequency of the radiation.We emit infra-red radiation,but a red-hot poker is hot enough to emit visible light. Because a black hole emits Hawking radiation, it has a temperature (known as the Hawking temperature) as we have seen earlier, although this is normally incredibly low. A black hole with a mass of one hundred times that of the Sun has a Hawking temperature less than a billionth of a degree above absolute zero (which is273 degrees below the freezing point of water)! This is one reason why Hawking radiation has not yet been detected: it is incredibly weak. But it is believed to be there.

Hawking radiation does however have an interesting consequence on the evolution of black holes: it is ultimately responsible for a black hole's eventual death. Think again about the two virtual particles. The energy of the real particle which escapes from the black hole has to be positive, but since the virtual particle pair appeared spontaneously from the vacuum, then the virtual particle sucked into the black hole must have negative energy to compensate. Because energy and mass are connected, the net effect of this process is that the black hole has had negative mass added to it, and therefore its mass will have decreased due to the emission of Hawking radiation.

Hawking had therefore discovered a mechanism by which a black hole can evaporate. Slowly, over time, the black hole will emit radiation and lose mass. This process is initially incredibly slow. It turns out that the larger a black hole is the smaller is its `surface gravity'. This is because even though the surface gravity depends on mass, which is larger for a big black hole, gravitational attraction follows an inverse-square law and more massive black holes are larger. The net result is that large black holes have very little surface gravity and this equates to a very low temperature.A large black hole therefore emits lessHawking radiation than a small black hole.

However, as a black hole evaporates and loses mass, the amount of Hawking radiation goes up as the surface gravity and hence temperature increases. Assuming the black hole isn't receiving any other energy, this makes the rate of mass loss faster and faster until, at the end of its life, the black hole simply pops out of existence. Thus the life of a black hole ends not with a bang but with that quiet pop. This evaporation process is only possible for black holes whose temperatures are higher than their surroundings. At the current epoch in cosmic history, the temperature of the Universe, measured from the spectral shape of the CosmicMicrowave Background radiation, is 2.7 degrees above absolute zero. Black holes with masses greater than a hundred million million kilos will not evaporate at the current epoch because their temperatures are lower than that of their surroundings. These black holes which have a slender fraction of the mass of the Sun, however, will be able to evaporate when the Universe has cooled more following further expansion. Up to this point in cosmic time, all black holes whose masses were less than one per cent of this slender value would have evaporated away by now.

The black hole information paradox

One question which arises from all of this is what happens to the information stored in the matter that fell into the black hole? One school of thought holds that this information is lost for ever, even if the black hole subsequently evaporates. Another point of view claims that that information is not lost. Because black holes evaporate, the argument goes, the information contained within the original matter that fell into the black hole must somehow be stored in the radiation from the black hole. Thus if you could analyse all the Hawking radiation from a black hole and understand it completely you would be able to reconstruct the details of all the matter that had originally fallen into the black hole. There was a famous bet between, on the one hand Stephen Hawking and Kip Thorne, and John Preskill on the other, about this very matter. Thorne and Hawking took the former position,while Preskill took the latter. The agreement was that the loser would reward the winner with an encyclopaedia of the winner's choice. In 2004, Hawking was sufficiently persuaded by the idea that information could indeed be encoded in the radiation from a black hole that he conceded the bet, supplying Preskill with an encyclopaedia about baseball (whether that constitutes a repository of meaningful information depends on your opinion of baseball); however, the matter is still debated.

Despite all these ingenious theoretical speculations, it is worth saying again that even ordinary Hawking radiation from a black hole has not yet been observed. The history of physics is littered with the relics of old, ingenious but ultimately wrong, theories.Experiments and observation have frequently been surprisingly effective at bringing forth unexpected results. Indeed,observations of spectacular phenomena have emerged that probably no-one at all would have predicted from first principles for black holes. One of the reasons that the faint Hawking radiation has not been observed is that many black holes we know about are at the centres of some of the brightest objects in the Universe, and these black holes are way too massive, and hence way too cold, to evaporate via Hawking radiation. These objects are extraordinarily bright for a completely different reason, which is examined in Chapter 6 and in Chapter 8.

Chapter 6 How do you weigh a black hole?

The Sun, the planets that orbit around it, together with dwarf planets (of which Pluto is the most famous example), asteroids,and comets collectively comprise the Solar System. The Solar System itself orbits within the disc of our Galaxy around its centre of mass at the Galactic Centre. The speed atwhich our Solar System travels around its circular path through the Galactic disc is about 7 km/s, and to complete an entire circuit around the Galactic Centre will take a couple of hundred million years. In addition to this orbital motion, the whole Solar System moves perpendicular to the Galactic plane. The kind ofmotion it exhibits is well known to physicists as simple harmonic motion with the restoring force, which pulls our Solar System back towards the equilibrium position of the plane of the Galaxy, coming from the gravitational pull of the stars and gas that comprise the Galactic disc. At the moment, we are about 45 light-years above this equilibrium point. In about 21 million years from now the Solar System will be at its extreme point 320 light-years above the Galactic plane. 43 million years after that, the Solar System will be back in the mid-plane of the Galaxy.When the Solar System lies in the centre of the Galactic plane then, the Earth will suffer maximum exposure to the cosmic rays that are whizzing around in the plane of the Galaxy, trapped along lines of magnetic field,and travelling around them on some kind of a cross between a helter-skelter and a tramline. There have been speculations that the Sun's motion through the Galactic plane could have been responsible for the mass exinction of dinosaurs. But this kind of speculation is hard to verify or refute because the timescales for this orbital motion are of course rather tricky for human observers, who don't tend to live longer than one century. This is a common problem in observational astronomy when we want to follow some process that changes on timescales much longer than the few centuries over which we've been making astronomical observations of any reasonable accuracy and thoroughness.

There are, however, orbital motions within the Galaxy that are significantly easier to measure, at least in the sense that the relevant timescales are commensurate with the attention spans of humans and their telescopes. Of particular interest in the context of black holes are the orbital motions of the stars in the innermost regions of theMilkyWay, that appears in a part of the sky known as SagittariusA*. Looking into this region, most easily seen from the southern hemisphere, one is looking towards the very centre of our own Galaxy, 27,000 light-years away from us. This is a particularly densely populated region of space, which leads us to two problems when we want to study the Galactic Centre. The first is that there is a relatively high space density of stars and the second is that there is lots of dust.

The first problem means you need to use a measurement technique that enables high resolution imaging, i.e. fine details can be separated from one another in the way that a telephoto lens gives finer detail on a given camera than a wide-angle lens does.Just using a larger telescope is invariably insufficient for this,but there are various techniques developed for untangling the turbulence in Earth's atmosphere through which we inevitably view all celestial objects, unless we put the telescope on a satellite above the atmosphere. Of particular importance is a technique known as adaptive optics. This technique corrects for atmospheric variations by observing the blurring of a bright star (called a guide star) and deforming the primary mirror of the telescope to cancel out this varying blurring. When a bright star isn't available in the part of sky that is of interest, a powerful collimated laser beam can be shone up to excite atoms in the atmosphere and the atmospheric corrections derived from that.

The second issue, the presence of vast quantities of dust towards the Galactic Centre, is problematic because it is hard to see optical light through dust, just as it is hard for ultra-violet light from the Sun to penetrate through the opacity of a sunhat. The solution to this problem is that one needs to observe at infra-red wavelengths rather than visible wavelengths.

How to measure the mass of the black hole at the Galactic Centre

Such infra-red observations have been championed by two groups,one led by Andrea Ghez in California and one led by Reinhard Genzel in Germany. The work of both teams independently provides a wonderfully clear measurement of the mass at the centre of the Galaxy. Figure 14 shows the data from Andrea Ghez and her team. Over the last few years they have made repeated observations right into the very heart of the Galactic Centre and watched how the stars have moved since the last time they observed them. Because the spectral types of these stars are known, their masses are known. Year by year, as the orbital path of each of these stars becomes apparent, the dynamical equations(known as Kepler's laws, the same laws that govern the motion of the planets around our Sun) enable Ghez and her team to solve for each orbit independently and deduce the mass of the `dark' region that is at the common focus of all these orbits. These independent solutions determine the mass of this dark region rather well. It is now known to be just over 4 million times the mass of our Sun,within a region whose radius is no more than 6 light-hours.Because the object is dark but extraordinarily massive, the only conclusion is that there is a mammoth black hole at the centre of our Galaxy.

14. Figure showing the successive positions of stars that orbit around the central black hole in our Milky Way.

There is no reason to believe that our Galaxy, theMilkyWay, is unique in having a black hole at its centre. On the contrary, it is strongly suspected that all galaxies may well have a black hole at their centres, at least the more massive ones. The reason for this is because of a seemingly fundamental relationship, discovered by John Magorrian, then at the University of Durham, and co-workers, between the mass of a black hole at the centre of a galaxy and the mass of the galaxy itself. Of course the business of measuring the mass of a black hole and the mass of a galaxy is tricky. The technique that works so beautifully at the centre of our Galaxy cannot be applied to external galaxies because they are simply too far away.

The masses of the central black holes at the hearts of elliptical galaxies exceed a million times the mass of our Sun and indeed extend up to and beyond a billion times the mass of our Sun. For this reason, they are often termed supermassive black holes.

Despite the difficulties in measuring the masses of black holes and the masses of galaxies, it has been found for a wide range of different galaxies that the mass of the central black hole scales with the mass of its host galaxy. This is thought to suggest that both the central black hole and the galaxy itself grew and evolved together across cosmic time.

Many black holes throughout the Galactic disc

Besides the single, central supermassive black hole at the heart of a galaxy, there are thought to bemillions of black holes distributed throughout the extent of each galaxy, and these are believed to have formed in a very different way from the galactic-central ones which grow by gradual accretion of infalling matter. These stellar mass black holes are formerly massive stars, once shining very brightly, with fusion powering away inside them keeping them very hot and pressurized, and crucially able to resist gravitational collapse.When their nuclear fuel is all used up, there is no longer any radiation pressure to hold up the star, and nothing to balance the inward force of gravity. For a star with a similar mass as our Sun, the collapse under gravity ultimately results in a compact object known as a white dwarf. The word compact has special meaning in astrophysics and connotes that the matter is dense in a way that is utterly distinct from normal matter. By the standards of normal matter, white dwarfs are compact because the matter has been extremely compressed. This matter is ionized, meaning that all the electrons are separate from their parent nuclei, yet cold (normally matter is only ionized at high temperature). The pressure that withstands the persistent inward gravitational pull arises from the electrons refusing to be compressed into too confined a region (a consequence of the Heisenberg uncertainty principle); the technical name for this effect is `electron degeneracy pressure'. Had the collapsing star,when it had used up all its fuel, been more massive, then the gravitational infall would have been greater still and the electrons and their counterpart protons would have fused together to form neutrons. These can form a much more compact object than a white dwarf-a neutron star.

But, if we are interested in black holes, then we must turn to stars which are considerably more massive than those which go on to produce white dwarfs or even neutron stars. A star above thismass will be very luminous while its fuel lasts and nuclear fusion can be sustained. Once all the fuel is used up, it's game over for the star and the lights will switch off. The star is now sufficiently massive that the gravitational force can overwhelm even the strong neutron degeneracy pressure and so the collapse is so powerful that even this pressure cannot balance gravity and the collapse leads inexorably to a black hole. The collapse of a massive star is often accompanied by the explosion of a spectacular supernova remnant, leaving a black hole as the only remnant at the original location of the progenitor star. In such explosions many elements,particularly those heavier than iron, are synthesized.

The first black hole to be securely identified from a determination of the masses of the two stars in a binary star system is called V404 Cyg. Jorge Casares and Phil Charles and their co-workers observed the orbits of the two stars very carefully and inferred from their analysis that this binary pair includes a compact object having a mass at least six times greater than the mass of our Sun,and is thus a black hole. (Its mass was later found to be twelve times the mass of the Sun.)

It is possible to make plausible estimates of the numbers of stars in galaxies and their masses.We can then estimate the number of‘stellar-mass' black holes in our Galaxy by considering how many massive stars would have formed early enough in its history to have evolved sufficiently by now to use up all their nuclear fuel via fusion. Even if only a very small proportion of stars in our Galaxy go on to form black holes, with more than 1011 objects in theMilky Way that still gives us a lot of black holes.

How can one measure the masses of these black holes that pervade galaxies? In fact for some stellar-remnant black holes, the technique is dynamically very similar to that used for the black hole at the centre of our Galaxy. The reason for this is that a very significant fraction of stars in our Galaxy, and therefore most probably in other galaxies also, come in pairs that formed binary star systems. It is easy to surmise how this might come about:gravitational forces are attractive and many two-body orbits are stable, so once two stars encounter one another and become gravitationally bound together, they are likely to remain so. For a binary system, if we can measure the time taken for the stars to do a complete loop around one another, a time known as the orbital period, and if we know the distance between them, then we are well on the way to finding their masses. If the compact object is in orbit around a normal (fusion fuelled) star of known spectral type and therefore known mass, then the mass of the compact star is straightforward to derive. If a compact object such as a black hole is a singleton and not in a binary, then the lack of dynamical informationmeans that there is no means of inferring its mass and or indeed of determining that it is a black hole. The smallest black hole that we can measure is a few times the mass of our Sun,but the heaviest stellar-mass black holes can exceed a hundred times the mass of our Sun.

The measurement of the mass of a black hole, given modern day technology, is tractable although it still requires a good measure of patience and tenacity. Given thatmass is one of essentially only two fundamental physical properties of a black hole such studies get us half-way to characterizing it! However, measuring the spin of a black hole is harder, and in Chapter 7 I describe the heroic efforts that are needed to try and do this.

Chapter 7 Eating more and growing bigger

How fast do they eat?

The popular notion of a black hole `sucking in everything' from its surroundings is only correct near the event horizon, and even then, only if the angular momentum of the infalling matter isn't too great. Far away from the black hole, the external gravitational field is identical to that of any other spherical body having the same mass. Therefore, a particle can orbit around a black hole in accordance with Newtonian dynamics, just as it would around any other star.What could unravel this pattern of going round and round in circles (or indeed ellipses) and pave the way for more exotic behaviour? The answer is that there is invariably more than one particle orbiting the black hole. The richness of the astrophysical phenomena we observe arises because there is a lot of matter orbiting around a black hole and this matter can interact with itself.What is more, gravity isn't the only law of physics that must be obeyed: so too must the law of conservation of angular momentum. Applying these laws to the bulk quantities of matter that may be attracted towards the black hole gives rise to remarkable observable phenomena, good examples of which are found in the case of exotic objects known as quasars. Quasars are objects at the centres of galaxies having a supermassive black hole at their very heart which, because of its effect on nearby matter,can cause it to outshine the collective light from all the stars in one of those galaxies, across all parts of the electromagnetic spectrum.We shall meet quasars, and other examples of `active galaxies', in Chapter 8, together with scaled-down counterparts of these called microquasars whose black holes are orders of magnitude less massive than those inside quasars. For now let's get back to thinking about the matter around a black hole.

As we have noted, you cannot directly observe an isolated black hole because it simply won't emit light; you can only detect a black hole by its interactions with other material. Any matter falling towards a black hole gains kinetic energy and by turbulence, that is to say swirling against other infallingmatter doing a similar thing, becomes hot. This heating ionizes the atoms leading to the emission of electromagnetic radiation. Thus, it is the interaction of the black hole on the nearby matter that leads to radiation being emitted from the vicinity of the black hole, rather than direct radiation from the black hole itself.

Black holes are not aloof, non-interacting entities in space. Their gravitational fields attract all matter, whether nearby gas or stars,towards them. Because gravitational attraction increases strongly with proximity, stars are ripped apart if they are unfortunate enough to have a close encounter with a black hole; an example is pictured in Figure 15. A certain fraction of the attracted matter will be entirely swallowed or accreted by the black hole. Matter doesn't just accelerate into the black hole whooshing through the event horizon. Rather, there is something of an elaborate courtship ritual as the gravitationally-attractedmatter draws near the black hole. Very often it is found that a particular geometry characterizes accreting matter: that of a disc. If the gravitational field were spherically symmetric, the black hole would play no role in determining the plane within which the gas would settle to form an accretion disc-the disc plane would be determined by the nature of the gas flow far from the black hole. If, however, the black hole has spin, accreted gas will eventually settle into the plane perpendicular to its spin axis, regardless of how it flows at large radii. If there is any rotation at all in the attracted matter,then this must be thought of in terms of the conservation of angular momentum that we met in Chapter 3 when we considered the rotation of material that ultimately collapsed to form a spinning black hole. The rotation means that the matter will be following (fairly circular but actually) spiralling-in orbits as it loses energy. Close to the black hole, the Lense-Thirring effect that we met in Chapter 3 means that at small radii the accretion disc may become aligned with the equatorial plane of the spinning black hole. (In this context, this effect is known as the Bardeen-Petterson effect.)

15. Artist's impression of an accretion disc (fromwhich a jet is shownto emanate-see Chapter 8) and a donor star which is being rippedapart by the gravitational tidal forces from the black hole which is atthe centre of the accretion disc.

If gas is a significant component of the collapsing matter then gas atoms can collide with other gas particles on their own orbits and these collisions result in electrons in those atoms being excited to higher energy states. When these electrons fall back to lower energy states they release photons whose energies are precisely the difference between the higher energy level of the electron and the lower energy level it has fallen to. The release of photons means that radiative energy leaves the collapsing gas cloud and so this loses energy.While energy is released in these processes, bulk angular momentum is not. Because angular momentum remains in the system, the coalescingmatter continues to rotate in whatever plane conserves the direction of the original net angular momentum.Thus, the attractedmatter will invariably form an accretion disc:a rather long-lived holding pattern formaterial orbiting the black hole. Depending on just how close to the black hole the orbiting material can get, the matter can get so hot that the radiation emitted from the accretion disc actually comprises X-ray photons,corresponding to high temperatures of ten million degrees (it doesn'tmatter too much whether the Kelvin or Celsius temperature scale is being used when the temperatures are quite this hot!).

A simple analysis of some familiar equations fromNewtonian physics shows that the gravitational energy release for a given amount of infalling mass depends on the ratio of its mass multiplied by that of the black hole it is spiralling towards, and how close to the black hole the infalling mass gets. For a given mass of attractor such as a black hole, the closer the infalling mass approaches it, the greater the gravitational potential energy released as can be seen in the cartoon in Figure 16. The energy that is available to be radiated out is the difference between the energy the infalling mass has far away before it is accelerated(calculated using Einstein's famous formula E = mc2, where E is energy, mis mass, and c is the speed of light) and the energy it has at the innermost stable circular orbit of the black hole.

Although fusion holds great hope as a future source of energy for Earth, it can only yield at most 0.7% of the available `E = mc2' energy. In contrast, significantlymore of the available rest mass can be released as energy from accreting material, via electromagnetic or other radiation. Quite how close to a black hole the accretingmaterial can get depends, as described in Chapter 4,on how fast the black hole is spinning. If the black hole is spinning fast, the holding pattern of the material can be orbiting much closer in, on much smaller orbits. In fact, accretion of mass onto a spinning black hole is the most efficient way known of using mass to get energy. This process is thought to be the mechanism by which quasars are fuelled. Quasars are the sites of the most powerful sustained energy release in the Universe and are discussed further in Chapter 8.

16. Diagram showing how the potential energy of a mass (a testparticle) decreases with decreasing distance to a black hole.

I've already mentioned there is an equivalence between mass and energy and for a Schwarzschild (non-rotating) black hole, an amount of energy equivalent to 6% of its original mass could in principle be liberated, and that Roy Kerr's solutions to the Einstein field equations show that the last stable circular orbit has a much smaller radius fromthe spinning black hole thanwould a non-rotating black hole of the same mass. In principle, vastlymore rotational energy can be extracted from a Kerr black hole, but only if the infalling matter is orbiting in the same sense as the black hole itself. If matter is orbiting in the opposite direction to the way the black hole is spinning, i.e. it is on a retrograde orbit, then not quite 4% of the rest energy could be released as electromagnetic radiation. If, however, the matter infalling towards a maximally spinning black hole were orbiting in the same sense as the black hole were spinning, then in principle a remarkable 42% of the rest energy could be released as radiation, if the matter could lose sufficient angular momentum that it could orbit the black hole as close as the innermost stable prograde circular orbit.

How fast do they eat?

The accretion rate of the black hole at the centre of our Galaxy,in Sagittarius A*, whose discovery we met in Chapter 6, is100-millionth of the mass of the Sun per year. This doesn't sound very much until you realize that this corresponds to an appetite of300 Earth masses per year. To account for the typical, immense luminosities of quasars, matter-infall rates amounting to a few times the mass of our Sun each year are required. To account for the typical luminosities of the smaller-scale microquasars that we shall also meet in Chapter 8, the required matter-infall rates might be one millionth of this value.

Another context in which a similar energy extraction process may be taking place is in gamma-ray bursts, usually referred to as GRBs. These are sudden flashes of intense beams of gamma rays that seem to be associated with violent explosions in distant galaxies. They were first observed by US satellites in the late 1960s and the received signals were initially suspected to be from Soviet nuclear weapons.

Given the ubiquity of matter spiralling into a black hole via a disc,physicistsfind it helpful tomake simple and instructive calculations to get a handle on themagnitudes of some of the important physical quantities: if ' one considers a spherical geometry rather than a disc geometry then some interesting limits emerge. A particularly illustrative example comes from the world of stars, which are much better approximations to spheres of plasma than are accretion discs. Sir Arthur Eddington pointed out that the radiation released by the excited electrons colliding with other ions in the hot gas of a star will exert a radiation pressure on any matter that it subsequently intercepts. Photons can `scatter' (which simplymeans`give energy and momentum to') electrons contained in the hot ionized plasma within the interior of a star. This outward pressure is communicated via electrostatic forces (the electrically-charged analogue of the gravitational force) to the positively charged ions such as the nuclei of hydrogen (also known as protons) and the nuclei of helium and other heavier elements that are present.

In the case of a star, the net radiation heads radially outwards and this resulting outward radiation pressure acts oppositely to the gravitational force that pulls matter inward towards the centre.For the more-or-less spherical geometry of a star, there is a maximum limit to the amount of outward radiation pressure before it overwhelms the inward gravitational pull and the star simply blows itself apart. This maximum radiation pressure is known as the Eddington limit. Higher radiation pressure inevitably follows from higher luminosity of radiation, and the luminosity of an object can be estimated from its brightness if we know the distance to the object. Therefore, with certain simplifying assumptions including approximating an accretion disc to a sphere, the amount of radiation pressure inside an object can be inferred. This simple method is sometimes used to make an indicative estimate of the mass of the black hole: from the observed luminosity of the radiation to emerge from the surrounding plasma, if it is deemed to be at the maximal limiting value of the `Eddington luminosity' (above which higher luminosity would give sufficiently high radiation pressure that it would exceed the gravity from the mass within and hence blow itself apart) then the mass can be estimated.

This Eddington luminosity can be thought of in terms of a maximum rate at which matter can accrete, for suitable assumptions about how efficient the process of accretion is. This gives a quantity called the Eddington rate which (for the assumed efficiency) is a maximal value. There are ways of breaking this particular maximum limit, not the least of which is the rejection of the assumption of spherical symmetry (this is fine for a star but manifestly doesn't apply to the disc-geometry of accretion discs that we need to consider in order to understand how black holes grow).

How to measure the speed of rotation within an accretion disc

Because of advances in astronomical technology it is now possible to measure the speed at which material is orbiting a black hole,at least for examples that are relatively close to Earth. One of the big challenges is that it is difficult to obtain information on a sufficiently fine angular scale. The spatial resolution required needs to be at least one hundred, if not one thousand, times finer than that routinely obtained by optical telescopes. In principle, the route to achieving finer resolution with a telescope would be to observe at shorter wavelengths and to build a larger telescope, in particular to reduce the ratio of the wavelength of observation to the diameter of the telescope being used. Unfortunately, the latter gets hideously expensive very quickly while the former takes the usual visible observing wavelengths into the ultra-violet regime, to which the atmosphere of the Earth is rather opaque. The route to achieving a smaller ratio of observing wavelength to telescope diameter is, counter-intuitively, to observe at radio wavelengths(much longer wavelengths than either visible or ultra-violet) for which the atmosphere and ionosphere are usually transparent, and to take the telescope diameter to be most of the Earth's diameter.

There are a few technical issues about this approach which need a little discussion: it turns out that thanks to some very useful mathematics developed by the French mathematician Jean Baptiste Joseph Fourier, it is possible to recover much of the signal that a full telescope aperture would observe, even if the actual collecting area only exists in a sparse subset of the full aperture that one would ideally prefer. If the signals from discrete antennas(each looking like an individual telescope-see Figure 17 showing the Very Long Baseline Array, known as the VLBA) are correlated together, it is possible to reconstruct images of small regions of the sky that have detail as fine as that which would be obtained if an Earth-sized telescope could have been fully built. Just to give an idea of how fine this resolution is, suppose that I was standing on top of the Empire State Building in New York, and you were in San Francisco.With this amount of resolution you would be able to resolve detail that is separated by the size of my little finger nail.

17. Artist's impression of the Very Long Baseline Array (VLBA) ofantennas that collectively give images with a resolution equal to thatwhich would be obtained by a telescope with an aperture a significantfraction of the diameter of the Earth.

18. The VLBA hasmeasured the distribution of discretemasersorbiting within the accretion disc of the galaxy NGC 4258 (also knownasMessier 106) around its central black hole whose mass is 40 milliontimes the mass of our Sun.

(I am glossing over the fact that the Earth is a sphere so there is no direct line of sight between San Francisco and the Empire State Building, but you get the idea.) This means that with instruments like the VLBA we can see individual features less than a light-month apart in other galaxies.

High resolution across an image in a spatial sense, and high resolution in a spectral sense (meaning that one can discern very precisely what the wavelengths of particular features are in a spectrum) is a very powerful combination.Making use of the Doppler effect, a team led by JimMoran of Harvard University used the VLBA to make observations of the accretion disc surrounding the central black hole of a nearby galaxy known as NGC 4258. They measured the variation in wavelength of a particular spectroscopic signal (a `watermaser' ) across the rotating accretion disc and used this redshifting and blueshifting, as the masing matter moved towards and away from the Earth, to detect the variation in the speed with which matter at a given distance orbits around the black hole. These exquisitely beautiful data confirmthat thematter orbits around the black hole just as Kepler's laws would describe, and these orbits are depicted in Figure 18.

Swirling matter

In the innermost stable orbit of a black hole whose mass is100 million times the mass of our Sun, the angular momentum is over 10,000 times smaller than the angular momentum of matter orbiting in a typical galaxy. It is clear that for matter to be accreted by the black hole, this requires the removal of the vast majority of this angular momentum, and this is accomplished by processes within the accretion disc. The orbits in an accretion disc may be regarded as a good approximation to circular although in fact they are subtly and gradually spiralling in. Kepler's laws say that the matter orbiting on the smaller radii will be moving faster than the matter on slightly larger orbits. This differential rotation allows a black hole to absorb the plasma that comprises the accretion disc:the rapidly rotating inner orbits friction burn against the neighbouring material on orbits with slightly larger radii. This difference in velocity will mean that the matter on slightly larger orbits will, by viscous turbulence effects, be dragged along a little faster and so correspondingly the matter on inner orbits will be slightly slowed. Therefore, because orbital motion has increased further out, angular momentum has been transferred to the outer material from the inner material, heating as it does so.

Overall, angular momentum is conserved, and the inner material can systematically lose angular momentum, making it more likely to be swallowed by the black hole. Note that if a blob of orbiting matter has too much angular momentum, it will stay further away from the centre of mass about which it is orbiting: it would be moving too fast to get any closer.What kind of viscous effects might be relevant to the plasma within an accretion disc?Inter-atomic viscosity can be small in this situation-the gaseous plasma of which the accretion disc is comprised is very far removed from the consistency of treacle. In fact, magnetic fields may be very important in transferring angular momentum out of accreting inflow.Where do the magnetic fields come from? The plasma in an accretion disc is very hot, and so the atoms are partially ionized into electrons and positively charged nucleons.Therefore, there are flows of charged particles and moving charges produce magnetic fields, as described by the equations of James Clerk Maxwell. Once even very weak magnetic fields exist, they can be stretched and amplified by differential rotation and modified by the turbulence of the plasma, up to levels at which they can give the required viscosity. This is the basis of what is known as the magnetorotational instability. The importance of this mechanism in this context was first realized by Steve Balbus and John Hawley in the early 1990s when working at the University of Virginia.

By viscous turbulence and probably other means, plasma can eventually lose angular momentum and orbit at smaller radii closer to the black hole. Once the gaseous plasma reaches the innermost stable orbit, no more friction is needed for it to slip down into the black hole, after which it will never be seen again,but it will have augmented the mass and spin of the black hole.

What do accretion discs look like,and how hot are they?

We have seen that viscous and turbulence effects play a significant role in removing angular momentum from the orbiting material so that it can orbit more closely to the black hole and be swallowed by it. A consequence of the viscous action, however, is that the bulk orbital spiralling motion gets converted into random thermal motion and hence the matter heats up. The greater the random thermal motion of matter, the more heat energy it has and the higher its temperature. As mentioned in Chapter 5, wherever there is heat, there will be thermal electromagnetic radiation.Every body emits thermal radiation, unless it is at absolute zero.

Such heating is what is responsible for the highly luminous radiation we observe from accretion discs. For the accretion discs that surround the supermassive black holes that are at the hearts of quasars, the characteristic size of an accretion disc is a billion kilometres and the bulk of the radiation from these accretion discs is in the optical and the ultra-violet region of the spectrum. For the accretion discs that surround the vastly less massive black holes in the so-called microquasars (that are discussed in Chapter 8),the accretion discs are a million times smaller in extent and the radiation is dominated by X-rays. The more massive a black hole is, the larger the innermost stable circular orbit is and hence the cooler the surrounding accretion disc will be.

The maximum temperature in an accretion disc around a supermassive black hole 100 times the mass of our Sun will be around 1million Kelvin while for a disc around a stellar-mass black hole, it can be up to a factor of 100 higher.

How do you measure how fast a black hole is spinning?

Given you can't actually directly see black holes, you can't see them spinning either. But there are nonetheless two main routes to measuring how fast a black hole is spinning. As discussed in Chapter 4, when black holes spin very fast, it is possible for matter to be in stable orbit around the black hole much closer in than would be possible if they were not spinning. It turns out that matter in these very tight orbits is heated by strong turbulent and viscous effects as it swirls in, and this immense heat can lead to X-rays being emitted, depending on how close to the black hole the matter has swirled in before being swallowed up. General relativity predicts that the shape of the spectral lines is affected by the distance the emittingmatter is from the black hole (arising from the gravitational redshift) in a way that has a characteristic signature. This signature arises from fluorescing iron atoms within this matter and the method of extracting information from X-ray light was pioneered by Andrew Fabian of Cambridge University.

These are challenging measurements to interpret, because of many different factors, such as the inclination of the accretion disc with respect to Earth, and indeed the nature of wind and outflowing matter from the surface of the accretion disc, in the vicinity of (along our line of sight to) its inner rim whose characteristics hold the key to unlock information about the black hole that is otherwise inaccessible. Other methods for measuring the spin of stellar mass black holes involvemeasuring a significant range of the X-ray spectrum and accounting for the different temperatures of the inner regions of the accretion disc (which are hotter) and the regions further out (that become gradually cooler).It is possible to estimate from the shape of the X-ray spectrum the inclination of the disc and from the highest temperature(assuming you know the mass of the black hole, and its distance from Earth) to infer how far from the black hole the innermost material is orbiting. Analogous methods to measure the spin of supermassive black holes at the hearts of quasars are being developed by Christine Done at Durham University. How close that matter is able to orbit (before being swallowed by the black hole) tells you how fast the black hole itself must be spinning.

Black holes are very messy eaters

It transpires that only a fraction (estimated to be 10%, though it can be very significantly higher) of the matter that gets attracted in towards a black hole gets as far as the event horizon and actually gets swallowed. Chapter 8 considers what happens to the matter infalling towards a black hole that doesn't actually get swallowed within the event horizon. From across the accretion disc itself, matter can blow off as a wind; from within the innermost radii of the accretion disc very rapid jets of plasma squirt out at speeds that are really quite close to the speed of light.As Chapter 8 shows, what doesn't get eaten by the black hole gets spun out and spat out rather spectacularly.

Chapter 8 Black holes and spin-offs

Black holes don't just suck

If our eyes could observe the sky at radio or at X-ray wavelengths,we would see that some galaxies are straddled by vast balloons or lobes of plasma. This plasma contains charged particles that move at speeds close to the speed of light and radiate powerfully across a range ofwavelengths. The plasma lobes exhibited by some of these galaxies (examples of `active galaxies') are created by jets,travelling at speeds so fast that they are comparable with the speed of light, that are squirted out from the immediate surroundings of a black hole, outside its event horizon. Roger Penrose showed in general terms how extraction of the spin energy of a black hole from its ergosphere might be possible in principle. Roger Blandford and Roman Znajek have shown explicitly how the energy stored in a spinning black hole could actually be transferred into electric and magnetic fields and thereby provide the power to produce these relativistic jets of plasma. There are also other explanations for the mechanism by which jets are launched from near black holes. However, which of these is correct is the subject of active and exciting current research.

Whatever the mechanism(s) turn out to be, these jets are highly focused, collimated flows ejected from the vicinity of the black hole, but of course outside the event horizon. The regions in between galaxies are not, in fact, empty space. Instead they are filled with a very diffuse and dilute gas termed the intergalactic medium. When the jets impinge on the intergalacticmedium,shock waves form within which spectacular particle acceleration occurs, and the energized plasma which originated in a jet from near the black hole billows up and flows out of the immediate shock region. As the plasma expands, it imparts enormous quantities of energy to the intergalacticmedium. There are many instances of these plasma jets extending over millions of light-years. Thus black holes have tremendous cosmic influence,many light years beyond their event horizons. In this chapter, I will describe the influence and interactions of black holes on and with their surroundings.

As discussed in Chapter 6, at the centre of (probably) most galaxies is a black hole, on to which matter accretes, giving rise to emission of electromagnetic radiation. Such galaxies are called active galaxies. In some of these galaxies, the process of accretion is extremely effective and the resulting emission of radiation extremely luminous. Such galaxies are called quasars (a term which derives from their original identification as `quasi-stellar radio sources', vastly distant, highly luminous points of radio emission).We now understand that quasars are the sites of the most powerful sustained energy release known in the Universe. Quasars radiate energy across all of the electromagnetic spectrum, from long wavelength radio waves, through optical(visual) wavelengths, to X-rays and beyond. The radio lobes,mentioned above, can be especially dramatic because they extend across distances of over hundreds of thousands of light-years (see Figure 19). The energy radiated at radio wavelengths arises from those large lobes-reservoirs of ultra-hot magnetized plasma,powered by jets that transport energy over vast distances in space.Highly energetic electrons (highly energetic here meaning travelling extremely close to the speed of light) experience forces across their direction of travel from the ambient magnetic fields that pervade the plasma lobes within which they are travelling.

19. This is aradio imageofagiantquasar, spanningover onemillionlight-years in extent.

This acceleration causes them to emit photons of radiation (which may be radio, or in rare, highly energetic instances, at shorter wavelengths still, all the way up to X-rays) known as synchrotron radiation.

To give a sense of the scale of the power produced by quasars,consider the following values. The LEDs by whose light I am working have a power output of ten watts. They are illuminated by electricity frommy local power stationwhich produces a few billion watts (a billion watts is 109 watts or a gigawatt). The Sun outputs about 4 x 1026 watts, morethan ahundredmillion billion timesthat from this power station. Our Galaxy, theMilkyWay, containsmore than a hundred billion stars, and its power output is approaching1037 watts. But the power produced by a quasar can exceed even the Galactic power output by more than a factor of 100. Remember,this power is being emitted not by a galaxy of one hundred billion stars but by the processes going on around a single black hole. Such radiation could do considerable damage to the health of living creatures here on Earth, so it is just as well for us that there are no examples of such powerful quasars too near our Galaxy!

Jets in quasars are thought to persist for a billion years or less, an idea that comes from estimates of the speed at which these objects' jets grow and from measurements of the size they have grown out to. A simple relationship between distance and time and speed therefore gives a guide to the likely durations of jet activity in the quasars that are observed across the cosmos.

As these radio-emitting lobes expand, their magnetic fields weaken as do the `internal' energies of the individual electrons in the lobes. These two effects serve to diminish the intensity of the radiation with time and with distance from the black hole; how dramatically this intensity falls off depends on how many highly energized electrons there are compared with how many less energetic ones there are. It's a property of synchrotron radiation that the lower the magnetic field strength is, the more energetic the electrons need to be to produce the radiation at the wavelength that your radio telescope is tuned to receive at. This compounds the diminishing of the synchrotron radiation as the plasma lobes expand into outer space. Not only do the electrons lose energy as the plasma expands, but because the magnetic field strength is weakening, only increasingly energetic electrons are relevant to what is observed by your telescope and, very often, there are vastly fewer of these than there are of the lower energy electrons anyway.As far as radio lobes of quasars are concerned, the lights can go out really quite rapidly.

The show isn't over, but the spectacle does move over to a different waveband. Something rather remarkable happens: the lobes light up in X-rays. This happens via a scattering process known as inverse Compton scattering. In the presence of a sufficiently large magnetic field, electrons can emit synchrotron radiation and thereby lose energy. Another mechanism of losing energy that is relevant to our discussion here happens via the interaction of these electrons with photons that comprise the Cosmic Microwave Background (CMB), the radiation that is left over from the Big Bang and which currently bathes the Universe in a cool microwave glow. It is possible for such an electron to collide with a photon from the CMB so that the photon ends up with a lot more energy than it had before the collision and the electron ends up with a lot less energy than it had before the collision (energy is conserved overall, remember). Of particular interest is that when the energies of the rapidly moving electrons reduce to a mere one thousand times the energy of an electron at rest (having previously been a hundred or a thousand times higher than this) their energies are perfectly matched so that they will upscatter CMB photons into the X-ray photons. The interaction of an energetic electron with a low-energy photon to yield a high-energy photon is somewhat analogous to the situation in snooker where the white cue ball (imagine this is an electron) collides with one of the red snooker balls (for the purposes of this illustration please overlook the fact that this ball isn'tmoving at the speed of light!) and the red ball gains a lot of energy at the expense of the cue ball.Whereas (hopefully) the red ball ends up in one of the pockets on the snooker table, the photon (which originally had a wavelength of about a millimetre) acquires about one million times as much energy as it had before the collision so that its wavelength becomes a million times shorter.

The Chandra satellite, launched by NASA in 1999, is sensitive to X-ray wavelengths and in fact can detect pairs of dumb-bell lobes in the X-rays just as a radio telescope can detect these double structures at cm-wavelengths. Figures 20 and 21 show in contour form double structures observed at radio wavelengths and in greyscale form the double structures in X-rays.

In fact if we were able to monitor the life cycle of one of these quasars throughout all these evolutionary stages (analogously to how a biologist might observe the life cycle of the frog from frogspawn, to tadpoles, to tadpoles with little legs, to little frogs with stumpy tails, to larger frogs to dead frogs) we would observe a cross-over fromthe double structures being radiant at radio wavelengths to becoming increasingly dominant in the X-ray region. First the radio structures would fade beyond detectability then the X-ray structures would fade beyond detectability. Of course, if the jets were to re-start, for example if the black hole were to get more fuel, then the jets would fuel new radio-emitting double lobes and then X-ray emitting lobes again. As we have seen in Figures 20 and 21, in some quasars we can see both the radio and the X-ray double structures at the same time but in others,only one or the other (Figure 22). In a couple of remarkable cases we see the X-ray double structure corresponding to a previous incarnation of jet activity, but also some new radio activity,at a different angle because the direction along which the oppositely-directed jets are launched has swung round, i.e. it has precessed; an example of this phenomenon is seen in Figure 21.

20. This giant quasar is half amillion light-years in extent, and has adouble-lobe structure at both radio (shown as contour lines) and X-ray(shown in greyscale) wavelengths.

The steadiness of the jet axis of many quasars and radio galaxies is a pointer to the steadiness of the spin of the supermassive black hole, acting like a gyroscope. Why some of these jet axes should precess but not others will be answered when we can discover what controls the angular momentum ofthejets at the launch point near the black hole. Whether this is the spin axis ofthe black hole itself, or whether it is the angular momentum vector ofthe inner part of the accretion disc, compounded no doubt by the Lense-Thirring or Bardeen-Petterson effects I mentioned in Chapters 3 and 7 respectively, is not yet clear and more data are required to fully elucidate the observed behaviour. But, there are clues from smaller objects closer to home that may suggest that the precession of jet axes is everything to do with the accretion disc's angular momentum.

21. The double-lobe structure observed in this quasar at radiowavelengths [contours] showing themore recent activity to bedifferently oriented from that showing at X-ray energies [greyscale](the relic emission revealed by inverse Compton scattering of CMBphotons) suggesting that the jet axismay have precessed as the jet axesinmicroquasars do.

22. This is an X-rayimage andshowsthe double-lobestructurestraddlingthis galaxywhichis onlydetectableat X-raywavelengths.

Microquasars

The quasars we have been discussing so far are all supermassive black holes that lie at the centres of active galaxies. However,it turns out that there is another class of objects that behave very similarly but are on a much, much smaller scale. These lower mass black holes can be observed rather closer to home,indeed located within our own Milky Way Galaxy, and they are called `microquasars'. Although the difference in scale size is vast,microquasars in our Galaxy and extragalactic quasars at the centres of other galaxies are both sources of plasma jets with analogous physical properties. Both of these are thought to be powered by the gravitational infall of matter onto a black hole. In the case of a microquasar, the black hole has a mass comparable with that of the Sun. In the case of a powerful extragalactic quasar, the mass of its black hole can be a hundred million times larger than the mass of our Sun. As far as the astrophysicist is concerned, an important advantage of the local examples is that being less massive,they evolve much more rapidly, on timescales of days rather than millions of years in the case of quasars. Nonetheless, as in the case of quasars, the jets which are squirted out from near the centre of all the activity are launched from outside the event horizon,and very likely from the innermost edge of the accretion disc.

Complex mechanisms are at play, and there isn't a simple relationship between the speed at which a jet is launched and the mass of the black hole with which it is associated. In the course of monitoring the jets in the black hole microquasar called Cygnus X-3 there are occasions when the speeds at which the jet plasma moves away from the black hole are found to vary. This has been measured by time-lapse astronomical measurements in which observations at successive times allow us to determine how fast the jet plasma is hurtling away from the vicinity of the black hole.Such measurements have shown on one occasion the jet speed to be 81% of the speed of light whereas four years later to be 67%of that speed. There is no suggestion that the jet speed is merely reducing with time, since fast and slower jets speeds in this microquasar appear to have been witnessed on a number of occasions since its discovery. Varying jet speeds seem to characterize another well known microquasar in our Galaxy, called SS433, that I shall describe in more detail below. The jet speed in this microquasar seems to change quite a bit as well, indeed it can be anywhere between 20 and 30% of the speed of light over just a few days.

The beauty of symmetry

Figure 23 shows a radio image of SS433, a microquasar in the Galaxy, which is a mere 18,000 light-years distant from us. The striking zigzag/corkscrew pattern is the structure of the plasma jets as they appear to us on the plane of the sky. The individual bolides of plasma that make up the jets are moving at tremendous speeds that vary between 20 and 30% of the speed of light. The directions along which the bolides are moving varies with time in a very persistently periodicway. In fact the axis alongwhich the jets are launched precesses in much the same way as does the paddle of a kayakist, in the frame of reference of the kayak, except on a timescale of six months rather than several seconds. This same behaviour is apparently taking place in at least some quasars(see Figure 21) albeit in that case in such slow motion that we are unable to appropriately time-sample the changes taking place.

The detailed appearance of the zigzag/corkscrew pattern on the sky depends directly on the physical motions of the bolides, as well as the time when the observation is made. One of the remarkable features of the jets is their symmetry: the physical motions of the components in the eastern jet are equal and opposite to those in the western jet: when one bolide of plasma is at 28% of the speed of light, so too is its counterpart in the oppositely-directed jet; for a different bolide of plasma moving at 22%of the speed of light, so too will its counterpart in the oppositely-directed jet. The fact that one jet appears to have a zigzag structure while the other appears to have a rather different corkscrew pattern is a consequence of the jet plasma always moving at speeds comparable with the speed of light, and well-known relativistic aberrations that occur under such circumstances. The power radiated by this microquasar is rather modest relative to that of an extragalactic quasar but it is still vast in comparison to the power of the Sun which seems somewhat puny, having a total luminosity of only 4 x 1026 watts, a factor of a hundred thousand smaller than that radiated from the microquasar in Figure 23.

23. The jets of themicroquasar SS433 as they appear at radiowavelengths.

Jet launch

The Virgo Cluster is a cluster of well over a thousand galaxies just over fifty million light-years distant from theMilkyWay. At its heart is a giant galaxy called M87 (an abbreviation of Messier 87,listed in the catalogue produced by the French astronomer Charles Messier). And, at its heart, is a supermassive black hole whose mass is three billion times that of our Sun. Emanating from this is a strong straight jet, as shown in Figure 24.

24. A jet of plasma squirted out at speeds close to that of light, fromthe supermassive black hole at the heart of the M87 galaxy.

This jet is readily visible at optical wavelengths, at radio wavelengths, and at X-ray wavelengths. It is thought that the infallingmatter accretes at a rate of two to three Sun's worth of mass per year, onto the very central nucleus where an accretion disc of the sort described in Chapter 6 is thought to be at work.The speed at which this jet propagates away from its launch point,likely at the innermost region of the accretion disc, is very close to the speed of light, and so we refer to it as a relativistic jet. Jet speeds close to the speed of light are revealed by successive monitoring with the VLBA instrument that I introduced in Chapter 7, and the Hubble Space Telescope and Chandra X-ray satellites which are each above Earth's atmosphere and thus attain higher sensitivity than if they were on the ground. At 50 million light-years from Earth an object moving at the speed of light would move across the sky at four milli-arcseconds per year.When we consider that an arcsecond is 1/3600 of a degree, then four-thousandths of this may sound like a tiny angle to measure,but such separations are easily resolvable with an instrument like the VLBA. The VLBA has already imaged the base of this jet to within less than about thirty Schwarzschild radii of its supermassive black hole.

Figure 25 shows an example of the lobes and plumes of radio emitting plasma fed by the relativistic jets from the supermassive black hole in M87.

By way of further illustration that expansive lobes are associated with relativistic jets, Figure 26 shows an example that extends6 degrees across the sky, and is shown to give a sense of scale with respect to the telescope array used to make the observation. The telescope, used by Ilana Feain and her colleagues, was the Australia Telescope Compact Array.

The mechanisms by which relativistic jets are launched from the vicinity of a black hole remain much closer to conjecture than to acceptance beyond all reasonable doubt. Nonetheless, various independent lines of research by entirely independent teams based in different countries around the world seem to be implying that the preponderance of evidence is that the basic emerging details are correct. Beyond the broad picture, however, the mechanisms and their detailed functioning are conjectural, but being patiently tested amid insufficient photons and selection effects. Proof doesn't belong in science but evidence very much does.We are hindered because even the most advanced imaging techniques deployed today cannot separate and resolve the smallest regions where most of the energy is released, but this is where numerical simulations on powerful computers can transcend the limitations of current technology. Indeed results from simulations of jet launch from accretion discs that fully account for general relativity effects are just being published.These simulations, with known input ingredients and axioms,allow jets and discs to evolve to size-scales where their properties can be confronted against state-of-the-art observations.

25. The radio-emitting lobes that are fed by the relativistic jetemanating out of the supermassive black hole at the centre of theM87 galaxy.

So what do we now know about the masses of black holes in the Universe? It seems that they fall into two main classes. First,those that have masses similar to those of stars. These stellar mass black holes come in between around three to thirty times the mass of our Sun and come from stars that have burned all their fuel.

26. Compositepicture showingan opticalimage ofthemoon andtheAustralia Telescope CompactArray, andaradio image ofCentaurusA.

Then there are the supermassive black holes which go all the way up to about ten billion solar masses. As we have discussed, these are found in the centres of galaxies including our own and are responsible for the extraordinary phenomena of active galaxies and quasars.

We have talked about things falling into a black hole, but what happens when a black hole falls into a black hole? This is not an abstract question, since it is known that black hole binaries can exist. In such objects two black holes are in orbit around each other. It is thought that, because of the emission of gravitational radiation, the black holes in a binary will begin to lose energy and spiral into each other. In the final stages of this spiralling, general relativity is pushed to breaking point and the black holes suddenly coalesce into a single black hole with a common event horizon.The energy released in the merger of two supermassive black holes in a binary system is staggering, potentially more than all the light in all the stars in the visible Universe.Most of this energy is dumped into gravitational waves, ripples in the curvature of spacetime, which propagate across the Universe at the speed of light. The hunt is on for evidence of these waves. The idea is that as a gravitational wave passes by a material object, like a long rod,its length will fluctuate up and down as the ripples in spacetime curvature flow through it. If you can measure these tiny length changes, using a technique such as laser interferometry, then you have got a method to detect gravitational waves produced elsewhere in the Universe. Both ground- and space-based gravitational wave detectors, examples of which have been built and more of which are planned, have the potential to pick up signals from black hole mergers. In fact, gravitational waves are so difficult to detect that you need a very strong source to have any chance of such experiments working, and a black hole merger is high on the list of candidates for such strong sources. At the time of writing, gravitational waves have not yet been directly detected,but the experiments are ongoing.

Our best theory of gravity, which comes from Einstein's general theory of relativity, has survived countless tests since its discovery in 1915. It has been shown to give far better agreement to experiment than Newton's theory which it supplanted. However, if general relativity is ever going to be tested up to its limits, you can confidently expect that black holes will prove to be the ultimate testing ground of this cornerstone of modern physics. Where gravity is the most intense in the smallest region of space, so that quantum effects should be important, is exactly where general relativity might break down. However, it might also be that general relativity breaks down on large scales in the Universe.Of course, a hot topic at present is the completeness of general relativity to explain the accelerated expansion of the Universe on the largest scales. Possible deviations away from general relativity are being discussed in connection with accelerated expansion and dark energy. If gravitational waves are detected from the mergers of black holes, or if observations extend our understanding of the fundamental physics which occurs in the vicinity of these fascinating objects, then there's a good chance that we will be able to see how well Einstein's theory holds up or whether it needs to be replaced by something new.

Why do we study black holes?

There are a number of reasons for investigating black holes and one is that they open up the exploration of physics parameter space that is otherwise simply inaccessble to the budgets of even an international consortium. Black hole systems represent the most extreme environments that we can explore, and as such probe the extremes of physics. They bring together both general relativity and quantum physics whose unification has not yet been achieved and remains very much a frontier of physics. A second reason is that trying to understand black hole phenomena arouses fascination in scientists and many thoughtful lay people, and provides a route by which many people can be stimulated by science and motivated to learn about the almighty magnificence of the Universe around us. A third and perhaps surprising reason is Earthly spin-offs. How could black hole research conceivably change our lives? The answer is that it has already done so. As I type these final sentences of this little book into my laptop, it simultaneously backs up my work onto my University server via the 802.11 WiFi protocol. This intricate and clever technology emerged directly out of a search for a particular signature, at radio wavelengths, of exploding black holes led by Ron Ekers to test a model suggested by (now Astronomer Royal, Lord) Martin Rees.Ingenious radio engineers in Australia, led by John O'Sullivan, in the course of devising interference suppression algorithms for the tricky business of detecting subtle signals from distant space realized that these could be applied to transform communication here on Earth. Black holes therefore have the power to rewrite physics, reinvigorate our imagination and even revolutionize our technology. There are many spin-offs from black holes-way beyond their event horizons.

Further reading

M. Begelman and M. Rees, Gravity's Fatal Attraction, 2nd ed.(Cambridge University Press, 2010).

J. Binney, Astrophysics: A Very Short Introduction (Oxford University Press, 2015).

J. B. Hartle, Gravity (Addison Wesley, 2003).

A. King, Stars: A Very Short Introduction (Oxford University Press,2012).

A. Liddle, An Introduction toModern Cosmology, 3rd edn.(Wiley-Blackwell, 2015).

F. Melia, The Galactic Supermassive Black Hole (Princeton University Press, 2007).

D. Raine and E. Thomas, Black Holes: An Introduction, 2nd edn.(Imperial College Press, 2010).

C. Scarf, Gravity's Engines: How Bubble-Blowing Black Holes Rule Galaxies, Stars, and Life in the Cosmos (Scientific American/Farrar, Straus and Giroux; Reprint edition, 2013).

R. Stannard, Relativity: A Very Short Introduction (Oxford University Press, 2008).

A. Steane, The Wonderful World of Relativity: A Precise Guide for the General Reader (Oxford University Press, 2011).

K. Thorne, Black Holes and TimeWarps (W.W. Norton, 1994).

Index

A

absolute zero 53, 54

accretion disc 64, 65, 72

active galaxies 77, 78

adaptive optics 57

angular momentum, conservation

of 26

area 48

Australia Telescope Compact

Array 88

B

Balbus, Steve 73

Bardeen, James 48

Bardeen-Petterson 65

Bekenstein, Jacob 48

binary star 61, 62

binary stars 8

black hole Kerr 26, 29, 30

black hole, Schwarzschild 26, 30

Blandford, Roger 77

C

Cape Canavaral 4

Carter, Brandon 29, 48

Casares, Jorge 61

Cavendish, Henry 7

centre of mass 4

Chandra satellite 81, 87

Chandrasekhar, Subrahmanyan 2

Charles, Phil 61

Christodoulou, Demetrios 32

chronology protection

conjecture 36

compact 60

cosmic censorship conjecture 30

CosmicMicrowave Background

(CMB) 80

D

dark star 6, 11

Descartes, René 12

diagrams, spacetime 15

dinosaurs 3

Done, Christine 76

E

E = mc2 66

Eardley, Douglas 33

eclipse, solar 23

Eddington limit 69

Eddington luminosity 69

Eddington rate 70

Eddington, Sir Arthur 2, 23, 69

Einstein-Rosen bridge 33

Ekers, Ron 93

electron degeneracy pressure 61

energy, kinetic 3

entropy 48

ergosphere 31, 32, 42

escape velocity 3, 4

event horizon 4

events 12

Ewing, Ann 1

extreme Kerr black hole 31

F

Fabian, Andrew 74

Feain, Ilana 89

Finkelstein, David 2

first law of thermodynamics 48, 51

Floyd, R. M. 48

Fornax cluster 3

Fourier, Jean Baptiste Joseph 70

frame dragging 29, 43

frame of reference 12

frame of reference, inertial 12

fusion 60

G

Göel, Kurt 34

Galactic Centre 56, 58

Galactic plane 56

gamma-ray bursts 68

general relativity 12

Genzel, Reinhard 58

geodesic 20

geodesic, null 22

Ghez, Andrea 58

gravitational constant, Newton's 4

gravitational potential well 13, 37

gravitational redshift 38

gravity 4

guide star 57

H

hair 28, 29

Hawking, Stephen 36, 48, 54

Hawking radiation 52, 53

Hawking temperature 53

Hawley, John 73

Heisenberg uncertainty

principle 51, 61

helium 6

Herschel,William 7

hole, white 33

Hubble Space Telescope 87

I

information paradox 54

information theory 48

intergalactic medium 78

inverse Compton scattering 80

K

Kepler's laws 58

Kerr, Roy 29, 42

Kerr black hole 26, 29, 30

Kerr black hole, extreme 31

kinetic energy 3

L

Laplace, Pierre-Simon 5, 6, 10

Lense-Thirring 29, 65

light, speed of 2

light cone 18

lobes, plasma 77

lobes, radio 78, 80

M

Magorrian, John 58

Maskelyne, Reverend Dr Nevil 8

Messier 106 72

metric 23

Michell, John 6

microquasars 64, 84

Minkowski, Hermann 12

Minkowski spacetime 12

Moran, Jim 72

N

naked singularity 30

Neptune 3

neutron degeneracy pressure 61

neutron star 61

Newton, Sir Isaac 7

Newton's gravitational constant 4

NGC 4258 72

null geodesic 22

O

O'Sullivan, John 93

Oppenheimer, Robert 1

P

Penrose, Roger 30, 32, 48, 77

photon 2

photon sphere 44

Planck area 50

point mass 4

potential well, gravitational 13

Preskill, John 54

prograde orbits 44

Q

quasars 63, 78

R

radio lobes 78, 80

radius, Schwarzschild 5

redshift 38

Rees, Martin 93

relativistic jet 87

relativity, general 12

relativity, special 12

retrograde orbits 44

Rosen, Nathan 33

Royal Astronomical Society 2

S

Schwarzschild, Karl 1

Schwarzschild black hole 26, 30

Schwarzschild radius 5

second law of thermodynamics 48

simple harmonic motion 56

simultaneity 19

singularity 4, 5

singularity, naked 30

Snyder, Hartland 1

solar eclipse 23

Solar System 56

spacetime 12

spacetime diagrams 15

spacetime, curvature 13

spacetime,Minkowski 12

special relativity 12

speed of light 2

spin 14

SS433 85, 86

star, dark 11

stars, binary 8

static limit 31, 45

steam engine 48

stellar mass black holes 60, 61

supermassive black holes 60

surface gravity 53

synchrotron radiation 79, 80

T

temperature 48

thermal radiation 52

thermodynamics, first law of 48, 51

thermodynamics, second law of 48

Thorne, Kip 54

tidal forces 41

time dilation 39

turbulence 64

V

V404 Cyg 61

vacuum 51

Very Long Baseline Array 71

virtual particles 52

VLBA 71, 72

von Zach, Franz Xaver 10

W

water maser 72

Wheeler, John 1

white dwarf 60

white hole 32, 33

WIFI 802.11 protocol 89

worldline 16

wormhole 33

Z

Znajek, Roman 77

-----------------------------------------------------

Light: A Very Short Introduction

Copyright:© Ian Walmsley 2015

Light: A Very Short Introduction was originally published in English in 2015. This translation

is published by arrangement with Oxford University Press. Dook Media Group Limited is

solely responsible for this translation from the original work and Oxford University Press shall

have no liability for any errors,omissions or inaccuracies or ambiguities in such translation or

for any losses caused by reliance thereon

中文版权：©2020 读客文化股份有限公司

经授权，读客文化股份有限公司拥有本书的中文（简体）版权

版权所有，不得翻印

图字：30-2020-006号

图书在版编目（C I P）数据

牛津通识课. 光 / [英] 伊恩·沃尔姆斯利

(Ian Walmsley) 著 ; 叶昊扬, 周应秋译. -- 海口 : 海

南出版社, 2020.4

书名原文：Light: A Very Short

Introduction

ISBN 978-7-5443-9273-0

Ⅰ. ①牛… Ⅱ. ①伊… ②叶… ③周… Ⅲ. ①科学知

识 - 普及读物 ② 光学 - 普及读物 Ⅳ. ① Z228 ② O43-49

中国版本图书馆CIP数据核字 (2020) 第061522号

-----------------------------------------------------

献给凯特、亚历克斯、纳撒尼尔与克莱尔。

目录

序言与致谢

01 光是什么 What is Light?

02 光线 Light Rays

03 光波 Waves

04 光的波粒二象性 Duality

05 光物质 Light Matters

06 光、空间与时间 Light, Space, and Time

07 探索光学前沿 Lighting the Frontiers

08 量子光学 Quantum Light

09 黎明时分 Twilight

索引

Preface and acknowledgements

Chapter 1 What is light?

Chapter 2 Light rays

Chapter 3 Waves

Chapter 4 Duality

Chapter 5 Light matters

Chapter 6 Light, space, and time

Chapter 7 Lighting the frontiers

Chapter 8 Quantum light

Chapter 9 Twilight

Further reading

Index

序言与致谢

因为有光，我们才能看到这个世界。这个显而易见的事实开启了一次漫长而引人入胜的征程。在这个征程中，有关自然世界是如何运作的非凡观点得到了发展，同样得到发展的还有建立现代科学所使用的工具和方法，从而使我们的征程保持着理论与实验齐头并进的态势。

光携带着有关我们周围环境的信息，从遥远的恒星和星系到我们身体中的细胞，再到单个原子和分子，不一而足。光也是很多能够提高我们生活质量的技术的基础：互联网是由光驱动的；世界上最精确的时钟依赖于光；那些最为微小的物体——从单个原子到活的生物细胞——都可以通过光来进行观察与操纵；至于与光息息相关的图像和显示器，更是无处不在。光还揭示了量子世界所有的怪异之处，激发了我们对世界的想象。你可能会惊讶地发现，从人类真正理解光的实质到现在，还不足100年时间。直到现在，我们仍然试图从这种理解中获得新的见解。

这本书探讨了人们是如何从无到有地建立起对光的理解，包括光的本质以及光的用途的问题。这是一次伟大的历程，从古代开始，就有来自世界各地的人为此作出贡献：从雅典的欧几里得与巴格达的海什木构想出光线的概念；到美国洛杉矶的西奥多·梅曼
[1]

(Ted Maiman)与日本德岛的中村修二开发了新的激光器；接着通过巴黎的奥古斯丁·菲涅耳
[2]

(Auguste Fresnel)与伦敦的托马斯·杨(Thomas Young)对光的波动性进行的研究；英国阿伯丁的詹姆斯·克拉克·麦克斯韦(James Clerk Maxwell)和德国柏林的海因里希·赫兹(Heinrich Hertz)从这些成果中发展出了电磁场概念；并最终由德国伯尔尼大学的阿尔伯特·爱因斯坦(Albert Einstein)与英国剑桥大学的保罗·狄拉克(Paul Dirac)博采众长，通过一个新的概念——量子场——解释了这些明显不相容的概念，即光是如何能够同时既是粒子又是波的。

对光的了解每加深一步，都会带来新的应用。例如，基于对光的折射的理解，用于矫正视力的眼镜得以发明。在光学领域，科学发现可以很快地转化成技术得以应用。光对现代世界的影响无疑是巨大的，但是却没有得到应有的重视。因此，联合国指定2015年为国际光年(International Year of Light)，来歌颂光以及它所带来的一切。

我想要感谢亚历克斯·沃尔姆斯利(Alex Walmsley)和拉莎·梅农(Latha Menon)，他们为本书的草稿提出了很多有用的评论，也要感谢我的同事们解答了一些具体技术的问题，还要感谢那些为本书提供插图的人。爱因斯坦曾经说过，“凡事都应该尽可能简单，但不应过分简单”(Everything should be made as simple as possible， but no simpler)。如果在本书中出现了与这个原则相违背的地方，那一定是我没有尽力遵从爱因斯坦规劝的缘故。

[1]
Ted是人们对西奥·梅多曼(Theodore Maiman)的昵称

[2]
作者误将奥古斯丁·菲涅耳的名写作Joseph。

01 光是什么 What is Light?

光，使我们看到周围的世界。我们通过对光的感知来收集物理世界的第一手信息，并观察它们的变化。从这个角度来说，光的这种承载与传递信息的能力，也许就是它最重要也是最显著的特征。

眼见为实

视觉帮助我们找到自己在周围环境中的位置，同时也帮助我们定义外部事物，为我们构建出一幅真实的世界图景。不仅如此，视觉所激发的想象力远超视觉本身。在图1里我们可以看到乔治·理奇蒙德(George Richmond)的画作《光的创造
》，它表现了光在人类心灵中占据了非常核心的位置。英语中还有很多由光的概念衍生出来的词语，例如insight(洞察力)、illumination(既可以译作光源，也可以译作启迪)、clarity(清晰，既可以表示画面或声音的清晰，也可以表示思维的清晰)。这些词汇都与人的品质或是世界的物理特性有关。在拉丁语中，有这样两个描述光的词语，一个是l u， x一个是l u m。e它n们分别从物质的角度与形而上学的角度对光进行描述。本书的重点放在前者，即从物质的角度来解析光的概念。在哲学、神学、心理学、艺术和文学领域，光的物理特性与其特有的诗意交织纵横，使得光也常被拿来作比喻，表达对世界的思索，毕竟几乎所有人都感知过光。正是由于光的物理特性，以及人们通过对光的思索而产生的意识观念，使光成为科学家与哲学家们数百年来经久不衰的研究对象。

图1　乔治·里奇蒙德《光的创造》

光赋予万物生命。毫不夸张地说，光与我们人类甚至地球得以存在的生物反应过程和化学反应过程息息相关。可以说，光塑造了我们对周围事物的认知。从我们的日常经验出发，也能理解光的这种重要性。例如，我们用光来进行照明，既可以是太阳或者月亮发出的自然光，也可以是人造光。大多数的常见光源都使用电力，但有时候我们也使用化学反应来制造光源，例如燃烧蜡烛。光源的不同特征会影响我们对周围环境的感知，因为不同的光源为它所在的物理空间营造了不同的“情绪”。

光使生命成为可能。地球上的能量主要源自太阳。光是太阳辐射能量的一种主要方式，包括可见光和我们无法直接观测到的不可见光。想象一下，你躺在阳光下的沙滩上，或者坐在室外的花园中，你身上感受到的“温度”就是因为太阳辐射出的某种不可见光的作用。这只是光的生理效应的一个例子。

地球为保证生命延续，持续进行着一系列令人惊叹的生化反应过程。在这一过程中，光扮演着非常重要的角色，在它的助力下，“无用分子”二氧化碳被转化为“有用分子”氧气。这一反应的逆反应，即将氧气转化为二氧化碳，来自生物的呼吸以及燃料的燃烧。

在太阳光数百万年时间的作用下，地球上的生态圈以及可以提供其他能源的地质特征得以形成。没有太阳能，不管是煤炭还是石油都不可能形成。但是，我们对于这些化石能源的利用正在改变太阳光影响地球的方式。太阳辐射的一些不可见光，例如紫外线，可以被地球和大气所吸收。但是其他不可见光，例如红外线，则会被大气反射回去。同理，由地球表面产生的红外线会被困在大气层之下，导致地球表面温度升高。

利用光进行通信

自人类诞生以来，图像一直都是人类文明的一部分。图像不仅影响着我们对世界的认识，还深深影响着我们对自身所处环境的认知。光学技术在图像方面作出了革命性的贡献。比如，通过胶片和数码摄像可以简单、快速地捕捉影像。这使得人们可以记录下人物、地点和事件来进行报道，并广泛传播出去(现在主要是通过互联网传播，而互联网的应用也离不开光学)。除此之外，它们还可以记录那些具有深远影响的事物，例如领袖与工人们的照片、令人惊叹的自然景观、毛骨悚然的战争场景，这些图像会以意想不到的方式使人们变得团结或分裂。例如，图像可以用来号召群众采取行动，激发同情心，以及使人们对共同拥有的经历进行更深刻的反思，等等。我们可以回想一下人类在月球上迈出第一步的场景(见图2)，它引发了全人类的强烈惊喜。捕获移动影像的技术为历史叙事增加了一个新的维度——你能够想象没有电视、电影和视频的生活吗？

图2　尼尔·阿姆斯特朗（Neil Armstrong）在月球上为登月同伴埃德温·奥尔德林（Edwin Aldrin）拍摄的一张照片，照片中奥尔德林在月球表面行走

现在，图像的生成与传播已经如此普遍，以至于我们在日常生活中根本不会有所留意。我们每天都使用发光显示屏，比如电视、电脑、平板和手机。这些设备都以光为媒介，为用户传送信息。几乎所有的远程通信都是以光为媒介，沿着名为光纤的细玻璃丝进行传输的。这正是互联网光纤宽带服务的基础，基于此，千家万户得以连接上互联网。即使在电视机和电脑里，光也非常重要。例如，刻在CD或DVD上的音乐、视频与图片都是通过光进行读取的。微型激光器的微型磁头被用来“读取”光盘，它将光盘上的信息转换成电信号并传输到显示屏上进行显示。我们上网、下载文件、收发邮件等活动都需要能够容纳巨大的信息量的传播媒介，而唯一能满足我们要求的，就是光。

在现代社会的交通运输中，光以信号灯的形式来规范我们的交通运行。从城镇的路灯到机场的着陆灯，光都是导航的重要组成部分。光在车辆维护方面也很重要。例如，激光被用来对齐汽车的车轮，又比如常见的光控点火器，可以用来驱动内燃机引擎。

可以说，光以多种多样的方式，承载着创造现代生活所需要的能量与信息。

光学

所有对光进行的研究统称为光学。光学是最古老的科学学科之一，它的历史发展进程为现代科学的产生开辟了一条极其重要的道路。光学领域中提出的新想法曾经为很多不同领域研究中新观点的产生提供了灵感，比如原子和分子动力学。通过对光的深入了解，人们开发出新的技术，这些技术也已经成为解开自然界中其他未解之谜的关键。例如，伽利略设计的光学望远镜不仅帮他观测到了木星的卫星，还帮助科学家们向“太阳系中的行星均围绕太阳运动”这一新发现迈出重要的一步。而这一发现反过来又极大地促进了万有引力定律(解释行星运动的规律)的发展。

光学这一学科可以追溯到公元前4世纪，一些希腊哲学家对光进行了研究。这之后的两千多年中，光学一直持续蓬勃发展。令人惊讶的是，尽管已经有很多具备卓越才能的学者前赴后继地研究，光学在两千多年后的今天仍然不断地绽放出新的光彩。时至今日，仍然有很多新的光学现象不断被发现。在过去的20年间，有十多个诺贝尔奖被颁发给了与光相关的科学研究，可以说，光学仍然处在现代科学的前沿。例如，在超低温条件下如何在超短时间内对原子和分子的运动进行控制和测量的研究，使钟表的时间精确度提升了1000倍；另一个例子则是研究如何才能够观测到活细胞内部，从而使我们能了解到其中的变化情况。

光是什么

要讨论光是什么，可以从光非常常见的一些性质入手：亮度、强度、颜色和温度。这些可感知的特性都说明了光是一种物质实体。但是，光到底是什么呢？

我们可以用家用灯泡作为例子，先来谈谈光的亮度。家用灯泡的功率通常有几十瓦(功率的单位为瓦特，简称为瓦，用W表示，代表每秒所消耗的能量)，具体数值根据灯泡型号不同而不同。一个50W的灯泡足以照亮整个房间，而汽车前照灯的功率一般略大一些，在60W到100W之间。足球场上用来照明的泛光灯的功率则更大，高达几千瓦。之后我会详细讨论光是如何由这些不同的光源产生的，但是通过功率的大小，我们已经对光的亮度有一个具体的概念了。毋庸置疑，太阳是亮度最大的光源之一。它辐射的能量巨大，其功率超过了1025W。(在数字1后面跟着25个0!)由于太阳的亮度是如此之大，即使它距离我们非常遥远，我们仍然不能直视太阳。

以上讨论的光，与我们相距越远看起来就越暗。因此，功率并不是衡量亮度的唯一指标。在某种程度上，亮度与我们从光源那里接收到的能量的比例有关。例如，一支激光笔的功率比灯泡的功率低很多，通常只有千分之几瓦(不到10-2W或者10mW)，但是它照射在屏幕上的时候看起来非常亮。这就引出了下一个与光的亮度有关的概念。

这个重要的概念就是光的强度
(更准确的表达是“辐照度
”，但是人们更熟悉的可能是“强度”这个术语)，即接收器每单位面积上接收到的光的能量。光的强度取决于光源的聚光能力。激光笔发射出的光看起来很亮，这是因为它的光束聚集在一个很小的点上，相比而言，太阳光则在一个很大的区域内扩散。因此，即使太阳输出的能量很大，但是它发出的光的强度却不及一支激光笔。

描述光源聚光能力的基本特征被称为“光源相干性
”。这与光源倾向于向某个特定方向发射光的特性有关。比如，太阳和灯泡总是向各个方向辐射光，这就是为什么我们在地球的任何角落都能看到太阳，在房间的任何地方都可以看到灯泡。但是激光笔只朝一个方向发射光，即激光笔所指向的那个方向。如果激光没有照射在某个表面，人们就无法看到激光，这是因为激光束具有明确的指向性。所以激光笔是很好的相干光源，灯泡则是非相干光源。

光的另一个决定性特征，可能也是它最明显的一个特征，就是光的颜色
。彩虹是雨水与阳光的相互作用而显现出来的多彩色带，色带由蓝色逐渐变化到红色，它体现了色谱的基本概念。事实上，彩色视觉模型的发展是光理论发展的一个中心环节。色彩不仅与感官紧密相连，还与物理学密切相关。这一点可以从艾萨克·牛顿爵士(Isaac Newton)(图3左图)与约翰·沃尔夫冈·冯·歌德(Johann Wolfgang von Goethe)(图3中图)分别做的探索颜色本质的实验中得到证实。牛顿是18世纪早期科学领域的领军人物，他在他的著作《光学
》中对光进行了定义，这一定义在长达两个世纪的时间里受到了广泛认同。歌德则是18世纪后期文学界的领军人物，他将科学理念融入他的作品中，但是他认为牛顿对于光的本质的认识大错特错。

图3　艾萨克·牛顿（左）、约翰·沃尔夫冈·冯·歌德（中）和罗莎琳·富兰克林（右）

牛顿所做的这个实验享誉世界。该实验的第一部分与笛卡儿(Descartes)以及其他人先前所做的相似：让太阳光穿过一个位于深色屏幕上的小孔，仅有一小束光可以穿过小孔。让这一小束光透过棱镜并照射在屏幕上。这时，我们就会在屏幕上看到类似彩虹的颜色带。牛顿认为这一系列颜色就是白光被分解后的颜色，且这些颜色具有普遍性。歌德被这一现象深深吸引，他从当地的一个贵族那里借来一些棱镜并自己动手做起了实验。他很快便得出结论，认为牛顿的实验完全是错误的，这是因为歌德自己发现了一套完全不同的颜色。

在歌德的实验中，他透过棱镜去看窗框。他和牛顿的做法完全相反，他在一片明亮的背景中观察一条黑线，因此，他看到的颜色和牛顿观察到的完全不同。相比于牛顿观察到的红色、绿色和蓝色，歌德观察到的则是青色、品红色和黄色。这一套颜色是牛顿所观察到的色谱的补色。将牛顿看到的颜色合在一起得到的是白色，将歌德看到的颜色合在一起得到的则是黑色。

歌德认为，颜色是我们感知到的一种事物，牛顿却认为这是光的一种固有特性。他们的观点其实都是正确的。今天，我们已经将颜色的物理属性与它的生理学特性(对颜色的感觉)分离开来了。个体对颜色的反应是各不相同的。事实上，基于这个原理，彩光甚至可以用来进行医学治疗。从艺术的角度来看，我们的意识脱胎于对某种特定颜色光的感知，这种解读十分重要，可以简单地理解成感知颜色是非常重要的。然而，从物理学角度来看，我们可以明确地为“颜色”这一标签赋予一个基本物理特性——频率，至少在我们进入量子光学领域之前可以这么做。

光的范围远远超出了可见光谱的范围。从蓝色可见光的一端向不可见光区域扩展，会依次经过紫外线、远紫外线谱区，接着延伸至X射线、γ射线谱区。从红色可见光的一端向反方向扩展，则会依次经过红外线、微波、无线电波直至T射线
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谱区(见图4)。要“看到”它们，仅仅用肉眼是不够的，我们还需要借助其他各式各样的工具，但至少我们已经知道这些“颜色”的光是存在的。例如，我们之所以能够感受到太阳的温度，是由于我们的皮肤吸收了太阳辐射出来的红外线；低频微波常常被用于手机通信，还可以通过加热食物中的水分来烹饪食物。波长较短的不可见光也很常见，例如太阳辐射出的紫外线会导致皮肤晒伤，而X射线常常被用于医学成像。

X射线也被应用在很多非医疗领域，例如可以利用X射线衍射图揭示分子或者固体的结构。将X射线照射到分子或者固体中时，如果其构成原子是规则排列的，那么经过这些原子散射出来的X射线会形成一定的图案。即使原子之间的距离是人类头发丝直径的万分之一，我们也可以从该图案中推断出原子的排列结构。最著名的例子也许就是半个多世纪前，詹姆斯·沃森(James Watson)和弗朗西斯·克里克(Francis Crick)根据罗莎琳·富兰克林(Rosalind Franklin)(图3右图)与莫里斯·威尔金斯(Maurice Wilkins)拍到的X射线衍射图确定了DNA的分子结构。这一发现让我们了解了分子的复制机制，为生物医学领域带来了巨大的变革。

图4　电磁波谱

这些应用都显示了光的重要性。从广义上讲，光帮助我们构建起现代世界，并让我们能够充分享受现代科技。这一切都仰仗19世纪许多科学家的基础研究工作，他们是：迈克尔·法拉第(Michael Faraday)、汉斯·克里斯钦·奥斯特(Hans Christian Oersted)、安德烈·马利·安培(AndréMarie Ampère)、查尔斯·奥古斯丁·德·库仑(Charles Augustin de Coulomb)、亚历山德罗·伏特(Alessandro Volta)、乔治·欧姆(Georg Ohm)、詹姆斯·克拉克·麦克斯韦(James Clerk Maxwell)和海因里希·赫兹(Heinrich Hertz)。可见光与其他与之大相径庭的不可见光，如微波和X射线之间，存在着某种联系，这种联系非常引人注目。能够发现这种联系可以说是这些科学家以及其他贡献者取得的一大胜利。

色域，或者称为光谱，为艺术和科学提供了工具。画家或者艺术家致力于探索如何对各种色彩进行组合，而光谱学家注重探索物质对不同颜色的反应。例如，在19世纪早期，约瑟夫·冯·弗劳恩霍夫(Joseph von Fraunhofer)通过观察太阳辐射出的某些特定颜色的光，从而确定了太阳存在的一些原子类型。他留意到太阳光谱中缺失了一些特征颜色，并指出这些颜色是某些特定原子的“指纹”。光谱研究是光谱学的领域之一，它利用光来识别不同的原子和分子。现在，光谱学是一项很重要的学科，对从健康监测到远程检测大气污染物等多个领域都有着重大影响。

除了这些为人们所熟知的性质，我还想指出光的另外一个性质。它也存在于我们日常生活中的各个方面，只不过没有光的其他性质表现得那么明显。它就是光的偏振性。

3D电影就是利用了光的偏振性。看3D电影需要观众戴上特殊的眼镜，眼镜的框架是硬纸板或者塑料，框架内夹着塑料片做的“镜片”。如果你拿两副这样的眼镜，把其中一副的左镜片平移到另一副的右镜片上，并透过这两个交叠的镜片去观察一个发光的灯泡，灯泡看起来会非常昏暗。或者，你可以把其中的一副眼镜相对于另外一副旋转90°并把两副眼镜的左镜片与左镜片(或右镜片与右镜片)重合，也可以观察到同样的现象。也就是说，光几乎不能透过如此交叠的两个镜片。

这个现象可以利用光的“方向”性进行解释。常见光源所发出的光并没有什么首选的传播方向。当你透过这种有调光作用的镜片观察一束光时，会发现光变得暗淡了一些，这是因为镜片选择了特定的光传播方向。左镜片允许某一个方向的光透过，右镜片允许的透光方向则与其相互垂直。这就是为什么当你将第二个镜片旋转90°并与第一个镜片对齐时，没有光可以透过：因为通过第一个镜片的光具有方向性，但是该方向并不是第二个镜片允许通过的方向。这种方向性特征就称为光的偏振。提出并理解偏振这个概念经历了大量细致的探索。偏振是基于光的应用的一个重要特征，而且对理解光的本质而言非常重要。

强度、颜色和偏振这些物理特性使得光可以用来辨别、测量和控制物质。基于这些特性，一系列工具得以发明，从而实现对物质甚至尺寸更小的对象进行研究和操控。在这一章所举的例子中，光几乎都扮演着信息载体的角色。无论是一张图片、一段光谱或者一次电话通话，光都扮演着信差的角色。除此之外，光还有其他的一些用途。例如，我们可以利用光的热效应对金属和其他材料进行精确切割。相比于用锯子，用高能激光加工厚达几厘米的金属片会更快、质量更好且浪费更少。在医药学方面，光也有着多种用途，从激光手术矫正视力到激活抗癌药物都有涉足。

光使我们能够在任意可想象的时间和空间维度上观察自然界。在时间维度上，我们既可以观测到宇宙形成的初始时刻，也可以观察到电子在原子、分子内部以难以想象的超高速度运动。在空间维度上，大至宇宙中星云的排布，小至石墨烯中碳原子的排列，都可以被观测到。光还帮助我们深入了解自然界赖以存在的基础，从量子物理学中的奇怪现象到DNA分子的结构，不胜枚举。

纵观光学的发展历程，我们可以看到对光的新发现使新技术得以应用，这些新技术反过来又促使许多科学领域产生新的发现。从眼镜的发明，到如今最精确的原子钟，再到现代成像、测试、通信技术，光在每一个阶段都有着不同的应用，为我们的生活方式带来了革命性的变化。尽管光学是一门古老的学科，但是这个新发现与创新所形成的循环使得光学依旧散发着蓬勃的生命力。本书将首先介绍我们是如何一步一步形成光的现代理论，接着讨论我们是如何使用光，从而对世界产生新的认识，产生改变世界的新能力。

[1]
即太赫兹射线。

02 光线 Light Rays

自拍的时候，你会很自然地将手机摄像头正对着自己，这样才能保证你的影像出现在照片中。这个我们习以为常的动作表明了光的本质：物体成像时要求物体(比如说自拍时候的你)必须与相机镜头连成一条直线。这条直线通常被称为“视线”。因此，光是一种由物体向观察者直线传播的物质。

事实上，这与我们对某些类型光源的了解完全一致。音乐会上引人注目的视觉效果是由激光制造出来的，五颜六色的光束被用来照亮舞台与表演者。激光笔则通常用在课堂上，以强调屏幕上的图像或文字。这些由相干光源产生的光束高度聚焦，即使穿越整个音乐厅也几乎不发散。这表明，激光是沿直线传播的——你将激光发射器指向哪个方向，它就会往哪个方向传播。

然而，太阳光并没有明显地表现出这种特性。这也是为什么古时候人们需要费一番周折才能解释这样一个现象：即使两个物体的物理尺寸完全相同，远处的那个物体看起来也要比近处的物体小。如果知道了光沿直线传播的特性，这个现象就非常好理解了。

在公元前300年左右，古希腊的欧几里得就已经用光的这一特性来解释“近大远小”的现象了，他的想法被记录进了最早的光学书籍之一
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。如图5所示，想象两条直线用来表示从物体传播到观察者的光线，一条将物体(图5中的支柱)的顶部与观察者的眼睛连接起来，另一条则是从物体的底部连接到眼睛。这两条线之间的夹角越大，我们感官上就会觉得像越大，反之同理。尽管离观察者较远的支柱与较近的支柱物理尺寸完全相同，但由于它与观察者间的连线夹角相比来说更小，因而远处的支柱看起来更小。我们把图5这样的图称为透视图。

图5　欧几里得用光线沿直线传播的原理解释了为什么相同尺寸的物体在离观察者更远时看起来更小

那么，构成光线的物质是什么？基于更早期的学说，欧几里得认为这种物质是从眼睛里发出的粒子，它来自想象中的体内火焰，照亮物体并被物体反射回观察者的眼中。如果这个说法成立，就表明不管外界是光明还是黑暗我们都能够看到东西，这显然与我们的生活经验相违背。尽管如此，粒子在物体和观察者之间沿着某一轨迹移动的想法仍然是一个强有力的学说。

11世纪的阿拉伯科学家海什木(Al-Hazen)修正了欧几里得的理论，从而逐渐形成我们现在所确信的理论：物体被来自太阳的光线(想象中的外部火焰，与体内火焰相对应)照亮，光线再通过反射传送到观察者。至于海什木是如何想到这个理论的，还流传着好几个故事，其中一个是关于他做的直视太阳的实验。直视太阳时眼睛会灼痛，他认为，如果构成光线的物质是由眼睛发出的，即“体内火焰”一直在燃烧，那么不管他有没有直视太阳，这种灼痛感会一直存在。因此他认为，物体成像所需的光源是来自外部，而不是由眼睛发出的。

在这个理论基础上，我们假设沿光线移动的是光的粒子，称为光子
。于是，光束的亮度就与一秒内光线中通过的光子数有关。为了理解物体是如何成像的，我们需要考虑当一个光子在镜面上反射以及穿过透镜时将会发生的情况，从而推导出“光学定律”。运用光学定律，可以设计出非常复杂的光学仪器，例如手术显微镜，用于“锁孔”手术
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的导管，以及放置在绕地轨道上用于观测遥远星系的大型光学望远镜。这些仪器深刻地影响着我们的生活和我们对世界的理解。

这些光粒子具有什么样的特性呢？粒子的常见属性包括其位置、行进方向和速度信息。我们作出如下假设并暂不深究：光粒子以光速移动；光子的位置可以指定为光线的起始位置；光子的运动方向则是光线的方向。在这些假设下，光子可以看作以光速从起始点射出，沿着光线的方向运动直到它遇到了某一物体的表面。

反射

当光传播到物体表面时会发生反射现象：光子从物体表面反弹，进而改变其运动方向，但这并不改变它在物体表面的位置，如图6所示。早在公元1世纪，亚历山大城的海伦就已经发现了光的“反射定律”，阐明了光子运动方向改变的规律：入射角(入射光线方向与入射点垂直于表面的方向之间的夹角)等于反射角(反射光线方向和入射点垂直于表面的方向之间的夹角)。这个定律在概念上十分简单却非常有力，我们可以用它来解释非常多的光学现象。

图6　光线分别反射在平面镜面(a)和曲面镜面(b和c)上

让我们先来看看由反射造成的左右反转现象。如果你把手表放到镜子前并观察它的镜像，你会看到镜中的秒针正沿着逆时针方向移动；当你移动你的右手时，镜中的你却在移动左手。这种“手性”的变化是镜像的标志——镜中反映的世界在这种意义上是真正的左右颠倒。

这一现象完全可以通过海伦的反射定律来解释。图7显示了镜面是如何使镜像发生了“手性”的颠倒。图中，顺时针方向运动的箭头是我们的观察对象，箭头上从每个点出发的光线同时由平面镜反射并重新排列，使得镜子中箭头的镜像指向逆时针方向。你也可以使用相同的方法来解释为什么指向左方的箭头其镜像指向右，反之亦然。但是，指向上方的箭头的镜像仍然指向上方，向下箭头的镜像仍然指向下方。

图7　顺时针旋转的时钟指针在镜子中变为逆时针旋转的光路示意图

反射成像

在浴室的平面镜子里，你可以看到左右反转的自己，但如果你对着一把抛光的勺子观察自己的反射图像，你会看到自己的形象被扭曲了：你的面部特征在勺子凹下的弧形表面上被放大了。事实上，勺子凹下的前表面有放大物体的效果，凸起的后表面则有缩小物体的效果。

为什么会出现这样的现象呢？从用于视力矫正的隐形眼镜到用于科学发现的太空望远镜，这些光学仪器的制造都运用了光的成像原理，因此弄清楚光是如何成像的非常重要。

到目前为止，我们只考虑了物体上某一点的某一道光线。实际上，光线通常是从物体上的各个点向四面八方散射的。如图8所示，假设多条光线组成的“光线束”从物体上的某个点出发并形成一个锥体，这个光锥在远离物体时发散。这些光线将在弧形镜面上的不同点处发生反射，因此形成了不同大小的入射角。尽管光线的反射方向不相同，但是在每个方向上的反射现象仍然满足海伦的反射定律。反射之后的光线会形成一个逆向的光锥，并最终会聚在同一个点上，这个点就是对应发出光线束的原始物体点的“像点”。

图8　物体通过曲面镜成像示意图。物体上某一点发出的锥形光束通过曲面镜的反射最终会聚到一个像点上

我们通常认为，物体的像是由物体上各个点所对应的像点组成的。像的大小由物体与曲面镜的距离以及曲面镜的聚焦能力决定，其中后者由曲面镜表面的曲率半径决定(例如，凹陷弧度越大的曲面镜表面曲率半径越小)。当物体更靠近镜子时，像可以比物体本身更大。像与原始物体之间大小的比率被称为放大率。

牛顿利用曲面镜可以放大成像的特性来设计望远镜，如图9所示。他的设计有一个显著的特点：不论是什么颜色的光线，望远镜对远处物体成像的大小是不变的(没有色差)。显然，牛顿巧妙地利用了反射定律里入射角必然与反射角相等的特性，使得无论光线的颜色是什么，只要光线的入射角度相同，反射角度就一定会相同。因此，每种颜色的像都将形成于同一位置，这就使所有颜色得以完美保留。

图9　牛顿的反射望远镜，它的成像没有色

折射

牛顿之所以发明了这种反射望远镜，是因为伽利略·伽利雷和约翰尼斯·开普勒(Johannes Kepler)等当代先驱所使用的望远镜受到了色差的严重影响。他们的望远镜成像时，在观测物体边缘总是有一个模糊的彩色光环，其原因在于这些望远镜是利用光的折射特性设计的。光的折射指的是当光从一种透明介质传递到另一种透明介质时传播方向发生弯曲的现象。

正是光的折射现象，使得浸入水中的铅笔看起来好像沿着水面被“折断”了。这就是光的折射定律，通常被称为斯涅尔定律，以荷兰物理学家威理博·斯涅尔(Willebrord Snell)的名字命名，他在17世纪早期就发现了这一定律。该定律表明，折射光线与入射点垂直于表面的方向间的夹角不仅与入射角有关，还与两个透明介质的特性有关。如图10所示，在铅笔看似被折断的例子中，这两个介质分别是空气与水。

“折射率”被用来度量透明介质的特性，它的大小反映了相应介质光学“刚度”的强弱。例如，光在具有较大折射率的介质中传播得更慢，这是因为光线更不容易“挪动”该介质分子中的原子与电子，即具有较大折射率的介质对光的阻力更大一些，我们可以理解成它的光学刚度更高一些。这就像在水池中奔跑，如果水不深，你的腿可以轻松移动；但如果水深达膝盖，你就没那么容易在水下自由行走了，因为你必须抵抗水的阻力。

图10　光线在空气和水的交界面上发生折

事实上，折射定律还可以用另一种方法推导而出。皮埃尔·德·费马(Pierre de Fermat)表明，当光从一个介质中的某个点传播到第二个介质中的某个点期间，它会寻找到一条特别的传播路径，使得光能用较短时间从高折射率的介质中穿过，用较长时间从低折射率的介质中穿过。这就要求光线在两种介质的交界面处发生弯曲。这就是有名的费马原理，它与斯涅尔定律异曲同工。

透镜成像

我们已经知道，光可以通过有弧度的镜面反射成像，与此类似，光也可以通过有弧度的透镜折射成像，其成像过程展示在图11中，来自物体上某点的一束光线通过透镜的折射最终聚焦在像的一个像点上。请注意图中透镜的形状，它的横截面是不是很像扁豆(lentil)？这就是透镜(lens)这个词的来源。

图11　光线通过透镜成像示意

从你的眼睛到手机摄像头，再到手术显微镜，透镜在成像设备中无处不在。成像仪器具有两个部件：透镜本身和光学检测仪。光学检测仪是将光转换成其他信号的仪器，通常是电信号。例如，视网膜就是眼睛的光学检测仪，而手机摄像头的光学检测仪则是固态光传感器，由一系列微小的硅片组成。

诚然，每个装置中的透镜都不尽相同，但基本原理是一样的。不论在哪种情况下，镜头与光学检测仪之间的距离都是关键的设计参数；另一个关键参数则是透镜的焦距
，它可以衡量透镜“弯曲光线”的能力。焦距由透镜的曲率以及厚度决定。要制造短焦距的透镜，需要采用曲度大且更厚的材料。这样的透镜通常用于需要高放大率的仪器，例如显微镜。

光的颜色改变，透镜材料的折射率也会随之改变，所以不同颜色的光在透镜表面会有不同程度的弯曲，导致每种颜色的焦点出现在不同的位置。这使得透镜成像的周围会出现不同颜色的“晕圈”。例如，在一个特定的光学检测仪平面，通常只有一种颜色可以准确聚焦，而其他颜色将失焦并形成光环。这种色差现象是否会导致严重后果需要具体情况具体分析。

我们最熟悉且最重要的成像工具之一就是我们的眼睛。它由前折射表面、角膜和可调节透镜依次组成，其中可调节透镜可以根据眼睛聚焦物体的远近而改变形状。物体通过这一系列眼部结构后，最终在眼睛后部的视网膜上形成图像。

在历史上，眼睛成像的原理一直令人们非常感兴趣，尤其是在笛卡儿做了一个关于眼睛成像的实验之后(见图12)。实验显示直立物体的图像经过眼睛成像后会上下颠倒。当然，我们眼睛看到的并不是上下颠倒的物体，很明显，大脑一定对原始视网膜信号进行了一些非凡的处理，校正了其与外部世界不一致的部分，使我们的感知变得准确。

光学仪器

众所周知，眼睛看清东西的能力(形状清晰、色彩鲜明)会随着年龄的增长而下降。最早的一些光学仪器就是开发作为视觉辅助的。眼镜可能是第一个这样的光学仪器，据称是由罗杰·培根(Roger Bacon)在13世纪时发明的，他被称作牛津的“疯狂修道士(mad friar)”。

眼镜通常是将简单的透镜，镶以镜框，佩戴在距离角膜(眼球的前表面)一定距离(通常是几毫米)的位置。 “隐形眼镜(contact lenses)”，顾名思义，则是将透镜直接与角膜接触(contact)。在这两种情况下，成像系统都是复合的，也就是说，成像系统由外部透镜、角膜和晶状体这几个部分组成。这样就可以通过外部透镜去补偿眼睛晶状体的缺陷，从而达到矫正视力的目的。这种矫正也可以通过激光手术直接改变眼睛前表面的形状来完成。激光辅助原位角膜磨削术(Laser-assisted Subepithelial Keratomileusis，缩写为LASIK)就是这样一种手术，它使用激光烧蚀角膜表面的一部分以改变其曲率，从而改变角膜的聚焦能力，即改变了眼睛的成像能力。

图12　笛卡儿关于眼睛成像的实验。实验显示眼底视网膜成的像是上下颠倒的
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许多其他成像工具的工作原理与眼睛非常相似，例如手机摄像头。手机摄像头通常非常小，但却能够拍出高质量的图像，可供我们在社交媒体上发布。手机的摄像头被放置在手机表面，硅基光电探测器阵列则被放置在手机内部。手机摄像得到高质量图像取决于两个方面：一是阵列中探测器的大小和数量，二是光学系统创建无色差、清晰、无失真图像的能力。

检测器阵列的“像素”数量大小一般用来描述图像质量的好坏：一个2400万像素的摄像头(探测器阵列包含2400万个传感器)通常被认为比800万像素的摄像头更好。像素可以被认为是最小可成像单位的图像大小。当探测器阵列中传感器数量很少时，被拍摄物体就只能被解析成少量的最小可成像单位，也就是说像素量很少，那么从拍出来的图像里就很难分辨出这个物体。因此，像素一般是越大越好，但前提是成像系统能够产生的最小图像单位比探测器元件还要小。

成像极限

在19世纪，德国科学家恩斯特·阿贝(Ernst Abbe)设计了一个简单的规则来描述成像极限，即像素尺寸大小。该规则适用于任何当时已知的成像系统。在阿贝准则中，一个像素的大小(S)与照射该物体的光的波长(λ)乘以透镜的焦距(f)再除以镜头直径(D)的结果成正比。

因此，具有大直径和短焦距的透镜将会有更小的像素尺寸，因而成像更为清晰。在任何透镜系统中，像素大小与该物体的光的一个波长相同时得到的物体图像，就是你能得到的最佳图像。实现最佳图像效果时所达到的像素大小大约为一个波长，这也是大多数光学仪器(例如相机和双筒望远镜)像素尺寸的极限。

在光学的许多重要应用中，设计和构建能够产出高质量图像的成像系统一直是重中之重。例如显微镜，它被广泛应用于从生物学研究到外科手术的多个领域中。最早的显微镜使用的是非常简单的透镜，尽管它很小，具有类似于球形抛光玻璃的形状，却为17世纪的罗伯特·胡克(Robert Hooke)等早期实验者提供了探索自然界中无法用肉眼看到的微小生物的工具。如图13位于上方的图片所示，胡克绘制的跳蚤图揭示了显微技术的力量，使更多的新发现成为可能。

相较起来，现代的科研显微镜设备更为复杂。它们由包含多个部件的复合透镜组成，使得成像的像素大小非常接近于光的波长，即之前提到的成像极限，或阿贝极限。图13位于下方的图片显示了一个由现代显微镜成像的例子。这是一张果蝇幼虫神经系统的合成图像，该幼虫即将孵化。它是通过位于幼虫细胞中的发光蛋白成像而成的。

图13　胡克通过早期显微镜观察到的跳蚤图(上图)，以及用现代荧光显微镜拍摄的果蝇幼虫的神经系统(下图)

阿贝极限适用于图像亮度与物体亮度成比例的光学系统。这样的光学系统被称为线性系统。事实上，阿贝极限可以被突破，但是需要通过非线性系统，在这种系统中，图像亮度与物体亮度的平方乃至更复杂的函数成比例。为了更全面地解释这些效应，需要更多地了解光的波动模型，这将是本书第3章的主题。

具有类似特性及复杂性的光学成像系统还被用于计算机芯片的制造中。要知道，电子电路元件都非常微小，连接芯片上两个晶体管的导线直径仅为250纳米。 复杂的器件和连接阵列通过一种被称为光刻的工艺被布置在硅片上。

为使设计师方便观察，芯片布局的绘制比例一般都足够大，绘制完成后，将芯片布局比例缩小并投影到芯片上；接着，这一图像将被蚀刻到晶片的表面涂层上；最后，通过一系列化学反应过程，图像映射到实际设备上。要完成这一系列步骤，成像系统必须具有非常高的分辨率，即像素尺寸要与设备连接线的尺寸数量级相同。在整个晶片上保持这种分辨率是一个很大的挑战，这需要对许多透镜元件精密组合，从而将所有像差减小到绝对最小值。图14就展示了这样一个例子，图中显示了该透镜的横截面，显示了透镜元件与光线路径的多样性。

图14　用于计算机芯片光刻的透镜的一部分。它由20多不同的透镜元件组成，可以形成500纳米的图像，个尺寸比其使用的光的波长的一半还要小

刚刚我们讨论了显微镜，现在我们来谈谈另一个极端——天文望远镜，它们有的在地面，有的在太空，尽管都是非常大的仪器，却是由相对简单的光学成像元件构成，通常只用一个弧形的反射表面和一个简单的“目镜”来调整光线，以便与现有探测器充分匹配。这些成像系统的显著特征就是它们的尺寸。当我们观测非常遥远的恒星时，它们看起来十分微弱，这是因为它们发出的光线几乎都没能到达地球。因此，尽可能多地收集这些光线是非常重要的，这往往需要一个非常大的透镜或镜面——直径达几十米或更大。制造这种尺寸的透镜是不切实际的，但镜片可以。因此，巨大的镜面被制造并安装在大型望远镜中。同时，为了收集足够多的光线来成像，往往需要长时间观察遥远的恒星。这导致了地面望远镜的另一个问题：大气层不是一成不变的，它的密度随着风、温度和湿度变化，这些波动往往会使光线偏离其传播方向。比如，恒星之所以看起来在“闪烁”，就是因为大气湍流使光线随机照向或偏离望远镜的探测器。

解决这个问题的方法之一就是直接将望远镜放在大气层外的太空中，哈勃太空望远镜就是一个例子。它成功获取了遥远恒星、星系和星云的壮观图像，观测到遥远太空中非凡的宇宙结构与运动。除此之外，还有其他的解决方案吗？光学工程师在过去20年中设计了一种巧妙的方法，为地面上的可见光望远镜成功解决了这个问题：将望远镜的镜面分割成多个区域，每个区域的镜面都可以倾斜，通过调节镜面不同区域的倾斜角度，就可以“操纵”光线，使它们全部被探测器所接收。如果你可以测量光线穿过大气层时产生的偏差，就可以通过调整镜面来补偿这一偏差。光学工程师们首先测量导星(位于上层大气中的人造光源)的光通过大气层的扭曲程度，然后根据这一信息来调整镜子不同区域的倾斜角度。用这种方式，地面望远镜成的像可以刚好达到阿贝极限。但是，将望远镜放置在太空仍然是必要的，这是因为有一些电磁波段会被大气吸收，例如X射线和紫外线，为了对它们进行观测，我们仍然需要太空望远镜。美国宇航局(North American Space Agency，缩写为NASA)和欧洲宇航局(European Space Agency，缩写为ESA)正在计划进行新的太空望远镜任务。

超颖材料和超级透镜

多年来，光学科学家们一直致力于建立卓越的光学系统，那么，是否存在这样一个具有完美的成像能力的透镜呢？从19世纪英国的詹姆斯·克拉克·麦克斯韦到20世纪苏联的维克托·韦谢拉戈(Victor Veselago)，许多伟大的物理学家都对这一问题充满了兴趣。韦谢拉戈考虑了这样一种奇特的材料：当光线射到这种材料表面后会并不会遵循斯涅尔定律，甚至与其完全相悖。斯涅尔定律是基于常见的“普通”材料，它们的折射率为正数，而韦谢拉戈提出的材料具有“负”的折射率。这种材料由许多微小结构组成，且每一个微小结构的尺寸都小于观测光的波长。这种特殊的结构赋予了“超颖材料”不同寻常的光学特性。举一个有代表性的例子，与光线在两种普通材料之间的界面上相比，当光线在普通和超颖材料之间的界面上产生折射时，折射方向将完全相反。

利用超颖材料独特的折射率，我们可以通过工程设计使它能弯曲从各个方向射来的光线。这样，本来会在材料表面发生散射的入射光线将围绕着超颖材料的表面发散出去，从而使超颖材料“隐形”。事实上，英国物理学家约翰·彭德里爵士(Sir John Pendry)表示，使用超颖材料制作隐形斗篷是完全有可能的。

超颖材料还有另一个不寻常的特性，就是能够对非常接近超颖材料的物体进行完美成像。如果使用超颖材料制造透镜，其表面可以做得非常平整，不需要像玻璃透镜那样有很大的弧度。这使得利用超颖材料制作的透镜很适合观察非常微小的物体，尤其是仅有数十纳米量级尺寸的纳米结构体。超颖透镜可以类比为21世纪的胡克显微镜技术了，也许它会开启一个新科学发现频繁涌现的新时代。

本章描述的所有成像系统都对物体进行了二维渲染
[4]

，毕竟我们通常对图像的理解就是平面的图片。那么，我们是不是能设想出一个可以制作三维图像的系统呢？这就需要我们对光本身有更深入的了解，我们将在第3章中就这一点展开讨论。

[1]
《光学》（Optics ）。

[2]
一种微创手术，切口比锁孔还小，使用包括光纤在内的特殊仪器和技术。

[3]
图中La Dioptrique 为法语，译作“屈光”，特指在眼部所发生的光的折射。

[4]
对三维物体进行二维渲染意即利用平面图像显示出三维物体的立体感。

03 光波 Waves

在第2章里，光被认为是由基本粒子组成，并沿着明确的轨迹而运动，我称之为“台球”模型。在这一模型中，光束可看作是由一个个分布紧凑的能量束集合而成，这与光是波的观点形成鲜明的对比。事实上，光的波动说与光的粒子说的发展可谓并驾齐驱，只不过与光的粒子说相比，光的波动学说要经过很多年的争论和实验之后，才被人们完全接受。

无法解释的现象？

在阳光下观察水面上漂浮的一小层薄油，你会在油层的边缘发现彩色的轮廓。正是这一观察激发了一个跨时代的想法——光是作为波运动的。牛顿是最早描述这种现象的人之一，但是这一现象对他的光粒子模型提出了挑战。为解释这一现象，牛顿势必要对他的模型进行严重的扭曲。而在海峡对岸，牛顿在光学上的竞争对手、法国科学院院长、荷兰人克里斯蒂安·惠更斯(Christian Huygens)则使用了光的波动模型来解释这一现象。这一解释被证明更加合适。因此，早在光学研究初期，波和粒子的概念就已经同时出现了。

不仅是这一种现象，还有其他的现象也不能够用光的粒子说来解释。例如17世纪中期弗朗西斯科·格里马尔迪(Francesco Grimaldi)的一些发现。他发现光线通过小孔(比如屏幕上的一个小孔)时会偏离直线。他注意到光线发散开来，且在光束的边缘看到了彩色的条纹，这种现象对于像头发或者薄纱这种小物体尤为明显。他总结说，当光照射在一个小或窄的物体上所形成的条纹说明了，当光经过这些物体边缘的时候偏离了其原始路径。如果光真的是由沿着直线运动的粒子组成，那么这样的固体物质肯定会投射出阴影，而不会导致光粒子偏离成奇怪的模式。

此外，令牛顿和他同时代的人都感到困惑的一个问题是，当光通过某些物体，尤其是一些晶体，例如方解石(一种自然矿物)时，会发生古怪的折射，这个现象用光的粒子说根本解释不清楚。图15中的例子就很好地体现了这个现象。用灯泡照亮一张纸上的单词“LIGHT”，且用两块方解石分别盖住单词的左右各一半。在图15a的左半边图像中，单词由一个错位成了两个，右半边图像中的单词也变成了两个，且错位的方向相反。将图中15a左半边上方的图像和右半边下方的图像结合起来，才是符合人们期望的、由纸反射的光经过晶体折射后看到的单词。而图15b似乎是由不同的折射率产生的。如图15b、15c图所示，通过在晶体上放置偏振器，可以分离由两个不同方向偏振光形成的图像。每个偏振光都有不同的折射率。这就是双折射现象
。

图15　展示双折射现象的一个实验。在入射光分别为非偏振光(a)、垂直偏振光(b)、水平偏振光时(c)，过一对方解石晶体观察写在纸上的单词LIGHT

所有的这些观测结果都表明光还有一些性质没有被解释清楚。这些性质分别是干涉
、衍射
与偏
振
。我们将在本章对这些现象进行探索，继续讲述光的波动说。

波长和频率

波的特点是什么？波是与介质有关的一种波动形式，例如池塘表面的水波，这些波是由水分子在水与空气界面处的上下运动形成的。这种运动的最高点和最低点即为水波的波峰和波谷，而水波本身沿着池水表面运动，也就是说水波的运动方向与水分子的运动方向垂直。因此，它被称为横波
。它的波速取决于水的深度等因素。

图16　水面上的圆形波：a.等高线，也称为波前；b.在某特定时刻，波的高度与距中心位置距离间的关系图；c.在水面某特定位置，波的高度和时间之间的关系图

如图16a所示，一块石头被抛入水中，圆形的表面波从石头入水处产生，并往外扩散，这是一种很常见的现象。相邻波峰之间的距离称为波长
(见图16b)。波峰到达岸边的速率称为波的频率
(见图16c)。波长和频率的乘积称为波速
。

很多个世纪以来，人们一直有个疑问，光究竟是由哪种波组成的？一些人认为波的存在需要某种介质。由于光的速度很大，所以这个介质必须非常坚硬，但是这样又会导致其他物体很难穿过它。比方说，我们之所以能够看到遥远的恒星，肯定是存在某种介质使得光得以在恒星和地球之间传播。地球在围绕太阳运转的过程中必然会不断地穿入并穿出这种介质。这种神秘的介质被称为“以太”，直到19世纪末，它才不再被视为一个有用的概念而被抛弃。

所以，光是什么样的波呢？这个问题最终由詹姆斯·克拉克·麦克斯韦(James Clerk Maxwell)在19世纪提供了答案。他指出这是一种新的实体的振动：电磁场。电磁场是作用在电荷和磁性材料上的力。例如，一块带有静电的布会吸附灰尘颗粒，一块磁铁会被吸附到冰箱门上。在第二个例子中，当你手拿着磁铁靠近冰箱门时，你的手就能感受到这种力：磁铁会加速靠近冰箱门，除非你给磁铁施加一个反向的作用力。

在上面两个例子中，都存在一种力将一个物体拉向另一个物体。在第一个例子中，布上的电荷产生电场，因而在离布一定距离之内的灰尘将受到源自该电场的力。同样，冰箱门受到的作用力源自磁铁产生的磁场。19世纪早期，迈克尔·法拉第(Michael Faraday)就已经证明了电场和磁场之间存在紧密的联系。麦克斯韦把电场和磁场合在一起，称为电磁场。在波动模型中，光可以看做是电磁场的高频振荡。基于这个观点，移动的电荷可以产生光波。我将在第5章中讨论这种方法以及其他产生光的方法。

干涉

如果将两块石头扔到水里相距较近的位置，那么从这两个位置就会产生两组圆形波向外扩散并最终相遇。在波与波叠加的地方，波峰会变得更高。在水面上也有另外一些可以连接成线的地方，尽管两个波都经过，却没有丝毫高低起伏。这些线的位置如图17所示，一般都是沿着波前(波源发出的振动经相同时间所到达的各个波峰点组成的面，见图17a中灰色的同心圆线，圆心则为波源位置)。

图17　a.水面上两个圆形波相互干涉。灰色的线是等相位线。b.两个波的波程相同，彼此之间发生相长干涉。c.两个波的波程相差半个波长，彼此之间发生相消干涉

这种现象被称为干涉，它是由两个波相遇时的振幅相加而产生的。如果两个波的峰值重合，则波峰的振幅变为原来的两倍。也就是说两个同相位的波，会发生相长干涉，即波的振幅加倍，见图17b。如果两个波是反相位的，也就是说其中一个波的波峰和另外一个波的波谷相遇，则合成波的振幅为零，使得这两个波彼此抵消，被称为相消干涉，见图17c。很显然，这样的现象不可能发生在粒子上，因为两个粒子怎么可能互相抵消呢？

1803年，托马斯·杨(Thomas Young)在一个著名实验中观察到了干涉现象，这一发现使得光的波动说成为解释光本质的主要理论。杨的实验简单而精妙。他用一个蜡烛当光源，蜡烛后面放一块屏幕，在屏幕上有两个距离很近的小孔。光线透过这两个小孔，投射在被放置在不远处的第二块屏幕上。如果只使用一个小孔(例如盖住另一个小孔)，那么在第二块屏幕上就会出现一个小小的光斑。然而，在两个小孔都开放的情况下，奇妙的现象发生了：第二块屏幕上出现的并不是一个两倍于之前亮度的光斑，而是在此基础上出现了条纹。这些条纹是由亮度几乎为零的直线组成，方向垂直于两个小孔的中心连线。图18是光线穿过两个小孔之后产生干涉现象的横截面图。这种条纹称为“杨氏条纹”，是光作为波运动的关键证据之一。

图18　托马斯·杨的实验。光透过一个小缝之后形成一个光滑的光强分布图。光透过两个小缝之后，形成一系列明暗条纹，这是典型的波动特征

我们之前提到牛顿做过的一个实验，光在两个靠得非常近的平面上反射时会产生彩色条纹。那么如何利用干涉原理来解释牛顿观察到的彩色条纹呢？我们知道，产生干涉现象需要两个波，其相对相位(两个波峰值的相对位置)可以调整。在牛顿的实验中，一束入射光被两个平面反射，从而被分成了两个波，就是在这两个波之间发生了干涉。如果两个反射面的距离等于光的波长，那么两个波的波峰相互重合，会形成一道亮条纹；如果两个反射面的距离等于半个波长，那么一个波的波峰和另一个波的波谷重合，从而发生相消干涉，产生“暗条纹”。因此，当你观察明暗条纹时，你会发现明暗条纹之间的间隔小于一个波长。对于波长约为500纳米的绿光，这一间隔甚至可以小于250纳米——约为头发直径的1/40。

当然，对于不同的波长，明暗条纹会出现在不同的地方。由于白光是由各种波长不同的光组成的，所以如果入射到平面上的光是白光，那么出现的条纹就会是彩色的。水面上油层边缘出现的彩色轮廓就是由于光波的干涉产生的。

干涉可以将微小的距离(与光的波长在同一个量级)转化为非常明显的光强度变化：最暗的地方光强度可以为零，而最亮的地方，其亮度可以达到单束光的强度的4倍。这种光强度的变化很容易被探测或观察到。因此，如果要测量的位移尺度在光波长的量级，干涉是一个很好的测量方法。很多光学传感器都是基于干涉效应的。

全息技术

干涉还可以用来制作真实的三维图像，它可以从任意角度观察图像，从而可以通过不同侧面展示成像对象。这种图像被称为全息图，与3D电影中所谓的合成图像不一样。全息图是通过记录物体散射出的光的完整波形制作成的。我们平常拍摄的二维图像只编码了波的强度，而波的相位信息却被丢失了。这是因为拍摄二维图像所使用的传感器只对波的强度做出响应，所以我们无法从这些图像中提取出相位信息。然而，要想对物体的形状进行编码，就需要利用相位信息。

干涉可以将相位信息编码为强度信息，这样光电探测器就可以记录目标波完整的振幅和相位信息。原理如图19所示。物体散射的光波与一束参考波发生干涉，其中参考波是由激光产生的已知形状的波。干涉图案则由传感器或者感光材料记录下来。这就是丹尼斯·加伯(Denis Gabor)于20世纪中期发明的全息技术。

图19　全息图是通过记录一束参考波和物体的散射光波之间的干涉条纹而形成的

与普通照片相比，观看全息图要复杂一些。首先，用一束参考波照亮全息图，其中一些光从全息图的编码图案中散射出来。这些散射光束有一个显著特性，它们再现了从原始物体散射出来的光束，因此当你的眼睛接收到这些散射光时，看起来就好像原始物体在你面前被重建了。在全息图周围移动时可以看到物体的不同侧面，因为这些从不同部分散射的光束编码了不同的信息。

全息图也可以由电脑制作并压印在金属或其他材料上。材料表面的起伏模仿了参考波与物体散射波的干涉图样：凸起的部分代表了亮条纹，凹进去的部分代表了暗条纹。同理，想观看这样的全息图也要用一个参考波照射，使得其材料上散射的光再现原物体发出的散射波前。这种全息图还被用来作为安全装置，包括在钞票上的使用[例如20英镑的纸钞上就印有一条18世纪苏格兰经济学家亚当·斯密(Adam Smith)的全息图]，因为它太难制作了，要借助很先进的工程技术才可以。

再次探讨成像极限

光的波动说还解释了为什么我们无法用显微镜观察极其微小的物体，正如阿贝(Abbe)所注意到的一样。小到半个微米(一米的百分之一或可见光波长的一半)的微小物体可以用一般的光学显微镜观察，而对于再小一些的物体，我们就需要用更加复杂的方法进行观察，这是因为光的波动特性限制了光斑的最小尺寸。

我之前提到过，两束光相遇会发生干涉从而产生暗条纹，也就是强度为零的区域。这些条纹的间距取决于两束光相交时的角度。如果角度很大，则条纹间距较小；反之，如果角度较小，则条纹间距较大。条纹的最小可能间距为一个波长；对于可见光而言，这个间距大约是一个微米。

如果这个干涉条纹图样被记录为全息图，那么当它再次被参考光束照亮时将会产生两束光，其方向与用来记录干涉条纹的光束方向一致。如果想用显微镜观察到这种条纹图，使用的透镜必须将这两束光都捕捉到才能形成干涉条纹，如果透镜只能捕捉到其中一束光，那么观察到的图像中就不会出现干涉条纹了。

这是我在第2章中介绍的阿贝准则的物理基础：成像系统的透镜捕捉到的两个光束之间的最大角度决定了所能观察到的物体的最小尺寸。很容易看出，透镜系统所能观察到的物体的最小尺寸大约等于穿过透镜的入射光的波长。因此传统的光学显微镜能够观察到比人的头发尺寸小50倍的微小物体，但是比这再小的尺寸就无法观察了。例如，光学显微镜可以用来观察生物细胞，但不能用来观察细胞核。

超分辨率成像

光学科学家和工程师们想出了很多巧妙的方法来绕过传统光学显微镜对观察目标在尺寸上的限制，这样他们就可以看到细胞内部，或者可以观察到比光的波长小百倍以上的物体。这些仪器使用了新材料和新工艺，比如把纳米级粒子附着到观测目标上，或者将会发光的分子插入细胞中。当它们被一束短波长的光照射时，可以发出长波的光(它们发出荧光)。由于它们的尺寸比显微透镜的分辨率小得多，根据阿贝公式，最终得到的图像会是一个尺寸受限于显微镜光学的斑点。但是我们可以用摄像机长时间观察附着在物体表面的纳米颗粒发出的荧光，并且确定光斑强度最强的位置，从而精确定位图像的中心点。这个技术被称为“光激活定位显微镜”(photo-activated localization microscopy，缩写为PALM)，由美国的埃里克·白兹格(Eric Betzig)发明。这个发明彻底改革了活细胞成像技术，使得人们可以在宽视野范围内更快地采集信息并获取更精确的深度分辨率。

在较大尺寸的荧光物体中测量微小结构的另一个方法是，先用一束光照射物体使其产生荧光，然后用第二束圆形光照射物体，使得光斑外围的荧光消失，只有中心的荧光点保持不灭。通过这样的方法，可以利用保留下来的尺寸很小的荧光点对物体进行精确定位，精确定位的方法跟我们之前描述的定位方法一样。这种方法叫做“受激发射损耗显微技术”(Stimulated Emission Depletion Microscopy，缩写为STED)，是由德国的斯特凡·赫尔(Stefan Hell)发明的。在第5章我会对受激发射的过程进行详细的描述。这些高分辨率成像的新技术使得科学家们得以观察细胞内部的结构，从而在生物学和医学领域中产生了巨大的影响。这种影响的重要性已经获得了认可——白兹格和赫尔获得2014年的诺贝尔化学奖。

阿贝准则反过来使用也是成立的：当光通过显微透镜照射在观测样本上时，聚焦形成的光斑直径不可能小于一个波长。而且聚焦的紧密度，也就是光斑的大小，取决于透镜和透镜照射面之间的夹角范围：角度范围越大，光束聚焦得越紧密。

干涉光束的角度的范围和明暗条纹尺寸之间的关系是波的一个基本特性。19世纪初期法国科学家约瑟夫·傅里叶(Joseph Fourier)对这一观点进行了量化，对光波的传播进行了详细的数学分析。傅里叶定理简单来说就是：要想光线聚焦的光斑尺寸越小，那么就得保证传播到这个光斑的入射光角度范围越广。

衍射

这解释了光的另外一个特征，即光在传播过程中会逐渐发散。这是因为根据定义，一束光的空间范围是有限的，它必须由一道道沿着不止一个方向传播的波组成。我们可以用激光笔来验证上述想法。激光笔发射出的光束直径大约是10微米(百万分之一米)，当它照射在屏幕上时，直径大约为1毫米(千分之一米)。如果激光照射的距离更远，例如照射到月球上去(大约40万千米)，那么光斑直径会高达24千米。这种现象就是衍射。

衍射在测定结构的形状和对称性方面有一些有趣的应用。例如，一束光照射在有小孔的屏幕上，当小孔的直径和波长相近时，光线会通过小孔发生衍射，且其光束的扩散程度与孔径的尺寸成反比。这些衍射光束在距离屏幕一段距离的地方会相互发生干涉，形成干涉条纹，也就是所谓的衍射图案，它反映了小孔的大小及相对位置。例如，如果小孔按照规律进行排列，那么经过该小孔产生的衍射图案就会显示出相应的规律性。使用衍射图案对物体进行测量的优势在于不需要非常昂贵或者复杂的透镜系统，也不需要让探测器非常靠近物体，只需要观察因为衍射而自然扩大的图案。

现在，我们假设屏幕被一个透明的固体材料所替代，比如说晶体蛋白结构。“小孔”则被蛋白质分子中的原子所替代。这些原子非常小，并且通过分子中的键相互连接，这些键的长度约为十亿分之一米(0.1纳米)。如果波长接近于这个尺寸的光照射在这种结构上，光就会发生衍射，分子本身的实际结构就可以由衍射图样确定出来。这是X射线衍射
的基础。正如在第1章中提到的，它曾因探索DNA的结构而闻名，现在也是生物化学领域很常见的工具，常常被用来探寻新分子(例如可能有助于开发药物的新分子)的结构。这一过程需要一束明亮的X射线源，以及将分子晶体化的方法。图20是牛肠病毒晶体的衍射图。

图20　使用现代同步辐射X射线源拍摄到的蛋白质晶体的射线衍射图

很明显，如果你想远距离传输光，那么衍射可能会是一个问题。衍射会使得光束的能量分散开来，因此，随着传输距离的增加，你需要的光学系统和传感器要越来越大才能够接收所有的能量。这对电信业来说非常重要，因为几乎所有通过远程通信传输的信息都被编码在光束里。

导波

为使远距离通信成为可能，就要对衍射进行管控，解决这一问题的方法就是使用波导，例如光纤。波导是一种经过精心设计使其截面具有特殊折射率的结构。例如，光纤内的折射率变化分布经过了特殊设计，使得直径为几百万分之一米的“芯”比周围“包层”的折射率更高。这样，光就被局限在折射率较高的“芯”里，沿着光纤移动而不发生衍射，从而完成远距离传输(例如通过海底光缆横跨大西洋)，同时光束的大小保持不变。从通信到传感器等广泛光信息基础设施，都是依靠这种控制光的方式来工作的。

偏振

光的波动模型的最后一个重要特征是偏振特性。回想一下，在横波中，波的振动方向与波传播方向相垂直。但是，与波的传播方向成直角的方向有两个，也就是说，横波有两个可能的波动方向。

以一根绳子上产生的波为例。如果你将绳子的一端上下快速移动，你会发现波是沿着绳子移动的。如果快速地左右移动绳子一端，也会发生类似的事情。不管是垂直于地面振动，还是水平于地面振动，这两种振动方向都与绳子的方向垂直，也就是与波的移动方向垂直。这样的波都被称为“横波”。

光波就是一种横波。水平偏振光有一个在水平面(相对于光具座
[1]

)上振荡的电场。类似地，垂直偏振的光束在垂直平面上振荡——还有其他更加复杂的偏振形式，这里就不赘述了。要解释双折射现象，我们可以先从晶体的结构入手。晶体由单位晶胞重复排列组合而成。作为构成晶体的最小几何单元，晶胞是由原子构成的特殊结构。这些晶胞本身可能是不对称的，光沿着晶胞的长轴或短轴传播时会发生不同的偏振，折射率也将随之不同。因此，当光通过这种晶体的时候，光的传播方向会发生不同程度的偏移。

众所周知，太阳眼镜就是利用了光的偏振特性。一些太阳眼镜使用塑料(例如塑料偏光薄片)做镜片来充当偏振片。偏振片只允许某个特定偏振方向(例如垂直偏振)的光通过，垂直于该特定方向的偏振光(例如水平偏振)则被偏振片所吸收。塑料偏光薄片是由橄榄球形状的分子组成的，这些分子在这种塑料聚合物中整齐排列并且像被“冻住”一样一动不动。这些分子优先吸收沿着分子排列轴方向偏振的光。一般来说，由于由物体散射的阳光会随机偏振(约为每个偏振方向的50%)，因此，过滤掉某一偏振方向的光就可以有效地将场景亮度降低一半。此外，太阳镜还可以减少眩光，即从光亮的平面(例如汽车的引擎盖或者风挡玻璃)反射的光线。这些平面倾向于反射偏振方向与该平面平行的光[这个现象被19世纪大卫·布鲁斯特爵士(Sir David Brewster)发现，并以他的名字命名]。戴上我们上面所说的太阳镜之后，这种反射光就因为其偏振方向被太阳镜挡住，因此看马路的时候视野会更加清晰。

透明双折射材料也可以在不吸收光的情况下改变光的偏振。这是因为光的传播速度取决于相对于材料“方向”的光的偏振方向。一些材料，例如一般的玻璃，是没有特定方向的：你可以任意旋转它而不改变其对光束的影响。但如前文所述，双折射材料中原子的排列有一个优先方向，即对称轴的方向。沿着这个方向，原子对光的响应是不同的。也就是说，沿着对称轴偏振的光的传播速度比垂直于对称轴偏振的光更慢。想象一下，光的偏振方向与对称轴的夹角为45°时可以假设有一半的光沿着对称轴方向偏振，另一半则垂直于对称轴方向偏振。如果后者的速度减慢得足够多，穿过材料之后透出来的光，将会沿-45°的方向偏振，相当于光的偏振方向被“旋转”了90°。

一些双折射材料可以通过主动调整分子排列轴的方向来控制偏振状态，例如对材料本身施加电压。一个典型的例子就是液晶(Liquid Crystals，缩写为LCs)，它由细长的分子组成，液晶中分子的方向可以通过施加电压的方式来控制。此外，通过施加压力或者应力，其他的一些材料也可以变成双折射材料，这是因为外力使得材料内部的分子发生“转动”或者让原子的排列方向发生了改变。利用这个现象可以构造力学传感器，它通过观察光传感器端输出的光的偏振状态来对力进行监测。

在两个偏振片之间放置一个双折射液晶，就可以通过电对光的强度进行控制。施加电压可以使分子重新定向，从而改变偏振光束在这一材料中的折射率。如果在液晶之后放置一个偏振片，那么根据施加的电压的高低可以控制通过偏振片光强的高低。将这样的“单元”构成阵列，且每一个单元由独立的电信号驱动，这样就构成了一个显示屏，每一个单元就是一个像素。这就是液晶显示屏(Liquid Crystal Display，缩写为LCD)的基础，通常用于电脑显示屏或者电视机。

事实上，这种显示屏还可以用来播放3D电影。在这样的电影中，我们感知到的深度其实是一种错觉，来自人类视觉的立体感。由于我们的两只眼睛间有几个厘米的距离，所以两只眼睛观看一个场景时感知的方位略有不同。这两幅图像在大脑中结合，让我们感知到深度。

这种错觉可以通过3D眼镜的偏振作用再现出来。两幅图片被同时投影在显示器或屏幕上，每一幅都是特定偏振的光产生的，而且是从略微不同的角度进行拍摄的。3D眼镜是由偏振方向不同的两个偏振片组成，使得左眼可以看到其中一幅图，右眼可以看到另外一幅。因为两幅图片发出的光都分别只与其中一个偏振片允许通过的方向一致，因此每只眼睛只能看到一幅图片，于是我们看到的场景就跟我们在自然界看到的景象一样，即物体和人看起来都是三维的。

光的波动模型的成功令人振奋，这让我们得以了解光的一些重要特性，从而利用这些认识来构建新的技术。光的粒子说同样令人惊叹。然而，光本质的这两种截然不同的学说都是必要的，这确实令人十分困惑。我现在就要转向这个难题。

[1]
一种多功能的通用光学仪器。

04 光的波粒二象性 Duality

有两种看待光的不同观点，一种将光视作粒子，另一种则是将光视为波，它们都包含着深刻的洞察力与价值。这两种不同的观点都各自启发了人们，不仅帮助我们加深了对自然世界的理解，还使相关新技术的开发和设计成为可能。然而值得注意的是，这两种观点中对光究竟是什么的概念似乎大相径庭。一方面，粒子模型将光视为一个固态的实体，具有能量，并沿着明确的轨迹移动；另一方面，波动模型将光描述为一个可扩散的实体，它穿过空间，与固态物体的运动无关。这两种观点怎么可能描述的是同一个概念？惠更斯及其同时代的人早就认识到了这种困境。作为对光本质的解释，这两种不同的观点针锋相对，一直持续到19世纪。

当麦克斯韦在发展他的电磁场理论时，他发现能够用此来解释光的波动性，正如我们在第3章中看到的那样。这一推理的胜利似乎证实了托马斯·杨(Thomas Young)和奥古斯丁·菲涅耳(Auguste Fresnel)分别做的两个实验(见第3章)，在这两个实验中他们揭示了两个基本现象，干涉与衍射，它们都不适宜用粒子模型解释。然而，光作为粒子沿着轨迹运行的概念仍然非常强大，它可以用来分析和设计光学系统。因此，科学家们需要重新考虑一下，有没有方法使光的粒子说与光的波动说握手言和呢？

再次审视光的轨迹

17世纪上半叶，法国人皮埃尔·德·费马(Pierre de Fermat)就折射现象提出了一种巧妙的解释，与斯涅尔的解释截然不同。让我们回顾一下斯涅尔定律，它描述了光在两个透明介质之间的界面处发生折射，即光的传播方向发生变化。其中，光的传播方向由它的入射和它撞击到界面的位置决定，其传播方向的改变程度则与这两种透明材料的折射率之比成正比。因此，最重要的似乎只是光和界面的局部特性。斯涅尔定律适用于轨迹上的任意一个点，就好像光可以凭着自己的“感觉”，在遇到新界面时调整方向。

图21　费马认为光传播的路径是连接起始点(A)和终点(B)且传播时间最短的路径。光穿过两个光学介质之间的界面，且光在两种介质中的传播速度不同

费马的想法则完全不同。他认为应该根据起点和终点来定义光的轨迹，如图21所示。他认为最应该问的问题是：光穿过空间中两点之间的轨迹是怎样的？在他看来，这个路径应该是耗时最短的路线。基于这一想法，费马异曲同工地给出了与斯涅尔相同的答案。这一成果是非凡而深刻的，因为费马的“最少时间原理”表明了光并不仅是基于光和界面的局部属性，而是对整体情况加以考虑：入射方向、初始位置、最终位置以及处于两个位置之间的一切因素。这一理论与光的粒子模型(粒子对其直接接触的周围环境进行反应的局部模型)相比，差别不言而喻。

这个想法被德国自然哲学家戈特弗里德·威廉·冯·莱布尼茨(Gottfried Wilhelm von Leibniz)所接受，他是与牛顿同时代的科学家，也是牛顿的竞争对手。莱布尼茨对费马所描述的折射过程的整体图景，以及其中所隐含的“优化”概念印象深刻：光对整个空间进行探索，最终仅选择在指定起点和终点之间传输时间最小化的路径。于是他开发了数学工具来分析这个想法，通过计算变化的微积分，可以计算出运动轨迹的微小变化对传输时间产生的影响。莱布尼茨认识到了费马原理中所提出观点的重要性，即光通过从一点到另一点的运动定义了“最佳”轨迹。

事实上，莱布尼茨也被这种最优化的概念所吸引，他将它提升为一个目的论原则，即世界的方方面面都处在某一个起点和某一个终点之间的最佳轨道上。当把这一原则应用到科学领域之外时，这种立场便显现出了其固有的矛盾。伏尔泰在他的小说《赣第德
》中便巧妙地讽刺了这一点，他将莱布尼茨的思想借潘葛洛斯博士之口说了出来。在书中，潘葛洛斯博士坚持认为任何发生的事情已经是穷尽所有可能性之后的最好安排，连自然灾害和人为灾难也皆是如此。

连接光波与光线

尽管如此，莱布尼茨的这一数学思想仍被证明是卓有成效的。19世纪著名的爱尔兰数学家威廉·卢云·哈密顿(William Rowan Hamilton)开始研究这些问题。他展示了如何将光的波动概念与粒子概念相结合。波可以通过波长、幅度和相位来定义(见图15)；粒子由粒子的位置、移动方向(见图5)定义，而粒子的集合则由其密度(在给定位置的粒子数量)和方向范围来定义。光在介质之间传播时，介质的光学特征由它们的折射率决定，这可能因空间而异。例如，在图20所示的介质界面处，折射率存在一个阶跃变化。

哈密顿表明，光到底是表现出粒子性更多一些，还是波动性更多一些，主要取决于空间中折射率变化的速率与光的波长之间的关系。换句话说，如果折射率变化速度的数值非常接近入射光一个波长的大小，那么光的波动性特征将会非常明显；如果折射率的变化速度基本不变或者非常慢，那么光的粒子特性就会比较明显。

哈密顿展示了在某些常见情况下，较简单的射线图是如何从较复杂的波动图表现出来的。当光的波长与其传播介质的大小相当时，光会表现出明显的波动特性，从而出现如衍射或干涉的波动现象。因此，当光照射的物体直径仅为几微米或者具有非常锋利的边缘时，例如鸟羽或蝴蝶翅膀上的精细结构，你会看到衍射图样。在另一种情况下，例如相机的镜头，其透镜的折射率是均匀的，即折射率的变化速率为零，光会表现出明显的粒子性，因而可以用粒子的运动轨迹来解释。

图22　哈密顿把光线与波前的概念联系起来，从而结合了光的粒子性与波动性

此外，哈密顿还表明，费马提出的光的轨迹理论与一个波的特性直接相关，这个特性就是波前。当波在空间中传播时，将相位相同的位置连接起来就是波前。例如，一块石头被投入池塘中，你看到池塘表面的每一个涟漪，即圆形的图案就是波前。这些涟漪是池塘表面上的水波“达到峰值”(或低谷)时的波前。因此，哈密顿指出光线可以被认为是以直角与波前相交的线，如图22所示，从而将相邻的波前与一个定义明确的光的轨迹这两个概念连接了起来。

哈密顿的“光学类比”

这个显著的结果引申出了另一个深刻的类比，即哈密顿的“光学类比”。他注意到，在那些众所周知的力学公式中，固态物体的运动和位置均是基于轨迹的概念上的。那么，这样的轨迹是否像光的轨迹一样存在着某种“最佳”情况呢？18世纪的皮埃尔·路易·莫佩尔蒂(Pierre Louis Maupertuis)就曾对此展开过研究。

莫佩尔蒂制定了一种方法来评估“作用量”的最佳值，其中作用量指向物体的运动轨迹，是物体的速度、移动距离与质量的乘积。他认为，对于物体在两点之间运动的实际轨迹，作用量应该是最小的。莫佩尔蒂的“最小作用量原理”在概念上与费马的“最短时间原则”非常相似。事实上，18世纪的瑞士数学家莱昂哈德·欧拉(Leonhard Euler)利用莱布尼茨的微积分，从莫佩尔蒂的原理推导出了著名的牛顿运动方程。由此，欧拉将“粒子通过环境感知其运动轨迹”与“粒子的运动路径受指定起点和终点之间的整个空间影响”这两种理论连接了起来。

哈密顿推导出了可以根据运动物体所处环境来描述物体作用量变化的方程。并且，这个方程与哈密顿为描述光线轨迹所推导的方程有着非常相似的形式(只不过在这一情况下，运动物体所处环境指的就是折射率如何随介质中位置的变化而变化)。因此，在固态物体的轨迹和虚构的波前之间存在着一种潜在的类比：也许所有物体都可能具有类似粒子的轨迹和类似波动的特性？事实上，哈密顿方程式及其同名函数对于思考理解光的下一个重大课题——量子力学——来说非常重要。

未解之谜

除此之外，还有很多现象暗示着科学界仍然存在许多新机遇，等待着人们去揭开谜底。大约在19世纪末期，即便哈密顿已经将光的粒子性与波动性联系起来了，仍然有一些关于光的未解之谜，这些谜题用主流模型是无法解释的。其中最重要的两个未解之谜，一个是有关热物体(包括太阳)的颜色，另一个则是有关不同原子在火焰中的颜色。

当物体被加热而升温时，它的颜色会发生改变。拿一块金属为例，随着它越来越热，它首先会发出红色的光，然后是橙色的光，接着则是白色的光。这一现象背后的原理是什么呢？这个问题困扰着当时许多伟大的科学家，包括麦克斯韦本人。依据麦克斯韦的理论，随着温度的升高，物体发出光的颜色理应变得越来越蓝，并最终发出不处于人类视觉范围内的紫外线。显然，这与现实生活中观察到的现象大相径庭。

第二个未解之谜则集中在研究原子发出的光上。约翰·巴耳末(Johannes Balmer)在这一问题上作出了开创性的贡献，我们将在第5章中更详细地研究这种机制。光谱中的颜色分布是光的重要特征，从这个角度来说，原子发出的光与太阳光非常不同(太阳是热物体的一个很好的例子)。太阳光具有我们非常熟悉的“彩虹”光谱(见图23a)，由从红色到紫色间的所有连续的颜色组成 。相比之下，一组原子发出的则是一组离散的颜色(见图23b)，即一组特定波长的“光谱线”。这些光谱线与所涉及的特定原子的内部结构有关。

这两种现象要求我们彻底修改对光的理解，因为它们无法用波动或粒子的当代模型解释。

图23　a、b分别是太阳(一个“黑体”)和霓虹灯发出的谱图。前者有连续的色带，后者则显示出特定颜色的离散谱线，这些谱线是氖原子的“指纹”

19世纪后期在柏林洪堡大学工作的马克斯·普朗克(Max Planck)首先提出了一个想法，用来解释热物体发出的光谱，这种热物体也常被称为“黑体”。他推测，当光和物质相互作用时，它们只能通过交换离散的“小包裹”来实现，这种“小包裹”可以是量子或能量。普朗克认识到他的想法是非常具有颠覆性的，尽管这将极大地改变我们对光的看法，但他仍不愿意太多地从这个角度去推断有关光的本质。他的想法使光重新被看作一种粒子，一种离散的带有固定能量的物质，可以被原子吸收或发射。

科学家们对光的理解似乎发生了倒退。毕竟，光的波动模型已经解释了迄今为止观察到的所有现象。并且，从哈密顿的工作中可以清楚地看出，即使是光的粒子性表现得最明显的现象，如光沿着特定路径传播，也可以用光的波动模型来解释。所以，光由粒子构成的这种想法似乎没有必要进行讨论了。当然，把光重新看做粒子只是一个计算性的“修复”，来解释现有理论无法解释的现象，它最终会被一个更合理的理论所替代。然而，结合巴尔默的观察实验，这个猜想终将从根本上改变物理学。

在普朗克提出光和物质之间进行离散能量交换的想法之后的几年里，阿尔伯特·爱因斯坦(Albert Einstein)利用这一想法解释了另一个长期无解的物理现象——光电效应。光电效应发生在光照在金属上时，一些电荷(带电的电子)会从金属中喷射出来。电子射出的速度取决于光的波长。光必须足够“蓝”，即具有足够短的波长，才能够使电子喷射出来。随着它变得越来越蓝，电子以越来越高的能量射出，速度也越来越快。

爱因斯坦指出，电子至少需要具有某一特定的能量才能脱离金属的束缚。不仅如此，他认为光的粒子中具有离散的能量，且这样的能量与光的频率成比例(其比例常数被称为普朗克常数h)。因此，当光照射到金属表面时，如果光的频率足够高(波长足够短)时，光的粒子可以将能量传递给电子，为电子提供足够的能量从而逃离金属的束缚。爱因斯坦的模型表明，光与物质之间离散能量交换的起源来自光实际的离散特征。这标志着光的粒子模型的完全复兴。

这一想法与巴耳末对原子产生离散光谱线的观察结果非常吻合。但是，为了完整解释离散光谱线的现象，显然需要着重解释为什么原子会通过这种“小包裹”的能量去发射光。彼时在曼彻斯特工作的丹麦物理学家尼尔斯·玻尔(Niels Bohr)提出了解释这一问题的关键。他认为，光之所以作为离散能量的“小包裹”被发射，是因为原子本身只能以某种构型存在。他认为原子类似于微小的行星系统：电子在围绕中心核的轨道上运转。电子可以在两个稳定的轨道之间“跳跃”，同时发射或吸收光。究竟是发射还是吸收光，则取决于电子是跳跃到更低还是更高能量的轨道上去。这些轨道或量子态的特征取决于原子本身：该原子有多少电子，还有其原子核的大小。因此，电子在两个量子态之间移动并且发射或吸收能量，是由原子本身的特性所决定的。这就是说，当光子的能量与原子中电子的两个量子态的能量差相同时，光的吸收或发射就成为可能。玻尔的想法巧妙地解释了巴耳末的观测结果，并肯定了光束作为离散粒子集合的想法。

所有这些进展都有可能破坏麦克斯韦理论所强烈肯定的光的波动模型。它们甚至超越了哈密顿试图将光的波动性与粒子性相协调的努力，因为这一全新的想法，即光束是离散粒子的集合，似乎是光的基本特质，而不仅是拿物体的大小与光的波长进行比较的结果。因此，科学家们重新审视了关于光的本质问题。

1908年，在剑桥工作的杰弗里·泰勒(Geoffrey Taylor)用极其微弱的光进行了杨氏双缝实验。光非常微弱，以至于任何时刻同时通过两个狭缝的光子平均下来不到一个，但他仍然看到了干涉条纹。这个结果很奇怪。如果我们认为从光源到探测器有两条路径，第一条路径是通过第一个狭缝，第二条则是通过另一条狭缝，那么一个光子从光源到达探测器的路径也有两条。然而，在同一时间内通过双缝的光子数只有一个，那么，单个光子是怎样形成干涉条纹的呢？这让当时的科学家们陷入了两难的境地。玻尔解决了这一难题。玻尔指出，一方面，光子总是会选择这两种路径中的一种，而另一方面，它表现得好像它同时通过了这两种路径一样。因此，即使是单个粒子也可能表现出类似波的行为。

光的波粒二象性

正如你可能想象的那样，要摆脱这个难题，需要一个真正革命性的想法。20世纪20年代在剑桥工作的物理学家保罗·狄拉克(Paul Dirac)认为，光的基本属性在于它既是粒子又是波，两种特性同时存在。现在，这一想法对你来说可能只是诡辩，一种没有回答任何问题的逻辑游戏，但它背后隐藏着深刻的洞见。狄拉克发展了麦克斯韦电磁场理论的量子力学版本。利用这一理论，狄拉克能向你展示，如果你使用像杨氏双缝干涉仪这样的装置来测量这些“量子场”，你会看到干涉效应这种体现光的波动性的现象。然而，如果你只是测量光的强度，那么只用去数光束中的光子数就可以了。

这一理论非常深刻，它将量子场设定为构建宇宙的基本实体——它不是粒子也不是波，而是既是粒子又是波，具有完全的波粒二象性。它完美地解释了光所展现出的所有现象，并提供了理解所有光学效应的框架。这些光学效应不仅包括牛顿、麦克斯韦和哈密顿的经典世界，还包括了普朗克、爱因斯坦和玻尔的量子世界。但是，这一理论实在是令人费解，因为它包含有一个完全非直觉的实体——量子场。光只是量子场的一个例子。

光既是波又是粒子的这一跨时代的理论激发了一些重要的新思想。例如，路易斯·德布罗意(Louis de Broglie)提出，如果这种波粒二象性存在于光中，那肯定也应该存在于所有其他事物上。因此，那些我们通常认为的由粒子构成的物质实体也应该具有“波动”的特征。他的想法超越了哈密顿所考虑的范围，甚至找到了物质波动性波长的定义。这一波长现在被称为德布罗意波长λdB
，它与粒子动量(质量与速度的乘积)成反比，比例常数为普朗克常数h。

λdB
=h/mv

这个波长公式表明，如果想观察到这种波动现象，必须使用质量非常轻或温度非常低(意味着移动速度非常慢)的粒子。使用分子代替光通过双缝干涉仪，一样可以形成干涉图样，如图24所示。这个结果简直令人难以置信。如果你把一个分子当做是一个非常轻的粒子，那么你将无法解释这个干涉图样的出现，因为你认为这个粒子只能通过这两个缝隙中的一个。然而，一个具有质量的粒子竟然可以同时通过两个缝隙并发生干涉，这个想法是非常惊人的。

图24　一次只让一个分子通过一个微缩版的杨氏双缝装置所形成的干涉图样。这两个很小的狭缝之间的距离仅为十亿分之一米

埃尔温·薛定谔(Erwin Schr
dinger)猜想，如果所有物质都表现出波的特性，那么肯定存在着一个描述其波动性的方程。从哪里开始寻找呢？他利用哈密顿通过“光学类比”推导出的方程，来描述粒子的“作用量”是如何演化的。通过对这一方程进行一个简单的补充(用到了普朗克常数)，薛定谔塑造了一个描述波动的函数。这就是薛定谔著名的“波函数”的来历。波函数具有许多非常类似于光波的特性，包括干涉和衍射，但是其描述的对象仍然是前量子力学时代语境下的具有明显质量与重量的粒子。那么，波函数描述的到底是什么呢？是实际的粒子本身，还是我们对粒子认知的某种简化呢？

光的强度是光的一个重要性质。如果将光看做是波，那么光的强度与其振幅的平方成正比。如果将光看做是粒子的集合，那么光的强度则与光束中的光子密度直接相关。类似地，波函数的平方与特定时间与空间中处于特定点的粒子的密度有关。但是，要想确定粒子在特定时刻的空间位置是不可能的。这种不确定性似乎是世界的基本属性，与“量子场是所有事物的核心”这一事实有着深刻的联系。

无即是有

认同这一事实的另一个结果就是，“什么也没有”实际上并不代表什么都不存在。换句话说，即使在一个完全没有物质(例如电子、原子)甚至光(光子)存在的空间里，仍然具有可测量的特性。这个空白的区域被称为“电磁量子真空”，是一种所有可提取的能量都被尽数去除的宇宙状态。与很多人的想象不同，它其实是一个容纳着很多活动的“大熔炉”，由波动的场组成却不包含任何光子。令人惊讶的是，量子真空中能够产生可以被观察到的现象。这不禁让我们发问，怎么能从“什么也没有”中产生出我们可以观测到的现象呢？

我们已经知道了，光可以被认为是电磁场的波动。请将这种波动所产生的场想象成海面上的涟漪。这些波动可以连续冲击海面上的任何船只，但是并不会将船上下移动或者将船推到某一条明确的波浪上。总的来说，船在这样的波动下并不会发生移动，仅仅是来回摇摆而已。现在将带电粒子(如电子)放在同样的想象场景中，这个带电粒子可以“感知”到电磁真空中的随机变化，并受到这些变化的连续冲击，就像海面上的涟漪一样。如果电子在原子中被束缚，那么这种冲击就是电子在其可能占据的量子态之间的能量的转变。由于原子吸收光子的频率取决于电子量子态间的能极差，因此，通过观察原子可能吸收的光的颜色变化，就可以知道电子在不同量子态间的能极差。这种变化微不足道，不到光的波长的十亿分之一。尽管非常微小，但是利用精确的频率测量技术，还是可以确定这种变化。20世纪50年代在纽约工作的威利斯·兰姆(Willis Lamb)是完成这一观测的第一人，并因此获得诺贝尔奖，他观测到的这种频率改变被称为“兰姆移位”。

对光双重身份的理解有许多层面。即使在前量子世界，光到底是波还是粒子的二元对立问题也需要解决。当时，通过了解光所体现的波动性质，以及与光相互作用的物体尺寸和性质，这一对立得到了解释。事实上，当物体的尺寸远大于光的波长且不具有锐利边缘时，物体的运动都可以解释成粒子沿着明确定义的路径做运动。而量子力学则提供了一种解释这种二元性的新观点。当光与物质相互作用时，光被视为一个或多或少带有能量的粒子，与此同时，它还保留了可以同时展现波动现象的能力。这个解决二元对立的方案引入了一个全新的概念：量子场。光粒子，即光子，是由量子场所激发，并且根据麦克斯韦量子版的光波方程进行传播。

量子场现在被认为是构成宇宙的基本实体，支撑着所有类型的物质和非物质，其中光可能是量子场最简单的一个例子。对此唯一的解释是，世界上的事物既不是粒子也不是波，而是兼而有之。这就是真实世界的本质。

05 光物质 Light Matters

光是如何产生的呢？在回答这个问题之前，让我们先看看身边多种多样的发光物体：首先是日常生活中的灯具：基于金属丝发光的普通灯泡；荧光管；我们之前提过的激光笔；从烤面包机到汽车仪表盘等电子设备上的指示灯；阳光，当然还有星光；在地球南北极地才可以有幸看到的极光
；不仅如此，还有萤火虫、萤科虫类以及船尾的磷光
[1]

等等。这些千差万别的物体是通过什么样的方式产生了一个共同的产物——光的呢？

这个问题的答案是，它们都涉及物质——都涉及电荷的转移。当这些电荷加速时，也就是说当它们改变运动速度或者方向时，就会产生光。这是一个简单的物理原理，对它的认识是电磁学理论的伟大成就之一。电场的起源是电荷，比如原子中的电子，其所产生的电场会延伸到整个空间，并吸引像质子一样的带异性电荷的粒子，且这种吸引力会随着其与电子间距离的增加而迅速减弱。正如我在第3章提到的，这是静电产生的力。

振荡原子与弯曲电子

现在假设电子突然运动起来，它周围的场也必定会随之改变，这是因为两者间有着千丝万缕的联系。图25描述了这种电场的变化，它看起来像一个“扭结”。位于电场中的质子并不会立刻感应到这种电场的变化，事实上，从电子发生运动到质子感知到电场变化，这之间有一个时间差。在这期间，“电子发生了运动”这一信息是以光速由电子向质子进行传播的。当质子感知到变化之后，质子会根据电子的运动方向而做出反应：如果电子靠近质子，那么质子受到的电场会变强，从而受到更大的力；如果电子远离质子，则质子受到的电场变弱，从而受到的力减小。

现在假设电子来回运动，它周围的电场也会随着这种振荡同步发生变化，并且传播到质子所在位置，质子受到这种变化的电场作用发生振荡。振荡的电场(以及相关的磁场，这里我们不展开讨论)正是我们所说的光。

图25　a.静止电荷的电场线；b.加速运动电子的电场线。当电子加速运动时，如图中电场线的转折(或“扭结”)所示的电场的变化，会以光速远离电子

由于最简单的氢原子只包含一个电子和一个质子，所以我们可以由氢原子入手，理解原子是如何产生光的。首先，让我们考虑一下，当一束光照射在基态原子上时会发生什么。光迫使原子内部的带电粒子——电子和质子——发生运动。但是由于电子比质子轻得多，在给定相同作用力的情况下，电子更容易运动，所以我们可以把质子看做是近似静止的，只考虑电子相对于质子的运动。事实上，电子以光的电场频率振荡，并随着电场的变化交替进行加速或减速。

这有点像帮孩子荡秋千的过程。使秋千荡起来的最好方法就是按照秋千的自然振荡周期同步推进，也就是说，在秋千每次运动到最低位置时推一把孩子。即便如此，想让孩子在秋千上荡得足够高也需要费一番力气。孩子荡到最高位置时的加速度最大，而在最低位置处的速度最大。原子内部的电子也是如此，光束的能量被原子吸收，并转变为电子的运动。

假设你现在停止推秋千，会发生什么呢？孩子会以越来越小的幅度呈弧线摆动，最后慢慢停下来。同样，原子也是如此。电子逐渐停止振荡，并把自身的动能转换为光能辐射出去。这就是光的辐射过程，也是例如霓虹灯、荧光灯和激光笔等众多光源发光的原理。

在上面的说明中，我假设原子内部的电子之所以发生振荡，是源自一些光束的照射，才导致了光的辐射过程。从某种意义上来说，这就引出了一个问题：最初的这些光是如何产生的呢？事实上，我们可以用其他方法来“激发”原子从而产生光。例如，人们可以简单地通过加热材料来达到这一目的，普通灯泡就是这样一个例子。让电流通过金属丝，金属丝会被加热到很高的温度(有几千摄氏度)。随着金属丝的温度越来越高，电子开始与原子互相碰撞，且碰撞的次数越来越多。这种碰撞激发了原子，也使得电子迅速地加速或者减速。通过这一过程产生的光具有很宽的颜色范围，具体会产生什么颜色的光取决于材料被加热后所达到的温度，而不取决于构成这种材料的原子类型。

电也可以通过其他途径产生光。例如，在发光二极管(light-emitting diodes，缩写为LED，常用于显示器的制造)中，通过它的电流或者说是电子流，可以被原子直接捕获。这种产生光的方法比利用热源产生光的效率要高得多。荧光管也是利用电流直接激发原子，但这发生在充满气体的灯管中。不仅如此，许多不同的化学或生物反应都可以释放能量，其中一些能量会以光的形式离开原子或分子。这还可以用来解释萤火虫是如何发光的。

正如我们之前提到的，加速度具有两个方面的含义：一个是速度大小的变化，正如之前提到的氢原子中电子和质子速度的变化；另一个则是方向的变化，哪怕速度保持恒定时也一样。加速度的方向变化在汽车转弯时很常见。当汽车转弯时，你被推到车门的一侧或者座位的一侧，并感受到有一种力使你随着车一起转向。当你转弯的速度越大，你感受到的力也越大。这表明你在加速，即使在行驶速度上并没有发生任何改变。

当带电粒子经历这种只改变运动方向而不改变速度的运动时，它们也会发出光。想象一下，一群电子被迫做圆周运动(你可以想象成它们被固定在旋转的车轮边缘处)时，由于这个角加速度的存在，它们会产生光。随着电子做圆周运动的速度不断增加，光的波长会变得越来越短，因而光子的能量也越来越大。以这种方式产生的光称为同步辐射
，这也是产生X射线的一种常用手段。它还与南北极
极光的产生有关：来自太阳的带电粒子进入大气层时受到地球磁场的作用进行螺旋运动从而产生极光。

量子光的生成过程

以上提到的这些基本机制是所有光源产生光的基础。但是当一些原子以群体的形式进行活动时，它们的行动方式会对最终辐射出的光的特性产生强烈影响。正如我在第1章中所提到的，普通灯泡发出的光与激光笔发出的光截然不同。为了理解这一点，我们需要深入研究原子的结构，因为原子的发光过程并不能完全类比成孩子荡千秋的过程。由于原子和分子是量子力学实体，因此对于原子的发光过程，我们需要考虑一下它们的量子特性。

就我们目前讨论的问题而言，原子或者分子的量子特性仅仅意味着它们中的电子只能保有固定的能级。如果使用我们的荡秋千模型，这就意味着荡秋千的最大摆动幅度不能为任意值，相反，幅度被限定为几个特定的值，也就是说它的值是量子化的。更具体地说，秋千摆动的能量来自离散的“小包裹”或量子单元。当你推动秋千的时候，你只能使秋千以一个或者多个量子单元进行摆动。在原子内部，这意味着当电子吸收或者发射出单个光子时，电子的能量只能以上述的不连续单位发生跃迁。与日常生活中的能量标准相比，电子发生跃迁需要的能量非常非常小。把你房间里的灯打开，它消耗能量的速率是每秒60焦耳(Joules)，即60瓦(W)。而灯泡中的原子发射的单个光子的能量大约为10-18
焦耳，因此，一个灯泡每秒发出超过10^18
个光子。

图26　一个原子吸收光子(a)、自发辐射(b)、受激辐射(c)的过程

只要用适当频率的光照射在原子上，原子就会进入激发态，如图26a所示(当然，我们还可以用其他的方式激发原子，例如给介质通电流等)。现在，根据量子理论中电子的跃迁运动可以推论出，当原子中的电子处于任一离散能级时，都是非常稳定的，因而不会主动发射光。电子就好比是放在橱柜中某一层架子上的球，从理论上来讲，它可以通过掉落到下一层架子上来降低能量，但这在实践中是不可能发生的，除非你稍微推一下它，不然球自己是不会滚落下来的。

这么看来，量子物理学似乎表明原子是不会发光的，因为你一旦把原子中的电子放在那些特定的轨道上，它们就会一直保持稳态，不会发光。事实上，除非电子处在最低能量状态，还存在一个推力将电子从较高能级跃迁到较低能级，否则是不会发光的。令人惊讶的是，这个推力是凭空产生的。

在第4章中，我提到了量子物理学最奇特的特征之一：即使是空旷的什么都不存在的空间，也充满热火朝天的“真空波动”。电磁场中的这些波动可以使原子中的电子跃迁到一个较低能级，并且，由于能级跃迁而产生的能量会以辐射光的形式释放出来。这个原子从较高能量的激发态跃迁到较低能量的基态，并释放出一个光子的过程，就叫自发辐射(见图26b)。每一个原子都能自发辐射。这一概念最初由爱因斯坦提出来，是为了解释光束与它所照射的物质之间的能量平衡关系。如果原子不发生自发辐射，那么原子就会保持住来自光束的能量。在这种情况下，我们平时到处都能看到的情况，即大部分事物都处于一个与其周围环境稳定平衡的状态，就基本上不可能存在了。

爱因斯坦认为自发辐射的核心奥秘就是它是一个随机过程。你不能确切地说出任何给定的原子何时会跃迁。你唯一可以说的是，平均来说，在一段时间(这取决于特定的原子，但是一般来说大约是一万亿分之一秒)内，在一个大的原子集合中，大约三分之二的原子会辐射光子。然而，这种基本随机性的起源一直是个谜，一直到1927年，保罗·狄拉克(Paul Dirac)的量子场理论指出，量子真空波动是这种随机性产生的根源。他说一个根本不包含光子的场可以扰乱受激原子的稳定性，这一观点与我们的直觉相悖。一直到20世纪50年代，兰姆(Lamb)的测量才证明狄拉克的解释是正确的。

这意味着，即便是我们在日常生活中习以为常的现象，例如由电视屏幕上的发光二极管(LED)生成图像，其核心也具有由量子力学产生的这种基本随机特性。与之相对，原子受到外界光的照射从而被迫释放能量辐射光子的过程被称为受激辐射
。这种将原子的能量回收到光场中的方式没有随机性。这使得激光的产生成为可能。

相干性：步调一致

当原子和带电粒子各自“随意运动”时，如果数量较多，那么它们辐射出的光就会是一组不协调的波
[2]

。即使是尺寸小到只有1毫米的发光二极管(LED)，里面也有大量的原子，所以这种情况是很常见的。

这种发出不协调光波的辐射有一个特征，就是每个原子都会随机发射光子，与周围的原子在做什么无关。因此，光是向各个不同方向辐射的，且光子会在不同的时刻被发射出来。实际上，辐射过程的随机性表现在原子所产生光强度的随机性上。

假如将一个光子探测器放在灯泡前面，我们可以看到探测器输出的电流非常嘈杂，这是因为照射到探测器上的光的强度变化快速且随机，说明在每个时刻到达探测器的光子数也是随机的。

如何才能使原子步调一致，从而使光波具有相干性呢？我们可以回想一下之前的类比：想象有一些秋千，且每一个秋千的摆动频率都是相同的。这些秋千开始进行随机摆动，那么就会出现以下两种情况：第一种情况是这些秋千的摆动是不同步的，即在任何时刻，各个秋千都会运动到其固定轨迹上的不同位置。第二种情况则是这些秋千的摆动是同步的，即相邻秋千间的轨迹差异是固定的，就好比足球比赛中场上观众按照顺序依次站立和坐下形成的人浪。在第一种情况下，从这些不相干的原子发出的光就像灯泡或者发光二极管发出的光，这种光是不相干的。在第二种情况下，原子们产生一致的振荡，它们产生的光以一种相干
的形式发出，所有的光子都往同一个方向辐射。这就是受激辐射
过程中会产生的情况(见图26c)，它是激光器的基础。

激光

激光器也许是20世纪光学领域最重要的发明。这个设备产生了非常有用的光束，革命性地改变了光的应用范围和性能。激光器可以作为一个特定的照明光源使用——例如在显微镜和光谱学中，不仅如此，还提供了一种能将大量能量沿特定路径引导到特定目标上的手段，从而控制物质的动力学。这类应用的一个极端例子就是用激光驱动原子聚变，使得新形式的核能得以利用，从而提供大量的能量。我们将在第7章对其进行讨论。

激光器包括一个光学放大器，也被称为增益介质，其原子通过受激辐射产生光。它被放置在两个反射镜(可能还有其他光学元件)所组成的光学腔中。随着原子不断地发射光子，光学腔内的光子数会逐渐增加，直到原子释放的能量与由反射镜从光学腔泄漏出来的能量达到平衡。说得更详细点，当放大器被接通时，从放大器辐射出去的光会被光学腔末端的反射镜反射回来，这就进一步刺激了受激原子的辐射，从而使光学腔内的亮度增加。在另一端的反射镜处，一部分光作为有效输出从腔中透射出去，一部分光则返回增益介质继续激发原子产生光子。当光通过放大器进入光学腔的速率等于光通过镜子透射出去的速率时，我们就说激光器处于阈值。超过这个阈值，放大器增益的任何增加(原子进入受激状态的速率)都会导致腔内强度的增加，从而导致输出光的增加。

光学腔对于激光的颜色有一定的限制。结果表明，获得最大增益的频率是那些在每次往返过程中都会发生相长干涉的光波所对应的频率。这意味着在腔内往返一次的长度应该等于半波长的倍数。满足这种谐振条件的频率即符合谐振腔模式。

激光器之所以重要，是因为它们发出的光是相干的：所有的光子都以相同的颜色朝着大致相同的方向运动。其中运动方向由光学腔决定，而颜色则由增益介质中的原子和光学腔共同决定。这就使得激光是以激光束的形式存在的，它与你想象中的“光线”非常相近。它在传播过程中仍然会因为衍射而发散，但是其发散程度已经微乎其微。这种特性也意味着激光可以用透镜或者平面镜聚焦成一个特别小的光斑。

除了相干性之外，与灯泡发出的光相比，激光的第二个优势是它的颜色更纯。换句话说，激光发出的光波长范围很窄，而灯泡发出的光的波长范围特别广。激光的光强度特别稳定(光探测器的探测结果中噪声很低)，可以连续发射或者作为光脉冲进行发射。

激光可以聚焦成非常小的光斑，这一能力使得它在显微镜技术中得到了各式各样的应用。例如，通过扫描在显微透镜焦点处目标物体上的激光光斑，并且检测从物体散射或者重新辐射出的光，可以构造出物体的三维图像。这个方法对于观察动物组织非常有用，这类光学显微镜在生物医学方面有着广泛的应用。

激光在制造业中的许多应用也是利用了这一特性。例如标记、切割、钻孔或者焊接金属等操作，都要求短时间内在金属的较小区域上聚集能量。高功率激光器可以产生以脉冲形式呈现的相干光束，聚焦能力强，因此成为这些材料加工操作的理想选择。

由于这些特性，激光在医学方面也得到了很多应用，这次涉及了皮肤、牙齿和头发等材料，常见如激光矫正视力和激光牙科等。激光也可以去除文身，利用激光加热皮肤里的文身墨水直到其被完全破坏。激光也可以除毛——但很可惜的是激光并不能反过来让毛发再生。其他一些人们所熟悉的设备，如CD、DVD、蓝光光碟(Blu-ray Disc)和一些计算机磁盘存储设备，也都是利用了激光的聚焦性能卓越这一特性，使得材料能够储存密度非常高的数据。

激光的颜色可以非常纯，因而可以利用光谱法来区分不同混合物中的原子和分子种类。正如第1章所提出的，不同的原子甚至不同的分子，由于它们的结构不同，因此具有不同的吸收和辐射光的特征频率。延伸一下我们本章中提出的类比，将这些原子和分子比作秋千，那么这些秋千中连接座椅的绳子长度不一，因此，这些原子或者分子的固有振荡频率由它们在混合物中的组合方式所决定。

事实上，每个原子和分子都有不同的辐射和吸收的频率范围，对应着不同的电子构型的激发。这些频率范围通常位于可见光光谱的蓝光区域，但有一些分子可吸收的光的波长要短得多，是人类不可见的。许多分子也可以吸收比可见光的红光波长还长的光。这种区别来自构成分子的原子核之间的振动。由于原子核比电子重得多，所以它们倾向于以更低的频率振荡。这组频率相当于分子的一种“指纹”，可用来确认分子类型。

当然，用这些“指纹”所确立的目录在化学中是很重要的，因为通过它可以识别出化学反应中所涉及的不同元素。它也被用于分子生物学；甚至在细胞生物学中，可以通过它来观察特定的标定分子，从而研究分子的运动。这种“指纹”对于天体物理学也相当重要，它可以确定恒星、星系、星云中存在的元素。在大气物理学和气象学中，则可以遥测污染物和颗粒。这种监测为评估气候变化的影响和成因方面提供了关键数据。

通过组合几个不同激光器所发出的激光，例如一个发出红光，一个发出绿光，一个发出蓝光，那么就有可能制造出一台激光投影仪。根据电脑或者互联网输出的视频信号来改变各个激光信号的强度 ——也许可以通过液晶单元的方式实现——那么色彩鲜艳、高饱和度的电影就可以投射到屏幕上。红、绿、蓝这三色光的组合足以构成一个完整的调色板，而激光可以在屏幕上产生非常明亮的图像。

X射线

当光的波长非常短，属于光谱的X射线区域时，就会产生一种特定的光谱。X射线的光子能量很高，不仅可以激发最外层的电子，甚至能激发原子中被束缚得最紧密的电子。这意味着X射线可以用来观察原子和分子的核心，并了解它们所处的环境，由此，我们就可以改变电子结合能
[3]

。X射线的吸收光谱技术在材料研究中有着广泛的应用，从检测微量污染物到研究玻璃的结构。如第3章所述，X射线衍射法也被用来研究晶体的结构。当X射线的波长接近于晶体中原子的间距时，晶体就充当了“衍射光栅”，使X射线向离散的方向散射。通过监测相机上的衍射图样，利用先进的反演算法重建高度复杂的晶体的三维结构。从分离出的生物和化学分子中提取特征，确定可能的新分子结构，对比进行设计，从而实现某一特定功能，这在现在已经是一个常规的流程。

同步加速器可以为这种光谱技术提供最好的光源。为了产生符合要求的具有短波长的X射线，同步加速器必须产生高能电子束，并且在一个环形轨道上对它进行加速。随着电子的加速运动，实验站会捕捉到闪烁的光，这导致了短暂的X射线暴，可以用于衍射成像。例如英国哈维尔的“钻石光源”1(Diamond Light Source)，电子束在一个超过半千米长的环内被加速至超过十亿伏特。下一代X射线光源正在使用线性粒子加速器来制造，这种加速器可1　位于英国牛津郡，是英国第一台第三代同步辐射光源。以产生极其明亮的X射线光束。如图20所示的X射线衍射图就是用钻石光源拍摄的。

超短光脉冲

激光也能够以短脉冲的形式发出，方法不止一种。能够产生最短光脉冲的方法称为锁模法
。锁模法要求增益介质具有较大的带宽，也就是说，它可以在比较宽的光谱范围内对光进行放大。这使得光学腔内多个不同种类的激光都可以获得增益。如果让这些不同种类的激光具有相同的相位，那么拥有不同频率的光波将在光学腔内叠加形成单个脉冲，并且在两面反射镜之间来回反射。脉冲有多短取决于锁定的频率的数目——频率分布的范围越宽，脉冲越短。

超短激光脉冲的获得使得时间分辨光谱技术成为可能。这种技术让我们得以利用闪频仪看到事物是如何随着时间变化的。利用光来“定格”快速运动的这一想法，可以追溯到19世纪末埃德沃德·迈布里奇(Eadweard Muybridge)的工作。他萌生了利用快速照相机快门来拍摄骏马奔跑的想法。由于马的腿移动得太快，人眼无法进行分辨，以至于当时还无法分辨马在跨步的过程中四条腿是否在某一时刻同时离地。为了解决这个问题，迈布里奇沿着跑道设置了许多相机，每一个相机快门都由一根横跨于跑道的线所操控，当马奔跑经过这些线时就会依次触发快门。这使得他能从马的反射光中提取出一个很短的光脉冲，这种光脉冲持续的时间比马腿移动的时间还要短。他这项研究的目的与成果就是告诉他的研究资助者利兰·斯坦福(Leland Stanford)，在马奔跑的过程中，马的四条腿在某一个瞬间可以同时离开地面。

传统相机的机械快门可以很快速地关闭，但是速度仍然不够快，因此仍然无法观察到某些形式的动物运动，例如蜂鸟翅膀的扇动。至于一些更快速的物理过程，例如爆炸发生在千分之一秒的时间尺度上，这么短时间内发生的变化是无法用传统相机捕捉到的。为了解决这个问题，麻省理工学院的哈罗德·埃哲顿(Harold Edgerton)在20世纪50年代发明了一种基于光学开关的新型非机械式快门。他可以用这种装置拍摄爆炸事件的静态照片。

这些开关我们可以称之为“被动”仪器，它们在打开状态时有一片允许光通过的空间，所以这种设备适用于照明良好的物体(例如沐浴在加利福尼亚阳光下的马)或者是本身就发出大量光的物体(例如爆炸)。我们可以想象一种“主动”的仪器，它可以产生短的光脉冲来照亮一个移动的物体，例如照相机的闪光灯所发出的光脉冲。与物体移动所需要的时间相比，一道持续时间更短的光照射在物体上时，就可以观察到某个瞬间物体定格住的图像，即使快门的速度比物体的运动速度要慢。第二个闪光会定格稍后的运动图像，依次往后推，这样就可以获得物体运动的动图了。

将在同一事件的重复实验中拍摄的序列帧组成一部电影可以说明运动对象的快速变化，即使其变化的速度已经远远超过人眼的识别程度。确实，这些稍纵即逝的事件竟然能够通过这种方式被观察到，真的很令人惊叹。埃哲顿于1931年发明了“频闪仪”。他的一些最具代表性的图像，例如子弹穿过苹果或者扑克牌(见图27)，都是用它拍摄的。

图27　频闪仪记录下一张图片，显示了运动中的子弹被定格的瞬间

使用现代脉冲激光作为“闪光”，不仅可以观察到运动的子弹定格的瞬间，还可以观察到参与化学反应的分子中原子的运动[因为这一发现，1999年的诺贝尔化学奖颁发给了艾哈迈德·泽维尔(Ahmed Zewail)]，甚至能看到在原子核周围以更快速度运动的电子。这些运动的时间尺度小得惊人。对于分子来说，它的时间尺度小于1秒的一万亿分之一(100×10-15
秒，即100飞秒)。而对于原子内的电子来说，其时间尺度为100×10-18
秒(100阿秒)。飞秒化学
[4]

和阿秒科学
[5]

都是研究光和物质相互作用的前沿领域，我在第7章将会作进一步讨论。

[1]
当波浪或者船只扰动了生活在海水中的某些微小浮游生物时，它们会发光。因此，这种磷光其实是一种生物发光。

[2]
例如波的方向、相位不一致等。

[3]
电子由被束缚状态转移到无穷远时所做的功，可以用来衡量电子被原子核吸引的紧密程度。

[4]
研究飞秒时间尺度内的化学反应过程和机理的一个领域。

[5]
阿秒时间尺度上的科学研究。

06 光、空间与时间 Light, Space, and Time

对于罗伯特·格罗斯泰斯特(Robert Grosseteste)来说，理解光的本质是理解整个世界的钥匙。格罗斯泰斯特曾担任英国的林肯主教，也是英国牛津大学在13世纪迎接的第一任校长，他非常崇尚古希腊人的作品。作为当时最主要的思想家之一，他在论文De Luce
（《论光
》)中是这样颂扬光的重要性的：“在我看来，光……是最首要的物质形态。光可以沿任意方向传播，因此一个发光点向各个方向传播的光可以瞬间形成一个任意尺寸的‘光球’。”

对于格罗斯泰斯特而言，光可以用来定义空间：光在传播途中所经过的区域即为空间。在他看来，如果没有光，就不会有空间，因此，物质以及物质所在空间的定义不可能脱离光的概念而存在。基于这个信念，格罗斯泰斯特还将光、空间与物质这三者之间的密切联系作了量化。这样的观点在随后的几个世纪里影响了宇宙学的发展。

时空

牛顿认为，空间这个概念既不需要被承认，也不需要被定义。他认为空间是一个早已存在的实体，就像是一个舞台，只等着演员上台表演精彩的剧目。因此，他提出的一系列力学定律中，很多都与物体在空间中的大规模运动密不可分。与牛顿不同，爱因斯坦则将光放在理解空间概念的核心地位。他认为可以通过信号从宇宙中一处发送到另一处的速度限制来定义时间和空间，正因为光速是一个确定的值，所以空间和时间这两个概念不可分割。爱因斯坦的相对论告诉我们，不能单独考虑空间或者时间中的一个，因为我们认知空间与时间时，都是利用对其进行局部测量的方式，但如果在一个正相对我们运动的系统上测量同一空间与时间，测量结果将发生改变，这也是源自光速的确定性。

光与时间、空间这种奇妙的关联是怎么产生的呢？让我们从牛顿空间的概念开始说起。让我们想象一个脚手架，如图28所示，固定长度的短棍相互连接形成了一个三维立体框架。牛顿认为，这样的结构早已存在于所有事件发生之前，事实上，所有事件都发生在该结构的某个地方。因此，只要在结构中确定一个参照点，事件的位置就可以通过参照点与事件之间的短棍数来确定。那么怎么确定事件的时间呢？在脚手架每个短棍的衔接处放置一个时钟，保证这些时钟在脚手架的任何位置都显示相同的时间，这样我们就可以很容易地确定事件的时间了。这样的时间被称为“通用时间”。

图28　图中的“脚手架”展示了一个代表空间的三维模型，每个格子的边由一个可测量距离的短棍表示。每一个节点上都有一个时钟，且都是同步的

现在，我们必须提出这样几个问题：首先，我们应该如何造一个可以计时的时钟？其次，我们应该如何确保它们在空间中保持同步？最后，我们应该如何确立长度标准呢？这些问题的答案都与光的属性密切相关。实际上，我们可以用光来定义长度：一米是光在1/299 792 458秒内在真空中行进的距离，这就回答了上述的第三个问题。由于长度的定义与时间息息相关，那么就回到了第一个问题：我们造出的时钟到底可以有多精确？

时钟

时钟最重要的特征是它以规则的时间间隔发出信号，并以此为周期不断重复下去。通过计数两个事件之间相隔的信号数或周期数，我们可以计算出事件之间的时间间隔。时钟越精确，就意味着每两个相邻信号之间的时间间隔越规则，周期越精准。老爷钟是一种机械钟，它的周期由钟摆的左右摇摆间隔确定，但是其精度很容易受到温度和湿度的影响。相比而言，电子手表的周期是依靠石英晶体的振荡，其振荡频率比钟摆的摆动周期更加规则，因此石英表计时一般比老爷钟更加精确。

世界上最精确的时钟是原子钟，它的计时功能与原子中电子的运动息息相关。我们知道，围绕在原子核周围的电子排列在不同的轨道上，因而存在不同的能量层级。通过吸收或释放某些特定频率的电磁波，电子可以在能量层级之间发生跃迁，即从一个稳定的能量层级跳跃到另一个稳定的能量层级。对于某些原子，比如铯原子，它发生电子跃迁时两个能量层级之间的能量差已经被精确定义了，因此只需要观测能量差出现的频率，即使得电子发生跃迁的电磁波频率，据此就可以定义时钟的周期了。

在实际操作中，我们使用微波照射铯原子，再慢慢改变微波的频率，直到电子开始在两个稳定的能量层级之间进行跃迁，我们就可以通过这一频率来定义时钟的周期。

构建这样的原子钟面临着很多技术挑战。首先，我们需要将原子冷却，使它们回归理想的初始状态；然后，我们要谨慎选择微波照射的方式，以最大化原子钟的灵敏度；最后，我们还要能够精准确定电子是否已经跃迁到较高能量层级的状态。现在基于铯原子的时钟已经成为测量时间的最准确方法，它在一亿年内的误差小于百万分之一秒。

原子钟提供了一个受国际肯定的时间标准，由一些政府实验室维护，例如美国国家标准与技术研究院(National Institute of Standards and Technology，缩写为NIST)、英国国家物理实验室(National Physical Laboratory，缩写为NPL)和德国联邦物理技术研究院(Physikalisch-Technische Bundesanstalt，缩写为PTB)等。时钟是很多技术的基石，例如，它们对于制定全球定位系统(global positioning system，缩写为GPS)的统一基准至关重要。现在，GPS已经运用到日常生活的方方面面，例如汽车的卫星导航系统等。可以说，时钟在我们的生活中几乎无处不在。

时钟的同步

下一个挑战是如何使两个时钟同步，使得它们可以被统一校正。其中一种方法是将信号从一个时钟发射到另一个，通过测量信号的延时来完成校正。具体做法是首先启动第一个时钟，当该时钟完成第一个时钟周期时，向另一个时钟发射一束光。管理第二个时钟的人收到光信号时，可以通过对比知道第二个时钟与第一个时钟间的延时情况，并利用这些信息进行时钟校正。由于时钟的构造都是一样的，我们假设它们计时周期也相同。

这样做会有一个有趣的结果。设想一下，为了让一个地球上的时钟与另一个放在遥远星系中某一颗行星上的时钟同步，你把一束光发射向那个行星，即使光速很快，由于距离实在太遥远，光到达那里还是要用很长时间。与此同时，你却在慢慢变老。所以，行星上的人接收到的这一校正信号，其实是你年轻时发出的信号，他看到的你也是很多年前发出信号时的你。

同理，当我们仰望星空，我们看到的实际上是源自很久很久以前从遥远恒星表面发出的光。当我们遥望更远的恒星和星系时，我们看见的是更久远的过去：一个数十亿年前的宇宙。从这个意义上说，我们接收到的光也有数十亿岁了，从它诞生的那一刻起，就一直在宇宙中穿行。光是我们在宇宙里能看见的最古老的东西。

当然，我们通常所说的时钟相距比较近。有这样一个有趣的现象，如果你把一个时钟放在一架飞机上，以大约每小时800千米的速度飞行，你会发现，它相较于地面上的时钟要走得慢一些，这是因为信号在两个时钟之间得以传递的最高速度是光速。

你可以参照图29明白其中的道理。一个人(标记为A)在地面上，而另一个人(标记为B)在高速运动的飞机上。A向离地面H高度处的一面镜子发射一道光。从A的角度看，这道光的行程是H；然而，从B的角度看，这个光信号的行程比H稍长，因为A相对于B在高速后退。既然信号的传递速度对A和B而言都是光速，而且他们根据发射信号和接收信号所记录的时间是一样的，那么唯一的解释就是从A的角度看，B的时钟走得比他的慢，而从B的角度看，A的时钟走得比自己的慢。这个现象被称为时间膨胀
。

图29　相对运动导致的时间膨胀。观察者A(地面上)和B(高速运动的飞机上)各自测量同一束光到达悬挂于高度H的镜子的时间。他们测出的时间并不相同，这是因为他们之间有相对运动

爱因斯坦用同样的方法表明了空间也同时在收缩。也就是说，对观察者A而言，观察者B所处三维空间框架中的短棍(如图28)应该比A的要短，反之，B也觉得A的比自己的短。

这两个效应的产生都是因为任何信号都有一个传播的最高速度，而且这个速度对每个人都是一样的。如果这一说法不成立，那么我们就可以自行选择一个三维空间框架，或者“参照系”，在这个框架中，信号以最快的速度传播。爱因斯坦的相对论指出了这个框架是不存在的，因此，牛顿提出的空间是恒定不变且预先存在的想法是不正确的。由于任何信号传播的最高速度都是光速，光对于定义空间和时间都至关重要。

那么，使用之前提到的用光信号去校正两个时钟到底能达到怎样的精度呢？一个提高校正精度的方法是让这束光尽可能地短，这样信号到达时的不确定性会最小。因此知道光束的长短是否有极限很重要。事实证明，这些极限确实存在，并且它们源自一种类似波的特性，这种特性限制了成像系统的分辨率，正如我们在第3章讨论的那样。

那么，光波的频率是如何确定的呢？想象这里有一个时钟，观察在单位时间间隔内我们可以接收到多少个波峰。通过的波峰数量越多，表明光波的频率越高。由于我们判断光波是否达到波峰的能力并不完美，所以频率的测量精度取决于我们重复测量的次数。如此说来，我们观测的时间越长，对频率的测定就越精确。值得注意的是，在此过程中，时间的测量也存在着不确定性。这种时间与频率测量精度间的权衡是波的基础：频率的不精确性与时间间隔的不确定性相乘为定值。约瑟夫·傅里叶(Joseph Fourier)首先指出了这一点，他是19世纪的法国数学家和科学家，他在建立光传播的波动模型方面作出了关键贡献。

超短光脉冲

傅里叶的定理对于时钟同步很重要。这一定理指出，如果要产生一个历时很短的短脉冲，我们必须有一个不确定性大的频率。换一种说法就是，一个短脉冲是由多种颜色的光构成的。这完全类似于阿贝所定义的光学成像的情况：为实现高分辨率成像，我们需要小焦距，需要收集来自较大范围角度的光线。正如阿贝所揭示的，光学成像分辨率的最小尺寸可被视作约等于光的波长，顺着这个类比推理，傅里叶表明，光脉冲最短持续时间应该就是光波的一个周期。

这在实践中意味着，在电磁频谱中的可见光区域，可以产生持续时间约为2飞秒的脉冲。令人惊讶的是，从激光中获得的光源现在已经可以成规模地产生这样的超短光脉冲了。它的实现是基于第5章中所描述的激光锁模技术。

尽管持续时间已经非常短了，它却并不是自然界中存在的最短光脉冲，甚至也不是实验室中可以产生的最短光脉冲。事实上，平均波长更短的光源产生的光脉冲会更短，这是因为若将波长缩短，光学周期也会跟着缩短，原则上就可以缩短脉冲的持续时间。用这种方法产生的光脉冲在目前保持着最短可控光脉冲的世界纪录。在具体操作上，我们将非常强的激光照射到原子气体上，经过被称为“高次谐波产生”的过程，一个频率是激光频率几十倍的光波就这样产生了。这样的光脉冲的持续时间为几十阿秒。这个数字让人难以置信，因为这一持续时间等于电子在原子内振荡所需的时间。

频率梳

第5章中我已经指出，在锁模激光器中，单个脉冲需要穿过一个光学腔。每当它遇到一个平面镜并发生反射时，其中一小部分光脉冲就会穿过平面镜并从腔体中射出。因此，在光学腔外部，光看起来就像一个“连续的”脉冲序列，且这些脉冲之间的间隔等于光在腔内的往返时间，通常是十亿分之一秒左右。观察这样的脉冲序列(见图30)，你会发现相邻两个脉冲之间的时间间隔要比这些脉冲的持续时间长得多，看起来就像梳子的齿一样。通过仔细调节产生脉冲的激光，可以使各个脉冲彼此相同，从而保证每个脉冲的电场在同一时间达到峰值。

图30　一系列几乎一模一样的单周期光脉冲。脉冲序列的频谱看起来像梳齿，因此被称为“频率梳”

频率梳中的每个“齿”在绝对频率处都有一个非常精确的位置。一组精确校准的频率对于构建精确时钟非常重要，因为它使得我们可以直接将光学频率与其他较低频率(通常是微波)比较，这种比较一般通过电子设备来实现。

使用这一方法，我们可以将铯原子钟的频率(处于微波波段)，与像锶原子或铝离子由于电子跃迁而产生的处于光学波段的频率进行直接比较。例如，现在卫星导航中使用的标准铯原子钟，可以完成时间同步并以相同的时间间隔进行计时，其一亿年内的误差小于百万分之一秒(误差在1×10-18
)。这一结果是由锶或铝中的光电子振荡频率的精度所决定的。

这种“光学钟表”可以非常精确地比较不同的频率，因此可以提供一种测试相对论原理的方法，从而使我们更好地理解光在定义空间和时间方面的作用。到目前为止，在所有物理量中——频率——也就是时间，是测量精度最高的。

光通信

频率梳在基于光的电信链路中也很重要。在第3章中，我们已经知道光波可以沿着光纤或玻璃“芯片”传播。长途电信基础设施就是利用这一现象，连接起世界各个角落的居民，同时它也是互联网技术的基础。光的通信之所以能得到如此广泛的应用，是因为与电线甚至微波蜂窝网络相比，它承载信息的能力更强。这使得大规模数据传输成为可能，比如需要通过因特网传输视频的情况。

许多电信公司提供“光纤宽带”服务。这些服务把宽带的速度作为关键卖点，宣传可以加速到每秒100兆字节(Mbps)来接收和传输数据。一个字节(byte)包含8个比特(bit)，而每一个比特只能是数字1或者0。信息以“0”和“1”组成的序列通过光纤发送，最终由计算机或移动电话将这些“0”和“1”的数字串解码为可以被人们轻松理解的视频、音频或文本消息。在光通信中，每一个比特的“0”或“1”的信息由光束的强弱表示：通常低强度为0，高强度为1。每秒送达的这些“0”和“1”的信号越多，通信速率也就越快。电信公司服务中说的Mbps，就是我们在该公司链路上传输和接收信息的速度。

为什么光通信这么好用呢？主要有两个原因。首先，光束不容易相互影响，因此只需要一根光纤就可以同时传输许多种光脉冲(通常颜色不同)，而不用担心信息发生混杂。这是因为制造光纤的玻璃不吸收光或仅吸收极少量光，因此不会加热和破坏其他脉冲序列。

此外，在玻璃中传播的光强度必须非常高，这样才能影响另一束光。举个例子，当两个激光器分别发出光束，即使这两个光束相互交叉，也不会出现光束扭曲或偏离其原始路径的现象 。(即使激光器具有巨大的功率，在真空中观察时也不会出现这样的现象。但是如果你在非真空的环境下观察，由于光的传播路径中充满空气，光束会出现扭曲或偏离其原始路径的现象。)这意味着在大多数材料中光束间的“串扰”非常微弱，因此可以同时传输许多光束而不会导致信号变差。这与沿着铜线传输电子的情况非常不同，它是在本地搭建“有线”通信链路的常用方式。由于电子通常会加热电线，导致电子自身的能量发生耗散，使信号更难被接收。因此，在这种情况下，不同信号的通道数量必须保持足够小，才能够避免这一问题。

采用光学通信的第二个原因是，光波会以非常高的频率振荡，这使得超短脉冲的产生成为可能，这一点我们在之前已经讨论过了。这意味着脉冲与脉冲之间的间隔可以非常小，因而每秒可以传输更多比特的信息。实际上，现在的商用长途系统已经可以达到40 Gbps的速率。相比之下，铜线中的电信号由于之前提到的热效应，使得带有信息的脉冲在持续时间和时间间隔上都受到限制，并且这种热效应会随着频率的增高而加剧，为信息的传递带来更多的限制。可以说，铜线在以比光纤通信传递速率低得多的情况下就已经筋疲力尽了。

基于光纤的光学通信网络可以支持色域非常广泛的光，这是因为能被玻璃传送的光的波长范围较宽。尤其在1.3~1.55μm波长范围内的光在光纤中几乎不发生散射或吸收损耗。在这些波长下，光子在光纤中耗损率约为每千米5％。这样微小的损耗可以通过在光纤中放大光的强度来弥补，从而使超远距离传输(例如横跨大西洋)成为可能，无须将光转换为电信号，或是将电信号转换为光。

电信频谱窗口被分成许多单独的频率“槽”，类似于图30中所示的频率梳。每个频谱分量是一个单独的通信信道。频率窗口中可以有150个左右这样的槽。在每个通信信道内，可以操作40 Gbps的光信号。因此，通信的总比特率为150乘以40 Gbps，即6 Tbps 。
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随着互联网的普及及其层出不穷的各种服务，我们对通信带宽的需求也在不断增长。这促使光学工程师们不断开拓创新，探索如何更充分地利用光的潜力。

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1 Tb，1 太比特（Terabyte），等于一万亿比特。

07 探索光学前沿 Lighting the Frontiers

光学有着悠久的历史，尽管它可能是自然哲学和科学中一直持续发展的最古老分支，时至今日，它仍然处在研究和应用的前沿。光学无处不在：它不仅可以作为检测、成像和通信的工具，也提供了探索、发现和解释新的基本效应的方法。

利用光可以创造出一些物理学上的极端条件，例如自然界中不存在的极端温度、极端压力和应力。这些极端条件或许也存在于最遥远的恒星中。光还可以用来观察甚至控制发生得极快的事件，例如发生在原子内部的电子运动。

此外，光还可以展示出量子世界的奇特特征。它揭示出，即使在日常条件下，这个非连续的世界中存在着许多与直觉相违背的方面。而这个非连续的世界却构成了我们日常经验中稳定可靠世界的基础。在这一章中，我将探索一些由光引领的前沿领域。之所以能够研究这些领域，是由于在光源、光学系统和探测器方面取得的巨大科技进步，使我们能够在空间和时间上精确控制光束的形状和强度。

光力学

光能够对物体施加作用力，这使得我们可以利用成形光束对小块材料进行“远程控制”。光可以用来移动物质，使其与其他物体接触，或者用来操控分子和原子的内部结构，迫使它们发生简单的化学反应，从而可以研究和开发具有特殊性质的材料。光的这种功能在很多研究领域都非常有用。

光之所以能够产生机械力，是因为光的每个光子都携带动量。例如，当光子从平面镜反射回来时，平面镜会受到一种力，这种力帮助光子改变了运动方向。这就像是消防水龙带中的水撞击墙面，在反弹回来时向墙面施加力一样。

类似地，当光子发生折射时，它的运动方向会发生改变，这也需要力的帮助。所以光子会对折射元件施加力。如果一束光入射到玻璃珠上，其中与玻璃珠几乎相切的光线的方向改变最大。当光线透穿过玻璃珠表面时，穿过玻璃珠下半部分的光子会向上运动。因此玻璃珠会受到一个反方向的力。随着光子的运动方向改变，光子在前进方向上(遇到玻璃珠之前的运动方向)的动量减小了，这说明光子对玻璃珠在前进方向上也有一个净力。这个力的强度取决于玻璃珠每秒折射的光子数。最终，如果这个光束中心的强度强于光束外围，那么玻璃珠就会被推向光束强度较高的部分，就好像光束将玻璃珠“捕获”了一样。

这个效应可以将聚焦的光束变成一个“光学镊子”。光学镊子能够抓住微小的物体，并且通过操控光束方向来控制物体的移动。光学镊子可应用于生物学，例如，它可以操控单个DNA链的位置和运动，还可以用来研究小分子马达
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的特征。具体来说，DNA、蛋白质和其他重要的生物分子都可以附着在这些玻璃珠的表面，因而光学镊子可以依照上述原理对它们进行操控。光学镊子可以在比光的波长还要小的精度上控制这些分子的位置，从而能够测量极小的力——例如生物细胞附着在表面或者其他细胞上的力，也可以在使用激光处理细胞(“细胞手术”)时，用光学镊子将细胞精确地固定在适当位置。除此之外，光学镊子还可以和其他的测试方法综合应用，例如和气溶胶的光散射或者光谱学相结合，可以用来发现可能造成大气污染的颗粒。

图31　一种由光的机械力控制的纳米级悬梁臂。图中的圆盘是直径约为30微米的微小镜面

光的机械力可以用来发现微小物体运动的全新状态。如图31所示的微型机械悬臂，其悬臂的运动就可以用光进行观察和控制。这种光力可以用来加热或者冷却悬臂的振动——就好像为机械手表的弹簧上弦或者放松一样——最终尽可能使其达到最安静静止的状态，只有运动的量子涨落才能干扰到这种完全静止的状态。光力也可以用来冷却比机械悬臂小得多的原子，并揭示出物质更奇特的量子态。

超冷

你体验过的最冷温度是多少？比冬天的牛津(大约2℃)、渥太华(-20℃)或南极(-50℃)还要冷吗？或许是液氮的温度(-200℃)？这些当然都很冷，但绝不是最冷的情况。研究发现，温度有一个最低极限，-273℃或者0开尔文(单位：K)。我们将其称为“绝对零度”，没有比这个温度再低的了。要达到这个温度需要物体保持绝对静止，此时，物体只受到量子力学的影响，使得其原子和分子产生轻微的抖动。

事实上，制造一台能达到绝对零度的机器是不可能的，但是使用“光学冰箱”可以达到非常接近绝对零度的温度的程度。当温度降低到一定程度时，原子几乎停止运动，这意味着原子的尺寸变大了(量子力学告诉我们，不能同时确定物体的精确位置和速度。如果原子完全停止运动，就意味着它必须向整个空间扩展)。因此，所有冷却的原子占据了空间中相同的区域，从而产生了一些非常奇特的新现象。

光学冰箱的工作原理是利用激光来“冷却”原子。想象有一束激光照射在一个从左向右移动的原子上，由于激光从右向左照射，所以会有一束光子直接撞击到原子上。为了使这些光子可以被原子吸收，激光根据原子运动的速度，被调节到某个特定频率。当原子从激光中吸收了一个光子时，就好像被光子当面“踢”了一下，从而降低了运动速度(更确切地说，光子的动量转移到了原子上。由于两者的初始动量方向相反，所以原子的动量减小，因此速度降低)。在之后的某个时刻原子必须重新发射光子，并且会受到与发射光子方向相反的力。但是由于原子发射光子的方向是随机的，这就意味着原子受力的方向也是随机的，因此原子可以向任意方向运动。

当你观察了足够多的吸收-散射过程，你就会发现，尽管光总是从同一个方向(激光束的入射方向)被吸收，但是原子却向各个方向发射光子，而不会偏向某个方向。这个现象导致的结果是，在与入射激光束相反方向运动的一组原子会慢慢停止运动，此后开始向各个方向随机运动。这样的随机运动对应着某一温度，这一温度与原子吸收光子到重新发射出去的时长成正比。

在这个方法的基础上有几个改良版本，每一种版本方法都是利用光将原子(和分子)冷却到更低的温度。在这种情况下，光就像一种“黏性流体”，其中的原子运动得越来越慢。一旦原子的速度降低到一定程度，甚至可以用光学镊子来捕获原子。此时就可以应用更加复杂的光学冷却技术，使温度降低到仅比绝对零度高十亿分之一摄氏度。

我之前提到，即使在绝对零度下原子依然会有“抖动”，这种抖动是量子力学引起的。可以将这种抖动的区域看作原子本身的空间区域。也就是说，根据量子力学，原子不仅以随机的方式在一个狭小的空间区域内游荡，还存在于整个空间区域内。对于被困在如此低温下的原子而言，该区域的大小可能是千分之一米。不过考虑到电子到原子核的距离只有十亿分之一米，那么这个原子所占的空间可以说是相当大了。更奇怪的是，几个原子可以同时占据这个同一空间区域。

这个概念是非常违反直觉的。我们常常认为原子就像一个个小小的台球，可以紧密地堆积在一起，就像组成固体材料中的元件结构一样。但是同时，由于原子在材料中位置不同，它们各自又保持着其独特的特性。但对于这些超低温的原子就不一样了，它们可以同时存在于任何地方，这是一种新的物质状态。这种状态由爱因斯坦和印度科学家萨特廷德拉·纳特·玻色
[2]

(Satyendra Nath Bose)发现，被称为玻色-爱因斯坦凝聚态(Bose-Einstein condensate)。

这种奇特的状态有一些显著的特性。例如，原子云
[3]

就是一种超流体
[4]

，在流动时没有黏性。此外，原子云可以被一分为二然后再重组在一起，从而使这两个被分离的原子云表现出量子干涉效应。这从本质上展示了一个大物体(包含许多原子，使其大小可见)所具有的量子特性。这种量子特性可以归因于每一个特定原子的不确定性——不确定它处于这一半还是另一半原子云中。我们必须考虑每个原子其实同时存在于这两个原子云中。

由于这些冷原子可以被光束束缚，所以也可以用几束光束创造出某种空间结构用来操纵原子。例如，当两个光束相遇时，会形成一个干涉图样(见第3章)，在干涉图样中有些区域强度高，有些区域强度低。冷原子们要不就都停留在强度高的区域，要不都停留在强度低的区域(可以通过选择特定波长的光来调整原子所在的区域)。随着光束强度的增大，原子会落入干涉图样中出现的“鸡蛋托盒”状的光陷阱中(见图32a)。它们落入的方式也很有趣。

图32　被光束缚在光学晶格
[5]

中的冷原子：a.光学晶格中个晶胞束缚有几百个原子(温度为几十微开尔文)；b.一些分布在各个“格子”中的单个原子(温度为纳开尔文)。

当原子足够冷时，它们并不喜欢待在鸡蛋托盒内的同一个“格子”里，因此最终原子的分布特别像一个完整的鸡蛋托盒——一个原子待在一个格子里，如图32b所示。这种情况下不存在超流体，因为原子们喜欢待在原地。事实上，这更像是一个“绝缘体”，因为所有的原子都没有动。通过调节光的强度，可以探究原子从完全自由流动到完全不流动的有趣过渡。

在量子力学的环境中实现对原子的控制，这使得科学家们能够探究与其他类型的材料(例如固态金属氧化物)相关的物质的新特性。尽管在这些材料上，我们很难实现同等精确度的控制和测量。现在我们可以观察到，冷原子气体
[6]

位于“鸡蛋托盒”中的单个原子，并观察当周围环境发生变化时它们会有怎样的反应。

我们可以用许多不同类型的原子来探究这种低温状态，并且利用光来构造复杂的俘获结构。当前的一个研究领域是利用冷原子来“模拟”其他量子系统。利用这种方法可以研究其他方法无法解决的复杂问题，促进我们对材料和结构产生新的理解，从而产生新的影响。这也许可以帮助我们理解甚至是设计出新的磁铁，可用于计算机数据存储、医疗的核磁共振成像设备，甚至用于悬浮列车的无摩擦发动机。

超快

光脉冲可以非常短。在第5章中，我说过它们可以和光学场的单个周期一样短。光谱中的可见光，其光脉冲大约会持续2飞秒。对于波长较短、频率较高的极紫外(extreme ultraviolet，缩写为EUV)区，其光脉冲持续的时间更短。目前测量到的最短光脉冲的持续时间小于100阿秒(10-18秒)。这些脉冲是目前可以受控产生的最短脉冲(尽管我们可以通过粒子对撞机观察到发生在更短时间尺度上的事件)。随着在X射线波段中出现了光的爆发，我们甚至可以期待产生持续时间更短的光脉冲。

这些数字简直小得让人难以置信，因此有必要选取一些参照物来帮助我们理解。宇宙的年龄是5× 1017秒，因此1秒和宇宙年龄的比值大约等于1阿秒和1秒的比值。或者从经济学的角度来看，如果美国的国债总量相当于1秒钟，那么1飞秒就相当于1美分。在这个尺度上，1阿秒几乎是没价值的。

在这个时间尺度上能发生什么事情呢？在第4章中我介绍了一个简单的原子模型，叫做玻尔模型。在这个模型中，电子受到电力的吸引而“环绕”原子核运动，就像行星受到万有引力的牵引绕太阳运动一样。对于简单原子(只有几个电子的原子)而言，电子绕轨道运行一周所需的时间约为150阿秒。如果我们想观察电子的运动，需要使用比150阿秒更短的光脉冲，才能使图像不致模糊。

频闪仪是与该话题最相关的一个设备。目前，研究人员已经使用了一种频闪仪的变体来观察原子和分子在基本微观层面上发生的迅速变化。在此应用中，一束激光的光脉冲被分为两个(或更多)部分，并在这两个部分之间引入一个延迟。其中，第一个脉冲先发射并照亮样品，其中一部分被样品吸收了。这“触发”了系统中的一些变化——电子在原子内部运动，或者化学键在分子或固体中振动。接着，第二个脉冲发射过去，其中一部分经由样品散射，而后被探测到。

重复进行该实验时，随着两个脉冲之间延迟时间的增加，探测到的散射光可以反映出样品的动态变化。从某种意义上来说，这是原子、分子或者固体变化的“电影”。这种“泵浦
[7]

探针”的方法已经被用来研究一些复杂的过程，例如在化学反应中，当两个分子通过它们之间的相互作用而被重构时发生了什么。这种方法还有一个更复杂的版本，就是利用不止两个，而是多个光脉冲。这些方法现在被用来研究许多极其有趣却令人费解的内容，从相互作用的原子、高温超导体到生物系统，等等。

我已经说过光学场的单一个周期是脉冲所能持续最短的时间。而我们可以利用由高次谐波产生的极紫外(EUV)脉冲，设计实验来测量光电场的振荡。测量脉冲场需要非常快，要比光周期快得多。我们可以利用波长更短的脉冲，它只有光学波长的二三十分之一。当一个电子被一个强光脉冲从原子上剥离时，就会产生这种波长非常短的脉冲。这个过程需要一个光学场，其强度相当于电子与原子核之间的结合力大小。这种脉冲很容易通过在锁模激光器的输出端增加一个光放大器来获得。

当电子被强烈的脉冲从原子上剥离出来后，电子会处在一个快速振荡的电场之中。如果电子是在电场振幅为零时被剥离的，电子就可以顺着光学波的下一个周期做“冲浪”运动——短暂地远离原子，然后再回来。当它返回时，速度会非常快，并且可以通过光的形式释放所有额外的能量，从而被原子重新捕获。在这种情况下，原子和电子重新结合时，会释放出非常短的脉冲。这个脉冲的波长只有几百亿分之一米，位于光谱的EUV区域，大约是产生它的光波波长的1/20。

现在想象这个EUV脉冲发射到另一个原子上。它的波长非常短，足以被原子吸收，并击出一个电子停留在原子周围。进一步设想，在同一时刻将待测量的短光脉冲也发射到这个原子上。这个脉冲的场将使停留的电子向某个方向加速，这一方向取决于电子被EUV脉冲从原子上被剥离时，所处的光学波周期位置。通过改变EUV脉冲和光脉冲之间的延迟，就可以测量电子的加速度。由于速度较大的电子有更多的能量，这使我们可以“看到”光脉冲场(见图33)，尽管该场振荡的时间非常短。

图33　光脉冲场的图像。两个相邻峰值之间的时间间隔为2.飞秒

这种泵浦探针光谱法可以应用在生物化学的研究中，例如研究光合作用的第一步反应，即植物利用阳光的能量，将空气中的二氧化碳转化为氧气。这一步需要以极高的效率在一个大的生物分子周围传输能量。该过程包含有一些非常有趣却不能被解释的特性——其能量的传输比人们预期的要快得多，效率也要高得多。如果我们能从这种在自然界中进化了上亿年的系统中，学习如何快速高效地传输能量，或许我们就能够应用这些知识改进诸如太阳能电池的设计之类，这将给社会带来极大的影响。

超强

电费账单告诉你上个月用了多少电。它以千瓦时(kW·h)为计量单位，你消费的每一度电都要付费。假设你在某个月使用了220千瓦时(这是英国每月的人均能耗)：你可以在这个月的四周内平均使用这些电，或者你也可以在第一周用光它，并在接下来的三周什么都不用。但是，你能想象在千万亿分之一秒内用完这些电吗？要在这么短的时间内用完这么多的电，你需要大量的电器，而且你还必须迅速地开关它们。因此，在这种情况下的用电峰值功率将会非常大。

光脉冲可以用来用完这些电。因为它们的持续时间特别短，而且包含了这么多能量。事实上，我们有可能产生某种脉冲，使其在某一时刻以相当于整个地球全部发电能力的功率提供能量。但你家里的灯并不会熄灭，这是因为脉冲太短，导致它们的总能量非常小，需要一台巨大的激光器来产生这种脉冲，其占地面积几乎赶得上一个足球场那么大。英国卢瑟福·阿普尔顿(Rutherford Appleton)实验室的火神激光器(VULCAN laser)就占地颇大。火神激光器可以让持续500飞秒的脉冲携带500焦耳(3.6×106J = kWh)的能量。500焦耳只是一个100瓦的灯泡在5秒内发出的能量。然而脉冲很短的持续时间意味着光的强度可以达到100万颗太阳的总量。位于加州利弗莫尔的美国国家点火装置(National Ignition Facility，缩写为NIF)
[8]

的激光器要比火神激光器大得多。还在计划中的欧洲光学基础设施(European Light Infrastructure)项目将建造一个比NIF峰值功率更大的系统。

这种非常短暂、非常强烈的光爆发可以用来改变物质的状态。光脉冲产生的最大电场大于原子内部的电子和原子核之间的引力场，所以有可能利用这个机制将原子中的电子剥离出来，从而形成一种新的物质状态——等离子体。这种剥离可以瞬间完成，比原子核运动的时间还要短，使得原子更紧密地排列在一起，因此等离子体的密度非常大，几乎与固体材料(如一块玻璃)的密度相同，然而与固体材料不同的是，等离子体的温度高达200万摄氏度。

这就是巨行星甚至一些恒星的核心所处的状态：高密度等离子体的粒子在百万倍于大气压力的压力下高速碰撞。可以在实验室获得这样的等离子体，而且它们的用途极为广泛。例如，我们可以通过它们了解恒星是如何工作的，它们的生命周期是怎样的，从而描述它们的进化阶段，如超新星爆炸和白矮星
[9]

等。其他的一些令天体物理学家感兴趣的现象也可以使用激光器进行实验研究。同时，天体物理学家也使用这种等离子体来探索行星科学。例如，我们可以从气态巨行星的质量和大小来推断它们的组成，但前提是我们要知道在如此高的压力下物质能被压缩到什么程度。

一些激光设备利用波长很短的光产生脉冲。这些脉冲由磁场中加速的电子产生，所以当它们沿着加速器急速下落时，它们会左右“摇摆”。这就产生了一种由短脉冲X射线组成的同步辐射。这类激光器通常使用粒子加速器的技术甚至硬件。比如斯坦福线性对撞机光源(Linear Collider Light Source，缩写为LCLS)和汉堡X射线自由电子激光器(X-ray Free Electron Laser，缩写为XFEL)。

基于最强烈的激光脉冲以及X射线短时增强的技术，科学家们能够在各种条件下检测等离子体。此外，激光在原子核之间施加的巨大压力，可以在适当的条件下使原子核融合在一起，在这个过程中会释放出大量的能量。这种“核聚变”可能使我们获得几乎无限的能源。将激光应用于核聚变在技术上要求极高，也是目前正在探索的实现核聚变的两种方法之一：另一种方法不涉及光，光只是在其中充当一种监测工具。不过这两种方法都使用了致密等离子体。

当激光脉冲穿过等离子体时，会产生一种波，类似于船只划过水面时会留下波纹。在等离子体的电场内距离10-6
米的两端电压可达到10万伏以上(这意味着约为高压电塔电线中10倍的电压，被加在只有人类头发十分之一的宽度上)。这样的电场强度比世界上用于研究基本粒子的最大机器，如日内瓦欧洲核子研究中心的大型强子对撞机(Large Hadron Collider，缩写为LHC)，所使用的加速场强度至少大1000倍。在未来，也许我们可以用激光制造出可以放在桌面上的小型设备，使电子能够加速到目前LHC所能达到的能量。

通过激光脉冲与物质相互作用产生的超强电场，也可以给较重的粒子加速，比如质子。目前质子束正作为一种癌症治疗的手段被研发，与目前使用的其他类型的放射治疗相比，重的粒子可以更精确、更深入地送达病变组织。

光的非凡特性使人们能够不断在广阔的范围里开创新领域。可以说，光是科学技术中一种无处不在的工具。

[1]
分子马达（molecular motor）是由生物大分子构成，利用生物化学能进行机械做功的纳米系统。生命体的一切活动都依赖于分子马达。

[2]
1894—1974，印度物理学家，奠-定爱了因玻斯色坦凝聚理论的基础。玻色子就是以他的名字命名的。

[3]
由大量原子构成，处于玻色-爱因斯坦凝聚态。

[4]
超流体是在超低温下的一种内部完全缺乏黏性的理想流体。

[5]
即文中描述的由多个光束相互干涉形成的光陷阱，可将冷原子“囚禁”于其中。

[6]
由单个原子组成的气体。

[7]
利用光将原子或者分子内部的电子从低能态激发到高能态的过程。

[8]
美国科学家制造的世界上最大的激光核聚变装置，能产生恒星内核温度和压力，被称为“人造小太阳”。

[9]
超新星爆炸和白矮星都是恒星进化到末期后可能出现的结果。

08 量子光学 Quantum Light

在第1章中，我介绍了光可以被视为粒子流，为方便起见，将其记为“光子”。事实证明，光子是真实的粒子，它可以被产生、研究、测量、储存与使用。尽管从某种意义上来说，光子用最简单的方式描述了光，但是制造单个光子却并不简单。大多数光源产生不同种类的光，其中包含的光子数量是不固定的。

例如，一个灯泡会产生一股向任意方向发射的光子流。如果你从某个方向观察灯泡发出的光，然后仅观察一小段时间——你也可以把这称为一个时间间隙——那么你可以数出在这段时间内发射出的光子数。但是，如果你把这个实验重复几次，你会发现每次数出来的光子数量都是随机的，有的时候多，有的时候少。光子的平均数量其实是固定的，只取决于灯泡的亮度。但是你却永远无法肯定，在给定的时间内，能从光束中测量出多少个光子。这就是“经典光”的特征之一，即光可以完全用波来描述。

激光也是这样。激光脉冲中包含的平均光子数可以很多，但对于任何给定的脉冲，实际测得的光子数都将大于或小于平均数。一个脉冲中光子数的变动范围近似于平均光子数的平方根。而每个脉冲中的光子数的变动与所有脉冲中平均光子数的比，被称为相对“噪声”，所以该“噪声”将随着平均光子数的增加而减小。

激光束有固有的强度噪声。这就限制了利用激光得到的图像质量。激光强度的波动意味着不能精确探测图像中两点间的距离。事实上，用低强度光获取的图像是非常不精确的，因为低强度光中的平均光子数很小(所以噪声大，导致物体很难被看清)，而且光子数在帧与帧之间的变化很大。获得精确结果的唯一方法是延长成像时间，从而增加到达目标物体的光子数量，再从中求取平均结果。平均信号可以降低相对强度噪声，从而得到分辨率更高的图像。其精度与所用光子数的平方根成正比。因为经典光束无法超越这一精度，所以该精度被称为“标准量子极限”。

另一方面，在平均光子数相同的情况下，利用量子光可以获得更好的平均效果，这是因为量子光的噪声远低于任何经典光的。但首先，你必须有一个量子光源。这样的光源有很多种，每种都能产生一种不同的量子光。那么接下来，先让我们来看一下使光具有原始量子态的源头——光子。

单光子

如何才能制造出单个光子呢？奥托·弗里施
[1]

(Otto Frisch)在1965年想出了一个可操作性很强的方案。他的想法很简单，首先将一个原子激发到激发态(关于如何施行请参阅第5章)，然后等它降至基态。在这个过程中，原子只会发出一个光子，这是因为单个原子只能存储一个“量子”能量。你可以知道原子什么时候发射出光子。因为发射光子的动量会给原子一个反向作用力，只要探测到了原子的运动，你就能确定此时原子发射出了光子，而且还可以根据原子的运动方向来确定光子的发射方向。

一些现代量子光源的工作原理与此类似，只是它们将原子困在两个平面镜(类似于激光器中的光学“腔”)之间，并快速激发原子，使其优先向沿着腔轴的方向发射光子，这就构成了一个稳定的单光子源。由于光子的发射具有严格的规律性，因而这种单光子光源是一种特别的“低噪声”源。如果在某个特定的时间段内观察这样一束光，你可以准确预测其中有多少个光子——只有一个。因此，这种光的强度异常稳定，与“嘈杂”的经典光束不同，它是一种很“安静”的光束。

此想法也被用于其他量子光源。你可以利用非线性光学效应构造一个非常简单的光源。具体来说，某些晶体可以使一个高能量光子分裂成两个能量较低的光子，每个光子大约是原始光子的一半。对于大多数材料来说，发生这种裂变的概率相当小。由于光子成对产生，你可以将其中的一个作为“前驱体”，作为表示另一个光子存在的信号(见图34)。这类光源是量子光学领域的主力军，它利用光的量子力学特性来探索量子物理学的基础，进而发展出一些新型信息技术。

图34　“前驱体”单光子光源，随机产生光子，当产生出一个光子时会由“前驱体”发出信号

正如经典的电磁波可以发生极化
[2]

一样，光子也可以发生偏振，因此，我们可以找到一个垂直偏振(用V表示)或水平偏振(用H表示)的光子。它们就像波一样，当我们通过观察光子能否通过水平方向的偏振器来测量其偏振方向时，会发现H光子(水平偏振的光子)总是可以通过偏振器，而V光子(垂直偏振的光子)总会被挡住，无法通过。

我们可以产生一个对角向偏振的光子，使其振荡角度与水平和垂直方向均呈45°。如果我们尝试观察这种对角向偏振光子能否通过水平偏振器时，其结果就存在不确定性，这非常奇怪。光子是光的最小“组分”，所以它不能再被分割。那么对角向偏振光子在通过水平偏振器时会发生什么呢？实际上，对角向偏振的光子有一半的概率通过偏振器，以一半的概率被反射回来(见图35)。

图35　一个对角向偏振(用D表示)的光子遇到一个偏振器，光子会随机地通过水平偏振器(用H表示)，或者通过垂直偏振器(用V表示)

这意味着如果你让对角向偏振(用D表示)的单光子通过水平方向的偏振器100万次，那么其中有50万次可以通过，而剩余的50万次则不能。量子力学非常奇怪的一点是，你无法预测每次实验的准确结果。这并不是因为光子有时是水平偏振的，有时是垂直偏振的，而是因为同一个光子既是水平又是垂直偏振的。因此，此随机结果从宇宙最基本的层面揭示了量子物理学所描述的内在不确定性。

在这种情况下，你可以用单光子做一些普通光不能实现的实验。例如，可以用光子的这种属性来生成随机数，方法是记录光子通过偏振器(标记为1)，还是被偏振器反射(标记为0)。由0和1组成的字符串中的随机性是由基础物理中的固有的特性保证的，而不只是来自投掷骰子或其他偶然事件中。因此，量子随机数生成器是一项新兴的业务，它们生成的随机性是无法被伪造的。

你也可以利用物理定律来保障通信链路的安全，而不是依赖电信供应商。这是基于光子的两个重要特性：第一，你不能同时在两个地方探测到同一个光子。因此，如果一个窃听者想通过捕获光子来获取你发送的信息，那么，你的信息不会被发出去，也就收不到任何回应，这个时候你就会意识到通信出了问题。当然，窃听者可能会很狡猾地给你发送一个“诱饵”光子，希望你能将这个含有伪造信息的光子当做你本该收到的光子。但是基于光子的第二个重要特性，你可以看出它是伪造的。因为在量子力学中，没有任何测量能够测得单个量子的所有信息。

结果示范如下，比如你想通过链路发送一个简单的二进制消息(由0和1组成)，并将一个垂直偏振光子标记为0，一个对角向偏振光子标记为1。如果偷听者(通常被称为Eve)检测发现光子是“垂直偏振”的，那么她依然不能确定光子是不是0，因为对角向偏振光子至少有一半概率也会给出“垂直偏振”的测量结果。所以Eve只能得到了一部分信息，而不是全部。

现在，假设消息的发送者(通常称为Alice，而你是接收者，可称为Bob)向你发送一个编码为1的光子。假设Eve测量该光子是否垂直偏振，并发现它通过了检测。为了伪装，她必须选择给你发送一个垂直偏振光子还是对角向偏振光子。她最好向你发送垂直偏振光子，因为这是根据测量结果得出的最有可能的情况。而作为接收者的你可以对接收到的光子进行对角向偏振测量。由于你知道Alice发送的部分信息，因此如果光子来自Eve，那么这个光子在50%的时间里会给出错误的结果。如果它来自Alice，你永远不会得到错误的结果。因此，通过比较接收到的信息与已知的Alice发送的部分信息，你就可以判断Eve是否篡改了你的传输链路。

然而，Eve可能想出更聪明的办法。她也许试图从Alice那里复制光子而不测量它。她可以先复制两份，并把原始光子发送给你。然后她就可以在其中一个副本上进行垂直偏振测量，在另一个副本上进行对角向偏振测量，这样她就可以在你毫不知情的情况下确定Alice发送给你的光子“比特”中的全部信息。然而，即使如此她的伎俩也还是无法得逞。因为量子力学的一个显著特点是，不可能制造出一台复印机能精确复制或克隆一个处于未知量子状态的单个粒子，这是违背物理定律的。由于物理上的这两个限制(“不可测量”和“不可克隆”)，我们可以在Alice和你之间建立一个安全的通信链路，用来传输秘密的随机比特流。

压缩光

其他种类的量子光相比经典光也有一些性能上的提升。我们知道，光是电磁场的振荡。几乎可以将激光束视作这种振荡的理想状态。然而，即使是激光，它的振幅中也有一些“噪声”。也就是说，每次测得的振幅，并不完全一样。如图36a，图中显示了每一点或每一相位的场的振荡不确定性。有一种特殊的量子光被称为“压缩光”，这种光的噪声会随着光场周期的相位而变化，如图36b所示。它在某些相位的噪声比其他相位的更大。结果表明，这样的场只能由成对的光子生成。如果你测量光子的数量，你只能得到偶数的结果。正是这些光子对的量子干涉形成了与相位相关的振幅噪声。

图36　压缩光a与激光b相比，a在其振荡的某些点上的场振幅噪声减小了

这一特性自有其应用价值。假设你想测量波的相位。回想一下，之前介绍过使用干涉仪时，光束的相移是由被测量的物体(比如某个特定分子)引发的。在光场波动最小的地方可以更精确地测量波的相位。事实上，在某些相位上，压缩光场的起伏比任何经典场的都要小，因此使用压缩光场的相位传感器将比使用经典光场的传感器更精确。它们甚至可以打破标准量子极限。

目前，这种测量方法仍然比较昂贵，因此只有在比其他方法具有明显优势时才会使用。例如，用大型光学干涉仪探测引力波，像德国汉诺威附近的GEO 600项目，就需要使用压缩光检测相移，而相移的变化又与引力波引起的光的相对路径距离的变化相对应。因此，可以通过测量相移的变化来判断引力波是否存在。当然，此时光的相对路径距离的变化非常小，如果与地球到太阳的距离相比，这段距离只有一个原子大小。

量子纠缠

当存在一个以上的量子光束时，事情会变得更加奇怪。光子会以某种方式缠绕在一起，导致我们无法区分任何一束光的属性——例如颜色、位置、方向或脉冲形状。这远远超出了波粒二象性的基本概念。它挑战了经典世界的观念，即在经典世界中可以确定物理实体的某种属性(如光束的频率、到达时间或水平/垂直偏振等等)。这些属性可以被测量，并且彼此自洽。但是，这并不适用于在某种状态下的成对光束，而这一点可以通过实验来验证。这是20世纪基础光学的伟大成就之一。

借助这一特性，我们可以利用量子光学来检验伟大的爱因斯坦、鲍里斯·波多尔斯基
[3]

(Boris Podolsky)和内森·罗森
[4]

(Nathan Rosen)的著名猜想，即判断他们对于粒子系统的量子力学描述是不是完整的，而且不需要借助任何其他信息就可以确定该系统的方方面面。约翰·贝尔
[5]

(John Bell)在20世纪60年代找到了一种量化这类问题的方法，并尽力尝试用实验来检验他的假设。这些实验一般被称为“贝尔实验”，其中最早实现也是目前最具说服力的研究中就使用了光子对，并且每对光子之间都彼此相关。正是这些相关性，使得量子粒子与经典粒子大为不同。为了更全面地了解这种量子效应的奇特性，我们有必要在此进行更深入的探讨。

相关性几乎无处不在。以下面这个简单的游戏为例。发牌人拿两副牌，一副牌的背面是绿色，另一副牌的背面是蓝色。发牌人从每副牌中各挑一张，其中一张牌给你，另一张给另一位玩家。当然，你们的牌背面的颜色总是不同的，但它们正面的花色却可能相同，因为每副牌中有一半正面是黑色花色，另一半是红色花色。事实上，你会认为在一半的时间里，两个人拿到的花色应该是相同的，这是因为出现红色红色和黑色黑色的概率为50%。

如果你和你的搭档每次都同时拿到红色或黑色的花色，这些卡片就被认为是“相关的”。这是你所能想象到的最强烈的相关。事实上，如果你们两个人在超过一半的时间里都得到了相同花色的牌，也可以说这些卡片是相关的，尽管这种相关性会比第一个例子中的“弱”。通过测量相关性，你可以确定发牌人是否在作弊，因为我们一般认为发牌人所用的是两副独立、完整的牌。

我们可以用偏振代替牌来解释光子的这种相关性。也就是说，一个水平偏振的光子可能被看作“红色”光子，而一个垂直偏振的光子可能被看作“黑色”光子。如果一个光源一次产生两个光子，就像之前描述的，它总是产生具有特定偏振方向的光子，比如一个垂直的和一个水平的，或者两个都是水平的，就可以说这个光源产生了相关的光子束。这种类型的相关性被称为“经典相关
”，因为它和经典对象(如扑克牌)的情况一样。

相关性在其本质上具有量子力学的特性。假设一对光子对有两种可能的初始状态，第一种是水平偏振，第二种是垂直偏振，或者第一种是垂直偏振，第二种是水平偏振。在经典世界中，两个粒子的这两种偏振组合是相互排斥的：也就是说这两个光子要么是水平-垂直偏振组合要么是垂直-水平偏振组合，并且每一种组合发生的概率都是50%。但是，正如单光子可以同时处于水平偏振和垂直偏振的叠加态一样，这对光子也可以处于叠加态，即水平-垂直偏振和垂直-水平偏振的叠加态，如图37所示。这种相关性比任何经典粒子更强，被称为纠缠。它是量子物理学中最神奇的性质，并产生了深远的影响。

图37　产生偏振纠缠光子的光源

这些都是贝尔实验所揭示出来的。在这样的测试中，你不仅要考虑每个粒子的水平偏振和垂直偏振之间相关的可能性，还要考虑对角向偏振(用D表示)和反对角向偏振(用A表示)之间相关的可能性，这两个偏振的方向角度都在水平和垂直偏振的正中间(对角向偏振光的一个例子展示在图35中。反对角向偏振的方向与对角向偏振的成直角)。用纸牌来类比的话，也就是说你看到的纸牌花色不是红色(相当于水平偏振)就是黑色(相当于垂直偏振)。或者你可以看到纸牌的背面，不是绿色(相当于对角向偏振)就是蓝色(相当于反对角向偏振)。

一个量子游戏

现在想象一个纸牌游戏，发牌人从任意一副牌中抽牌并发给每个玩家一张牌。这意味着，每个玩家手中有一张牌的正面花色(用“正”表示)为红色(用R表示)或黑色(用B表示)，牌的背面颜色(用“背”表示)为绿色(用g表示)或蓝色(用b表示)。发牌人选择用以下的方式发牌：如果一个玩家只能看到他自己牌的正面，另一个玩家只看到他自己牌的背面，用(正，背)表示，那么在这种情况下，两位玩家间永远不会出现(R， B)
[6]

的结果。同样，如果第一个玩家看他自己牌的背面，另一个看他自己牌的正面，即(背，正)，那么他们也永远不会看到(B， R)的结果。然而，当两个玩家都看的是牌的正面(正，正)，他们有时会看到(R， R)。由此，你可以根据逻辑推理得知，如果他们都看牌的背面(背，背)，他们就一定会看到为(g， g)。这就是经典的纸牌游戏中会发生的情况。

但事实上，当你用量子相关的光子(或其他粒子)做这样的游戏时，结果将完全不同。当第一个玩家测量水平偏振、第二个玩家测量对角向偏振(或者两个玩家调换)时，结果发现他们永远也得不到(V = 0， D = 1)和(D = 1， V = 0)这两个结果。而当他们都使用对角向偏振进行测量时，他们有时会得到结果(D = 1， D = 1)。如果据此进行逻辑推理，当他们都使用水平方向的偏振片测量光子时，他们应该有时会得到结果(H = 1， H = 1)，但是，当他们真正做这个实验时，他们却永远不会得到这个结果。这种量子卡牌游戏的所有可能结果都在图表1的表格中。这样的实验是可操作的，而且已经使用光子验证过了。

图表1　一个量子纸牌游戏可能结果的概率表

事物的定域属性

那么到底发生了什么呢？这是量子物理学一个根本的怪异之处：量子卡牌游戏的结论是，光源产生光子时，光子的偏振并没有被预先确定。这就好比从一副卡牌中取出背面颜色未定的牌。这与我们的经验相悖，每张纸牌的正面有一定有特定花色，背面一定有特定颜色。无论我们是否清楚，甚至是发牌人是否清楚花色或者颜色是什么，我们都会非常确信，当这些牌被发给我们时，它们确实具有特定的花色和颜色。我们当然不希望它们的这些属性被我们的行为影响。但是量子力学却告诉我们，我们不能预先确定纸牌的花色和颜色。

只有通过测量才能给出确定的结果。但是我们不能简单地认为，测量出来的结果就是之前不知道的、预先设置的光子特性。事实上，当光源产生单个光子时，你不能事先确定光子的偏振，因而实际测量的结果并不是其事先具有的偏振，而是如果没有测量，你将永远不知道其偏振状态。用纸牌游戏来说，如果你企图设计出一种发牌方式得到相同的效果，你会发现那是不可能的，除非这些纸牌可以同时以红黑或绿蓝的方式叠加
[7]

。对光子来说也是一样，它们必须处在水平和垂直偏振的叠加态，形成某种特定的相关性，这种相关性被称为“量子纠缠”。

纠缠是一个非常奇怪的概念，我们不可能从普通日常的角度来考虑它，例如之前举的纸牌游戏的例子。然而，纠缠也很常见。它出现在许多量子尺度的事物中，甚至也发生在日常生活中。例如，分子中电子之间的相关性就是纠缠；在构成分子的原子之间，甚至是相对较小的原子之间也可以通过纠缠形成化学键；纠缠还造就了像超导体这样的特殊物质。

令人惊讶的是，纠缠也可以被运用到现实技术中。你很难想象这样一个神秘而抽象的概念可以有任何实际用途，但它确实有用。它使很多信息处理的方法得以实现，而这些方法是不能够通过来回发送经典波来实现的。

事实上，所有的信息处理系统都是建立在物质实体之上，这表明，这些系统必定反映了其组成部分的物理原理(通常是经典物理)。这使得人们看到了新的机遇，即可以基于量子力学来建造新的系统，如在计算、通信和测量技术方面创造新技术，并以前所未有的方式超越当代技术。例如，未来通信的安全性将由自然法则所保障；未来的计算机能够解决现在我们根本“无法计算”的问题；未来的成像系统可以让我们看到从未看到过的物体。

光在创建这样的系统中起着重要的作用。例如，光纤网络的基础设施可以用来在双方之间绝对安全地发放随机的“量子密钥”(0和1的随机字符串)，然后再利用“量子密钥”来编码需要传递的消息。这样的网络还可以用来连接小型量子处理器，最终组成分布式量子计算机。事实上，研究也表明，原则上可以完全不借助光来建造量子计算机，尽管这种方法极具挑战性。这些技术的结合为量子互联网的未来带来了希望，这是一种与我们目前使用的技术完全不同的通信和处理信息的方式，而且都将通过光来实现。

[1]
1904—1979，英国核物理学家。

[2]
改变电磁波电场强度的方向等性质，光学上被称为偏振。

[3]
1896—1966，美国物理学家，为了论证量子力备性，于1993年与爱因斯坦和内·森罗森一起提出了EPR佯谬。

[4]
1909—1995，以色列物理学家，与爱因斯斯·波多尔斯基一起提出了EPR佯谬。

[5]
1928—1990，爱尔兰物理学家，发展了量子力的贝尔定理。

[6]
原文为(R， b)是红色蓝色之意可以出现，疑为出错误。

[7]
即纸牌处在一种状态下，使得它的正面花色同时既是红色也是黑色，背面颜色既是蓝色也是绿色。

09 黎明时分 Twilight

德谟克利特的原子

和牛顿的光粒子

是红海海岸上的沙粒

在那里以色列的帐篷竟是如此闪耀。

——威廉·布莱克，

《嘲笑吧，嘲笑吧，伏尔泰，卢梭》

光，有着如此悠长的历史与广泛的应用，因此这本薄薄的书必定无法涵盖关于它的所有话题。尤其是那些在可见光区域之外的电磁光谱上观察到的令人惊叹的发现，以及日常生活中随处可见的光学仪器，这些都没有在书中得到详尽的描述。

从多镜面望远镜(直径可达几十米，其自适应控制的反射镜面可以抵消由大气湍流引起的空中观测目标的闪烁现象)到大规模同步加速器(对电子加速直到它们辐射强烈的X射线，可以用来观察自然或人造材料的结构，从而揭示例如生物重要分子或工程金属的结构)，我们已经拥有了无数各式各样的成像设备。无论如何，我希望你已经感受到了光之美，知道了人类为揭开光的神秘面纱所经历的旅程，也了解了各种光之谜是如何被一一解开的。

与此同时，光学技术的蓬勃发展，也开辟了新的探索领域和应用领域，并常常取得出人意料的成果。正如过去的几个世纪一样，光将持续向我们展示新的谜题，不断激发我们的想象力，并使我们研制出新的设备。

全书完

索引

3D films 3D 电影

γ-rays γ 射线

A

Abbe, Ernst 恩斯特·阿贝

Abbe's criterion 阿贝准则

aether 以太

Al-Hazen 海什木

aluminum 铝

Ampère, André-Marie 安德烈·马利·安培

angle of incidence 入射角

angle of reflection 反射角

astronomy 天文

atom 原子

attoscience 阿秒科学

aurorae 极光

B

Bacon, Roger 罗杰·培根

Balmer, Johannes 约翰·巴耳末

beams 质子束

Bell tests 贝尔实验

Bell, John 约翰·贝尔

Betzig, Eric 埃里克·白兹格

binoculars 双筒望远镜

birefringence 双折射

birefringent materials 双折射材料

black bodies 黑体

Blake, William 威廉·布莱克

Blu-ray 蓝光

Bohr, Niels 尼尔斯·玻尔

Bose, Satyendra Nath 萨特廷德拉·纳特·玻色

Bose-Einstein condensate 玻色- 爱因斯坦凝聚态

Brewster, Sir David 大卫·布鲁斯特爵士

brightness 亮度

Broglie, Louis de 路易斯·德布罗意

bundle 束

C

caesium 铯

calcite 方解石

chromatic aberration 色差

classical 经典相关

coherence 相干性

compact disc 光碟（CD）

constructive 相长

contact lenses 隐形眼镜

copper 铜

cornea 角膜

correlations 相关性

Coulomb, Charles Augustin de 查尔斯·奥古斯丁·德·库仑

Crick, Francis 弗朗西斯·克里克

D

De Luce 论光

destructive 相消

Diamond Light Source 钻石光源

diffraction 衍射

digital video disc 数字影盘（DVD）

Dirac, Paul 保罗·狄拉克

E

Edgerton, Harold 哈罗德·埃哲顿

Einstein, Albert 阿尔伯特·爱因斯坦

electric charges 电荷

electromagnetic field 电磁场

electron 电子

emitting diode 发光二极管

entanglement 纠缠

Euclid 欧几里得

Euler, Leonhart 莱昂哈德·欧拉

European Light Infrastructure 欧洲光学基础设施

extreme ultraviolet 极紫外（EUV）

F

Faraday, Michael 迈克尔·法拉第

femtochemistry 飞秒化学

Fermat, Pierre de 皮埃尔·德·费马

fibre optic broadband 光纤宽带

fields 量子场

fluorescent 荧光

focal length 焦距

Fourier, Joseph 约瑟夫·傅里叶

Franklin, Rosalind 罗莎琳·富兰克林

Fraunhofer, Joseph von 约瑟夫·冯·弗劳恩霍夫

frequency 频率

Fresnel, Auguste 奥古斯丁·菲涅耳

fringes 条纹

Frisch, Otto 奥托·弗里施

G

Gabor, Denis 丹尼斯·加伯

Galilei, Galileo 伽利略·伽利雷

global positioning system 全球定位系统（GPS）

Goethe, Johann Wolfgang von 约翰·沃尔夫冈·冯·歌德

Grimaldi, Francesco 弗朗西斯科·格里马尔迪

Grosseteste, Robert 罗伯特·格罗斯泰斯特

guide star 导星

H

Hamilton equation 哈密顿方程式

Hamilton, William 威廉·哈密顿

handedness 手性

Hell, Stefan 斯特凡·赫尔

herald 前驱体

Hertz, Heinrich 海因里希·赫兹

high-harmonic generation 高次谐波产生

hologram 全息图

Hooke, Robert 罗伯特·胡克

Hubble Space Telescope 哈勃太空望远镜

Huygens, Christian 克里斯蒂安·惠更斯

I

incoherent 不相干的

information 信息

infrared 红外线

intensity 强度

interference 干涉

Internet 互联网

irradiance 辐照度

K

Kepler, Johannes 约翰尼斯·开普勒

key distribution 量子密钥

L

Lamb, Willis 威利斯·兰姆

Large Hadron Collider 大型强子对撞机

laser 激光或激光器

laser light pulses 激光脉冲

laser projector 激光投影仪

LASIK 激光辅助原位角膜磨削术

Leibniz, Gottfried Wilhelm 戈特弗里德·威廉·冯·莱布尼茨

lens 透镜

Light classical 经典光

light sources 光源

liquid crystal display 液晶显示器（LCD）

liquid crystals 液晶

lithography 光刻

M

magnetic materials 磁性材料

magnification 放大率

Maupertuis, Pierre Louis 皮埃尔·路易·莫佩尔蒂

Maxwell, James Clerk 詹姆斯·克拉克·麦克斯韦

metamaterials 超颖材料

microscope 显微镜

microwaves 微波

mirror 平面镜

mode-locked laser 锁模激光器

mode-locking 锁模法

modes 模式

molecules 分子

Muybridge, Eadweard 埃德沃德·迈布里奇

N

National Ignition Facility 美国国家点火装置

National Institute of Standards

and Technology

美国国家标准与技术研究院

National Physical Laboratory 英国国家物理实验室

Newton, Isaac 艾萨克·牛顿

no-cloning theorem 不可克隆理论

no-measurement theorem 不可测量理论

normal materials 普通材料

normal to surface 与表面垂直

O

Oersted, Hans Christian 汉斯·克里斯钦·奥斯特

Ohm, Georg 乔治·欧姆

optical 光学的

optical analogy 光学类比

optical cavity 光学腔

optical clockwork 光学钟表

optical fibres 光纤

optical telecommunications 光学通信

optical tweezers 光学镊子

optics 光学

P

Pendry, John 约翰·彭德里

photo-activated localizationmicroscopy
光激活定位显微镜

photoelectric effect 光电效应

photon 光子

Physikalisch-TechnischeBundesanstalt
德国联邦物理技术研究院

pixel 像素

Planck, Max 马克斯·普朗克

plasma 等离子体

Podolsky, Boris 鲍里斯·波多尔斯基

polarization 偏振

polarizer 偏振片

protein 蛋白质

proton 质子

Q

quanta 光子

quantum 量子光

quantum entanglement 量子纠缠

R

radio waves 无线电波

random number generators 量子随机数字生成器

ray 光线

reference wave 参考波

reflection 反射

refraction 折射

refractive index 折射率

relativity 相对论

Rosen, Nathan 内森·罗森

ruler 长度标准

Rutherford Appleton Laboratory 卢瑟福·阿普尔顿实验室

S

Schrödinger, Erwin 埃尔温·薛定谔

shift 频率改变

Smith, Adam 亚当·斯密

Snell, Willebrord 威理博·斯涅尔

space-time 时空

spectral line 光谱线

spectroscopy 光谱学

spectrum 光谱

spontaneous emission 自发辐射

squeezed 压缩光

standard quantum limit 标准量子极限

Stanford, Leland 利兰·斯坦福

stimulated emission 受激辐射

stimulated emission depletionmicroscopy
受激发射损耗显微技术

stroboscope 频闪仪

strontium 锶

super-resolution 超分辨率

synchrotron 同步加速器

T

Taylor, Geoffrey 杰弗里·泰勒

telescope 望远镜

time dilation 时间膨胀

transverse wave 横波

T-rays T 射线

U

ultraviolet 紫外线

V

vacuum 量子真空

vacuum fluctuations 真空波动

Veselago, Victor 维克托·韦谢拉戈

Volta, Allessandro 亚历山德罗·伏特

Voltaire 伏尔泰

W

warmth 温度

Watson, James 詹姆斯·沃森

Watts 瓦特

wave 波

wave function 波函数

wave guide 导波

wavefronts 波前

wavelength 波长

wave-particle duality 波粒二象性

Wilkins, Maurice 莫里斯·威尔金斯

X

X-ray Free Electron Laser X 射线自由电子激光器

X-rays X 射线

Y

Young, Thomas 托马斯·杨

Z

Zewail, Ahmed 艾哈迈德·泽维尔

To Kate, Alex, Nathaniel, and Clair

Contents

Preface and acknowledgements

1 What is light?

2 Light rays

3 Waves

4 Duality

5 Light matters

66 Light, space, and time

7 Lighting the frontiers

8 Quantum light

9 Twilight

Further reading

Index

Preface and acknowledgements

Light enables us to see things. This tautology is the starting point of a long and fascinating trail from which developed both extraordinary views of how the natural world behaves and the very tools and methods on which modern science is built-explanations that are commensurate with experiments.

Light carries information about our surroundings, from distant stars and galaxies to the cells in our bodies to individual atoms and molecules. It is the basis of many technologies that enhance our quality of life: the Internet is powered by light; the most precise clocks in the world rely on light; the tiniest objects, from individual atoms, to live biological cells, can be observed and manipulated using light; images and displays are everywhere. Light reveals the full strangeness of the quantum world and inspires our imagination about the world. Yet it might surprise you to know that what light actually is was only really understood less than a hundred years ago, and even now we are ekeing out new insights from that understanding.

This book explores how people have come to our current view of what light is and what it does. It’s a great story, reaching back into the ancient world, with a global cast of contributors, from Euclid in Athens and Al-Hazen in Baghdad, conceiving the idea of light rays, to Ted Maiman in Los Angeles and Shuji Nakamura in Tokushima developing new lasers, by way of Joseph Fresnel in Paris and Thomas Young in London thinking about light waves, to James Clerk Maxwell in Aberdeen and Heinrich Hertz in Berlin developing from these ideas the concept of electromagnetic fields, that finally culminated in Albert Einstein in Bern and Paul Dirac in Cambridge explaining these apparently mutually incompatible facts by a radical new concept-the quantum field-that showed how it is possible to be both a particle and a wave at the same time.

At each step, new understanding (for example, of refraction) has led to new applications (such as eyeglasses for correcting vision): the path from discovery to technology is often very short when light is involved. The impact of light on the modern world is immense, and often unrealized. For this reason, 2015 has been designated by the United Nations as the International Year of Light: a celebration of light and what is made possible by it.

I should like to record my thanks to Alex Walmsley and Latha Menon for helpful comments on drafts of this book, and to many colleagues for responding to specific technical questions as well as those who kindly provided illustrations for the figures. Errors and statements that go beyond the exhortation, attributed to Einstein, to make things as simple as possible, but not simpler, are due to me.

INTERNATIONAL YEAR OF LIGHT 2015

Chapter 1 What is light?

Light enables us to see the world around us. It provides the means by which our sense of sight gleans the most direct information about the physical arrangement of the world and how it is changing. Indeed, the capacity of light to carry and convey information is perhaps its most important, and remarkable, characteristic.

Seeing is believing

Sight enables us to locate ourselves in our surroundings, defining things outside ourselves that allow us to construct a true picture of the world. And sight inspires the imagination beyond the physical sensation of vision itself. George Richmond’s painting,

The Creation of Light, shown in Figure 1, illustrates the central place light has in our psyche. Indeed, words deriving from the idea of light-insight, illumination, clarity, for example-pertain to human, as well as physical, qualities. In fact, Latin has two words to describe light, lux and lumen, denoting both the material and the metaphysical aspects of light. It is the former with which this book is primarily concerned. The intertwining of the physical and the poetic has made light a metaphor for thinking about the world, in philosophy, theology, psychology, art, and literature. Because it is something of which almost everyone has direct experience, the physical basis of light and how it facilitates this powerful sense has made it an object of study for philosophers and more recently scientists, for centuries.

1. The Creation of Light by George Richmond.

Light gives life. Literally, light plays a vital role in the biological and chemical processes that underpin our and our planet's existence. Figuratively, light frames our perception of our surroundings. Our common everyday experiences illustrate the central importance of light in this regard. Of course we use it for illuminating our environment, either naturally, by the Sun or Moon, or artificially. Most common light sources use electricity, but on occasion we still use chemical reactions to generate light; burning candles, for example. The diferent character of the illumination has an efect on how we perceive our surroundings: it sets a ‘mood’ for the physical space.

Light has a very fundamental role in making possible life itself. The primary source of energy for the Earth is ultimately the Sun. And the means by which energy is transmitted from the Sun is light, both the visible components we can see, as well as some invisible ones we cannot see directly. Think, for example, of lying on a beach or sitting out in the garden in the sunshine: the warmth we feel is a consequence of some of the ‘invisible light’ radiating from the Sun. This is just one example of the physiological efects of light.

But at the very core of our planet’s ability to sustain life is an awesome biochemical process that converts ‘waste’ moleculescarbon dioxide-into ‘useful’ ones-oxygen, using sunlight as a source of energy. The reverse process, conversion of oxygen into carbon dioxide, occurs during respiration, as well as from the things we burn to power our everyday world.

The Sun’s light has over the course of millions of years enabled the formation of the current biosphere and the geology that provides other sources of energy. Neither coal nor oil could have been made without energy from the Sun. And our use of these resources is changing the way in which light from the Sun afects our planet. Some of the invisible light from the Sun-ultraviolet light-is still absorbed by the Earth and its atmosphere. But the other invisible part-infrared light-is reflected back by atmospheric gases. By the same mechanism, infrared radiation is trapped on the planet, contributing to increased planetary surface temperature.

Light enables communication

Pictures have been part of human culture since the beginning of the species. The impact of images on how we conceive of the world, and how we make sense of our place in it, is immeasurable. Optical technology has contributed to this in ways that are utterly transformative. For instance the ability to capture images easily and rapidly, by means of film-based and digital photography, allows us to record places, people, and things as reports that can be widely distributed (nowadays by an optically enabled Internet) and which have lasting impact: images of leaders and workers, awe-inspiring scenes of the natural world, and horrifying scenes of war. These can bind or fragment people in unexpected ways: calling populations to action, inciting acts of compassion, and giving deeper insight into shared experience. Recall the astonishing sense of wonder the sight of man’s first steps on the Moon (see Figure 2) invoked. The ability to capture moving images adds a completely new dimension by enabling new narrative and documentary capabilities. Can you imagine life without television or movies, without video?

Nowadays, the generation and transmission of images is so prevalent we hardly think of it. We use self-luminous displays every day: televisions, computers, tablets, even smartphones. All of these bring information to you and receive it from you using light as a medium. Almost all long-distance telecommunications travel on light beams, guided along thin strands of glass called optical fibres. This is the basis of fibre optical broadband services that link our homes to the Internet. Even inside computers and televisions light plays a role. For instance, the music, video, or images that are locked in a CD or DVD are accessed using light. A tiny moving head based on a miniature laser ‘reads’ the disc and converts the information coded on it into electrical signals that can then be sent to the display screen. All our surfing, downloading, and emailing activity now requires such immense information capacity that light is the only feasible medium for conveying it.

2. Neil Armstrong’s photograph of Edwin Aldrin walking on the Moon.

Transportation in the modern world uses light as the means by which we signal and regulate our movements. From streetlights in towns, to landing lights on aircraft, light is an essential part of navigation. And it even plays a role in maintaining our vehicles. For instance, lasers are used to align the wheels of a car, and light-enabled distribution of ignition power to drive an internal combustion engine is not uncommon.

In many, many ways, light carries the energy and information that makes modern life possible.

Optics

The field of enquiry that constitutes the study of light is called optics. Optics is among the oldest of the sciences, and its historical development forms one of the most important paths in the emergence of modern science. Ideas arising in optics have stimulated new ways of thinking for very disparate fields, such as the mechanics of motion of atoms and molecules. And technologies enabled by deeper understanding of light have been central in unlocking other secrets of the natural world. Galileo’s telescope designs, for instance, were critical in his observation of the moons of Jupiter, which was a vital step in moving towards a view of the solar system in which planets moved around the Sun. This, in turn, was important in developing the laws of gravity that govern planetary motion.

The origins of optics lie in the work of the Greek philosophers of the 4th century bce, and the field has continued to flourish for the past two millennia. It is perhaps surprising that we can still discover new things about light after such a long period of attention by many clever people. Yet optics remains at the forefront of current science: more than ten Nobel Prizes in the past twenty years have been awarded for research in which light has played a central role, from controlling and measuring the motion of atoms and molecules, at unimaginably low temperatures and on timescales of breathtaking brevity, to improving the precision of clocks a thousandfold, to enabling us to look inside living cells and watch what happens as they change.

What is light?

A good place to start is with some of the things commonly associated with light: brightness, intensity, colour, and warmth.

These are all tangible properties that suggest light is a physical entity. But what, exactly, is it?

We may consider what it means for light to be bright by taking a particular source of light-a household light bulb. These come in various sizes, but all have powers of several tens of Watts (the unit in which power is measured, labelled W, and signifying the energy consumed per second of operation). A 50 W light bulb gives suicient light by which to see things inside a house. Car headlights are typically of slightly greater power, approximately between 60 W and 100 W. The floodlights at a football ground are of much larger power, up to several thousand Watts. I will discuss later exactly how these diferent sources generate light, but these powers will give a sense of the brightness of the corresponding lighting. Of course, one of the brightest sources is the Sun. It has a massive power output, more than 1025 W (1 with 25 zeroes after it), which makes it impossible to look at directly even though it is a very great distance away.

This brings us to the next concept associated with how bright a light is. Light of the kind discussed above looks dimmer the more distant it is. So power alone is not the only criterion determining brightness. It is related in some way to the fraction of the power that we can receive from the light source. For example, a laser pointer typically has much, much lower power output than a light bulb, often only a few thousandths of a Watt (10-2
W or 10 mW). Yet it appears very bright when it is pointed at a screen.

What is important here is the intensity of the light generated by the source-the power per unit area of the receiver. (This is more properly the irradiance, but intensity is perhaps a more familiar term.) The intensity of a light source is related to the ability to concentrate the light. A laser pointer appears to be very bright because its light beam is concentrated on a small spot on the screen, whereas the Sun’s light is difused over a very wide area.

Therefore, although the Sun has a very great power output, the light it produces is not as intense as that of a laser pointer.

The underlying property that describes our ability to concentrate light is called the source coherence. This is related to the source’s propensity to send light in a particular direction. For instance, both the Sun and a light bulb radiate light into all directions-the Sun can be seen from every place on Earth, and a light bulb from wherever you stand in a room. But a laser pointer only puts out light in a single direction-that in which you point it. So you cannot see the laser beam unless you look at the surface on which it is incident. Because of the property that its beam has a well-defined direction, the laser pointer is said to be a coherent light source, whereas the light bulb is an incoherent light source.

Another defining characteristic of light, perhaps its most evident property, is colour. The rainbow embodies the fundamental idea of a spectrum of colours-a palette emerging from the conjunction of rain and sunlight-from blue at one end to red at the other. A central strand in the development of theories of light has been the development of models of colour vision. Colour is intimately tied to perception, as well as to physics. An illustration of this is found in the experiments on the nature of colours undertaken by Sir Isaac Newton (Figure 3), a dominant figure of early 18th-century science, and whose book Opticks defined the view of light for two centuries, and by Johann Wolfgang von Goethe (Figure 3), a dominant figure of late 18th-century literature, who incorporated scientific ideas in his writings, but nonetheless believed Newton to be profoundly wrong about the nature of light.

The first part of Newton’s famous experiment (similar to ones undertaken by Descartes and others previously to him) was to allow a small beam of light from the Sun, defined by a hole in a dark screen, to pass through a prism, and thence to fall upon a screen. The familiar rainbow colours emerge. Goethe was fascinated by this efect, and borrowed some prisms from a local aristocrat with which to experiment for himself. He concluded quickly that Newton’s experiment was wrong-in the sense that his claim of the universality of colour dissection from white light was not true. Goethe had himself discovered a very diferent set of colours.

3. Isaac Newton (left), Johann Wolfgang von Goethe (middle), and Rosalind Franklin (right).

The experiment Goethe undertook was to look through the prism at the mullion of a window. That is, he looked at a dark line against a bright background, the very opposite of what Newton had done. What he saw was a very diferent spectrum from Newton. Not the red, green, and blue of the Newtonian spectrum but rather a new palette of cyan, magenta, and yellow; the so-called complementary colours of the Newtonian spectrum. Combining Newton’s colours produces a white image-combining Goethe’s produces a black one.

Goethe espoused the idea that colours are the things perceived; Newton defined them as intrinsic properties of light. They were both right. Nowadays we are content to separate the physical attribute of colour from its physiological efects, the sensation of colour. We each react diferently to colours-indeed, coloured light can even be used as a therapy. From an artistic point of view, the interpretation that our consciousness realizes from the sensations associated with light of a particular colour is a critical matter-perception is vitally important. Yet from a physical point of view there is an underlying property that we can assign to the label ‘colour’ unambiguously: its frequency-at least until we get into the realm of quantum light.

The reach of light extends beyond the visible spectrum, at the blue end into the invisible realm of the ultraviolet and the extreme ultraviolet to X-rays and γ-rays. At the other lie the infrared, microwaves, radio waves, and eventually T-rays (Figure 4). To see these, we need diferent instruments than our eyes alone. Nonetheless, we know that light of these colours exists. For instance, the warmth of the Sun is due to infrared light that is absorbed by our skin. At lower frequencies microwaves are used for cellular phone communications as well as for cooking, by heating the water in the food being prepared. The invisible colours at shorter wavelengths are also familiar. Sunburn is caused by ultraviolet light, while X-rays are used routinely in medical imaging.

X-rays are also used in many non-medical applications. For example, the patterns made when X-rays scatter from a regular arrangement of atoms in a molecule or solid enable that arrangement to be determined, even though the atoms are spaced very, very close together, at distances more than 10,000 times smaller than a human hair. X-ray difraction images can reveal the very structure of the molecule or solid, with profound implications. Perhaps the most famous example is the structure of DNA molecules identified by James Watson and Francis Crick more than half a century ago, based on X-ray images taken by Rosalind Franklin (Figure 3) and Maurice Wilkins. Knowing how molecules replicate revolutionized biomedicine.

These applications are indicative of the importance of light-in its broadest sense-in making possible our modern world, and impact our ability to enjoy it to its full. They rest on the fundamental work of a number of scientists in the 19th century-Michael Faraday,

4. The spectrum of electromagnetic waves.

Hans Christian Oersted, André-Marie Ampère, Charles Augustin de Coulomb, Alessandro Volta, Georg Ohm, James Clerk Maxwell, and Heinrich Hertz. That there exists a connection between visible light and other apparently disjoint things like microwaves and X-rays is remarkable, and it was the triumph of scientific enquiry by these men and others who made and identified these connections.

The gamut of colours, or spectrum, provides a tool for art and science. Whereas a painter or artist explores ways in which colours themselves are juxtaposed or combined, a spectroscopist explores ways in which matter responds to diferent colours. For example, in the early 19th century Joseph von Fraunhofer determined some of the types of atoms that are present in the Sun by looking carefully at the particular colours of light that the Sun emits. He noticed that characteristic colours were missing from the Sun’s spectrum and noted that these colours were ‘fingerprints’ for particular atoms. The study of spectra is the domain of spectroscopy, which uses light to identify diferent atoms or molecules. It is a vital research activity today, with impact in many areas from health monitoring to remote sensing of the atmosphere for pollutants.

Apart from these familiar properties of light, there is one further property I want to point out. It, too, is something that we all know about from our everyday lives, though perhaps in a less explicit way than we experience the other properties of light. It is polarization.

If you have watched a 3D movie, then you have seen this property being exploited. Watching such a movie requires you to wear special spectacles with cardboard or plastic frames that have pieces of plastic for the ‘lenses’. If you take two pairs of these spectacles and slide the left lens of one over the right lens of the other, then look through them at a light bulb, you will see a very,very dim image of the bulb. Alternatively if you rotate one of the spectacles through 90 degrees with respect to the other and put either the two left lenses or the two right lenses over one another you will see something very similar-almost no transmission of light through the pair of glasses.

This can be explained by assigning a property of ‘orientation’ to the light. Most common light sources emit light without a preferred orientation. When you look at a light through these spectacles it will appear dimmer, indicating that they have selected a particular orientation. The left lens allows one orientation to pass, the right lens an orientation that is at right angles to the first. That’s why when you put a second lens oriented at right angles to the first, nothing will be transmitted through it: the light passing through the first lens has the ‘wrong’ orientation to pass through the second. This characteristic of orientation is called polarization. It took a great deal of careful exploration to come up with and to understand the idea of polarization, but it is an important feature for technologies based on light, and indeed for understanding what light actually is.

These physical characteristics of intensity, colour, and polarization are what enables light to be used to discern, to measure, and to control properties of material substances, and therefore to form the basis of a host of tools for studying and manipulating matter and even small objects. In the examples above, light almost always plays the role of an information carrier. Whether it is conveying an image or a spectrum or a phone conversation, it acts as a messenger. But light can also be used in an active way. For instance, the heating properties of light can be used to cut metal and other materials very precisely. Thick plates of metal, up to a centimetre or so, can be machined using high-power lasers more rapidly, with a higher quality finish and less waste, than using a saw. And light is used in medicine in various ways, from correcting vision through laser surgery to activating drugs for anti-cancer therapies.

Light enables us to view the natural world at every time scale and distance scale imaginable; from the earliest moments of the universe to the unimaginably fast motion of electrons in atoms and molecules; from the large-scale arrangement of clusters of galaxies across the universe to the atomic arrangement of carbon atoms in graphene. It provides us with insight into the very foundations of the natural world, from the weirdness of quantum physics to the structure of DNA molecules.

The story of optics is one in which new discoveries about light have enabled new technologies that have, in turn, given rise to new discoveries across many fields of science. At each stage, from the invention of eyeglasses to the most precise atomic clocks, to modern technologies for imaging, measuring, and communications, light has given new applications that have revolutionized how we live. This cycle of discovery and innovation makes the study of light a vibrant discipline, even as it is among the most venerable. How we came to a modern understanding of what light is, and therefore how we could use it, both for new understanding of the world and for new capabilities that change the world, is the tale that forms the rest of the book.

Chapter 2 Light rays

Taking a selfie requires that the phone camera is pointed towards you. It’s obvious that this is necessary if you are to be in the picture. But this simple fact indicates something about the nature of light: to see an image of an object, there has to be a straight line between the object (in this case you) and the camera lens. This is usually called the ‘line of sight’. Thus light is something that propagates in a straight line from the object to the viewer.Indeed, this is what we might expect from our knowledge of certain types of light source. Eye-catching visual efects at concerts are generated using lasers, illuminating the stage and the performers with coloured light beams. Laser pointers are commonly used at talks or lectures to emphasize images or words on a screen. The beam produced by these coherent light sources is highly focused, hardly diverging at all even across a big hall. It goes in a straight line-you point the device in the direction where you want the light to go, and it does so.

Because sunlight does not obviously exhibit this characteristic, it required some thinking to determine that the propagation of light in a straight line was exactly what was needed to understand why distant objects appeared to be smaller than nearer ones, even when it was known that they were, in fact, exactly the same size physically.

5. Euclid’s construction of rays showing why objects of the same size look smaller when they are further away.

The insight that the concept of straight-line propagation could explain this efect is attributed to Euclid, working in Greece in around 300 bce. His idea, from one of the earliest books on optics, is illustrated in Figure 5. Imagine two lines-let’s call them rays-one connecting the top of the object (a pillar in this case) to the observer’s eye, and one connecting the bottom of the object to the eye. The angle between these is related to the apparent size of the image of this object that we perceive. A more distant pillar, the same physical size as the first, produces two rays whose angle of intersection at the observer is smaller-hence the pillar appears smaller. This is what we call perspective in the image.

What is the stuf that traverses the rays? Euclid (building on earlier ideas) thought that it was particles sent out from the eye itself (from an imaginary internal fire) that illuminate the object and are reflected back to the observer. But this suggests that we would be able to see things whether or not it was dark outside. Nonetheless, the idea of stuf moving along a trajectory between object and observer remained a powerful concept.

It was modified by Al-Hazen in the 11th century to a form that we now use routinely: objects are illuminated by rays from the Sun (the external fire) and are scattered towards the observer. There are several stories about how he came to this idea-including doing an experiment when he looked directly at the Sun, and determined that the painful sensation he experienced would be there all the time if the ‘internal fire’ were burning all the time. Thus, he argued, the source of the light necessary to generate the image was external.

Let us, for the sake of this argument, assume that what moves along these rays are particles of light: call them photons. The brightness of the beam is related to the number of photons traversing the ray in one second. In order to understand how an image of an object is formed, we’ll need to consider what happens when one of these photons is reflected of a mirrored surface, as well as what happens at a lens. This will lead to the ‘laws of optics’ that are used for designing very complex optical instruments such as surgical microscopes, and catheters for ‘keyhole’ surgery, as well as massive optical telescopes placed in orbit above the Earth for observing distant galaxies. The impact of these instruments on our life and our understanding of the world is immense.

What sort of properties do these particles of light possess? The usual sorts of attributes assigned to a particle are its position, its direction of travel, and its speed. For now, assume that it moves at the ‘speed of light’, without going into detail about what that actually is. The position of a photon might then specify the starting position of the ‘ray’ and the direction of the photon’s motion would be the direction of the ray. The photon heads of from its starting point in this direction at the speed of light until it encounters the surface of the object.

Relection

When it hits the object, the light is reflected. What happens is that the photon ‘bounces’ of the surface, changing its direction, but not its position on the surface. The situation is shown in Figure 6. The manner in which the direction is changed is specified by the ‘law of reflection’, discovered by Hero of Alexandria in the 1st century. It states that the angle of incidence (that is, the angle between the incoming ray direction and the direction perpendicular to the surface at the point of incidence) is equal to the angle of reflection (that is, the angle between the outgoing ray direction and the direction perpendicular to the surface at the point of incidence). There are some surprising consequences of this conceptually simple and yet extremely powerful law.

6. Rays of light reflecting of a. aflat mirror and b. and c. a curved mirror.

The apparent left—right inversion associated with reflections follows from this idea. If you hold up your watch to a mirror and look at its reflection, you’ll see that its second hand is moving in an anticlockwise direction, and that when you move your right hand, your doppelg
nger moves his or her left hand. This change of ‘handedness’ is the hallmark of the image through the looking glass-the world reflected in a mirror is in that sense really topsy-turvy.

This can be explained entirely by Hero’s law of reflection. Figure 7 shows how a mirror generates a reflection with opposite handedness. The clockwise-pointing arrow is the object. Rays from each point on the arrow reflect of the mirror and are rearranged so that the arrow seen in the mirror is pointing anticlockwise. You can use the same construction to show that a left-pointing arrow is seen in the mirror as a right-pointing arrow and vice versa, but an up-pointing arrow remains pointing up, and a down-pointing arrow points down in the reflection.

Imaging using relectio

If, instead of looking at your opposite-handed self in a flat bathroom mirror, you see your reflection in a polished spoon, then you see a distorted form of your image: magnified features on curved backgrounds. The concave front surface of the spoon magnifies the object and the convex back surface demagnifies it.

7. The change of handedness of objects reflected in a mirror.

Why is this? Since the formation of images is perhaps the most important application of optical instruments-ranging from contact lenses for vision correction to space telescopes for scientific discovery-it’s worth understanding exactly how this happens.

Up to now, I‘ve considered only a single ray of light from one point on the object. In fact, rays usually scatter in all directions from each object point. Consider a ‘bundle’ of such rays all coming from a single point on the object, forming a cone around the original ray. This cone of rays diverges as it moves away from the object, as shown in Figure 8. The rays hit the curved mirror surface at diferent points and therefore also at diferent angles of incidence. Thus they reflect in diferent directions, each one still satisfying Hero’s law of reflection.

8. Image formation by a ray bundle using a curved mirror. The rays from one point on the object meet at one point in the image.

In fact they now form a converging cone, and eventually all meet at a single point. This is the ‘image’ point of the original object point.

An image as we normally consider it is made up of multiple such image points arising from diferent object points. The size of the image is determined by the distance of the object from the mirror and the focusing power of the mirror, specified by the radius of curvature of surface (e.g. a more concave mirror has a smaller radius of surface curvature). The image can be bigger than the object when the object is closer to the mirror than the image. The ratio of image to object size is called the magnification.

The image-magnifying feature of a curved mirror was used by Newton to design a telescope, shown in Figure 9. His design has a remarkable property: it forms images of distant objects that are the same size for every colour (said to be free from ‘chromatic aberration’). Newton cleverly used the property that the angle of a reflected ray for a fixed angle of the incident ray is the same no matter what the colour of the light. The image of each colour is therefore formed in the same place-all the colours register perfectly, guaranteed by physics.

9. Newton’s reflecting telescope enabled images without chromatic aberration.

Refraction

Newton invented this instrument because the telescopes used by contemporary pioneers such as Galileo Galilei and Johannes Kepler sufered seriously from chromatic aberration. The images formed by their telescopes always had a blurred coloured halo around the edge of the object. The reason for this is that they were designed using a diferent property of light rays-refraction: the phenomenon that light rays bend when they go from one transparent medium to another.

It is the refraction of light that produces the ‘kink’ observed in a pencil partially immersed in a bowl of water. This is described by the law of refraction, commonly known as Snell’s law, after Dutchman Willebrord Snell, an early 17th-century proponent. This law says that the angle the exiting ray makes with a line perpendicular to the surface is related to the angle of the incoming ray by the properties of the two media that form the interface-in our example the surface of the water. This is illustrated in Figure 10.The particular property of the media that is relevant here is the ‘refractive index’. The refractive index can be thought of as being a measure of the optical ‘stifness’ of the medium as experienced by a light ray. So light travels more slowly in a medium with a larger refractive index because the molecules of the medium are slightly more resistant to having their atoms and electrons moved by the light. It is like running in a pool of water. If the depth is very small, your legs can move easily and you can run fast. If the water is up to your knees, it’s harder, because you have to work against the resistance of the water.In fact, the law of refraction can be derived from this analogy. Pierre de Fermat showed that when light goes from a point in one medium to a point in another medium, it seeks a ray that traverses a shorter time in the medium with high refractive index and a longer time in the medium with a lower refractive index. This requires the light ray to bend at this interface between the two media, and Fermat’s principle turns out to be entirely the same as Snell’s law.

10. Refraction of a ray at the interface between air and water.

Imaging using lenses

Now, just as a curved reflecting surface can form an image of an object, so can a curved transparent surface. How this happens is shown in Figure 11. A bundle of rays from a point on the object are brought to focus at the image. Notice the shape that does this-it has the same cross section as a lentil. This is the origin of the word ‘lens’.

Lenses are ubiquitous in image-forming devices, from your eyes to mobile phone cameras to surgical microscopes. Imaging instruments have two components: the lens itself, and a light detector, which converts the light into, typically, an electrical signal. In the case of your eyes, this is the retina, whereas for the mobile phone it is an array of minute pieces of silicon that form solid-state light sensors.

11. Image formation by a ray bundle using a lens.

The lenses in each of these devices are diferent, of course, but the basic principle is the same for each. In every case the location of the lens with respect to the detector is a key design parameter, as is the focal length of the lens which quantifies its ‘ray-bending’ power. The focal length is set by the curvature of the surfaces of the lens and its thickness. More strongly curved surfaces and thicker materials are used to make lenses with short focal lengths, and these are used usually in instruments where a high magnification is needed, such as a microscope.

Because the refractive index of the lens material usually depends on the colour of light, rays of diferent colours are bent by diferent amounts at the surface, leading to a focus for each colour occurring in a diferent position. This gives an image that has ‘haloes’ of diferent colour around it. For example, only one colour may be properly in focus at a particular detector plane; the others will be out of focus, and form the halo. Whether this chromatic aberration is an important efect or not depends on the particular application.

One of the most familiar, and indeed most important image-forming instruments of this type is the eye. It consists of a front-refracting surface-the cornea-and an adjustable lens, which changes shape as you focus on things at diferent distances. These elements form images on the retina at the back of the eye.

Historically, the formation of images by the eye was of great interest, since an experiment by Descartes (see Figure 12) showed that the image of an upright object was upside down. Of course,we don’t perceive the object in this way, so it was clear that the brain undertakes some remarkable processing between the raw retinal signals and the perception of the external world.

Optical instruments

As many of us are all too aware, the ability of the eye to form high-quality images (sharp, undistorted, and in colour) can degrade as we age. One of the earliest applications of optical instruments was developed as an aid to sight under such circumstances.Eyeglasses were perhaps the first optical technology, purportedly invented by Roger Bacon—the ‘mad friar’ of Oxford—in the13th century.

The corrective elements are often simple lenses, placed either in a frame at some distance (a few millimetres) from the cornea(the front surface of the eyeball), or ‘contact lenses’ placed,as the name suggests, in contact with the cornea. In both cases the imaging system is compound, that is, it consists of several elements—the external lens, the cornea and the internal ocular lens. This functional form provides the necessary degrees of freedom to correct most kinds of vision by enabling the external lens to compensate for the imperfections of the internal lens.This can also be done by directly altering the shape of the front surface of the eye by laser surgery. One approach, laser-assisted in situ keratomileusis (LASIK), uses the laser to ablate part of the surface of the cornea. This changes its curvature, thereby altering its focusing power, and thus the image-forming capabilities of the eye.

Many other image-forming instruments work on very similar principles to the eye. The camera of a mobile phone, for instance,has a lens near the surface of the phone, and a silicon-based photodetector array inside the device. The mobile phone lens is often very small, and yet must provide images of sufficient quality that they are intelligible, and thus make sense when they are posted on Facebook. This requires that both the detector array and the imaging system are adequate to the task of producing a high-quality image. The quality of the image depends on two things—the size and the number of detectors in the array, and the ability of the optical system to create a sharp,undistorted image with all colours properly registered. That is,an image free from ‘aberrations’.

12. Descartes’ experiment to show the image formed by an eye is upside down.

The specification of the number of ‘pixels’ of the detector array is often used as a proxy for the quality of the image. A 24 megapixel camera (one in which the detector array contains 24 million sensors) is often considered better than an 8 megapixel one. A pixel can be thought of as the size of the image of a point object.If it is possible to resolve only a small number of points—because there are only a few elements in the detector—then it is hard to tell much about the object. The more pixels, then, the better. But only if the imaging system can produce a point image that is smaller than one detector element.

Limits to imaging

In the 19th century, the German scientist Ernst Abbe devised a simple rule for the minimum size of any image that was applicable to all imaging systems then known. Abbe’s criterion says that the size (S) of the image of a point object is proportional to the wavelength (λ) of the light illuminating the object multiplied by the focal length (f) of the lens and divided by the lens diameter (D):

S= 1.22 S × λf/D.

Thus, lenses with a big diameter and a short focal length will produce the tiniest images of point-like objects. It’s easy to see that about the best you can do in any lens system you could actually make is an image size of approximately one wavelength.This is the fundamental limit to the pixel size for lenses used in most optical instruments, such as cameras and binoculars.

Designing and building imaging systems that can deliver high-quality images has been at the heart of many important applications of optics. Microscopes, for example, are used in applications from biological research to surgery. The earliest microscopes used very simple lenses—small, nearly spherical polished glass shapes that provided early experimenters like Robert Hooke in the 17th century with the means to explore new features of the natural world, too small to be seen by the unaided eye. His drawing of a flea, shown in Figure 13, was a revelation of the power of technology to enable new discovery.

Modern research microscopes are much more sophisticated devices.They consist of a multi-element compound lens that can form images with pixels very close to the wavelength of the illumination light—just at the Abbe limit. Figure 13 also shows an example of what is possible using a modern imaging microscope. It is a composite image of the nervous system of a fruit-fly larva, about to hatch, made by viewing light-emitting proteins located in the cells.

Abbe’s criterion applies to all optical systems in which the image brightness is proportional to the brightness of the object. These are called linear systems. But it’s possible to go beyond this limit by means of nonlinear systems, where the image brightness is proportional to the square or even more complicated function of the object brightness. A fuller explanation of these effects requires knowing a bit more about the wave model of light, which is the subject of Chapter 3.

Optical imaging systems of similar properties and complexity are used in another imaging application—the making of computer chips. Individual electronic circuit elements are extremely tiny.

13. Hooke’s diagram of a flea observed by means of an earlymicroscope (top), and the nervous system of a fruit-fly larva (bottom)taken with a modern fluorescence microscope.

A wire connecting two transistors on a chip may have a diameter of only 250 nanometres (nm). (A nanometre is one billionth of a metre,or 10-9
m. For comparison, a human hair is approximately 10,000nm in diameter.) The complex array of devices and connections is laid out on a silicon wafer by means of a process called lithography.Essentially, the chip layout is drawn at a large enough scale to be visible to the human designers, then a demagnified image is projected on to the chip. The image is etched into a surface coating on the wafer, and a series of chemical processes then maps the image into real devices. The imaging system must be able to provide extraordinary resolution in the image—with pixel sizes of the order of the line size of the device. Maintaining this resolution over an entire wafer is a real challenge, requiring many lens elements properly designed to reduce all aberrations to an absolute minimum.An example of such a lens is shown in cross section in Figure 14,showing the multiplicity of lens elements and ray paths.

At the other extreme, both ground- and space-based telescopes for astronomy are very large instruments with relatively simple optical imaging components, often consisting of just one curved reflecting surface and a simple ‘eyepiece’ to adjust the rays so as to make best use of the available detectors. The distinctive feature of these imaging systems is their size. The most distant stars are very, very faint. Hardly any of their light makes it to the Earth. It is therefore very important to collect as much of it as possible. This requires a very big lens or mirror—several tens of metres or more in diameter. It is not practical to build lenses of this size, hence the ubiquity of mirrors in large telescopes.It is also necessary to look at distant stars for a long time in order to gather enough light to form an image. And this leads to another problem for ground-based telescopes: the atmosphere is not static. It changes in density with wind, temperature, and moisture. These fluctuations tend to make rays deviate from their course from star to telescope, causing the star to ‘twinkle’as its light is deflected randomly onto and off the detector due to atmospheric turbulence.

One way to deal with this problem is to put the telescope outside the atmosphere, in space. The Hubble Space Telescope is an example. It produced spectacular images of distant stars, galaxies,and nebulae, showing extraordinary structures and movement in the far reaches of space. However, optical engineers have in the past two decades devised a clever way to deal with this problem for ground-based telescopes operating with visible light. What they do is to make the telescope mirrors in segments, the tilt of each segment being adjustable. Thus it is possible to ‘steer’ the rays hitting different parts of the telescope mirror so that they all hit the detector. If you can measure the deviation that a ray experiences as it traverses the atmosphere, then you can configure the mirror to compensate for that deviation. And that’s what the engineers do. They measure how light from a guide star—an artificial light source in the upper atmosphere—is distorted and use that information to adapt the tilt of the mirror’s segments.In this way images right at the Abbe limit can be produced.Space telescopes are still needed though, to probe the wavelength ranges, such as X-rays and UV, that are absorbed by the atmosphere, and several missions for new ones are planned by the North American Space Agency (NASA) and the European Space Agency (ESA).

14. Section of a lens used for photolithography of computer chips. It consists of more than twenty diferent lens elements, and produces images of 500 nm in size using light of less than half that wavelength.

Metamaterials and super lenses

For many years, optical scientists have been fascinated with the question of what makes a good optical system. Is there a lens that can form the perfect image of an object? This question has intrigued many great physicists, from James Clerk Maxwell in England in the19th century to Victor Veselago in the USSR in the 20th century.Veselago thought about materials that behave in strange ways—in which light bends in a way opposite to that predicted by Snell’s law.Snell’s law is based on the positive refractive indices that are found in common ‘normal’ materials. Veselago considered materials with a ‘negative’ refractive index. Such materials can be made up of tiny structures that are each less than a wavelength of light in size.This kind of special construction gives ‘metamaterials’ such unusual optical properties. In particular, refraction takes place at the interface between normal and metamaterials such that the light rays bend in the opposite direction with respect to the interface than between two normal materials.

The strange refractive indices of these materials can be engineered to bend light rays in all directions, allowing the incoming rays which would normally be scattered by the object to instead be guided around it. Indeed, British physicist Sir John Pendry showed that it is possible to build an invisibility cloak using these designer materials.

Another of the unusual properties metamaterials possess is the ability to make perfect images of objects that are very close to a slab of the metamaterial. Even a flat surface is sufficient to make a lens,which makes them suited to viewing very tiny objects—so-called nanostructures, because they have sizes of the order of tens of nanometres. This is the 21st-century version of Hooke’s technology,and will perhaps unleash a similarly fruitful era of discovery.

All of the imaging systems described in this chapter make two-dimensional renderings of objects. That’s normally the way we experience and think about images—as flat pictures. But what if it were possible to conceive of a system that could make three-dimensional images? Remarkably it is, but that requires a deeper view of light itself, which we will consider in Chapter 3.

Chapter 3 Waves

Chapter 2 explored the idea of light as consisting of fundamental particles, moving along well-defined trajectories. This ‘billiard ball’ model, in which a light beam is a collection of individual,compact, and well-localized bundles of energy, stands in contrast to the alternative view, which is that light is a wave. This conception of light has been pursued in parallel with the particle view of light, although it took many years of discussion and experimentation for the wave picture to become fully accepted.

Unexplained phenomena?

If you look, when the Sun is shining, at a pool of water on which is floating a thin layer of oil, you will see coloured margins that map out the contours of the oil layer. It was this observation that stimulated historical thinking about light as a wave motion.Newton was one of the first to describe this effect, which provided a challenge to his particle model of light. Newton needed to make severe contortions to his model to account for this observation.Across the Channel, Newton’s rival in optics and President of the Académie Fran
aise, Dutchman Christiaan Huygens, was able to explain this effect using a wave model of light. This turned out to be an altogether more elegant solution. So the ideas of wave and particle have been around simultaneously since the early days of the scientific study of light.

Other observations, such as those made by Francesco Grimaldi in the mid-17th century, gradually accrued evidence that did not fit with the particle model. Grimaldi saw that light rays deviated from straight lines when they passed through small apertures,such as a tiny hole in a screen. He noted that the light was diffused and that the edges of the beam were fringed with colour, especially pronounced for small objects such as a hair or a piece of gauze. He concluded that the striations seen when light was incident on a small or narrow object were evidence that the light had been bent from its original path as it passed the edges of these objects. If light really consisted of particles moving along straight rays, such solid objects would surely just cast a shadow, and not cause light particles to deviate into strange patterns.

Further, the problem well known to Newton and his contemporaries of the bizarre way in which light was refracted through certain materials, notably crystals such as calcite—a naturally occurring mineral—confounded explanation in terms of simple particles. An example of this behaviour is shown in Figure 15. The word LIGHT, written on a sheet of paper, is illuminated by a light bulb. Two pieces of calcite have been placed over each half of the writing. In the left half of Figure15(a), two images of the word appear, displaced with respect to each other. In the right half, the two images are displaced in the opposite direction. The lower image in the left half and the upper in the right are just as one would expect from ordinary refraction of light reflected from the paper, seen through the crystal. But the second set of images appears to arise as if from a different refractive index. By placing a polarizer over the crystal, as shown in Figure 15(b)and 15(c), it is possible to isolate images formed by two different orientations of polarized light. Each polarization experiences a different refractive index. This is the phenomenon of birefringence.

15. An illustration of birefringence. The image of the word LIGHT viewed through a pair of calcite crystals, using a. unpolarized light, b. vertically polarized light, and c. horizontally polarized light.

These observations all pointed to features of light that demanded explanation. They are known respectively as interference,diffraction, and polarization. We will explore these phenomena in this chapter, developing a picture of light as wave motion.

Wavelength and wave frequency

What are the characteristics of wave motion? Waves are a form of undulation associated with a medium, for example water waves on the surface of a pond. These waves consist of the up-and-down motion of water molecules at the interface between the liquid and the air. The highest and lowest points of this motion become the peaks and troughs of the water wave, while the wave itself moves across the surface—that is, at right angles to the motion of the water molecules. For this reason it is called a transverse wave. Its speed depends on the depth of the water, among other things.

The circular surface waves that radiate away from the point at which a stone is cast into the water, as shown in Figure 16a, are a familiar effect. The distance between successive peaks is called the wavelength (Figure 16b), and the rate at which peaks hit the shore is called the frequency (Figure 16c). The product of these two quantities is the speed of the wave.

The puzzle for many centuries was what kind of undulations constituted light. It was assumed that some medium would need to exist in order to support a wave. And since the speed of light is so large, this would need to be a very stiff medium. But a stiff medium would surely make it difficult for other bodies to move through it. For instance, because we can see distant stars, there should surely be some medium to support the propagation of light between the Earth and the star. Since the Earth moves around the Sun, the planet would be continually swept by a ‘wind’as it travelled through such a medium. This enigmatic medium was called the ‘aether’, and it was not until the end of the19th century that it was finally discarded as a useful concept.

16. A circular wave on a water surface: a. contours of equal height, called wavefronts, b. wave height vs distance from centre at a particular instant, c. wave height vs time at a particular location.

So, what sort of wave is light? This was also finally answered in the19th century by James Clerk Maxwell, who showed that it is an oscillation of a new kind of entity: the electromagnetic field. This field is effectively a force that acts on electric charges and magnetic materials. For example, a cloth charged with static electricity will attract dust particles to it. A magnet will be attracted to the door of a refrigerator. In the latter case you can feel this force as you place the magnet close to the door: the magnet accelerates towards the door unless an opposing force is supplied.

In both cases, a force pulls one object to the other, so that at some distance away from the cloth the dust particle feels this force due to the electric field generated by the charges on the cloth. And similarly for the refrigerator door, due to the magnetic field generated by the magnet. In the early 19th century, Michael Faraday had shown the close connections between electric and magnetic fields. Maxwell brought them together, as the electromagnetic force field. It turns out that in the wave model,light can be considered as very high frequency oscillations of the electromagnetic field. One consequence of this idea is that moving electric charges can generate light waves. I’ll discuss this, and other methods for making light, in Chapter 5.

Interference

If two stones are dropped in the water next to one another, the resulting two sets of expanding circular waves collide. Some of the peaks are therefore higher, where the waves reinforce each other. But there are also lines of flat water, where there is no up-and-down movement of the water surface, even though the waves generated by both stones’ disturbance of the water are passing through all points along these lines. The location of such lines is shown in Figure 17, along with the wavefronts—the locus of points on the peaks of the waves emanating from each source.

17. a. Two interfering circular waves on a water surface. The dashed lines are contours of equal phase. b. Constructive interference between paths of equal length. c. Destructive interference between paths difering by half a wavelength.

This phenomenon is known as interference, and it arises from the addition of the amplitude of two waves when they meet. If the peaks of the two waves coincide, the resulting peak is twice the size, or amplitude, of either wave. The waves are said to be in phase, and the interference is constructive. This is shown in the middle diagram of Figure 17. If, however, the waves are exactly out of phase, so that the peaks of one coincide with the troughs of the other, then the resultant wave has an amplitude of zero: the waves have ‘cancelled’ one another or interfered destructively. This is shown in the bottom diagram of Figure 17. It is immediately clear that such a phenomenon could not happen with particles, for how could two particles cancel one another?

It was the observation of interference effects in a famous experiment by Thomas Young in 1803 that really put the wave picture of light as the leading candidate as an explanation of the nature of light. Young’s experiment was very simple, and very elegant. He took a candle as a light source, and placed it behind a screen in which there were two holes a very small distance apart. The light shining through these holes could be seen on a second screen some distance away. Now, if only a single hole was used—say by covering up the second—then the light made a single spot on the screen. When both holes were open, however,something marvellous happened—instead of just a spot of twice the brightness, the spot now had striations. These are generally nearly straight lines of zero intensity perpendicular to the line joining the centre of the two spots, as shown in cross-section in Figure 18 arising from the interference of the waves passing through the two holes. They are called ‘Young’s fringes’, and are one of the key pieces of evidence for light as a wave motion.

How does interference explain the coloured ‘fringes’ observed by Newton in reflections from two surfaces very close together? What is needed for interference to occur is two waves, the relative phase of which (that is, the relative positions of the peaks of the two waves) can be adjusted. In Newton’s experiment, interference occurs because a single incident beam of light is partially reflected at the two surfaces and thus split into two waves. If the distance between the two surfaces is equal to a single wavelength of the light, then the peaks of the two reflected waves coincide, and there is a bright fringe. If, however, the distance is just half of the wavelength, then the peak of one lines up with the trough of the second and there is a ‘dark fringe’ owing to destructive interference. Thus, when you look at the surface the bright and dark fringes map out the contours of the separation of the surface with a resolution of less than one wavelength. For green light, with a wavelength of approximately one-half of a millionth of a metre,or 500 nm, the separation can be determined to better than 250nm—a precision of about 1/40th of the diameter of a human hair.

18. Thomas Young’s experiment. The light from one slit produces asmooth intensity pattern. When both slits are open ‘fringes’ appear,characteristic of wave-like behaviour.

Of course, for a different wavelength the bright and dark fringes will occur in a different place, so that the surface shows fringes of colour when illuminated with white light. It is interference of light waves that causes the colours in a thin film of oil floating on water.

Interference transforms very small distances, on the order of the wavelength of light, into very big changes in light intensity—from no light to four times as bright as the individual constituent waves. Such changes in intensity are easy to detect or see, and thus interference is a very good way to measure small changes in displacement on the scale of the wavelength of light. Many optical sensors are based on interference effects.

Holography

Interference is also the means by which one can make true 3D images, that is, images that can be viewed from different angles and reveal different aspects of the object. These are different to the synthetic images in so-called 3D films, and are called holograms. Holograms are made by recording the full waveform of light scattered from an object. The sort of 2D images we’re used to from photography encode only the amplitude of the waves. The phase information is lost. This is because detectors only respond to amplitude, so there is no way in the sorts of images we have looked at previously to extract phase. Nonetheless, it is the phase of the wavefronts scattered from an object that encodes its shape.

What interference enables is the encoding of phase into intensity,so that photodetectors can register patterns in which the full amplitude and phase information of the object wave is recorded.The principle is shown in Figure 19. The wave scattered from the object interferes with a reference wave that has a well-known shape, often generated by a laser. The interference pattern is recorded on a detector or in light-sensitive materials: this is the hologram itself, invented by Denis Gabor in the middle part of the 20th century.

19. A hologram is constructed by recording the interference fringes between a reference beam of light and one scattered from the object.

Viewing the image is a little more complicated than with an ordinary photograph. First, a reference beam illuminates the hologram and some of its light is scattered from the patterns encoded in the material. These scattered beams have the remarkable property that they reproduce the beams scattered from the original object, so that as your eyes receive them, it appears that the object is reconstructed in front of you. Moving around the image reveals different aspects of the object, because the beams scattered from those different parts encode different information.

Holograms can also be computer generated and embossed in metals or other materials. The idea is that the surface shape mimics the interference pattern of the reference and object waves,so that raised parts correspond to bright fringes and low parts to dark fringes. Again, illuminating this with a reference wave causes scattered light to imitate the wavefronts of the chosen object.This kind of hologram is used as a security device, including on some banknotes (such as the UK ￡20 note, which has a strip of holographic images of the 18th century Scottish economist Adam Smith on it), because they are hard to make and require advanced engineering to copy.

Limits to imaging, redux

The wave picture of light also explains why we can’t see infinitesimally small objects using a microscope, just as Abbe realized. Very tiny things—down to about half of one micron (one millionth of a metre, or about half a wavelength of visible light)can be seen using an ordinary light microscope. Much more sophisticated methods are required to see even smaller things.The reason is that the wave nature of light puts a lower limit on the size of a spot of light.

I noted previously that when two light beams meet, they interfere to give regions of zero amplitude—dark fringes. The distance between these fringes is actually determined by the angle at which the two beams intersect. If the angle is very large, the fringe spacing is small; if the angle is small, the fringe spacing is larger.The smallest possible separation of the fringes is one wavelength,or about one micron for visible light.

Now, if this fringe pattern is recorded as a hologram, then when it is illuminated again with the reference beam two beams will emerge in the directions of the light beams that were used to record the interference pattern. In order to see such a fringe pattern with a microscope the lens must capture both of these beams to form an image of the fringes. If this didn’t happen, say because the lens could only capture one beam, then there would be no interference fringes in the image.

This is the physical basis of Abbe’s criterion that I introduced in Chapter 2: the maximum angle between two beams captured by the lens of an imaging system sets the minimum object size that can be resolved. It’s straightforward to see then that the best any lens system can do is to see object sizes of about the wavelength of the illumination. Thus conventional light microscopes can see very tiny objects, about fifty times smaller than a human hair,but not much smaller than this. They can be used to look at biological cells, but not the cell nuclei, for instance.

Super-resolution imaging

Optical scientists and engineers have found a number of very clever ways to get around the object size limits posed by conventional microscopes, so that they can see inside cells, or view objects that are more than one hundred times smaller than the wavelength of light. These instruments make use of new materials and processes, such as the ability to attach nanometre-scale particles to the objects you wish to see, or to insert molecules that emit light into cells. These emit light (they fluoresce) at a long wavelength when they are illuminated by a beam of light at shorter wavelengths. Since they are much smaller than the resolution of the microscope lens, the resulting image is a spot the size of which is entirely limited by the microscope optics, according to Abbe’s formula. But the exact centre of this image can be located very precisely by using a camera to take a long look at the fluorescence of the attached nanoparticles and determine the position of the maximum intensity of the spot. This approach is called photo-activated localization microscopy, or PALM, and was invented by Eric Betzig in the US. It has revolutionized live cell imaging, allowing faster acquisition and precise depth resolution over a wide field of view.

Another method for measuring small structures in larger fluorescent objects is to shine a second annular beam on them that causes the objects illuminated by this beam to have their fluorescence extinguished, so that the remaining fluorescence can be located precisely by the same approach as described previously.This method is called stimulated emission depletion microscopy,or STED, and was invented by Stefan Hell in Germany. I will describe the process of stimulated emission in more detail in Chapter 5. These novel ways of making high-resolution images that enable intracellular structures to be imaged have had enormous impact in biology and medicine. Indeed the significance of this impact was recognized when the 2014 Nobel Prize in Chemistry was awarded to Betzig and Hell.

The process identified by Abbe works in reverse, too. When applied to the illumination of a sample by means of a microscope lens, it says that a light beam cannot be focused to a spot much smaller in diameter than a wavelength. Again, the tightness of the focus depends on the range of angles that the lens can produce on the side that faces towards the object: the broader the range of ray directions, the tighter the focus of the light.

The relationship between the range of angles between interfering beams and the size of the fringe structures turns out to be a very fundamental property of waves. This idea was quantified by Joseph Fourier, a French scientist of the early 19th century, who provided a detailed mathematical analysis of light wave propagation.Fourier’s theorem says in simple terms that the smaller you focus light, the broader the range of wave directions you need to achieve this spot.

Diffraction

This explains another feature of light beams—they gradually diverge as they propagate. This is because a beam of light, which by definition has a limited spatial extent, must be made up of waves that propagate in more than one direction. The idea can be tested using a laser pointer. The beam emitted by the laser itself is about 10 μm (ten millionths of a metre) or so in diameter. When it reaches the screen, it is about 1 mm (a thousandth of a metre)in diameter. And if it were sent further away, say to the Moon(approximately 400,000 km), then it would be about 24 km in diameter! This phenomenon is called diffraction.

Diffraction has some interesting applications in determining the shape and symmetry of structures. For instance, when you shine a beam of light on a screen with small holes in it, of diameter comparable to the wavelength of the light, the light diffracts through the apertures, spreading in inverse proportion to the size of the aperture. These diffracted beams interfere some distance away from the screen, and the resulting interference fringes—the so-called diffraction pattern—tell something about the size and relative location of the apertures. For instance, if they are in a regular array, then the diffraction pattern will also show regularities. The advantage of using such patterns to measure this type of object is that you don’t need to have very expensive or complicated lens systems or detectors close to the object—you simply look at the pattern when it has naturally expanded due to diffraction.

Now, imagine that the screen is replaced by a transparent solid material, say a crystallized protein structure. The ‘holes’ are replaced by the atoms in the protein molecule, which are very small indeed and are connected to one another by bonds in the molecule that are about one tenth of a billionth of a metre (0.1 nm) in length.If light with a wavelength of about this size illuminates such a structure, then the light will be diffracted. The actual structure of the molecule itself can be determined from the diffraction pattern.This is the basis of X-ray diffraction. As noted in Chapter 1, it was famously used in the effort to find the structure of DNA and is now a very common tool in biochemistry, used regularly for finding out the structure of new molecules that might be useful in developing drugs for example. It requires a bright X-ray light source, as well as a means to make crystals out of the molecules. Figure 20 shows a diffraction pattern from a crystal of bovine enterovirus.

20. An X-ray difraction pattern of a protein crystal taken using a modern synchrotron X-ray source.

It’s clear that if you want to transmit light over long distances,then diffraction could be a problem. It will cause the energy in the light beam to spread out, so that you would need a bigger and bigger optical system and detector to capture all of it. This is important for telecommunications, since nearly all of the information transmitted over long-distance communications links is encoded on to light beams.

Guided waves

The means to manage diffraction so that long-distance communication is possible is to use wave guides, such as optical fibres. A wave guide is a structure that has a carefully designed profile for the refractive index. For example, the index variation across an optical fibre is arranged so that the ‘core’, with a diameter of a few millionths of a metre, has a higher index than the surrounding ‘cladding’. The light is confined to this higher index core and moves along the fibre without diffracting,remaining the same size over very long distances—across the Atlantic Ocean via undersea cables, for example. This means of controlling light is the basis of a wide-ranging optical information infrastructure, from communications to sensors.

Polarization

The final important feature of the wave model is the characteristic of polarization. Recall that in transverse waves the undulations occur in a direction at right angles to the direction of propagation of the wave. Importantly there are two such directions for these undulations.

Consider waves on a string, for instance. If you move one end of a rope up and down rapidly, you can see the undulations move along the rope. A similar thing happens if you move the end left and right equally rapidly. Both vertical and horizontal oscillations are at right angles to the motion of the wave down the rope. The waves are said to be ‘transverse’.

Light waves behave similarly. For example, horizontally polarized light has an electric field that oscillates in a horizontal plane(relative to, say, an optical bench). Similarly, the field of a vertically polarized light beam oscillates in a vertical plane. (There are more complicated forms of polarization too, but these will suffice for now.) The phenomenon of birefringence can be explained by noting that a crystal is a structure of atoms in very specific and highly repeatable units. These ‘unit cells’, consisting of a few atoms, may themselves be asymmetric. Depending on whether the light is polarized along the long axis or the short axis of the unit cell, it will experience a different refractive index, and thus will be deviated by different amounts as it propagates through a block of such material.

One of the well-known ways in which polarization of light is exploited is in sunglasses. Some of these use lenses made of plastic material (for example, a sheet of Polaroid plastic) that acts as a polarizer—that is, an element which transmits light of a particular polarization (say vertical) and absorbs that of the orthogonal polarization (horizontal). Polaroid is made from rugby-ball shaped molecules that are aligned and ‘frozen’ in the plastic polymer. These molecules preferentially absorb light that is polarized along the axis of alignment of the molecules.Since generally sunlight scattered from objects has a random polarization (roughly 50 per cent of each polarization direction),then filtering out light of one polarization effectively reduces the brightness of the scene by half. Further, polarized sunglasses reduce glare: that is, light reflected from shiny flat surfaces, such as the hood and windscreen of cars. These surfaces tend to reflect a higher proportion of light polarized in a direction parallel to the surface (an effect discovered in the 19th century by Sir David Brewster and now named for him). Such reflections are blocked by spectacles that are constructed in the manner noted here,making for clearer vision of the road.

Transparent birefringent materials can also change the polarization of light without absorbing the light. This is because the speed of light depends on the direction of polarization with respect to the ‘orientation’ of the material. Some materials, such as ordinary glass, have no special orientation: you can rotate the material with no change in the effect on a light beam. As noted above, atoms in birefringent materials are arranged in such a way that there is a preferential direction—the symmetry axis—along which atoms respond differently to light. That is,light polarized along the symmetry axis will go slower (say) than light polarized perpendicular to the axis. Now, imagine that the light is polarized at 45 degrees to the symmetry axis. We can consider that half of this light is then polarized along the symmetry direction and half polarized at right angles to this direction. If the latter is slowed down by a sufficient amount,then the light emerging at the other face of the material can be polarized at -45 degrees. Thus the direction of polarization has been ‘rotated’ by 90 degrees.

Some birefringent materials can be used to control the state of polarization, by actively adjusting the orientation of the alignment axis of the molecules, say, using an applied voltage across the material itself. An example of this is a class of materials called liquid crystals (LCs), which consist of elongated molecules. The orientation of the molecules in an LC can be controlled by applying a voltage across them. Other materials become birefringent when forces or stresses are applied, because the force causes the molecules to rotate or the atoms to change alignment. This phenomenon enables the construction of force sensors by monitoring the state of polarization of light at the output of the optical sensor.

Placing a piece of birefringent LC between two polarizers also allows control of the light intensity by means of an electrical connection. Applying a voltage reorients the molecules, thus changing the refractive index seen by a polarized light beam. If a polarizer is placed after the LC then depending on the applied voltage a greater or lesser amount of light will be transmitted through the final polarizer. An array of such ‘cells’, each driven by a separate electrical signal, can be used to form a display where each cell is a single pixel. This is the basis of a liquid crystal display (LCD), and is often used for computer display screens and television sets.

In fact, such displays can be used to show 3D movies. The illusion of depth in these movies derives from the stereography of human vision. Each of our eyes sees a scene from a slightly different location, since they are a few centimetres apart in our skulls. The two images are combined in our brains to give us a perception of depth.

This illusion is reproduced using 3D glasses by means of polarization. Two images are projected on to the display or screen.Each of these is generated using light of a specific polarization,and each is shot from a slightly different vantage point. The 3D glasses are polarizers set at different orientations that allow transmission of one scene to the left eye and one to the right, each completely blocking the alternate image that has the ‘wrong’polarization. Thus we have a sense that the scene is as we would perceive it in the natural world—that is, the illusion of a three-dimensional arrangement of objects and people.

The successes of the wave model of light have been stunning,allowing us to understand some important characteristics of light and to use this understanding to build new technologies. And the successes of the ray picture of light have been equally amazing.Yet it is certainly puzzling that two apparently very different views of what light is should be necessary. It is to this conundrum that I now turn.

Chapter 4 Duality

The two different views of light, as a particle and as a wave, both contain insight and value. They have each enabled both new understanding of the natural world and the development and design of new technologies. Yet they appear to be vastly different in their conception of what light actually is. On the one hand, the particle model views light as a localized entity, a bundle of energy,that moves along a well-defined trajectory. On the other hand, the wave model describes light as a diffuse entity, permeating through space with no connection to the motion of solid things. How can these two pictures possibly refer to the same thing? This dilemma was recognized early on by Huygens and his contemporaries,but the two views remained in tension, as alternative descriptions of light, until the 19th century.

When Maxwell developed his theory of electromagnetic fields,he was able to use this to explain the properties of light as wave motion of those fields, as we saw in Chapter 3. This triumph of reasoning appeared to confirm the experiments of Thomas Young and Auguste Fresnel (described in Chapter 3) by providing an explanation of two fundamental phenomena, interference and diffraction, that did not easily fit within the particle model.Yet the concept of trajectories remained, and still remains, an extraordinarily powerful one for the analysis and design of optical systems. So there’s an uneasy truce of these two pictures—a dualism within classical physics—that requires some consideration.How can they be reconciled?

Looking at trajectories again

In the 17th century the Frenchman Pierre de Fermat proposed an ingenious formulation of refraction that was very different from that of Snell. Recall that Snell’s law deals with the change of direction of a ray of light at an interface between two transparent media. The ray, defined by the direction in which it is travelling towards the interface and the point at which it hits the interface,has its direction altered by an amount proportional to the ratio of the refractive indices of the two materials. It is only the local properties of the ray and interface that are important. Snell’s law applies at each point along the trajectory, as if the ray is‘feeling’ its way along, adjusting direction when it encounters a new interface.

Fermat’s conception was radically different. He argued that one should define the trajectory in terms of starting and ending points, as shown in Figure 21. He suggested that the question to ask is: what is the path that the light takes to traverse the space between the two points? He proposed that it should take the path that minimizes the time of flight between the two points. That this gives the same answer as Snell is remarkable and profound.Fermat’s ‘principle of least time’ suggests that the light considers the overall picture of the situation, and that the notion of a ray is one that takes into account both the initial and final positions and directions as well as everything in between. The contrast with the local model of a particle reacting to its immediate environment is telling.

21. Fermat’s conception of a light ray as a path of least time connecting the start and end of the trajectory. The ray crosses an interface between two optical media in which light moves at diferent speeds.

This idea was taken up by the German natural philosopher Gottfried Wilhelm von Leibniz, who was Newton’s contemporary and antagonist. Leibniz was impressed by the holistic picture of the process described by Fermat, and the concept of‘optimization’ that it implied: a ray explores the whole of space and picks just that path that will minimize its transit time between the specified beginning and end points. He developed the mathematical tools for analysing this idea—the calculus of variations—by which the effects small changes on a trajectory would have on the time taken to traverse the modified trajectory could be calculated. Leibniz recognized the importance of the notion that Fermat’s principle provided: the movement of light from one point to another defines an ‘optimal’trajectory.

Indeed, so taken was Leibniz by this concept of optimization that he elevated it to a teleological principle: that the world itself, in all its aspects, was on the optimal trajectory between a starting point and a finishing point. The contradictions inherent in such a position, when applied outside of the realm of science, were ably lampooned by Voltaire in his novel Candide, where Leibniz’s ideas are put into the mouth of Dr Pangloss, who insists disasters both natural and man-made were nonetheless evidence that this is the‘best of all possible worlds’.

Connecting waves and rays

Nonetheless, Leibniz’s mathematical ideas proved to be very fruitful. They were taken up by the renowned Irish mathematician William Rowan Hamilton in the 19th century. He showed formally how the idea of a wave can be allied to that of a collection of particles. Waves can be defined by their wavelength, amplitude,and phase (see Figure 15). Particles are defined by their position and direction of travel (see Figure 5), and a collection of particles by their density (i.e. the number of them at a given position) and range of directions. The media in which the light moves are characterized by their refractive indices. This can vary across space. For example, at the interface shown in Figure 20 there is a step change in the refractive index across the boundary between the two media.

Hamilton showed that what was important was how rapidly the refractive index changed in space compared with the length of an optical wave. That is, if the changes in index took place on a scale of close to a wavelength, then the wave character of light was evident. If it varied more smoothly and very slowly in space then the particle picture provided an adequate description.He showed how the simpler ray picture emerges from the more complex wave picture in certain commonly encountered situations. The appearance of wave-like phenomena, such as diffraction and interference, occurs when the size scales of the wavelength of light and the structures in which it propagates are similar. Thus you see diffraction patterns arising when the object that the light hits is a few microns in diameter, or has a very sharp edge, such as the delicate structure in a bird’s feather, or a butterfly wing. Otherwise, as in the case of a camera lens, the trajectory provides a sufficient description, since the refractive index is uniform throughout the glass of the lens itself.

22. Hamilton’s idea of rays as connecting wavefronts-thus joining the two primary conceptions of light.

Further, Hamilton showed that Fermat’s trajectories related directly to a property of the wave—the wavefronts. These are the loci of points at which the wave has the same phase at each point in space. For instance, when you see the ripples on the surface of a pond after a stone has been cast into it, the circular patterns are just these wavefronts. They are the places on the surface where the wave ‘peaks’ (or troughs) at a given instant of time. Now, what Hamilton noted was that rays could be considered as lines that intersected the wavefronts at right angles,as shown in Figure 22, thus connecting adjacent wavefronts by a well-defined trajectory.

Hamilton’s ‘optical analogy’

This remarkable result suggested another profound comparison—Hamilton’s so-called ‘optical analogy’. What he noted was that the well-known formulation of mechanics—the motion and position of solid bodies of matter—was based on the idea of trajectories.The idea that these may also be in some sense ‘optimal’ had been considered by Pierre Louis Maupertuis in the 18th century.

Maupertuis had formulated a way to evaluate the optimal value of a quantity called the ‘action’—essentially the velocity of the body multiplied by the distance it moves (and times its mass)—along the body’s trajectory.

He argued that the action should be minimal for an actual trajectory between two points, just as in Fermat’s argument that the time taken to traverse a light ray should be minimal. Maupertuis’‘principle of least action’ is very similar in concept to Fermat’s‘principle of least time’. Indeed, Leonhard Euler, a Swiss mathematician, showed how to use Leibniz’s calculus to derive Newton’s famous equations of motion from Maupertuis’ principle.Thus Euler connected a description of a trajectory in terms of a particle sensing its way through its environment to one in which the whole of space between the specified starting and finishing points influences the path.

What Hamilton did was to find equations that encapsulated the variations in action in terms of a simple description of the specific environment in which the body was moving. And this equation turns out to have a very similar form to the one he found for describing the trajectories of light rays (for which the environmental description is just how the refractive index changes with position in the medium). So there is a hint of a latent analogy between the trajectories of solid objects and a fictive wavefront: perhaps all bodies might have both particle-like trajectories and wave-like properties? Indeed, Hamilton’s equation, and his eponymous function, turns out to be very important in thinking about the next big step in understanding light—quantum mechanics.

Unsolved puzzles

This was by no means the only hint of a new opportunity for science. About this time, towards the end of the 19th century, light still offered a few puzzles that were unexplainable in terms of the prevailing models of its properties, even with the reconciliation that Hamilton had provided. Two of the most important of these were: the colour of hot objects (including the Sun), and the colour of different atoms in a flame.

When things are heated up, they change colour. Take a lump of metal. As it gets hotter and hotter it first glows red, then orange,and then white. Why does this happen? This question stumped many of the great scientists of the time, including Maxwell himself.The problem was that Maxwell’s theory of light, when applied to this problem, indicated that the colour should get bluer and bluer as the temperature increased, without a limit, eventually moving out of the range of human vision into the ultraviolet—beyond blue—region of the spectrum. But this does not happen in practice.

The second example arose from the study of light emitted by atoms, pioneered by a Swiss schoolmaster, Johannes Balmer. We’ll look at this mechanism in more detail in Chapter 5, but the important feature of the light is in the distribution of colours in its spectrum, shown in Figure 23a. In this respect it is very different from sunlight (the Sun is a good example of a hot body), which has the familiar ‘rainbow’ spectrum, shown in Figure 23b, consisting of all colours continuously from red to violet (and beyond at each end—just not visible to us). By contrast, a collection of atoms emits a discrete set of colours—a set of spectral ‘lines’ of particular wavelengths—specifically associated with the internal structure of the particular atom involved.

Both of these phenomena required a radical revision of thinking about light, because they could not be explained within the contemporary models of wave motion and atomic structure.

Max Planck, working at Humboldt University in Berlin in the late19th century, first came up with an idea to explain the spectrum emitted by hot objects—so-called ‘black bodies’. He conjectured that when light and matter interact, they do so only by exchanging discrete ‘packets’, or quanta, or energy. Planck recognized the revolutionary nature of his idea, and was therefore reluctant to infer too much about light itself from it, though it would eventually dramatically change our view of what light is. His notion revived the idea of light as a stream of particles—discrete objects that carried a fixed amount of energy that could be absorbed by atoms or emitted by them.

23. Spectrum of light emitted from a. the Sun (a ‘black body’), andb. a neon lamp. The former has continuous band of colours, whereaslatter shows the discrete lines of particular colours that are a‘fingerprint’ of the neon atoms.

This seemed like a retrograde step: the wave model of light could explain all of the hitherto observed effects, and it was clear from Hamilton’s work that even trajectory-like behaviour, previously the most obvious evidence of a particle-like entity, emerged from a wave model of light in certain common situations. So the idea of a particle of light appeared not to be necessary. Surely it was simply a calculational ‘fix’, thought up to get out of a tight spot,and would eventually be replaced by a more reasonably consistent picture of light. However, combined with Balmer’s observations,this conjecture was set to radically change physics.

In the years immediately after Planck’s suggestion, Albert Einstein used the idea of discrete exchanges of energy between light and matter to expose another piece of physics that had eluded explanation—the photoelectric effect. This effect is seen when light shines on a piece of metal. Some electric charges—electrons,in fact—are ejected from the metal. The speed with which the electrons are ejected depends on the wavelength of the light. The light must be sufficiently ‘blue’, that is have a short enough wavelength, in order to see any electrons emitted at all. As it gets bluer and bluer, the electrons are ejected with more and more energy, and thus higher and higher speed.

Einstein explained this by noting that the electrons required a minimum amount of energy to escape the clutches of the metal,and by assigning discrete amounts of energy to a particle of light—the photon—proportional to the frequency of the light (the constant of proportionality being known as Planck’s constant, h),so that when the frequency of the light is high enough (and thus the wavelength short enough) the light, when it is absorbed, can provide enough energy for an electron to escape. His model suggested that the origin of the discrete exchange of energy between light and matter that is central to Planck’s notion arises from the actual discrete character of light—a full revival of the particle model.

This idea chimes nicely with Balmer’s observations of discrete line spectra of light emission from atoms. But a full explanation of this phenomenon clearly requires a bit more thought about why atoms would deliver light in such packets. The key idea came from Niels Bohr, a Danish physicist working in Manchester. He suggested that the reason light was emitted as discrete packets of energy was that the atoms themselves could only exist in certain configurations. He imagined atoms as analogous to tiny planetary systems: electrons in orbit around a central nucleus. The electron can ‘jump’ between two stable orbits, emitting or absorbing light as it does so (depending on whether the jump is to an orbit of lower or higher energy). The character of these orbits—or quantum states—depends on the details of the atom: how many electrons and the size of the nucleus. Therefore the energy given or taken up when an electron moves between two quantum states is a signature of the particular atom itself. So when the energy of a light particle—or photon—matches that of the difference in energy of two quantum states of the electron in an atom, then absorption or emission is possible. Bohr’s ideas explained Balmer’s observations neatly, and added some weight to the idea of light beams as a collection of discrete particles.

All these developments had the potential to undermine the wave model of light that had been so strongly affirmed by Maxwell’s theory. They went beyond even Hamilton’s reconciliation of trajectories and wave motion, since they appeared to be fundamental,not simply the result of an approximation about size and scale. Thus they reopened the question of the nature of light once again.

In 1908, George Taylor, working in Cambridge, performed Young’s double-slit experiment with exceptionally feeble light—so weak that on average there was less than one photon in the apparatus at any time. Yet he still saw interference fringes. That outcome is very strange. If we think of one path from the light source to the detector as being via one slit, and a second path via the other slit, then there are two ways that the photon can get from source to detector. The evidence of interference fringes posed a dilemma that caught the attention of the leading scientists of the day. Bohr captured the difficulty, noting that we would ‘be obliged to say, on the one hand, that the photon always chooses one of the two ways, and on the other that it behaves as if it passed through both’. Even single particles can exhibit wave-like behaviour.

Waving altogether

As you might imagine, it took a truly radical thought to figure a way out of this conundrum. That thought occurred to Paul Dirac,a physicist working at Cambridge in the 1920s. Dirac suggested that the fundamental property of light was that it was both a particle and a wave at the same time. Now, this might appear to you as simply sophistry, a logical trick that resolves nothing. But there is much more behind it than a slogan. What Dirac did was to develop a quantum mechanical version of Maxwell’s theory of electromagnetic fields. Using this he was able to show that, if you measured these ‘quantum fields’ using a set-up like Young’s double-slit interferometer, you would see interference effects characteristic of wave-like behaviour. Whereas, if you simply measured the intensity of the light, you would be effectively counting the number of photons in the beam.

This turned out to be a very profound step. It set the quantum field up as the fundamental entity on which the universe is built—neither particle nor wave, but both at once; complete wave–particle duality. It is a beautiful reconciliation of all the phenomena that light exhibits, and provides a framework in which to understand all optical effects, both those from the classical world of Newton, Maxwell, and Hamilton and those of the quantum world of Planck, Einstein, and Bohr. But the cost is a perplexing and non-intuitive entity at the heart of nature—a quantum field—of which light is but one example.

The radical idea that light was both wave and particle stimulated some major new ideas. For instance, Louis de Broglie suggested that if this kind of dualism existed for light, surely it should for all other things too. So, material bodies that we normally had considered only as collections of particles should also have‘wave-like’ properties, taking the next step beyond what Hamilton had considered. He even defined what the wavelength should be(now called the de Broglie wavelength λdB
)—proportional to the inverse of the particle’s momentum (i.e. its mass and velocity,the constant of proportionality again being Planck’s constant):

λdB
=h/mv

This suggests that to look for such effects you should use either very light particles or very cold ones that are moving very, very slowly. Such effects can be observed. Figure 24 shows an interference pattern made using a double-slit-like interferometer,but using molecules instead of light. The implications of this are mind-boggling. If you think of a molecule as just a very light particle, then you cannot explain the pattern, because you consider that it must have passed through one slit or the other.However, the idea that a particle with mass could be so delocalized as to have passed effectively through both slits to interfere with itself is astounding and beggars belief.

If material objects also behave as waves, then, Erwin Schr
dinger conjectured, surely there must be a wave equation describing their behaviour. Where to start looking for such a thing? He took the equation that Hamilton had developed, by means of his optical analogy, to describe how the ‘action’ of a particle evolved. A simple addition to this equation, involving Planck’s constant, moulded it into one that described wave motion. This was the origin of Schr
dinger’s famous ‘wave function’. The wave function has a number of properties very analogous to optical waves, including interference and diffraction, but nonetheless refers to things that in the language of pre-quantum physics are palpably particles possessing mass and weight. As a consequence, there are still questions as to what the wave function actually describes. Is it the actual particle itself, or is it a sort of shorthand for what we know about the particle?

24. An interference pattern made using molecules passing one at atime through a tiny version of Young’s apparatus—two very small slitsseparated by billionths of a metre.

An important quantity for light is its intensity, proportional to the square of the amplitude of the field. This is related directly to the density of photons in the light beam. Similarly, the square of the wave function is related to the density of particles at a particular point in space at a particular time. But it is impossible to say for certain that a particle occupies a specific position at a specific instant. This indeterminacy seems to be a very fundamental property of the world, and it is related deeply to the fact that quantum fields lie at the heart of things.

Nothing is something

Another consequence of this fact is that ‘nothing’ is actually something. That is, the complete absence of matter (e.g. electrons or atoms) or light (i.e. photons) still has measurable properties.This void is called the ‘electromagnetic quantum vacuum’, and is the state of the universe from which all extractable energy has been removed. Yet it is a seething mass of activity, consisting of fluctuating fields but containing no photons whatsoever. What is even more surprising is that the quantum vacuum has observable consequences. How can this ‘nothing’ give rise to an effect we can see?

We’ve seen that light can be thought of as a wave motion of the electromagnetic field. Imagine this field as ripples on the surface of the sea. These would buffet about any boat, but would not move the boat up and down or push it along as a well-defined wave might. On average, the boat does not move, but it nonetheless rocks back and forth. Now imagine the same thing for a charged particle like an electron. It ‘feels’ the random changes in the electromagnetic vacuum, being buffeted by these. If the electron is bound in an atom, this buffeting is revealed as a shift of the energy of the quantum states that the electron may occupy. Since the frequency of the photon that the atom may absorb depends on the difference in energy of two such states, these changes can be seen in a change of the colour of light that the atom may absorb. The changes are tiny—a shift of less than one billionth of the wavelength of the light—but measurement techniques for frequencies are so precise that such changes can indeed be determined. The first person to do this, Willis Lamb, working in New York in the 1950s, won a Nobel Prize for showing this frequency shift, which is now named for him.

The dual identity of light has numerous facets. Even in the pre-quantum world, the dichotomy of ray and wave demanded a resolution. That came about by understanding the nature of the wave motion that light embodied, and the scale and nature of objects with which it interacted. Particle-like behaviour—motion along a well-defined trajectory—is sufficient to describe the situation when all objects are much bigger than the wavelength of light, and have no sharp edges. Quantum mechanics puts a new twist on this duality. Light acts as a particle of more or less well-defined energy when it interacts with matter. Yet it retains its ability to exhibit wave-like phenomena at the same time. The resolution is a new concept: the quantum field.Light particles—photons—are excitations of this field, which propagates according to quantum versions of Maxwell’s equations for light waves.

Quantum fields, of which light is perhaps the simplest example,are now regarded as being the fundamental entities of the universe, underpinning all types of material and non-material things. The only explanation is that the stuff of the world is neither particle nor wave but both. This is the nature of reality.

Chapter 5 Light matters

How do you generate light? There many different ways: common light bulbs, based on glowing metal filaments, as well as‘fluorescent’ tubes; laser pointers; tell-tale lights on electrical equipment, from toasters to car dashboards; sunlight and starlight; even, for those in the northern and southern extremities of the planet, the aurorae; fireflies and glow-worms, and the phosphorescence in the wake of boats. What is the means by which these very different things all generate the same thing:light?

The key is that they all involve matter. More specifically, they involve electric charges moving about. When these charges accelerate—that is, when they change their speed or their direction of motion—then a simple law of physics is that they emit light. Understanding this was one of the great achievements of the theory of electromagnetism. An electric field has its origin in an electric charge, such as an electron in an atom. The electric field,attracting oppositely charged particles, such as protons, extends throughout all space, although it gets weaker quite quickly as you move away from the electron. As I noted in Chapter 3, this is the force that arises from static electricity.

Oscillating atoms and bending electrons

Now say the electron moves with a sudden jerk. The field surrounding it must move also, since it is linked inextricably to the electron. The change in the field is illustrated in Figure 25, as a ‘kink’. A remote proton will notice that the electron has moved only when the change in the field that arises from the electron movement has had time to make its way to the proton. This will take time since the kink, and therefore the information that the electron has moved, propagates at about the speed of light.When the change does get to the proton, it will move according to whether the electron moved closer to it (thus making the field experienced by the proton stronger, so that it feels a stronger force) or further away (leading to a weaker field and a weaker force).

Now say the electron were to move back and forth. Then changes would occur in the field surrounding it in synchrony with this oscillation and propagate away to the proton, which would then be induced to oscillate in turn as it received this information. But an oscillating electric field (and associated magnetic field, but that need not bother us here) is exactly what we mean by light.

25. Lines in the electric field of a. a stationary electron and b. anaccelerating electron. When the electron accelerates, the changes inthe field—the ‘kinks’ in the field lines—propagate away from theelectron at the speed of light.

Since a hydrogen atom—the simplest one—consists of a single electron and a single proton, we can understand from this picture how atoms can generate light. First, let’s think about what happens when light irradiates an atom sitting quietly on its own.The light forces both charged particles—the electron and the proton—inside the atom to move. But since the electron is much lighter than the proton, it moves more easily with a given application of force, and we can consider its motion with respect to the more or less stationary proton. In fact, the electron oscillates at the frequency of the light’s electric field, being alternately accelerated or decelerated as the electric field varies.

This process is a bit like pushing a child on a swing. The best way to get the swing to oscillate is to push on it in synchrony with the natural oscillation period—a gentle push each time the swing reaches the bottom of its motion. Even so, it takes effort to get the child up to a height that thrills him or her. The child experiences maximum acceleration at the apices of the swing’s oscillation, and maximum speed as she passes under the point of suspension. So it is with the atomic electrons—the energy of the light beam is absorbed by the atom, and converted into the motion of electrons.

Let’s say you now stop pushing on the swing. What happens? The child gradually swings in arcs of lesser and lesser amplitude to rest. Again, so it is with the atom. The electrons gradually stop oscillating, and give up their motional energy by reradiating light. This is the process of light emission, and is the basis of many light sources, such as neon signs, fluorescent lights, and laser pointers.

Now in this picture I have assumed that some light beam itself is used initially to get the atomic electrons oscillating. But in a sense that begs the question of how one generates light in the first place.In fact it is possible to use other means to ‘excite’ the atoms. First,one can simply heat up the material. This is what is done in an ordinary light bulb, where by passing an electric current through a metal filament the metal heats up to a very high temperature—several thousand degrees. As the material heats up, the electrons start to jostle and collide with the atoms and with one another more and more, and this both excites the atoms and causes the electrons to accelerate and decelerate rapidly. This produces a very broad range of colours that depends only on the temperature to which the material is heated, and not upon the particular type of atoms of which it is made.

Electricity may also be used in other ways. In light-emitting diodes (LEDs) for example, as used in displays, an electrical current—or flow of electrons through the material—can be captured directly by an atom, so the light is generated much more efficiently than in a thermal source. A fluorescent tube also uses an electrical current to directly excite atoms, only this time in a nebulous gas with which the tube is filled. Finally, many different chemical or biological reactions can release energy, some of which leaves the atoms or molecules in the form of light. This is the origin of the light given off by fireflies, for example.

We noted previously that acceleration has two parts to it: it can mean a change of speed, as we have just seen for the electron and proton in a hydrogen atom, or it can mean a change of direction without a change in speed. This latter characteristic of acceleration is familiar from the experience of going around corners in a car: you are pushed against the door or the side of the seat and experience a force that turns you with the car. The force is larger the faster you are moving as you enter the turn, and this is an indication that you are accelerating, even though you may not be speeding up or slowing down.

Even this kind of acceleration, when experienced by charged particles, causes them to radiate light. Imagine a bunch of electrons forced to move in a circle, as if they were stuck on the rim of a rotating wheel. They generate light, the wavelength of which gets shorter and shorter (so the photon energy gets larger and larger) the faster they move around the circuit, because of this angular acceleration. The light generated in this way is called synchrotron radiation, and it is a common means to generate X-rays. It is also related to the light seen in the northern and southern aurorae, which are produced when charged particles from the Sun are forced to spiral by the Earth’s magnetic field as they enter the atmosphere.

Quantum light emission processes

These basic mechanisms underpin all light sources. But the details of how the atoms act as a group can have a strong influence on the characteristics of the light that is eventually emitted—as I noted in Chapter 1, a light bulb emits a very different sort of light than a laser pointer, for instance. In order to understand this, we need to delve a little deeper into the structure of atoms, since the process of emitting light from an atom is not completely encompassed by the analogy with swings. Something needs to be added in order to accommodate the fact that atoms and molecules are quantum mechanical entities.

For our purpose this simply means that the electrons in the atom or molecule can only hold energy in fixed amounts. Using our swing model, it means that the maximum extension of the swing amplitude cannot be anything you like. Rather, it is restricted to certain particular values: it is quantized. More particularly, the energy of the swing comes in discrete packets, or quanta, and when you push it you can only make it jump by one or more quanta. In the atom, this means the energy of the electron can change only in the same discrete units when it absorbs or emits a single photon.The energies involved in making these jumps are very small by everyday standards. Take a light in your house. This consumes energy at a rate of, say, 60 W, or 60 Joules per second. A single photon emitted by the atoms in the light bulb possesses about one billion billionth of a Joule. So a light bulb is emitting more than ten billion billion photons per second.

26. An atom undergoing a. absorption, b. spontaneous emission, andc. stimulated emission.

An atom can be prepared in an excited state simply by shining light of the right frequency on it, as shown in Figure 26a.(Of course, this begs the question, but we’ve also seen that the excitation can also be accomplished in other ways, for instance by running an electrical current through the medium.) Now,according to quantum theory a corollary of the ‘jumpiness’ of the electron motion is that the atomic electrons are pretty much stable against the emission of light once in one of these discrete states.They are like a ball on a shelf in a cupboard—in principle it can lower its energy by dropping to a lower shelf, but this cannot happen in practice unless you give it a little push so that it rolls off the shelf.

So it would appear that quantum physics suggests that atoms cannot emit light, since once you have put them in these stable states—that’s it. Well, it turns out that, except for the lowestenergy state of the electron in the atom, a push is available to allow the electron to drop from a more energetic state to a less energetic state. And the surprising thing is that the shove arises from nothing.

In Chapter 4, I noted one of the strangest features of quantum physics: even the emptiness of space is a seething background of activity, filled with ‘vacuum fluctuations’. These fluctuations in the electromagnetic field can cause the atomic electron to drop to a lower energy level and to give up the energy difference in the form of emitted light. This process, by which an atom (or molecule)undergoes a transition from one stable state (the excited state) to another of lower energy (the ground state), emitting a photon on the way, is called spontaneous emission (Figure 26b). It is something that each atom does on its own. It was originally proposed by Einstein in order to account for the proper energy balance between a light beam and the matter on which it was shining. If spontaneous emission does not occur, then the atoms hold on to the energy from the light beam and the situation we see everywhere around us, where most things are in a stable state in equilibrium with their surroundings, would be impossible.

Einstein understood the central mystery of spontaneous emission:that it was a random process. You just cannot say exactly when any given atom will make a jump. All you can say is that on average, after some amount of time (that depends on the particular atoms, but is roughly 1,000 billionth of a second), in a large collection of atoms, about two-thirds of them will have emitted a photon. But the origin of the fundamental randomness remained a mystery until, in 1927, Paul Dirac’s quantum field theory introduced the idea that quantum vacuum fluctuations were at the root of this. The notion that a field containing no photons at all can cause an excited atom to be unstable is at odds with our intuition, and it took until the 1950s for Lamb’s measurements to show that Dirac’s explanation was right.

What this means is that even everyday occurrences—the picture generated on a TV screen by means of LEDs, for example—have at their heart this fundamentally random characteristic arising from quantum mechanics. By contrast, the emission of light by atoms when they are pushed to give up their energy by the application of another light field is called stimulated emission (Figure 26b). This form of recouping energy from atoms into the light field does not have random character. And this makes possible a very different kind of light: that of the laser.

Coherence: acting all together

When atoms and charged particles behave individually, ‘doing their own thing’, the light they emit when there are many of them is a sort of uncoordinated set of waves. Even a very small LED,with a size of much less than a millimetre, contains a vast number of atoms, so this is a common situation.

A feature of this uncoordinated emission is that each atom emits its photons at random, with no acknowledgement of what the adjacent atoms are doing: the light goes off in many different directions, and the photons are all emitted at different times. In effect, the randomness of the emission process is reflected in the randomness of the resulting light intensity.

Let’s say we put a photo detector in front of a light bulb. (A photo detector works like a light bulb in reverse. It uses the photoelectric effect—light incident on it produces an electrical current that can be measured.) What we would see is that the electrical current from the detector was very noisy, because the light incident on the detector has an intensity that changes quickly and randomly,corresponding to the arrival of random numbers of photons at each instant of time.

But what if it were possible to coordinate the atoms, so that they acted together? We can think back to our earlier analogy: imagine a collection of swings, each with the same oscillation frequency.The swings may be all oscillating at random: that is, with each at a different point in its repetitive trajectory at any instant. Or, they may be in synchrony, with the differences in trajectory between adjacent swings being a fixed amount—like a wave caused by the adjacent spectators in the crowd at a football match standing up and sitting down in sequence. In the first case, the light that is emitted from these uncorrelated atoms is like that from a light bulb or LED and is said to be incoherent. In the second case,however, the atoms oscillate in lock-step, and the light they emit is given off in a coherent fashion—all of the photons are emitted in the same direction. This is what happens in stimulated emission(Figure 26c), and is the basis for the laser.

Laser light

The laser is perhaps the most important invention in optics in the last century. This device produces extraordinarily useful beams of light that have revolutionized the range and capabilities of applications. Not only is it a specific source of illumination, in microscopy and spectroscopy for example, but it also provides a means to direct significant energy on to a particular target in a tailored way, and thereby to control the dynamics of matter. An extreme example of the latter application is laser-driven fusion of atoms, discussed in Chapter 7, that may enable new forms of nuclear energy which can draw upon a very large supply of fuel.

A laser consists of an optical amplifier, or gain medium, that generates light from atoms by means of stimulated emission,placed between two mirrors (and possibly other optical elements)that form an optical cavity. The number of photons in the cavity builds up as the atoms emit light until there is a balance between the energy put into the light beam from the atoms, and the energy leaking out of the cavity through the mirrors. As the amplifier is turned on, by providing a means to excite the atoms, the light emitted from the amplifier is reflected back into it by the end mirror of the cavity. That causes further stimulation of radiation from the excited atoms, and thus the light in the cavity increases in brightness. At the other mirror, some of the light is transmitted out of the cavity as a useful output. Some is reflected back into the gain medium. When the rate at which light is put into the cavity by the amplifier equals the rate at which it is extracted through the output mirror, the laser is said to be at threshold. Beyond this point, any increase in the amplifier gain (the rate at which atoms are put into their excited states) leads to an increase in the intra-cavity intensity, and thus to an increase in the output light.The optical cavity also imposes a restriction on the colours of the laser. It turns out that the frequencies that experience the most gain are those for which the light waves add with constructive interference on each round trip. This means that the length of one round trip of the cavity should be equal to a multiple of half of a wavelength. The frequencies that satisfy this resonant condition are said to be the cavity modes.

The reason that lasers are important is related to the fact that the light they emit is coherent: all the photons go in more or less the same direction, with the same colour. The direction is defined by the laser cavity: the colour by the atoms in the gain medium and the allowed modes of the cavity. This leads to the property that the light is in the form of a beam—the laser beam—which is about as close to a ‘ray’ of light as you can imagine. It diverges as it propagates due to diffraction, but has the smallest divergence possible. This property also means that it can be focused to a very small spot using lenses or mirrors.

A second feature that contrasts the light emitted from lasers with that from light bulbs is that laser light is usually very pure in colour. In other words, it consists of only a few wavelengths,whereas lamps often emit a broad range of wavelengths. The light intensity is very stable (registering as very low noise in a photodetector output), and the light can be emitted continuously or as a sequence of pulses.

The ability of laser light to be focused to a very small spot makes it useful for microscopy, and there are a number of different ways in which, by scanning the laser spot across an object at the focus of the microscope lens, and detecting the light scattered or re-emitted from the object, three-dimensional images of the object can be made.This approach is very useful in looking at animal tissue, for example,and optical microscopies of this kind are widely used in biomedicine.

Many applications of lasers in manufacturing also stem from this property of laser light. The ability to mark, cut, drill, or weld metals, for instance, requires that a lot of energy be deposited in a small region of the metal in a short time. So high-power lasers producing coherent light beams in the form of pulses that can be focused are ideal for such materials processing.

Similar properties are needed for some medical applications of lasers, also involving materials—this time skin, teeth, or hair.Laser correction of vision and laser dentistry are now commonplace, as is the use of lasers to remove tattoos by heating up the ink until the drops break up, and for hair removal—although unfortunately not hair regrowth! Other familiar devices that make use of laser light’s ability to address a very small spot are the CD, DVD, Blu-ray, and some computer disk storage devices. Very tiny spots of light in the recording medium allow the very high-density storage of data in the material.

The very pure colours achievable with laser light make it possible to distinguish the constituent atoms and molecules of different mixtures by means of spectroscopy. As noted in Chapter 1, different atoms, and indeed different molecules, have characteristic frequencies at which they absorb and radiate light, due to their different structures. Extending the analogy developed in this chapter, they are like swings in which the chains or ropes holding the seat are of different lengths—their natural oscillation frequencies are dependent upon the way in which they are put together.

In fact, each atom and molecule has a range of different absorption and emission frequencies, corresponding to the excitation of different electron configurations. Typically these lie in the blue part of the visible light spectrum, but some molecules absorb at much shorter wavelengths, invisible to humans. Many molecules also absorb light at wavelengths longer than the red end of the visible spectrum. This absorption arises from the vibrations between the atomic nuclei that make up the molecule. Since nuclei are much heavier than electrons, they tend to oscillate at much lower frequencies. This set of frequencies is a sort of molecular‘fingerprint’ that enables identification of a particular species.

The catalogue of these fingerprints is of importance, of course, in chemistry, since it allows the different elements involved in a reaction to be identified. It is also used in molecular biology, and even in cell biology, when the movement of particular ‘tag’molecules can be studied. It is critical, too, for astrophysics, in which the elements present in astronomical objects—stars,galaxies, nebulae—can be determined, as well as in atmospheric physics and meteorology, for the remote sensing of pollutants or particles. Such monitoring provides key data in assessing the impact and origin of climate change.

By combining the outputs of several different lasers—say one emitting red light, one green, and one blue—it is possible to make a laser projector. By changing the intensities of each laser individually according to the video signal output of a computer or Internet link, perhaps by means of a liquid crystal cell, movies can be projected on a big screen with vivid, highly saturated colours.The combination of red, green, and blue (RGB) light is sufficient to make up a complete colour palette and lasers produce very bright images on a screen.

X-rays

When the wavelength of the light is very short, in the X-ray region of the spectrum, a different kind of spectroscopy arises.X-ray photons are energetic enough to excite the most tightly bound of the electrons in atoms—not just the outermost electrons. This means that X-rays can be used to look into the heart of atoms and molecules, and to understand their local environment, which can shift the binding energies of the electrons. X-ray absorption spectroscopy is widely used in the study of materials for a variety of applications, from detecting trace pollutants to understanding the structure of glasses. As noted in Chapter 3, X-rays are also used to study the structure of crystals by means of diffraction. When the X-ray wavelength is close to the spacing between atoms in the crystal, then the crystal acts as a ‘diffraction grating’ and scatters the X-rays in discrete directions. By detecting these diffraction patterns on a camera, it is possible to reconstruct the three-dimensional structure of highly complex crystals using advanced inversion algorithms.Today this is a routine process for characterizing isolated biologically and chemically relevant molecules, determining the structures of possible new molecules in order to design them for a specific function.

Some of the best light sources for this sort of spectroscopy are synchrotrons. In order to produce X-rays at the required short wavelengths, synchrotrons have to produce very energetic electron beams, and accelerate them around a big ring. Experimental stations catch a glint of light as the electrons rush by, leading to short bursts of X-rays that are used for diffraction imaging. For example, the Diamond Light Source at Harwell in England accelerates electrons to more than a billion volts in a ring that is more than half a kilometre long. The next generation of X-ray light sources is being built using linear particle accelerators, which produce extremely bright X-rays beams. The X-ray diffraction pattern shown in Figure 20 was taken using the Diamond synchrotron.

Ultrashort light pulses

Laser light can also come in short bursts. There are several ways to arrange for this to happen. The method that produces the briefest pulses is called mode-locking. This requires a gain medium that has a large bandwidth—that is, it can amplify light over a broad spectrum. This allows several of the modes of the optical cavity to experience gain. If it is also arranged that these modes all have the same phase, then light waves of many different frequencies add constructively to yield a single pulse inside the cavity, bouncing back and forth between the mirrors. The brevity of the pulse is determined by how many frequencies are locked—the wider the range of frequencies, the shorter the pulse.

The possibility of creating very short duration laser light pulses enables a kind of measurement called dynamical or time-resolved spectroscopy. It allows us to see how things change in time, based on an old principle: the stroboscope. The general idea of how you use light to ‘freeze’ rapid motion stems back to the work of Eadweard Muybridge in the late 19th century. He invented the idea of using a fast camera shutter to photograph a horse trotting.The legs of a horse move too fast for the human eye to resolve, and it was not known at that time whether all four legs left the ground at any point during the stride. To settle the matter, Muybridge set up a bank of cameras, each of which had its shutter opened by a trip wire, which was triggered when the horse passed the camera.This enabled him to ‘slice’ a short pulse from the light reflected from the horse. The duration of this pulse of light was shorter than the time over which the horse’s legs moved. The outcome of his work was that he was able to inform Leland Stanford, the funder of his research, that in fact there is a point in a horse’s stride at which none of its legs touch the ground.

Mechanical shutters on conventional cameras could close very fast, but not fast enough to see some forms of animal motion,such as the flapping of the wings of a hummingbird. Even faster physical events such as an explosion, where things change on timescales of thousandths of a second, were out of reach. To solve this problem, Harold Edgerton at MIT in the 1950s invented a new kind of non-mechanical shutter, based on an optical switch.He was able to take ‘still’ photographs of explosions, for instance,using this device.

These shutters are what we might call ‘passive’ instruments. They simply allow a slice of light to pass through when they are open,so are suitable to events that are well illuminated (the horse in California sunshine) or emit a lot of light themselves (the explosion). But we can imagine an ‘active’ instrument, one that generates a short pulse of light to illuminate a moving object.Think of the light pulses emitted by the flash unit on a camera.A flash of light with a duration that is short compared to the time taken for the thing we’re looking at to move provides an image of the object ‘frozen’ in time, even when using a camera shutter speed that is much longer than the changes of the object. A second flash freezes the motion at a later time. The same is the case for subsequent flashes.

A movie composed of the sequence of frames taken on repeated trials of the event reveals very rapid changes in the system, on a timescale that is much faster than could be observed by the eye.Indeed, the brevity of events that can be seen in this way is truly breathtaking. Edgerton invented a ‘stroboscope’ of this kind in1931, and some of his most iconic images, such as a bullet passing through an apple or a playing card (Figure 27), were taken with this device.

27. A bullet frozen in motion using stroboscopic imaging.

Using modern pulsed lasers as the ‘flash’ it is possible to observe not just the frozen motion of bullets but even the motion of atoms in a molecule involved in a chemical reaction (for which the 1999Nobel Prize in Chemistry was given to Ahmed Zewail) and the much, much faster motion of electrons whizzing around the nucleus of an atom. The timescales for these motions are staggeringly small—less than one tenth of a million-millionth of a second(100 × 10-15
seconds, or 100 femtoseconds (100 fs)) in the case of molecules, and a few tens of billion-billionths of a second(100 × 10-18
seconds, or 100 attoseconds (100 as)) in the case of atomic electrons. These fields—femtochemistry and attoscience respectively—are at the forefront of what is possible in the interaction of light and matter. I shall consider them further in Chapter 7.

Chapter 6 Light, space, and time

Robert Grosseteste, Bishop of Lincoln and the first Chancellor of the University of Oxford in the 13th century, was one of the leading thinkers of his day, and a proponent of the works of the ancient Greeks. For him, as for many philosophers, the challenge of understanding light’s nature was critical to understanding the world. In Grosseteste’s treatise on the subject, entitled De Luce,he extols the primary importance of light: ‘The first corporeal form …is in my opinion light. For light of its very nature diffuses itself in every direction in such a way that a point of light will produce instantaneously a sphere of light of any size whatsoever’.

For Grosseteste, light defines space by its propagation instantly throughout the universe. Without light, there is no space, and therefore no forum in which events can take place. Matter, and thus the spatial extension of objects, are coupled to light, but cannot be separately defined. This intimate connection between light, space, and matter—in Grosseteste’s hands amenable to quantifiable description—informed the development of ideas regarding cosmology in the subsequent centuries.

Space-time

For Newton, space neither admitted nor demanded definition. He thought of space as a pre-existing entity, a sort of theatre in which events played themselves out. Large-scale motion of bodies in the heavens was integral to his idea of a set of universal laws. Einstein,by contrast, places light at the centre of space. For him, it defines space and time by virtue of setting the speed limit for signals sent from one part of the universe to another. The fact that there is a finite maximum speed turns out to make space and time inseparable. Einstein’s theory of relativity teaches us that we cannot think of one without thinking of the other. This is because our perception of space and time is based on local measurements of distances and time intervals. These measures appear differently to those moving relative to us, because of the speed limit imposed by light.

How does this strange entwining of space and time by light arise?Let’s start with Newton’s conception of space. We can think of this as a sort of scaffold—a collection of imaginary rods of fixed length all connected together in a three-dimensional framework, as shown in Figure 28. Newton thought that this sort of structure pre-existed any event, and indeed that all events took place somewhere in this structure. Events can therefore be specified by their distance from a fixed point in the frame by counting the number of rods to reach the location of the event. Of course events occur at a certain time, too, so the scaffold must be equipped with clocks to measure the time. If a clock is placed at the junction of each of the rods, they all show the same time everywhere in space,and we can easily define a ‘universal time’.

Now we must ask several questions. First, how should we build a clock? Second, how should we ensure that they are all synchronized across space? Third, how should we build a ruler?These questions all have answers that are intimately related to the properties of light. Indeed, the answer to the last is this: one metre is the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second. It is therefore linked to the answer to the first question: how accurate a clock can be built.

28. A scafold representing space made up of a 3D lattice of measuring rods. At each intersection is a clock, all synchronized.

Clocks

The primary characteristic of a clock is that it ‘ticks’. That is, it signals at regular intervals of time. By counting the number of ticks between events, we can assign a time interval between them. The more precise a clock is, the more regular the intervals between the ticks. In a grandfather clock, the ‘ticks’ are provided by the regular swings of a long pendulum. In an electronic wristwatch, the ‘ticks’are the oscillations of a piece of quartz crystal. These are much more regular than the swings of a pendulum, which can be affected by the temperature and humidity of the place where the grandfather clock is located. Therefore the quartz watch is said to keep better time than the grandfather clock.

The most accurate clocks in the world are based on the highly regular clicks of electrons moving around in atoms. We’ve seen that atomic electrons can jump between different stable energy levels within an atom. For some atoms, the difference in energy between these levels is extremely well defined, and the rate at which electrons jump between the two can therefore be used to define a set of ticks, based on the frequency of the light used to push the electrons up and down between the two energy states.

The idea is simple enough: illuminate an atom with microwaves(recall that microwaves are just like light, but with a much lower frequency—billions of oscillations of the electric field per second rather than millions of billions as in the case of visible light). Then slowly change the frequency of the microwaves until the electrons move between the atomic energy levels most efficiently. This defines the number of cycles per second of the microwave radiation—the rate of ticks of the clock—in terms of the energy level spacing of electrons in a particular atom.

There are many technical challenges to building such an atomic clock—cooling the atoms, preparing them in the right initial state,illuminating with microwaves in a clever way to maximize the sensitivity, detecting that the electrons are indeed in the higher state at a given time—but clocks based on caesium atoms are now the most accurate way to measure time, with a rate of ticking that deviates from complete and utter regularity by only one millionth of a second in one hundred million years.

These clocks provide a time standard that is agreed internationally and maintained by government laboratories such as the National Institute of Standards and Technology (NIST) in the US, the National Physical Laboratory (NPL) in the UK, and PhysikalischTechnische Bundesanstalt (PTB) in Germany. They are crucial components of many technologies that underpin our daily lives. For instance, they are vital for the global positioning system (GPS) that is the basis for navigation, including the satnav commonly used in cars.

Clock synchronization

The next challenge is to synchronize the two clocks, so that they are calibrated. One way to do this is by sending a signal from one clock to another. You start the first clock, sending a pulse of light to the other clock telling it when your first ‘tick’ occurred. The person in charge of that clock then knows what fraction of tick her clock is behind yours (since the clocks are the same construction,we can assume they tick at the same rate) and can use this information in setting the correct time.

There’s an interesting consequence to this. Imagine you want to synchronize your clock on Earth to that on a distant planet, in a far-away galaxy. You send your pulse of light off into the direction of the planet, and then you wait. As the planet is far away, it might take a very long time for the light to get there, even given the high velocity of light. Meanwhile you are getting older and older. The person who receives your synchronization message will have received it from the young you—she will see you as you were when you sent the message.

Likewise when we look at the night sky, and see the distant stars,we are seeing images of them by receiving light that left their surfaces a long, long time ago. And as we look to stars or galaxies that are even farther away, so we look into the deeper and deeper past, seeing the universe as it was billions of years ago. In that sense, the light that reaches us is also billions of years old—it has been travelling across space for an age since its birth in the remote past. Light is the oldest thing we can see in the universe.

Our clocks, though, are a bit closer together. An interesting fact is that when you put one of these clocks on an aeroplane moving at 800 kph or so, you find that it ticks slower than one on the ground. That is, if you set the clocks to tell the same time, you will find that the one in the aeroplane appears from the ground to be ticking at a slower rate than the ground-based one. This is a consequence of the maximum speed at which signals can be conveyed between the two clocks—the speed of light.

You can see this by looking at the situation in Figure 29. There,person A is on the ground and person B is in an aeroplane moving at high speed. B watches as A sends a light pulse to a mirror suspended at height H above the ground. From A’s point of view,the light pulse travels distance H. However, from B’s perspective that signal will travel a slightly longer distance than H since A appears to be moving backwards at high speed relative to B.Therefore, because the signal travels at light speed according to both A and B, and both record the same number of ticks between sending and receiving the signal, then the only explanation is that B’s clock is ticking slower than A’s clock when seen from A, and A’s clock is ticking slower than B’s when seen from B. This effect is called time dilation.

29. Time dilation due to relative motion. Observers A and B bothmeasure the time for a pulse to arrive at the suspended mirror. Theymeasure different times because they are moving relative to oneanother.

Einstein argued in a similar way that space should also contract.That is, a rod of B’s imaginary scaffold should look smaller to A than an identical rod in his possession. And vice versa: A’s rod looks shorter to B than her own.

Both of these effects arise because there is a maximum speed at which signals of any kind can propagate, and this speed is the same for everyone. If that were not the case, then one could determine a preferred scaffold, or ‘frame of reference’, in which the signals went at the highest speed. Einstein’s work on relativity showed that there is no preferred frame, so that Newton’s idea of a fixed, pre-defined space could not be the case. Since the maximum speed for signals of any kind turns out to be light speed, light is crucial in defining space and time.

It’s worth asking how precisely we might be able to synchronize two clocks by the ‘light pulse’ method discussed previously. You can see that one way to do it is by making the light pulse as brief as possible, so that the uncertainty over when it arrives is minimal.Thus it is important to know if there are limits to the brevity of light pulses. It turns out that there are, and they arise from a similar sort of wave property that limits the resolution of imaging systems, as we saw in Chapter 3.

We might start by asking how it is that we determine the frequency of a light wave. Imagine taking one of our clocks and asking how many peaks of the wave reach us during the interval between two ticks. The greater the number of peaks, the higher the frequency. The precision with which we can determine the frequency depends on how many times we repeat this measurement, since our ability actually to tell whether we have reached the peak of a wave may not be perfect. Thus, the longer we count, the more precise our determination of frequency. This trade-off is fundamental for waves—the imprecision in frequency multiplied by the uncertainty in the time interval is a fixed product. This was first understood by Joseph Fourier, a19th-century French mathematician and scientist who played a key role in formulating the wave model of light propagation.

Ultrashort light pulses

Fourier’s theorem is important for clock synchronization, since it says that if we want a short pulse, we must have an indefinite frequency. Another way to say this is that a short burst of light is constituted by a broad range of colours. That’s entirely analogous to the situation Abbe identified for imaging optics: a high-resolution image, demanding a small focus, requires a wide range of ray angles to be collected. In fact, the analogy goes further. Just as Abbe showed the smallest size of a focal spot could be approximately one wavelength of the illuminating light, so Fourier showed that the shortest-duration pulse is a single cycle of the field.

What this means in practice is that for light in the visible region of the spectrum, it is possible to produce pulses with a duration of about 2 fs. Amazingly, light sources derived from lasers can now routinely produce pulses of such startling brevity. They are based on the mode-locking technique described in Chapter 5.

But these are not the shortest bursts of light that occur in nature,nor even the shortest that can be produced in a laboratory.That honour goes to light sources with much shorter average wavelengths. For instance, using the single-cycle argument you can easily see that if the wavelength is shortened, then the duration of an optical cycle is reduced and in principle the duration of the pulse can be reduced. This approach currently holds the record for the world’s shortest controllable light pulses.By shining very intense laser light on an atomic gas, a process known as high-harmonic generation produces light waves with a frequency multiples of several tens of the driving laser frequency.This allows pulses with durations of several tens of attoseconds(10-18
s, or a billion billionth of a second). These are unimaginably short bursts of light, with duration equal to the time it takes an electron to oscillate within an atom.

Frequency combs

In Chapter 5, I stated that in a mode-locked laser a single pulse traverses the optical cavity. Each time it bounces off one of the mirrors, a little bit of the light pulse is transmitted through the mirror and exits the cavity. As a consequence, outside the cavity the light appears as a ‘continuous’ sequence of pulses spaced by the round-trip time of the light in the cavity, typically a billionth of a second or so. A ‘snapshot’ of such a train of pulses would show these very short bursts separated from each other by a delay that is long compared to their duration, like the teeth of a comb (as shown in Figure 30). And the pulses can be made identical to one another by careful adjustment of the laser producing them, so that the electric field of each of the pulses peaks at exactly the same time with respect to the intensity envelope of the pulse.

It turns out that this configuration means that each of the ‘teeth’in the frequency comb has a very precise position at an absolute frequency. A precisely calibrated set of frequencies is a very important tool for building accurate clocks. This is because it allows a direct comparison of optical frequencies to lower (usually microwave) frequencies, which can be counted by means of electronics.

Thus frequencies in the microwave region inhabited by the caesium atomic clock can be compared simply to much more precise electronic transitions in the optical region of the spectrum in, for example, strontium atoms or aluminium ions. Therefore the standard caesium atomic clocks used in satellite navigation,for instance, can now all be synchronized and to tick at the same rate to within one part in a billion billion (i.e. 1:10-18
), due to the precision of the optical electron oscillation frequency within strontium or aluminium.

30. Train of identical nearly single-cycle optical pulses. The spectrum of the pulse train looks like the teeth of a comb, hence it is called a frequency comb.

‘Optical clockwork’ of this kind allows the comparison of disparate frequencies with such remarkable precision that it provides a means to test the tenets of relativity, and thus to understand better the role of light in defining space and time. Frequency, and thus time, is the physical quantity that can be measured with the highest precision of any quantity, by far.

Optical telecommunications

Frequency combs are also important in telecommunications links based on light. In Chapter 3, I described how optical waves could be guided along a fibre or in a glass ‘chip’. This phenomenon underpins the long-distance telecommunications infrastructure that connects people across different continents and powers the Internet. The reason it is so effective is that light-based communications have much more capacity for carrying information than do electrical wires, or even microwave cellular networks. This makes possible massive data transmission, such as that needed to deliver video on demand over the Internet.

Many telecommunications companies offer ‘fibre optic broadband’deals. A key feature of these packages is the high speed—up to 100megabytes per second (MBps)—at which data may be received and transmitted. A byte is a number of bits, each of which is a 1 or a 0. Information is sent over fibres as a sequence of ‘bits’, which are decoded by your computer or mobile phone into intelligible video, audio, or text messages. In optical communications, the bits are represented by the intensity of the light beam—typically low intensity is a 0 and higher intensity a 1. The more of these that arrive per second, the faster the communication rate. The MBps speed of the package specifies how rapidly we can transmit and receive information over that company’s link.

Why is optics so good for communications? There are two reasons.First, light beams don’t easily influence each other, so that a single fibre can support many light pulses (usually of different colours)simultaneously without the messages getting scrambled up. The reason for this is that the glass of which the fibre is made does not absorb light (or only absorbs it in tiny amounts), and so does not heat up and disrupt other pulse trains.

Further, a light beam propagating in glass has to be very intense in order for it to influence another light beam. For instance, when you cross the beams from two laser pointers you don’t see either beam distort or deviate from its original path even though the two beams pass right through each other. (If your laser pointers had enormous power, you might just see such an effect, but only because the room is full of air. In a vacuum they would still not influence each other.) This means that the ‘crosstalk’ between light beams is very weak in most materials, so that many beams can be present at once without causing a degradation of the signal. This is very different from electrons moving down a copper wire, which is the usual way in which local ‘wired’ communications links function. Electrons tend to heat up the wire, dissipating their energy. This makes the signals harder to receive, and thus the number of different signal channels has to be kept small enough to avoid this problem.

Second, light waves oscillate at very high frequencies, and this allows very short pulses to be generated, as described earlier. This means that the pulses can be spaced very close together in time,making the transmission of more bits of information per second possible. Indeed rates of 40 Gbps (a Gb, or Gigabit, is a billion bits)are possible in current-generation commercial long-haul systems.Electrical signals in copper wires are limited in the duration and spacing of pulses coding the information by the heating effects noted previously, which tend to get worse at higher frequencies.Copper wires run out of steam, as it were, at much lower bit rates.

Fibre-based optical networks can also support a very wide range of colours of light. Glass transmits a broad range of wavelengths,with particularly low scatter and absorption loss in a spectral window from 1.3–1.55 μm. The rate at which photons are lost in fibre at these wavelengths is about 5 per cent per kilometre. These losses can be made up by amplifying the light while in the fibre so that transmission over very long distances (such as across the Atlantic Ocean) is possible without any conversion of the light to electrical signals or vice versa.

The telecommunications spectral window is divided into many individual frequency ‘slots’—much like the frequency comb shown in Figure 30. Each spectral component is a separate communications channel. There can be 150 or so slots in the window. Within each channel, a 40 Gbps optical signal can be operated. Therefore the total bit rate for communications is 150times 40 Gbps, or 6 Tbps (1 Tb, 1 terabit, is 1,000 billion bits).

The ever-increasing demand for communications bandwidth due to increased use of the Internet and the services it provides have spurred optical engineers to new heights of creativity in harnessing the potential of light.

Chapter 7 Lighting the frontiers

Despite its long history as possibly the oldest continuous branch of natural philosophy and science, optics remains at the forefront of research and application. It is ubiquitous: as a tool for sensing,imaging, and communications, as well as providing ways to explore, discover, and illustrate new fundamental effects.

Light can generate conditions at the extremes of what is known to be possible according to physics, such as extremes of temperature and extremes of pressure and stress that do not exist naturally,except perhaps in the remotest of stars. And light can be used to observe and even control really fast events, such as the movement of electrons inside atoms.

Further, light can exhibit strange features associated with the quantum world, revealing even in everyday conditions some of the counter-intuitive aspects of the fitful world of randomness that underpins the stable, solid world of our normal experience. In this chapter, I will explore some of the frontiers to which, and across which, light is currently taking us. Exploration of these frontiers is possible because of the great technological strides that have been made in light sources, optical systems, and detectors, which enable exquisite control over the shape and intensity, in both space and time, a light beam can take.

Light mechanics

Light can exert forces on objects. This allows ‘remote control’ of bits of material using shaped light beams. Light can be used to move matter around, and bring it into contact with other objects,or to manipulate the internal configuration of atoms and molecules, forcing them into, for example, simple chemical reactions, in ways that allow both the study and exploitation of unusual material properties. That’s an extraordinarily powerful feature in many areas of research and study.

The concept of mechanical force arising from light has its origins in the momentum carried by each photon. For instance, when a photon is reflected from a mirror, that mirror experiences a force that provides the exertion needed to redirect the photon, just as water from a fire hose hitting a wall exerts a force on the wall by virtue of its bouncing off.

Similarly, when a photon is refracted it changes direction, and this, too, requires a force. Thus the photon exerts a force on the refracting element. If a light beam is incident on a glass bead, rays that are nearly tangential to the bead will experience the greatest change in direction. A photon traversing the ray in the lower half of the bead is directed upward as it propagates through the glass surfaces. The bead therefore experiences a force in the opposite direction. Since the momentum of the photon in the forward direction (the direction it was moving before encountering the bead) is reduced, there is also a net force in the forward direction.The strength of this force depends on how many photons are refracted per second. A light beam that is more intense at a position near the centre of the beam than on its periphery will therefore drag the bead towards the higher-intensity part of the beam.

This effect can be used to make a focused light beam into an‘optical tweezer’, which is able to hold on to a minute object and move it around as the light beam is steered. Optical tweezers find applications, for example, in biology, by enabling control of the position and movement of individual strands of DNA and the characterization of tiny molecular motors. Specifically, DNA,proteins, and other biologically important molecules can be stuck on to these beads and can therefore be handled using optical tweezers. Their position can be controlled with a precision of much less than the wavelength of light. This allows extremely small forces to be measured—such as happens when biological cells adhere to surfaces or other cells—as well as to hold the cells in places as they are operated on using other lasers (so-called cellular surgery). Optical tweezers can be combined with various other test methods, such as light scattering from aerosols, or spectroscopy, to characterize particles that may be pollutants in the atmosphere.

These opto-mechanical forces can also be used to access completely new states of motion of small objects. In particular, it is now possible to build tiny mechanical cantilevers, illustrated in Figure 31, and to both observe and control their motion using light. Light forces can be used to cool or heat the oscillations of the cantilever—like running down or winding up a watch spring—and eventually to bring it into the quietest state possible,where only quantum fluctuations of the motion disturb the complete stasis of the lever. Light forces can also be used to cool atoms—much smaller objects—and this reveals even more strange quantum states of matter.

31. A nano-scale cantilever controlled using light forces. The discs are tiny mirrors about 30 μm in diameter.

Ultra-cold

What’s the coldest thing you’ve experienced? Colder than winter in Oxford (approximately 2°C), or in Ottawa (-20°C), or the South Pole (-50°C)? Or perhaps the effects of liquid nitrogen, at-200°C. These are certainly cold, but by no means the coldest things possible. It turns out that there is a lower limit for temperature: -273°C, or 0 K (Kelvin), below which it is not possible to cool things further. This is the temperature at which things are as still as they’re going to get, with just the effects of quantum mechanics to cause a little jiggling about of atoms and molecules.

It’s not actually possible to build a machine to get to absolute zero but it is possible to get very close using an ‘optical refrigerator’.In fact, you can get cold enough to make the atoms almost stop moving. What this means is that their size gets bigger. (Quantum mechanics tells us that you can’t simultaneously specify the precise location and speed of an object. If the atom is completely stopped,then it must be extended over all space.) Therefore all atoms in the cloud that has been refrigerated occupy the same region of space,and this gives rise to some very strange new phenomena.

An optical refrigerator works by using lasers to ‘cool’ atoms.Imagine a laser beam shining on an atom that is moving from left to right, say. The laser shines from the right to left, so that a stream of photons hits the atom. The laser is tuned in frequency to be absorbed by atoms that are moving at a particular velocity.Now, when the atom absorbs a photon from the laser beam, it gets a kick from the photon, and thus slows down. (More specifically,the momentum of the photon is transferred to the atom. Since it is in the opposite direction to the initial momentum of the atom, it reduces the momentum, and thus the speed of the atom.) The atom must re-emit the photon at some later time, and it will get a kick in the opposite direction to that in which it emits the photon.But the direction in which it re-emits the photon is random—it can go in any direction at all.

If you look at enough of these absorption-scattering events, then you will find that, although the light is always absorbed from one direction (the incoming laser beam) it is emitted uniformly in all directions—no one direction is preferred. The consequence of this is that on average a collection of atoms moving in a direction opposite to the laser beam grinds to a halt, and is left with random motion representing a temperature that is proportional to how long it holds on to the light before re-emitting it.

There are several refinements of this approach, each of which uses light to cool atoms (and molecules) to even lower temperatures,and for which light acts like a ‘viscous fluid’ in which the atoms move slower and slower. It is even possible to use light to trap atoms using optical tweezers once they are slow enough. This allows the application of yet more sophisticated optical cooling techniques, by which it is possible to get to temperatures of a billionth of a degree above absolute zero.

I referred to some residual ‘jiggling’ of the atoms that happens even at zero temperature, arising from quantum mechanics. The range of this jiggling can be thought of as the spatial extent of the atom itself. That is, according to quantum mechanics the atom isn’t just wandering around in a random fashion over a small region of space, but rather it is actually present across all that region at once. For atoms trapped at such low temperatures the size of that region may be several thousandths of a metre. That’s a remarkably large atom, given that the distance of the electron from the atomic nucleus is less than one tenth of a billionth of a metre. What’s even stranger is that several atoms can occupy this region of space at the same time.

That’s conceptually very counter-intuitive. We often think of atoms as being like little billiard balls, that can be packed close together, as in a solid material, but which retain their individual distinction by virtue of their location inside the material. That’s not the case for these very cold atoms. They are each everywhere at once, in a new state of matter identified by Einstein and the Indian scientist Satyendra Nath Bose and called, not surprisingly,a Bose–Einstein condensate.

This very strange state has some remarkable properties. For instance, it is a superfluid, which flows without viscosity. Further,it is possible to split the entire atomic cloud in half and recombine it to show quantum interference between the two separated parts,essentially demonstrating that a big object (containing many atoms and of a palpably visible size) exhibits quantum character,attributable to the uncertainty of whether an atom is in one part of the cloud or the other. One has to think of each atom occupying both separate components at the same time.

Because these cold atoms can be trapped in light beams, it is also possible to create spatial structures out of several light beams that can be used to manipulate the atoms. For instance, when two light beams coincide they form an interference pattern (see Chapter 3)in which there are regions of high and low intensity. Cold atoms like to settle in one or other of these regions (you can adjust which one by choosing a particular wavelength of the light). As the intensity of the light beams is turned up, the atoms fall into the‘egg-crate’-like optical traps that appear in the intensity pattern, as shown in Figure 32a. And they do so in very interesting ways.

32. Cold atoms trapped in an optical lattice: a. a few hundred atoms per cell (several 10s μK), b. individual atoms at each site (a few nK).

When the atoms are cold enough, they don’t like to be located at the same ‘site’ in this egg-crate, so the resulting distribution of atoms is very like a full egg carton—one atom at each site, as shown in Figure 32b. In this case there is no superfluidity, since the atoms like to stay put. It is more like an ‘insulator’, as nothing moves. By turning the light intensity up and down it is possible to explore this interesting transition between completely free flow and no flow at all.

The ability to do this in a system that is fully quantum mechanical allows scientists to explore new properties of matter that are relevant to other types of materials (for example, solid-state metal oxides) over which it is difficult to exert the same degree of precision control and measurement. In cold atomic gases it is now possible to look at atoms in these egg-crates individually and see what they are doing as changes are made to their environment.

It is possible to explore this low-temperature regime with many different kinds of atoms, and to build complicated trapping structures using light. The idea of using cold atoms to ‘simulate’other quantum systems is a current area of research. It allows exploration of complex problems that cannot be solved in other ways, and is expected to lead to a new understanding of materials and structures that will have impact in new ways—perhaps helping to understand and even design new magnets that will be used for applications such as data storage for computers,magnetic resonance imaging machines for healthcare, or even friction-free motors for levitating trains.

Ultrafast

Light pulses can be extremely brief. In Chapter 5, I stated that they can be as short as a single cycle of the optical field. For light in the visible region of the spectrum, that’s about 2 fs. For light in the extreme ultraviolet region, which is of shorter wavelength and higher frequency, the durations can be much shorter. The shortest yet measured is less than 100 as (10-18
s) long. These are currently the shortest pulses that can be controllably generated (although we can observe events that happen on a much shorter timescale by means of particle colliders). And with the advent of bursts of light in the X-ray region of the spectrum, we can expect that even shorter timescales are possible.

Since these numbers are so mind-bogglingly small, it is helpful to put them into context. The age of the universe is approximately5 × 1017 s. Thus the ratio of one second to the age of the universe is approximately the same as the ratio of one attosecond to one second. Or to put it in an economic context, if the national debt of the US is equivalent to a second, then one cent would be equivalent to a femtosecond. On this scale, a single attosecond is virtually worthless.

What sort of things can happen on this timescale? In Chapter 4,I introduced a simple model of an atom—called the Bohr model—in which electrons ‘orbit’ an atomic nucleus, attracted to it by electric forces in much the same way as planets orbit the Sun, attracted by gravitational forces. The time taken to execute these orbits for simple atoms (that is, those with only a few electrons) is about 150as. So if we want to look at this motion, we might need to use pulses shorter than this, so we don’t just see a blur.

The idea of the stroboscope is the one most relevant to our story,since a variant is used by researchers today to look at the really speedy changes that go on at the fundamental level of atoms and molecules. In this application the light pulses from a laser are split into two (or more) parts, with a delay introduced between them.The first pulse in the sequence illuminates the sample, and some of it is absorbed. This ‘triggers’ some changes in the system—electrons move around in the atom, or bonds vibrate in molecules or solids. An instant later the second pulse arrives and some of it is again scattered from the sample and detected.

As the delay between the two pulses increases in repeated runs of this experiment, the detected scattered light maps out the dynamical changes of the sample. In a sense it makes a ‘movie’ of the atom or molecule or solid as it changes. This ‘pump-and-probe’ scheme has been used to get into the guts of what happens, for instance, during a chemical reaction, when two molecules are reconfigured by their interaction. More sophisticated versions of this kind of approach exist using several light pulses. These approaches are being used now to explore many fundamental features of extremely interesting and puzzling materials, from interacting atoms and high-temperature superconductors to biological systems.

I’ve noted that the shortest pulse it is possible to generate is a single cycle of the optical field. It turns out that you can devise an experiment to measure the oscillations of the optical electric field using the extreme ultraviolet (EUV) pulses produced by highharmonic generation. What is needed to measure the pulse field is a very fast process, one that is much faster than the optical cycle itself.That can be provided by a pulse with much shorter wavelengths,about twenty or thirty times shorter than that of the optical wavelength. Pulses of such brevity are generated when an electron is ripped off an atom by means of a strong optical pulse. This requires an optical field whose strength is comparable to the binding force of the electron to the atomic nucleus. Such pulses are readily available by adding optical amplifiers to the output of a mode-locked laser.

When the electron is liberated by such an intense pulse, it finds itself sitting in a rapidly oscillating electric field, and, if its liberation occurs near a time when the field has zero amplitude,the electron can ‘surf ’ along the next cycle of the optical wave,taking an excursion away from the atom, and then back again.When it returns it is moving very fast, and when it recollides with the atom it can be recaptured by emitting all of its extra energy as light. In this case a very short pulse is emitted as the electron recombines, having a very short wavelength of perhaps a few tens of billionths of a metre, in the EUV region of the spectrum, about twenty times shorter than the optical wave that generated it.

Now imagine that this EUV pulse shines on another atom. It has a sufficiently short wavelength such that it is absorbed by the atom,and knocks off an electron, which then sits near the atom. Imagine further that the atom is simultaneously illuminated with the short optical pulse we seek to measure. The field of this pulse accelerates the electron in one direction or another depending on the part of the optical cycle at which the electron is liberated by the EUV pulse. By changing the delay between the EUV pulse and the optical pulse, the acceleration of the electron can be measured since faster electrons, which have been accelerated to a greater degree, have more energy. In this way it is possible to ‘see’ an optical pulse field (Figure 33), despite the extraordinarily short timescale of the oscillations of the field.

An example of an application of the methods of pump-and-probe spectroscopy in biochemistry is the study of the first steps in the process of photosynthesis, by which plants convert carbon dioxide from the air into oxygen using sunlight as an energy source. The processes by which this happens involve transporting energy around a big biological molecule with remarkably high efficiency.The means by which this happens has some very interesting and poorly understood features—it is faster than one might expect and much more efficient. If we could learn from systems that have evolved naturally over eons how to do this, perhaps our understanding would enable us to apply it to things like improving the design of solar cells, which would have an enormous impact on society.

33. Direct image of the electric field of an optical pulse. The time between two adjacent peaks is approximately 2.5 fs.

Ultra-intense

Your electricity bill tells you how much energy you used in the previous month. It is measured in units of kilowatt-hours (kWh),and you are charged for each unit that you consume. Let’s say that you used 220 kWh in some month (this is the average monthly energy consumption in the UK). Now, you could use all this energy at the same rate across all four weeks of the month. Or you could use it in the first week, and use nothing in the subsequent three weeks. But can you imagine using it all in a million billionth of a second? You’d need to have an awful lot of appliances to use that much energy in such a short time, and you’d need to be able to switch them on and off impossibly quickly. But the peak rate or power would be immense.It is possible to produce light pulses that can achieve this. That is,they are incredibly brief and contain this amount of energy. In fact, it is possible to produce a pulse that delivers energy at a rate equal to the entire electricity generating capacity of the planet at a given instant. But the lights in your house won’t go out, because the pulses are so brief that the total energy in them is very small.

Lasers that produce pulses of this kind are massive instruments,occupying large buildings that are a significant fraction of a football field in size. One example is the VULCAN laser at the Rutherford Appleton Laboratory in England. VULCAN produces pulses with 500 Joules of energy (1 J = kWh) in a pulse of 500 fs duration. 500 J is the energy emitted by a 100 W light bulb in five seconds. Yet the brevity of the pulse means that the intensity of the light can be as high as a million suns. The laser at the National Ignition Facility (NIF) in Livermore, California is much, much bigger than this. And the proposed European Light Infrastructure project is set to deliver a system capable of even greater peak power than that at NIF.

Such very brief, very intense light bursts can be used to alter states of matter. The electric field at the most intense moment of the light pulse is larger than the attractive field between the electrons and nuclei that holds atoms together. So it is possible to strip the electrons off the atoms to form a new state of matter—a plasma.And it’s possible to do this in an instant, shorter than the time over which the atomic nuclei can move, so that the plasma is very dense—nearly the same density as in a solid block of material such as a piece of glass, except now at two million degrees Celsius.

These are the conditions inside the cores of the giant planets and even some stars: very high-density plasmas with particles colliding with each other at high speed and at pressures of a million times that of our own atmosphere. It is possible to use this new laboratory-accessible state of matter for several things. For instance, we can begin to understand how stars work, what their life cycle is, and to characterize their stages of evolution, such as supernovae explosions and white dwarfs. Other situations of interest to astrophysicists are also amenable to experimental exploration using lasers. Astrophysicists also use such plasmas to probe the frontiers of planetary science. For instance, it is possible to infer the composition of the gas giants from their mass and size,but only if the degree to which matter can be compressed at such high pressures is known.

Some laser facilities generate pulses using light of very short wavelengths. These pulses are produced by accelerating electrons in magnetic fields, so that they ‘wiggle’ from side to side as they whiz down the accelerator. This produces a kind of synchrotron radiation consisting of short bursts of X-rays. Often these kinds of lasers use techniques, and indeed hardware, from particle accelerators. Examples of these are the Stanford Linear Collider Light Source (LCLS) and the Hamburg X-ray Free Electron Laser (XFEL).

The techniques afforded by the most intense laser pulses, in conjunction with short bursts of X-rays, enable scientists to diagnose plasmas in a wide range of conditions. Further, the immense pressure exerted by lasers between atomic nuclei can cause them, under the right conditions, to fuse together, releasing a large amount of energy in the process. This ‘nuclear fusion’ is a possible route to an almost unlimited source of energy. This application of lasers is extremely technically demanding, and is one of two methods that are being explored to achieve fusion:the other does not involve light except as a way to monitor the process. Both make use of dense plasmas.

As the laser pulses move through these plasmas, they generate a wave, very similar to the wake that trails a boat moving across a water surface. The electric fields in the plasma wave can reach more than 100,000 V over 10-6
m (that’s about ten times the voltage in the big power lines on pylons, over a distance of less than one tenth of a human hair’s breadth.) These field strengths are at least 1,000 times bigger than the accelerating fields used in the world’s biggest machines for studying fundamental particles,such as the Large Hadron Collider (LHC) at CERN in Geneva. It may be possible using laser methods eventually to build table-top devices that can accelerate electrons to similar energies as currently possible in the LHC.

It is also possible to accelerate heavier particles, such as protons,by means of the extraordinarily strong electric fields generated by the interaction of laser pulses with matter. Proton beams are currently being explored as a cancer treatment, since the delivery of heavy particles to diseased tissue can be done more precisely and at greater depths than is currently possible using other types of radiation therapy.

The extraordinary properties of light continue to enable new realms of discovery, across a wide range of fields. Light is a ubiquitous tool for science and technology.

Chapter 8 Quantum light

In Chapter 1, I introduced the idea that light could be construed as a stream of particles, which I labelled ‘photons’ for convenience.It turns out that these are real particles, which can be produced,played with, measured, stored, and used for doing things. However,even though photons are in a sense the simplest expression of light, making individual photons is not so simple. Most light sources generate light of a different kind, for which the number of photons is not fixed.

A light bulb, for instance, produces a stream of photons that sprays everywhere. If you looked at the light going in just one direction from the bulb, and then examined just a short temporal section of the beam—a time slot, if you like—then you’d be able to count some photons in that slot. But if you repeated the experiment several times, you’d find that the number of photons was random,sometimes large and other times small. The average number of photons would be fixed, depending on the brightness of the bulb,but you’d never be able to say with certainty how many photons you would measure in the beam at a given time. That’s one of the characteristics of ‘classical light’—light that can be described entirely in terms of waves.

Laser light is also of this kind. The average number of photons in a pulse of laser light can be large, but for any given pulse the actual number of photons will be bigger or smaller than the average.The spread of photon numbers in a pulse is approximately the square root of the average number, so that the relative ‘noise’—the variation in the number of photons in each pulse compared to the mean number over all pulses—gets smaller the higher the average number of photons.

Thus a laser beam has intrinsic intensity noise. This sets a limit on the quality of images you can get with laser illumination.The fluctuations in the laser intensity mean that detecting the separation of two points in an image is imprecise. In fact it is very imprecise for low-intensity light, where the mean photon number is small (so the object is hard to see) and the variation in photon number from frame to frame is large. The only way to get precise measurements is to look for longer, thus increasing the number of photons illuminating the object, and averaging the results over many laser pulses. The relative intensity noise is reduced by this signal averaging, leading to a better-resolved image. The precision increases in proportion to the square root of the number of photons used. This is called the ‘standard quantum limit’, since no classical light beam can beat it.

Quantum light, on the other hand, allows you to achieve much better results in signal averaging for the same average number of photons, since quantum light can have much lower noise than any classical light. But first, you have to build a quantum light source. There are many kinds of such a source, each producing a distinct kind of quantum light. But we might consider, to be concrete, a source that generates the primitive quantum state of light—a photon.

Single photons

So how could you make just a single, individual photon? There’s a very practical scheme, invented by Otto Frisch in 1965. His idea was simple. Take a single atom and put it in its excited state (see

Chapter 5 for a discussion of how to do this). Then wait for it to drop to its ground state. When it does, it emits just one photon,since only one ‘quantum’ of energy can be stored in a single atom.You can tell when the atom has emitted the photon, because it recoils from the ‘kick’ provided by the photon’s momentum. If you detect the atom moving, you can determine both that the single photon is on its way and the direction in which it is going.

Some modern quantum light sources operate in a similar way to this, only they corral the atom between two mirrors (an optical‘cavity’ similar to that of a laser), and excite it very quickly so that it emits preferentially into a direction defined by the cavity axis. This makes a reliable source of single photons. It is an especially ‘low noise’ source, since the photons are emitted with strict regularity.If you looked at a given time slot in such a beam, you’d be able to predict with certainty how many photons would be in it—just one.Therefore the intensity is exceptionally stable—it is a ‘quiet’ light beam, in contrast to the ‘noisy’ classical one.

The idea is also used in other quantum light sources. In particular,you can construct a very simple light source using nonlinear optical effects. Specifically, there are crystals that enable one input photon with high energy to be split into two photons with lower energy, each about half of the original input photon. The probability that this fission takes place is rather small, for most materials.But since the photons are produced in pairs, you can use one as a ‘herald’, to signal the presence of the other (Figure 34). Such light sources are the workhorse of the field of quantum optics,which uses the quantum mechanical features of light to explore the foundations of quantum physics, as well as to enable new kinds of information technologies.

Just as classical electromagnetic waves can be polarized, so can photons. So we might find a vertically polarized (V) photon or a horizontally polarized (H) photon. These would behave just like waves, in that if we measured the polarization of the photon by seeing if it passed through a polarizer oriented horizontally, then we’d find that the H-photon always passed through and the V-photon never.

34. A ‘heralded’ single photon light source, generating photonsrandomly, but with a signal that indicates when one has been prepared.

What’s strange here is that we can construct a diagonally polarized photon, oscillating with the field at 45 degrees to both the horizontal and vertical. But if we now try to see if the photon passes through the horizontal polarizer, then there is an ambiguity. The photon is the smallest ‘piece’ of light, so can’t be divided further. How should it behave at the polarizer? What happens is that it is transmitted with a probability of one-half, and reflected with equal probability(illustrated in Figure 35).

In practice what that implies is that if you try the experiment of putting a diagonally polarized (D) single photon into a horizontally oriented polarizer a million times, then 500,000 times it will go through. And the very strange thing about quantum mechanics is that you cannot tell on any given trial what will happen. This is not because the photon can be considered sometimes to be H-polarized and sometimes V-polarized. Rather it is because the photon is both H and V-polarized, simultaneously. The random outcomes of a measurement of the photon’s polarization therefore reveal the intrinsic uncertainty that inhabits the most fundamental level of the universe as described by quantum physics.

35. A diagonally polarized photon encounters a polarizer, and exits randomly through one output or the other.

Of course, you can make a virtue out of necessity in such circumstances. You can do practical things with single photons that are unimaginable with ordinary light. For instance, this property of photons can be used to generate random numbers,by measuring whether the photon is transmitted (labelling the outcome, say, 1) or reflected (labelled 0). The randomness in the string of zeroes and ones is inherent in the underlying physics,not just in the manufacture and casting of dice, or other contingencies. For this reason quantum random number generators are an emerging business—you can’t fake the randomness they provide.

A second example: you can make communications links for which the security is guaranteed by the laws of physics, rather than by trusting your telecoms supplier. This is because of two important properties of photons. First, you cannot detect them in two places at once. For that reason, if an eavesdropper grabs the photon to capture the information you are sending, then of course you don’t get the photon. So you receive no information, and you are aware that something’s wrong.

But if the eavesdropper is clever, she will send a ‘decoy’ photon that she hopes will fake the message. But you can tell that it’s a fake! The reason you can know this is that in quantum mechanics there is no measurement that can tell you everything about a single quantum particle.

Consider the following scenario. You want to send a simple binary message (0s and 1s) over this link, say a vertically polarized photon for 0 and a diagonally polarized photon for 1. If the eavesdropper (usually known as Eve) measures the photon and gets the answer ‘vertically polarized’, she could not be certain that the photon was a 0, since the diagonally polarized photon would give her the same answer at least half the time. So she gets some information, but not everything.

Now, let’s say the sender of the message (conventionally called Alice—you, the receiver, are Bob) sends you a photon coded as 1.Let’s say Eve measures this in the vertical orientation and gets a positive result. She must choose whether to send you a vertically or diagonally polarized photon. One strategy is to send you a vertically polarized photon, since that’s the most likely source of her result. Now you measure the diagonal polarization. If your photon is from Eve, it will give you the wrong result 50 per cent of the time. If it is from Alice, you will never get the wrong result.So by comparing a section of the received message with what Alice sent, you can tell if Eve is tampering with your line.

However, Eve might be even cleverer. She may try to copy the photon from Alice without measuring it. She could make two copies in fact, sending you the original. Then she can make a vertical polarization measurement on one copy and a diagonal polarization measurement on the second, and she would have determined the full information about the photon ‘bit’ that Alice sent you without you ever knowing. However, she would be thwarted. A remarkable feature of quantum mechanics is that there is no possibility of building a copying machine that can do this—make an exact replica, or clone, of a single particle in an unknown quantum state. It is simply forbidden by the laws of physics. Because of these two constraints imposed by physics—‘no measurement’ and ‘no cloning’—it is possible to build a secure communications link that can transmit a secret stream of random bits between Alice and you.

Squeezed light

There are other kinds of quantum light that provide different sorts of enhancements. Recall that light is oscillations of the electromagnetic field. A laser beam most nearly mimics this ideal behaviour. Yet even it has some ‘noise’ in the amplitude. That is,each time you measure the field amplitude, you get a different answer. The situation is sketched in Figure 36a, which shows some uncertainty about the field at each point, or phase, of its oscillation.There is a particular type of quantum light—called ‘squeezed light’—for which this noise varies with the point in the cycle of the field, as shown in Figure 36b. It is bigger at some phases than at others. It turns out that such a field is composed of only pairs of photons. If you measure the number of photons, you will only ever find an even number. The quantum interference of all these pairs is the origin of the phase-dependent amplitude noise.

There are certain things you can do with such a state. Imagine that you wanted to make a measurement of the phase of the wave.(Recall that that is what you do in an interferometer, and the phase shift is something induced on the light beam by an object you’d like to measure, such as the presence of a particular molecule.) The phase can be determined much more precisely at points in the wave oscillation where the fluctuations of the field are smallest. In fact, the fluctuations in the squeezed light field are smaller at some phases than any classical field, so that phase sensors using such a field will be more precise than sensors using classical fields. In fact they will break the standard quantum limit.

This is a costly approach to sensing at present, so it is only used where there is a clear advantage to be had—for instance in the detection of gravity waves by means of very large optical interferometers, such as the GEO 600 project near Hanover in Germany. By using squeezed light, this instrument can detect phase shifts that correspond to a relative path length change of the light equivalent to the size of an atom compared to the distance from the Earth to the Sun.

36. Squeezed light a. has reduced noise in its field amplitude at certain points in its oscillation as compared to laser light b.

Quantum entanglement

Things get even stranger when we consider more than one quantum light beam. Photons can be entwined in such a way that it is impossible to ascribe a property to either of them individually—for example, a colour, position, direction, or pulse shape. This goes well beyond the fundamental notion of wave–particle duality. It challenges the very notion that in the classical world it is possible to assign real values of properties to physical entities (e.g. in the case of light beams, say frequency and time of arrival, or H- and V-polarization)—in a way that can be revealed by a local measurement in a self-consistent fashion. The fact that this cannot be done for pairs of light beams prepared in certain states,and can be proven so by experiment, is one of the great triumphs of fundamental optical science in the 20th century.

By means of this property, it is possible to use quantum optics to explore the famous conjecture of Einstein, Boris Podolsky, and Nathan Rosen concerning whether a quantum mechanical description of a system of particles can be considered complete,requiring no other information to determine everything about the system. John Bell discovered in the 1960s a means to quantify such a question, and the quest to build an experiment to actually test his hypothesis began in earnest. These are known colloquially as ‘Bell tests’, and the earliest and currently most convincing work uses pairs of photons, each of which is correlated with the other. It is the nature of these correlations that is so different for quantum particles than for classical ones. It’s worth exploring this in a bit more depth in order to get a fuller sense of the strangeness of this quantum effect.

Correlations can be found in almost every situation. Consider for instance the following simple game. A dealer takes two packs of cards, one with green backs and the other with blue backs. The dealer picks one card from each pack and gives one to you and another to your partner. Each of you looks at your card. They always have different colours on the back, of course, but they may have the same colour (red or black) on the front. In fact, you’d expect this to occur half the time, since each of you would expect individually to get either red or black with equal probability (half of the cards in each deck are black and half red).

If you and your partner found that every time you both got red or both got black, you’d say that the cards were ‘correlated’. This is about as strong a correlation as you can imagine. In fact, if you both got the same colour more than half the time, you’d also be able to claim the cards were correlated, though clearly the correlations would be ‘weaker’ than in the first instance. By measuring the correlations, you could determine whether the dealer was cheating,since you might assume she’d start with two independent,complete decks.

We can make an analogy of this kind of correlation for photons using polarization instead of suit for the cards. That is, a horizontally polarized photon might be termed a ‘red’ photon,and a vertically polarized photon a ‘black’ one. Then if a source produces photons two at a time, as described above, you can say that it produces correlated photon beams if it always produces photons with a prescribed polarization, say one vertical and one horizontal, or both horizontal. This type of correlation is termed‘classical’, since it has a complete analogy to the situation with classical objects like playing cards.

There is a feature of correlations that has an intrinsic quantum mechanical aspect. Let’s say there are two possible states in which the photon pair can be prepared—the first H-polarized and the second V-polarized or vice versa. In the classical world these two situations for two particles are mutually exclusive: either HV or VH is possible, each with a probability of one-half. But, just as the single photon can be in a superposition H and V, so can the pair:HV and VH, shown in Figure 37. This turns out to be a much stronger correlation than is possible with any classical particles,and is called entanglement. It is the most enigmatic property of quantum physics, and has extraordinary consequences.

These are revealed by means of Bell tests. In such a test, you have to consider not only the possibility of correlations in the H and V polarizations of each particle, but also those in the diagonal (D)and anti-diagonal (A) polarizations, each oriented half way between the horizontal and the vertical. (Diagonally polarized light, for example, is shown in Figure 35. Anti-diagonal polarization is oriented at right angles to the D direction.) The analogy with the cards is that you can look at the front of the cards and observe either red (equivalent to H) or black (equivalent to V) suits. Or you could look at the backs and see green (equivalent to D) or blue(equivalent to A).

37. A light source for generating polarization entangled photons.

A quantum game

Now imagine a card game in which the dealer chooses from either pack and gives one card to each player. That means that each player will have a card that could be either red (R) or black (B) on the front (F) and either green (g) or blue (b) on the back (B). The dealer chooses to hand out cards in such a way that if one player looks at the front of his card, and the other the back of hers (F,B),then they never find the result (R,b). Similarly if the first player looks at the back of his card and the other the front of hers (B,F),then they never find the outcome (b,R). However, when they both look at the front of their cards (F,F) they sometimes see (R,R).From this, you would conclude logically that in such a case, had they looked at the front of their cards (B,B) they would have seen(g,g). That’s what would happen for obviously classical things like cards.

38. Table of the probabilities of possible outcomes for a quantum card game.

But in fact, when you take photons (or other particles) that are quantum correlated and do such an experiment it doesn’t turn out that way. What happens is that when the players make measurements of the polarizations using, for the first player, a horizontally oriented polarizer, and, for the second player, a diagonally polarized photon (or vice versa), they never get the results (V = 0, D = 1) and (D = 1, V = 0). Likewise, when they both measure using diagonally oriented polarizers, they sometimes get the result (D = 1, D = 1). Therefore you would logically conclude that when they measured the photons using a horizontally oriented polarizer, they would sometimes get the result (H = 1, H = 1).But, when they do this experiment, they never get this outcome!The table of possible results of such a quantum card game are shown in Figure 38. Such experiments can, and have been, done using photon pairs. It’s not fiction.

Local properties of things

So what is going on? This is the fundamentally weird thing about quantum physics: the conclusion of the quantum card game is that the photons cannot have predetermined values of their polarization when they are prepared at the source. It is as if the cards could not have been of definite suits from a deck with a well-specified card-back colour. This goes against all intuition about cards: they surely have definite properties of a specific suit on the front of each card and a specific colour on the back. No matter whether we know or even the dealer knows what these values are or not, we don’t doubt that the cards actually have these properties when they are given to us. And we certainly don’t expect that anything we do to them changes those properties. But quantum mechanics tells us that we cannot assign colours to the cards a priori.

It is the measurements that give definiteness in the outcomes.We cannot claim the measurements simply reveal predetermined properties of the photons, which are unknown to the players.It is actually that you cannot assign definite polarizations to the individual photons when they are produced by the source in such a way as to give the outcomes that are actually seen. If you try to devise a way of dealing cards that gives such a result, you’ll find that it is impossible. The cards would need to have the possibility that they can be simultaneously in superpositions of red and black or green and blue, in particular ways. Just so the photons—it is necessary for them to be in superpositions of H and V in a way that gives very specific types of correlations. It is this type of correlation that is termed ‘quantum entanglement’.

Entanglement is a very weird concept. It is not possible to find a way to think about it in terms of common everyday objects—as the playing card example was intended to show. Yet entanglement is also very common. It appears in many things at the quantum scale,even in everyday conditions: in the correlations between electrons in molecules, giving rise to bonds between the atoms making up the molecule, or even relatively small atoms themselves, as well as exotic materials like superconductors.

Surprisingly, entanglement also turns out to have technological implications. You’d hardly think that such an arcane and abstract idea could possibly have any application, but it does. It enables a raft of information processing approaches that cannot be replicated by sending classical waves back and forth.Indeed, the very idea that all information processing systems are at bottom built of something suggests that the design principles of these machines must reflect the underlying physics of the constituent parts—usually classical physics. This has led to the understanding that basing computing, communications, and measurement on quantum mechanics provides new opportunities for technologies that surpass those of the current generation in unimaginable ways: communications whose security is guaranteed by the laws of nature; computers that can solve ‘uncomputable’problems; imaging systems that reveal an object that they are not even looking at.

Light plays an important part in implementing such systems. The infrastructure of optical fibre networks, for instance, can be used to distribute random ‘quantum keys’ (random strings of 0s and 1s)completely securely between two parties, which can then be used to encode messages. Such networks can also be used to connect small-scale quantum processors, eventually becoming a distributed quantum computer. Indeed, it has been shown that in principle it is possible to build a quantum computer completely out of light,though it is extremely challenging to do so. Combining these technologies holds the promise in the future of a quantum Internet,a radically different way to communicate and process information from the technology we currently use, and all enabled by light.

Chapter 9 Twilight

The atoms of Democritus

And Newton’s particles of light

Are sands upon the Red Sea shore

Where Israel’s tents do shine so bright.

William Blake, ‘Mock on, Mock on,

Voltaire, Rousseau’

It is inevitable that in a book of this brevity—covering a topic with as long a history and as broad a range of applications as light—many things simply can’t be covered. In particular, the fantastic discoveries arising from looking at other regions of the electromagnetic spectrum than the visible, and the ubiquity of optical devices in everyday life are very incompletely described.

The myriad versions of imaging devices, from multi-mirror telescopes (with diameters of tens of metres, and adaptively controlled reflectors to null the effects of the twinkling sky) to massive synchrotrons (accelerating electrons to the point that they radiate intense X-rays for looking at tiny material structures, both man-made and natural, to reveal the structure of, for instance,biologically important molecules or engineered metals) are only hinted at. But no matter: I hope that you are convinced of the beauty of light, and that a tour through its mysteries and how they were unravelled is as interesting a story as you could want.

Meanwhile, the science and technology of optics is vibrant,opening up new areas for exploration and new applications, often with unexpected fruitfulness. Light continues to reveal new mysteries and to inspire new devices: it still engages and fires our imagination as it has done for centuries.

Further reading

Non-technical books

O. Darrigol, A History of Optics from Greek Antiquity to the Nineteenth Century, 2012 (Oxford: Oxford University Press).

H. E. Edgerton and J. R. Killian, Moments of Vision: The Stroboscopic Revolution in Photography, 1979 (Cambridge, MA: The MIT Press).

J. P. Harbison and R. E. Nahory, Lasers: Harnessing the Atom’s Light,1997 (New York: Scientific American Library, W. H. Freeman& Co).

J. Hecht, City of Light: The Story of Fiber Optics, 2004 (New York:Oxford University Press).

J. Hecht, Beam: The Race to Make the Laser, 2005 (Oxford: Oxford University Press).

M. Kemp, The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat, 1992 (New Haven: Yale University Press).

A. Zajonc, Catching the Light, 1993 (Oxford: Oxford University Press).Specialist texts

M. Bass et al., Handbook of Optics, 2000 (New York: McGraw-Hill).

M. Born and E. Wolf, Principles of Optics, 7th ed., 1999 (Cambridge:Cambridge University Press).

R. W. Boyd, Nonlinear Optics, 3rd ed., 2004 (New York: Academic Press).

J. W. Goodman, Statistical Optics, 2000 (New York: Wiley Interscience).

J. W. Goodman, Introduction to Fourier Optics, 2004 (New York:Roberts & Co.).

H. Hariharan, Basics of Interferometry, 2nd ed., 2003 (New York:Academic Press).

S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms,Cavities and Photons, 2006 (Oxford: Oxford University Press).

E. Hecht, Optics, 4th ed., 2001 (Reading, MA: Addison Wesley).

S. M. Hooker and C. Webb, Laser Physics, 2010 (Oxford: Oxford University Press).

J. Mertz, Introduction to Optical Microscopy, 2010 (New York:Roberts & Co.).

L. Novotny and B. Hecht, Principles of Nano-optics, 2nd ed., 2012(Cambridge: Cambridge University Press).

V. Vedral, Introduction to Quantum Information Science, 2006(Oxford: Oxford University Press).

W. Welford, Optics, 3rd ed., 1988 (Oxford: Oxford University Press).

Index

3D films 12, 41, 50

γ-rays 10, 11

A

Abbe, Ernst 27, 43, 90

Abbe’s criterion 27, 28, 32, 44

absorption 61, 72, 77–8, 94, 99

action 57, 63

aether 37

Al-Hazen 16

aluminium 91, 92

Ampere, Andre-Marie 12

angle of incidence 17, 19of reflection 17of refraction 22

astronomy 30

atom 14, 46–9, 58–61, 68–78, 82,85–6, 98–106, 111, 121

attoscience 82

aurorae 71

B

Bacon, Roger 25

Balmer, Johannes 58

Bell, John 117

Bell tests 117–18

Betzig, Eric 44

binoculars 28

birefringence 36, 48

birefringent materials 49

black bodies 58–9

Blake, William 123

Blu-ray 77

Bohr, Niels 61

Bose, Satyendra Nath 100

Bose–Einstein condensate 100

Brewster, David 49

brightness 6, 17, 28

butterfly wing 55

C

caesium 86, 91

calcite 35,

camera 15, 25, 27, 44, 55, 79–81

candles 3

CD (compact disc) 4, 77

chromatic aberration 21–4

clock 84, 85–9, 91

coherence 8, 74–7

colour 8–12, 21, 24, 58, 76–8

constructive 38–9, 76

contact lenses 25

copper 93–4

cornea 24–5

correlations 117–18, 121

classical 117

correlations (cont.)

quantum 118

Coulomb, Charles Augustin de 12

Crick, Francis 10

D

de Broglie, Louis 63

De Luce 83 see also Grossteste

destructive 38–9

Diamond Light Source 79

diffraction 10, 36, 45–7, 55, 79

Dirac, Paul 62, 73

DVD (digital video disc) 4, 77

E

Edgerton, Harold 80, 82

Einstein, Albert 60, 73, 84, 88–9, 100

electric charges 37, 38, 43, 60, 67

electromagnetic field 37–8, 52, 62,65, 72, 115

electron 60–1, 65, 67, 68–72, 78–9,82, 85–6, 93, 102–7, 123

energy 3, 7, 59–61, 65–6, 69–73,75, 85–6, 104–7, 131

entanglement 116, 118, 121

Euclid 16

Euler, Leonhart 57

European Light Infrastructure 106

eyeglasses 25

F

Faraday, Michael 10, 38

feather 55

femtochemistry 82

Fermat, Pierre de 23, 53–4

fibre optic broadband 4, 92

fluorescent 44, 67, 70

focal length 24, 27

force 37, 50, 68, 70, 96–8, 102

Fourier, Joseph 45, 89–90

Franklin, Rosalind 9, 10

Fraunhofer, Joseph von 12

frequency 10, 36–8, 60, 86, 89, 94,99, 102

comb 90–2

shift 66

Fresnel, Auguste 52

fringes 39–41, 43, 46, 61–2

Frisch, Otto 110

G

Gabor, Denis 42

Galilei, Galileo 6, 22

glass 4, 28, 49, 79, 92–4, 96

global positioning system (GPS) 86

Goethe, Johann Wolfgang von 8–9

Grimaldi, Francesco 35

Grosseteste, Robert 83

guide star 32

H

Hamilton, William 55–8

Hamilton equation 57

handedness 18

Hell, Stefan 45

Hertz, Heinrich 12

high-harmonic generation 90, 103

hologram 41–3

Hooke, Robert 28

Hubble Space Telescope 30

Huygens, Christian 34, 52

I

images 4, 10, 15–17, 18–25, 27–30,32–3, 35–6, 41–5, 50–1, 76, 78,81–2, 87, 90, 110, 123

incoherent 8, 74

information 1, 4, 13, 41, 47, 68, 92,113–14, 122

infrared 3, 10

intensity 7, 41, 50, 62, 64, 74, 76,92, 100, 101, 110–11

interference 36, 38–43, 46, 61–3,76, 100

Internet 4, 78, 92, 122

irradiance 7

K

Kepler, Johannes 22

L

Lamb, Willis 66

Large Hadron Collider 108

laser 4, 5, 7–8, 13, 15, 25, 45, 73,75–9, 82, 90, 93, 98–9, 106–8,109–10, 115

laser light pulses 76–7, 79–82,90–1, 93, 103, 106–8, 110

laser projector 78

LASIK 25

Leibniz, Gottfried Wilhelm 54–5

lens 12–13, 23–7, 28, 31, 32–3,43–5, 48, 55, 76

light

bulb 7, 8, 67, 69–70, 71, 74, 76,106, 109

classical 109–11

emitting diode 70, 73, 74

quantum 10, 61–3, 66, 71–3,109–10

quanta 59, 71

squeezed 105–6

light sources 3, 7, 13, 15, 71, 79, 90,109, 111

liquid crystal display (LCD) 50

liquid crystals 50, 78

lithography 29

M

magnetic materials 37

magnification 20, 24

Maupertuis, Pierre Louis 56–7

Maxwell, James Clerk 12, 32,37–8, 52, 58

metamaterials 32–3

microscope 17, 28, 43, 44–5

microwaves 10, 11, 86, 91, 92

mirror 18, 19–20, 32, 75

mode-locked laser 90

mode-locking 79, 90

modes 76, 80

molecules 10, 12, 23, 36, 46, 49,50, 77–8, 82, 103

Muybridge, Eadweard 80

N

National Ignition Facility 106

National Institute of Standards and Technology 86

National Physical Laboratory 86

Newton, Isaac 8–9, 20–2, 34, 40,83–4

no-cloning theorem 115

no-measurement theorem 115

normal

materials 32

to surface 17

O

Oersted, Hans Christian 12

Ohm, Georg 12

optical

analogy 56, 63 see also Hamilton

cavity 75–6, 80, 90–1, 111

clockwork 92

fibres 4, 47, 92, 94, 122

refrigerator 98

telecommunications 4, 47,112–14

tweezers 97

optics 6, 17, 28, 75, 90, 93

opto-mechanics 97

P

Pendry, John 33

photo-activated localization

microscopy 44

photoelectric effect 60, 74

Light

photograph 4, 41, 42, 80

photon 17, 60, 64, 65, 71, 73, 74,78, 94, 96, 99, 109–15, 116,118, 120, 121

herald 111

Physikalisch-Technische

Bundesanstalt 86

pixel 27, 28, 42, 50

Planck, Max 58–9

plasma 106–8

Podolsky, Boris 117

polarization 12, 13, 36, 48–51, 111,112, 114, 118–19, 120–1

polarizer 36, 48, 50, 112, 120

protein 28, 46, 97

proton 68–9, 108

beams 108

pump-and-probe 103, 104

Q

quantum

enhanced metrology 116

entanglement 116, 121

fields 62, 66, 73

key distribution 122

noise, laser light 110

noise, squeezed light 115

non-locality 121

random number generators 113

vacuum 65

R

radio waves 11

ray 15–17, 21, 22–4, 30, 32, 35,53, 54, 55–6

bundle 19–20, 23

reference wave 41–3

reflection 17–19

refraction 22–3, 32, 53

refractive index 23, 24, 32, 33, 36,47, 48, 50, 53, 55

relativity 84, 89

Rosen, Nathan 117

ruler 84

Rutherford Appleton

Laboratory 106

S

Schr
dinger, Erwin 63

security 43, 113

Smith, Adam 43

Snell, Willdebrord 22–3, 32, 53

space-time 83–4

spectral ‘lines’ 58

spectroscopy 12, 77, 78–9, 80, 104

spectrum 8, 9, 12, 58, 90, 102

speed of light 17, 36, 49, 68, 84, 87,88–9

spontaneous emission 73

standard quantum limit 110, 115

Stanford, Leland 80

starlight 67

stimulated emission 45, 72, 75

stimulated emission depletion

microscopy 45

stroboscope 80, 82, 103

strontium 91–2

Sun 3, 7, 8, 10, 12, 16

sunlight 3, 8, 49, 58, 104

super-resolution 44

synchrotron 47, 71, 79, 107, 123

radiation 71, 107

T

Taylor, George 61

telescope 6, 20–2, 30, 32, 123

time dilation 83

transverse wave 36, 48

T-rays 10

U

ultraviolet 3, 10, 58, 102

extreme (EUV) 104

V vacuum fluctuations 72, 73

Veselago, Victor 32

Volta, Allessandro 12

Voltaire 54, 123

W

warmth 3, 6, 10

Watson, James 10

Watts 7

wave 34, 36–41, 43, 45, 48, 55–6,60, 62–5, 66, 89, 93, 108, 115

wave function 63–5

wave guide 47

wavefronts 38, 41, 56

wavelength 11, 27, 36, 40–1, 43, 44,55, 60, 63, 76, 79, 90, 94, 107

wave–particle duality 52, 62, 116

Wilkins, Maurice 10

X

X-ray Free Electron Laser 107

X-rays 10, 46–7, 71, 78–9, 107, 123

Y

Young, Thomas 39, 52, 61–2

Z

Zewail, Ahmed 82

-----------------------------------------------------

Planets: A Very Short Introduction

Copyright:© David A. Rothery 2010

Planets: A Very Short Introduction was originally published in English in 2010. This

translation is published by arrangement with Oxford University Press. Dook Media Group

Limited is solely responsible for this translation from the original work and Oxford University

Press shall have no liability for any errors, omissions or inaccuracies or ambiguities in such

translation or for any losses caused by reliance thereon

中文版权：©2020 读客文化股份有限公司

经授权，读客文化股份有限公司拥有本书的中文（简体）版权

版权所有，不得翻印

图字：30-2020-006号

图书在版编目（C I P）数据

牛津通识课. 行星 / [英] 戴维·罗瑟里

(David A. Rothery) 著 ; 刘悦译. -- 海口 ： 海南出版

社, 2020.4

书名原文：Planets: A Very Short

Introduction

ISBN 978-7-5443-9273-0

Ⅰ. ①牛… Ⅱ. ①戴… ②刘… Ⅲ. ①科学知识 - 普

及读物 ② 行星 - 普及读物 Ⅳ. ① Z228 ② P185-49

中国版本图书馆CIP数据核字 (2020) 第061525号

-----------------------------------------------------

目录

引言

01 太阳系 The Solar System

02 岩质行星 Rocky Planets

03 巨行星 Giant Planets

04 巨行星的卫星和光环 Giant Planets' Satellites and Rings

05 小行星 Asteroids

06 海外天体 Trans-Neptunian Objects

07 系外行星 Exoplanets

索引

Introduction

Chapter 1 The Solar System

Chapter 2 Rocky planets

Chapter 3 Giant planets

Chapter 4 Giant planets’ satellites and rings

Chapter 5 Asteroids

Chapter 6 Trans-Neptunian objects

Chapter 7 Exoplanets

Further reading

Index

引言

在1816年的一首十四行诗中，年轻的英国诗人约翰·济慈(John Keats)回顾了他阅读荷马作品新译本的体验。他写道：“在这金色王国(realms of gold)中，呼吸纯粹而宁静。”并继续写道：

忽见新星映入眼帘

我就像天空的守望者

或像壮士科尔特斯

鹰眼般远眺着太平洋

伫立在达连山峰上，我沉默无言

而徒留从者

面面相觑，愕然猜忌

济慈关于行星的新比喻，要么是受到1781年威廉·赫歇尔爵士(Sir William Herschel)发现天王星事件的启发，要么是受到1801—1807年之间新发现四颗小行星事件的启发。然而由于时间更近，后者在人们的记忆中更加清晰。像济慈这样的天文门外汉认为那四颗小行星是新的“行星”，不足为奇，放在今天，这四颗小行星会因太小而无法获得行星资格。

然而，当我的眼睛通过小型望远镜看到土星时，我仍沉浸在“金色王国”中，即使这种新奇感有时会变得暗淡。比如，在看到一个新发现的遥远冰球在数码照片上只是单个像素时；或者在看到另一颗恒星出现微小的摆动，得到其有木星大小的伴星线索时。

但是，对我来说，每当从宇宙飞船传回的新的行星景观展现在我面前时，真正的“科尔特斯体验”就会重现。尽管在某些情况下，这种新的行星景观是一个云图。我们对太阳系的探索已经达到了一个阶段，我们能够把其他行星和它们的大型卫星看作是一个独立世界：具有和我们自己的行星——地球一样复杂和迷人的地理、地质和气象。理论上，这其中的许多地方是你我可以进入的，虽然它们一般不适合野餐，但我们至少可以在那里跳来跳去，铲起一把泥土，爬上一座小山，或者滑下山谷，甚至可以在某些地方找到生命。在这本书中，我将与你分享我们所知的太阳系中的行星起源、演化，特别是当今的状况。天文学家目前正式承认的太阳系内行星只有八颗，冥王星已经被降级，我在后面会提到这件事。就我这样的地质学家而言，还有很多大到足以和行星相提并论的天体，尽管它们数量众多，无法一一说明，但是这些天体都很吸引人，所以我不会忽视它们。

最后，我将转向描述“系外行星”，即围绕其他恒星运行的行星。第一颗系外行星是1995年被发现的。迄今为止，已有几百颗系外行星被记录在案。我们无法观测到它们的任何细节，但我们有足够的信息可以来对比这些系外行星系统布局和我们太阳家族的异同。

01 太阳系 The Solar System

历史上的行星

在受到光污染和烟雾的“诅咒”之前，人们对夜空的熟悉程度要高于今天。天空中的行星在古代文化中被认为是特别的，因为它们是在“固定星星”背景上会移动的“漫游星星”。在古代，人们知道的行星有五颗：水星、金星、火星、木星和土星，只有这些行星是可以用肉眼直接看到的。当然，天空中的太阳和月亮也能直接用肉眼看到，不过太阳和月亮看起来是明亮的圆形，而行星看起来像是四处游荡的光点。人们也因此认为太阳、月亮与行星是不一样的。在人类存在的大部分时间里，地球被想象成万物的中心，它与天空中的天体无关，所以那时候没有人认为地球是一颗行星。

其实在很早之前，人们就意识到地球和其他行星一样，是一个绕着太阳旋转的岩质球，而且地球是行星中的一员。这是一次思想上的飞跃。这个飞跃的过程很缓慢，并且伴随着很多的假象曙光。

公元前5世纪，古希腊哲学家阿那克萨戈拉(Anaxagoras)正确地推断出月球是一个反射太阳光的特殊球形天体，但因为这样的推断，他被流放了。在接下来的几个世纪里，许多中国的天文学家也提出过类似的想法。直到17世纪，通过望远镜的观测，月球是一个球体的想法才深入人心。

至于行星，在它们是以太阳为运动中心的“日心说”这种反直觉的观点被接受以前，通常被认为是围绕地球旋转的光点。最早提出地球绕着太阳转的书面记录可以追溯到公元前9世纪的印度文本。尽管如此，这之后的天文学家提出的一些关于地球绕着太阳转的观念，尤其是来自古希腊和伊斯兰智者的建议以及1543年尼古拉斯·哥白尼(Nicolaus Copernicus)提出的学说，在18世纪前都没有被广泛认可。而伽利略(利用他的望远镜看到了月球上的山脉、金星的相位和围绕木星运行的四颗小卫星)从1633年直至1642年去世，一直被教会软禁在家中，一部分原因就是他提倡日心说。

17世纪初，人们通过望远镜发现行星小归小，却是可辨别的圆盘，而恒星仍然只是一个光点。由此，人们从根本上将行星和恒星区分开来，并为把其他行星看作是和地球相近的天体铺平了道路。顺便说一下，现在我们知道恒星比行星要亮得多，但恒星(除了太阳)距离我们太远了，即使用最先进的现代望远镜，也只能观测到极少数恒星的表面细节。在照片上，明亮的恒星看起来比暗弱的恒星大，但这只是一种光学效应，因为明亮的恒星形成的模糊光斑更大，所以看起来比较大。

开普勒的行星运动定律

1609年，约翰内斯·开普勒(Johannes Kepler)认识到，行星(包括地球)绕太阳运行的路径(轨道)是椭圆，而不是规范的正圆。艾萨克·牛顿(Isaac Newton)在1687年利用对引力的深刻理解，对行星绕太阳的运动进行了解释。多亏了开普勒和牛顿，行星才在人类的理解中找到了它们应有的位置。随后，人们又逐渐推断出行星相对于地球的距离和大小。

椭圆，就是你可能会想到的“卵形”。在数学上，椭圆被定义为一条围绕两点(椭圆的两个焦点)绘制的闭合曲线，且从两个焦点到曲线上任意一点的距离之和相同。圆是一种特殊的椭圆，两个焦点在圆的中心重合。两个焦点距离越远，椭圆就越扁长，或者说越“偏心”。开普勒推断，行星沿着椭圆轨道运行，太阳位于椭圆轨道的其中一个焦点，另一个焦点是空的。在椭圆轨道上，离太阳最近的点称为“近日点”(perihelion，希腊语中表示“最接近太阳”)，离太阳最远的点称为“远日点”(aphelion，希腊语中表示“离太阳最远”)。行星的轨道不是高度偏心的，如果你从平面图上看，会发现它们看起来很像圆。例如，当火星处于远日点时，它与太阳的距离与它处在近日点时相差不到21%。对地球来说，处在远日点和处在近日点，它与太阳的距离相差不到4%。

开普勒因他的行星运动三定律而闻名。简单地说，开普勒第一定律就是：每颗行星都在一个椭圆轨道上运行，太阳在椭圆轨道的其中一个焦点上。开普勒第二定律描述了行星沿轨道运转速度的变化：行星越靠近太阳，其移动速度越快(原因可用后来的牛顿的引力理论解释)。开普勒第二定律也可表述为：在相等的时间内，连接地球和太阳的虚构线扫出的面积相等。开普勒第三定律将行星的轨道周期(行星绕太阳一周所需时间)和行星与太阳的平均距离联系起来。开普勒第三定律可表述为：轨道周期的平方与平均距离的立方成正比。行星到太阳的平均距离等于其椭圆轨道长轴长度的一半(也称为“半长轴”)，也可以说，行星到太阳的平均距离等于其近日点和远日点之间直线距离的一半。开普勒的行星运动定律使精确计算其他行星轨道的大小成为可能，但其结果的精确程度却受限于人们对地球轨道大小测量的不确定性。早在1672年，天文学家们就利用在多个地点同时对火星进行观测，测得了地球和太阳的距离，大约为1.4亿千米，这十分接近149 597 871千米这一正确值。之后在1761年和1769年，天文学家们又通过对金星凌日的观测，将地球和太阳的距离估值修正为153±1百万千米(1769年的观测要求库克船长亲自在塔希提岛驻扎)。虽然科学的进步使得关于太阳系规模和性质的模型变得更加自洽和简洁，但罗马教皇对印刷“日心说”书籍的禁令直到1822年才被撤销。

你可能会认为，一旦确定了地球与一颗行星间的距离，计算行星大小的工作将会变得很容易。但即使是利用大型望远镜，观测到的行星盘也是很小的，再加上地球大气层的干扰，我们对行星视角大小(或者说是行星看起来有多大)的测量存在巨大的不确定性。例如，当威廉·赫歇尔在1781年发现天王星时，他测量的天王星的盘比实际要大8%。要用望远镜测量一颗行星的大小，最精确的方法不是测量它看起来有多大，而是计算它从一颗恒星前面经过的时间。行星从一颗恒星前面经过的现象被称作“掩星”，这非常罕见，但到19世纪末，利用“掩星”的方法，许多行星的大小已经被相当精确地确定了(表1)。

如果说天王星的发现是出于偶然，那海王星则是经过慎重的搜寻后，才在1846年被发现的。当时天王星的轨道被发现存在微小的扰动，这使得天王星的轨道不再是一个完美的椭圆，而是存在扭曲。对这种扰动最好的解释是，一颗看不见的外行星的引力影响了它，海王星因此被发现了。当海王星的轨道被记录了足够长的时间后，它似乎也显示出了扰动，指向另一颗未被发现的行星。这引发了1930年对发现冥王星的研究。起初，天文学家认为这颗新发现的第九大行星的大小和质量一定与天王星和海王星相似，但在1955年，天文学家们证明冥王星不可能比地球大；1971年，冥王星大小的估算结果减少到火星的大小；1978年，人们发现冥王星表面的主要成分是具有高度反射性的甲烷冰，这意味着冥王星的实际尺寸必须更小，才能与它的总亮度保持一致。如今，我们知道冥王星的直径只有2390千米，甚至比水星还要小，质量也比水星要小得多。尽管海王星轨道的“扰动”很幸运地激发了对冥王星的搜索，但现在认为，海王星的轨道扰动不过是观测误差而已。

冥王星在2006年失去了官方承认的行星地位，这是一个有争议的决定，但在我看来是正确的。在解释这是为什么之前，我将回顾一下我们现在所理解的太阳系的性质。

表1　行星的大小(赤道直径

*卡米尔·弗莱马里恩（C.Flammarion），《大众天文学
》（Popular Astronomy ）（查托与温达斯，皮卡迪利大街）

回顾太阳系

太阳

太阳系的中心是太阳。它是一颗相当普通的恒星，其核心的核聚变将氢转化为氦，为太阳提供能量。太阳的直径是地球的109倍，质量约是地球的

333 000倍。太阳的质量是太阳系中所有其他天体质量总和的740倍。太阳的引力是如此强大，以至于太阳系中天体绕太阳运行的轨道几乎都是开普勒认定的完美椭圆。尽管行星间存在的轨道扰动是可测量的，但这些扰动非常微小，几乎可以忽略。

行星

表2总结了行星的一些基本性质。为避免使用非常大的数字，表中引用的数据是行星的某一性质相对于地球的比较值。地球与太阳的距离用“天文单位(Astronomical Units)”来表示，简记为AU，定义为地球到太阳的平均距离，可以简化地记为1.5亿千米。行星的轨道周期是指其绕太阳一周所需要的时间，当然，这里的时间指的是该行星自己的“年”。由开普勒第三定律可知，本表中行星的轨道周期和其与太阳的距离是相互联系的，也就是说，行星轨道周期(单位为地球年)的平方等于其到太阳平均距离(单位为AU)的立方。地球的质量非常接近6×1024千克(6×1021吨)，因此，在描述其他行星的基本性质时，不引用如千克、秒和米这样的标准科学单位，而用其与地球这一性质的比较值，是很方便的。

自转周期是行星绕其自转轴旋转一圈所用的时间。对快速旋转的行星来说，这大约等同于行星上从一个日出到下一个日出的时间(行星自身“一天的长度”)。但快速旋转的行星的自转周期和其“一天的长度”之间的关系并不确定，这是因为行星的轨道运动不断地改变着行星相对太阳的方向。地球的自转周期为23小时56分钟，但它实际需要24小时才能将太阳带回天空中的同一点。从行星的角度来看，除非自转引起了行星表面某一点朝向太阳的方向发生了改变，否则太阳在单轨道运行的过程中是完全绕着行星的天空移动的。如果一颗行星的自转被潮汐锁定，那么它每绕太阳一圈就会自转一次(同步自转)，并且它的某一表面将永远朝向太阳。水星并不是这样的，它每公转两次就会精确地自转三次，也就是说，它每公转两次就会相对太阳
自转一次，所以水星上一天时间相当于两年。

表2　行星的相对性质

*其与太阳的距离为平均距离。年和天分别为地球年和地球天。行星的大小见表1

四颗内行星和四颗外行星的性质有许多不同。内行星(水星、金星、地球和火星)与外行星(木星、土星、天王星和海王星)相比，体积相对较小，质量也较低。两者的密度也有差别，内行星的密度比外行星大。内行星被称为“类地行星”，这意味着它们“和地球类似”。四颗外行星被称为“巨行星”，有些人也把它们称为“气态巨行星”，以反映它们含有许多的氢和氦；还有一些人专门用“气态巨行星”来形容木星和土星，因为它俩的气体含量要高于另外两颗外行星，尽管另外两颗外行星含有的气体的质量都超过了一个地球质量。

图1　太阳系图，以实际的相对大小显示行星轨道。行星轨道只有轻微的偏心，所以看起来和圆没什么区别。火星轨道内未标记的圆圈是地球轨道，不是太阳。金星和水星的轨道太小，无法包含在图内。冥王星不是一颗行星，图中显示它的轨道是因为它代表了海王星轨道之外的大量小天体

图1中除了金星和水星，其他行星都按照轨道等比例排列。金星和水星的轨道太小了，难以显示在图中。图1还包括了冥王星轨道的一部分，放到以后讨论。其中有一个行星轨道的性质我还没有提到，即行星轨道几乎都在同一平面上，没有这一性质，就无法绘制出这样一幅星图。地球的轨道面也因此能被当成一个方便的参考平面，被称为“黄道”。相对于地球的轨道，冥王星的轨道倾角为17.1°，水星的轨道倾角为7°，金星的轨道倾角为3.4°，其他行星的轨道倾角都小于3°。

当冥王星接近近日点时，它就位于海王星的轨道内侧。冥王星和海王星不会发生碰撞，因为它们的轨道倾角不同，阻止了它们的路径相交，而且，每当冥王星经过海王星的轨道时，海王星总是在太阳的另一边。这是因为海王星每完成三次公转，冥王星恰好完成两次，这种关系被称为3∶2轨道共振。

除了轨道几乎共面，每颗行星绕太阳公转的方向也是一样的：从地球北极上方一个假想的有利位置进行观测，就会发现行星都是逆时针运行的。除金星和天王星，其他行星的自转也都表现为逆时针运动。由于逆时针运动很普通，它被称为“顺行”，而顺时针轨道运动或旋转则被认为是向后的，被称为“逆行”。

除了天王星，每颗行星的自转轴相对其公转轨道垂直平面的倾角都小于30°。水星自转轴倾角几乎是“完美的”，只有0.1°；地球的自转轴倾角为23.5°。从数万年的时间尺度上来看，行星自转轴的指向方向和倾斜程度都是会变化的，但从一个公转周期的时间尺度上来看，它们又是恒定的。轴倾角是行星上有四季的原因，当地球处在自转轴北端倾斜向太阳的那部分公转轨道时，北半球是夏天；6个月后，地球处在太阳的另一边，北半球是冬天。金星与天王星的自转与公转方向不一致。金星的自转轴倾角只有2.7°，它在逆行方向上的自转非常缓慢，这使得它一天的长度为116.7个地球日。而天王星的转轴倾角为82.1°，并进行快速逆行自转。天王星以前很可能遭遇过一场灾难性撞击，它被撞翻了，从开始的顺行自转变成现在这样，轨道倾角变为 97.9°(180°减去82.1°)。这样的灾难能解释天王星的逆行自转。

行星的卫星

除了水星和金星，太阳系内所有的行星都有卫星或自己的“月球”。这些较小的天体离行星足够近，可以绕行星公转，而不绕太阳公转。严格来说，行星和它的卫星都围绕着它们共同的质心(或“引力中心”)运行。由于行星比它的卫星要大得多，所以它们的引力中心在行星内部。但通常情况下，我们完全可以认为卫星绕着它的行星转。大多数行星卫星的公转轨道都靠近其所在行星的赤道面，而且几乎所有的大型卫星都有顺行的公转轨道，即沿着行星自转的方向运行。

当然，地球的卫星是月球(Moon ，这里要用大写的M)。月球是一个例外，因为与地球相比，月球相对较大，其直径为地球直径的27%，质量为地球质量的1.2%。巧合的是，月球与地球的距离使月球的大小看起来几乎与太阳相同。虽然太阳比月球大得多，但太阳离地球距离相对更远。当月球正好经过地球和太阳之间时，它会遮挡太阳的圆盘，导致日食。如果月球绕地球公转的轨道恰好与地球的公转轨道共面，那么在月球的每个公转周期(每个月)，都会发生日食。但是月球的公转轨道与黄道的夹角为5.2°，所以日食很少见。月球的公转轨道与黄道有两个交点，只有当月球位于其中一个交点，并恰好经过地球和太阳之间时，才会发生日食。大约2600年前，尽管还没有完全理解日食发生的原因，巴比伦天文学家就已经算出了这些事件的周期性的本质并预测了何时会发生日食。这是巴比伦天文学家的伟大成就之一。

火星有2颗小卫星。木星有4颗直径超过3000千米的卫星(伽利略发现的)，以及最近统计发现的59颗直径小于200千米(大多数小于4千米)的卫星。土星已知的卫星总数与木星相近，但土星只有1颗卫星能与木星最大的卫星相匹敌。天王星有5颗直径在400~1600千米之间的卫星，还有22颗已知的较小天王星卫星。海王星有1颗大卫星和12颗已知的小卫星。木星和土星大多数小的外部卫星(直径为几千米)是用望远镜(而不是访问这两颗行星的飞船)发现的，而对于天王星和海王星来说，肯定还有很多巨行星的微小卫星有待发现。用望远镜观测天王星和海王星的卫星尤其困难，主要原因有两个：一、这两颗行星的卫星离太阳远，没有那么明亮；二、它们离地球更远，所以即使它们和较近的卫星有同样的亮度，看起来也更暗弱。

在地质学上较大的卫星是非常有趣的事物，稍后我会详细介绍它们。所有的卫星对行星科学家来说都是有用的，因为可以利用它们给行星称重。由于卫星要小得多，行星的质量几乎完全占据了行星-卫星系统的主导地位。行星绕太阳的公转轨道依赖于该行星与太阳的距离以及太阳的质量，相应地，卫星的公转轨道周期也只取决于它与行星中心的平均距离和它们的总质量(可以用开普勒第三定律中的牛顿引力定律来计算)。

小行星、海外天体和彗星

这本书是关于行星的，不是关于整个太阳系的。值得注意的是，尽管其他天体都很小，并且它们的总质量相对来说微不足道，但这些天体的数量远远超过了行星及其卫星的数量总和。虽然行星科学家已经意识到这些“垃圾”天体的界定有些模糊，但它们大致可以被分为三类：小行星、海外天体和彗星。

小行星大小的上限是直径950千米(最大的小行星——谷神星的直径)，但是没有下限。已有一些只有几十米宽的小行星，它们在接近地球时被探测到，还有一些更小的小行星掉落在地面上的残骸，被称为陨石。以前的人们认为小行星是被摧毁的行星的碎片，现在我们认为小行星不是行星的碎片。所有小行星的质量总和可能还不到地球质量的千分之一。有些小行星的不规则形状证明，它们已经经历过相互碰撞。

毫无例外，小行星的轨道运动都是顺行的。大多数小行星的轨道倾角小于20°，但它们轨道的偏心率通常比行星大。大多数小行星的轨道位于火星和木星之间，也就是所谓的“小行星带”。有些小行星离太阳更近，从地球轨道内侧穿过，有少数小行星甚至从水星轨道内侧穿过，还有一些已知的小行星在土星之外的轨道上运行。与陨石一样，大多数小行星是由岩石或碳组成的，但也有一些小行星是由铁和镍构成。据我们所知，小行星的成分往往没有那么多岩质，而是会有更多碳质，且最终随着小行星与太阳距离的变大而更加冰质化。

在海王星轨道之外，距离太阳30~55AU的地方，小型冰质天体变得很常见，甚至还有几个体积超过最大小行星的其他天体，这个区域通常被称为“柯伊伯带”，以荷兰裔美国人杰拉德·柯伊伯(Gerard Kuiper)的名字命名。柯伊伯在1951年预测，该区域是太阳系诞生后留下的冰质团。1943年，爱尔兰人肯尼斯·埃奇沃思(Kenneth Edgeworth)在一本不太知名的杂志上也发表过类似的言论，所以有些人更愿意把这条带称为“埃奇沃思-柯伊伯带”。第一个柯伊伯带天体是在1992年被发现并确认的，而到现在已经有数百颗柯伊伯带天体被编入了目录，包括冥王星。那些近日点距海王星轨道不远，但远日点与海王星的轨道距离达到约100 AU的类似天体被称为“黄道离散天体(Scattered Disk Objects)”，这些天体与柯伊伯带一起，组成了一个被称为“海王星外天体”(TransNeptunian Objects， TNOs)的大家族。海外天体的轨道都是顺行的，它们的总质量可能是小行星带天体总质量的200倍左右(约等于地球质量的五分之一)，总共可能有近10万颗大小超过100千米的海外天体。2005年发现的一个“黄道离散天体”，后来被命名为阋神星(Eris)，它似乎比冥王星稍大。我们对阋神星和冥王星的质量测算结果很有信心，因为它们都有轨道记录良好的卫星，而这些轨道记录表明阋神星的质量比冥王星大28%。

彗星自古以来就为人所知，这是因为当彗星接近太阳时，那由气体和尘埃组成的尾巴将会伸展到天空中，这使得彗星瞬间看起来非常壮观。然而，彗星的固体部分只是一小块积满灰尘的冰(被称为“脏雪球”)。在大多数情况下，这部分只有几千米宽。大部分时间彗星都离太阳很远，只有当它们足够接近时，来自太阳的热量才会让它形成尾巴。彗星形成尾巴的情况很少发生，因为它的轨道偏心率很高，近日点通常在地球轨道内，远日点则在木星轨道附近或在木星轨道之外。有些彗星来自更远的地方，它们的轨道看起来像抛物线(无限长的椭圆)，在历史记录中，它们只接近过太阳一次。这样的彗星属于“长周期”彗星，似乎是从距太阳约50 000AU处，围绕太阳的不规则的壳中分离出来的——这个壳被称作奥尔特云(Ort Cloud)。相比之下，“短周期”彗星很可能源于黄道离散天体。通过与一个同类天体的近距离接触，这些黄道离散天体被扰动到一个近日点与太阳距离较小的偏心轨道上。那些轨道周期为数百年的彗星的远日点仍然处在散盘中，但通过与一颗巨行星的近距离接触，它们的远日点可以被推到离太阳更近的地方，例如，哈雷彗星的远日点在海王星轨道附近，其轨道周期为75
[1]

年，而恩克彗星的远日点在木星轨道附近，轨道周期只有3.3年。彗星每次经过太阳时，太阳的热量会使彗星变暖，并使彗星因为蒸发失去质量。因此，在经过近日点不到1000次之后，彗星可能会变成由无冰岩石和尘埃组成的惰性物质，很难与小行星区分开来。

考虑到短周期彗星的来源，你可能也会猜到，它们的轨道是顺行的，轨道平面接近黄道。长周期彗星则没有这样的限制，它们的轨道平面可以是高度倾斜或者逆行的。

什么是行星

冥王星为什么会被踢出行星俱乐部

1930年，冥王星成为第一个被发现的海外天体。即使在我们都知道冥王星的尺寸很小之后(1978年发现了冥王星最大的卫星，因此确定了冥王星的质量)，人们还是倾向于将冥王星视为第九颗行星。但随后，柯伊伯带(Kuiper belt)里已知天体的数量增加到数百个，而且其中一些天体的大小与冥王星不相上下。若我们还将冥王星归为行星，而将其他柯伊伯带天体归为别的，这种分类显然很不合理。从逻辑上讲，当阋神星被证实比冥王星更重，可能还更大时，我们或者将所有的海外天体都称为行星，或者不称任何一个海外天体是行星。尽管如此，还是有许多人出于情感或历史原因，主张保留冥王星的行星地位。

因为“行星”一词从未被准确定义，所以将冥王星踢出“行星”俱乐部这一决定受到了阻碍。最终，2006年在布拉格举行了一次激烈的国际天文学联合会，会议上代表们投票通过了一些界定“行星”的标准，这基本解决了是否将冥王星踢出“行星”俱乐部的问题。在国际天文学联合会的规定中，有两个没有争议的标准是：第一，行星必须有足够的质量，使其自身的引力能够克服“刚体力”，呈现出流体静力学平衡的形状，即近似球形；第二，行星必须围绕太阳公转。第二个标准排除了像我们月球这样的大型卫星。

而关于行星的第三个标准才是决定性的那个：要被算作一颗行星，一个天体必须“清除了其轨道周围的所有天体”，仅剩下的是比它小得多的天体。这项测试，冥王星失败了。冥王星还没有将它的轨道周围清除干净，它与许多大小相似的天体共用了一个轨道区域，甚至还有质量大得多的海王星。但是海王星却通过了行星测试，因为它比同一轨道区域的其他任何天体(如冥王星)都要大几千倍。

采取了大胆但完全合乎逻辑的步骤后，冥王星被逐出行星俱乐部，国际天文学联合会似乎立刻就后悔了，然后为它创造了两个新的类别，是两个哦!在2006年的布拉格会议上，新造词——“矮行星”被定义为“一个轨道绕太阳的天体，它有足够的质量使得引力能将它拉成近球形，但没有清除其轨道附近的天体，并且它本身不是卫星”。要远程确定一个天体的形状是否“接近球形”是一件很困难且很有争议的事情，但国际天文学联合会还是采纳了这个定义，给冥王星、阋神星和谷神星(最大的小行星)颁发了一个安慰奖——称它们为“矮行星”。当时，国际天文学联合会承认其他大型海外天体在经过适当测量后，也可以被列为矮行星。在2008年，一个名叫鸟神星(Makemake)的柯伊伯带天体被发现了。我们认为鸟神星的大小约为冥王星的三分之二，通过了形状测试。鸟神星被承认为第四个矮行星，紧随其后的第五个矮行星被称为妊神星(Haumea)。

但国际天文学联合会似乎又后悔把类冥王星天体与谷神星混在一起，于是在2008年，又发明了一个新的术语——“类冥矮行星”，用来表示轨道平均距离大于海王星以外的矮行星。如此一来，谷神星就变成了唯一不属于类冥矮行星的矮行星，且目前可以肯定已发现的小行星中，再也没有大到能被归入矮行星这一类别的了。但是，可能还是有许多未被发现或未被详细记录的大型海外天体，它们将加入冥王星、阋神星、鸟神星和妊神星的行列，成为类冥矮行星和矮行星。顺便说一句，阋神星(Eris)是根据古希腊纷争女神命名的(想到阋神星引发的争议，这个名字恰如其分)，而鸟神星(Makemake)和妊神星(Haumea)则分别是根据太平洋岛屿上掌管生育的神祇命名的。

这一切是如何发生的

越来越多的行星

直到最近，可能还有人认为行星是宇宙中的稀有物，但现在看来，行星显然是恒星形成过程中的一个常见副产品。因此，太阳系的存在只是太阳起源的一个结果。

人们认为，巨大的星云因自身引力坍缩形成了恒星。星云的主要成分是氢，还混合了其他一些气体和被称为星际尘埃的微小固体颗粒。星云收缩时，大部分物质会集中到位于中心的一个天体上。因为引力能在物质陨落的过程中转化为热能，这个天体会变得越来越热，最终，天体中心的压力和温度升得非常之高，氢原子核产生核聚变形成氦。在这一阶段的中心天体可以被称为恒星。星云在收缩的最后阶段会遗留下一些物质，行星就是由此形成的。在星云收缩的过程中，基于角动量守恒原理，星云任何一点初始旋转都会被加速，未被吸收到恒星中的物质会集中在恒星赤道面的圆盘上，和恒星沿相同的方向旋转。

这个旋转的圆盘就是行星形成的地方。产生我们太阳系的星云被称为太阳星云，“星云”(nebula)在拉丁语中是“云”的意思，天文学家们用它来表示太空中巨大团块的气体、尘埃或者两者的混合物。我们有充分的理由确信，太阳星云的组成大约是71%的氢、27%的氦、1%的氧、0.3%的碳，以及0.1%的氮、氖、镁、硅和铁。在太阳星云中，几乎所有的原始尘埃都可能被初期太阳的热量汽化了，但很快，星云内的环境就冷了下来，足够使新的尘埃颗粒凝结，通过化合作用它们变成了化合物，而不是单元素物质。氦不能形成化合物，所以大部分的可凝结化合物都包含有氢或氧。

在合适的局部温度和压力条件下，如果附近还有可用的各种元素——比如硅和各种金属——氧能够与它们结合，在星云内部形成一系列叫作硅酸盐的化合物。这是地球上常见的矿物，熔融岩石冷却时会结晶形成硅酸盐，但在太阳星云中，硅酸盐是直接从气体中生长出来的。只有当温度低到足以形成含氢化合物时，氢才会被结合进固体颗粒中，这种情况多数都发生在距离太阳超过5AU的地方。在与太阳距离为5AU的地方，存在一条被称为“冰线”的分界线；在这条所谓的“冰线”之外，由氢和氧组成的水分子可以凝结成小块的冰。在离太阳更远的地方，会形成更容易挥发的化合物：氢与碳结合形成甲烷，氢与氮结合形成氨，碳与氧结合形成一氧化碳或二氧化碳。在距离太阳约30AU处，温度低到氮可以凝结成氮冰。基于行星科学词汇的一个技巧，任何由水、甲烷、氨、一氧化碳、二氧化碳或氮(或这些物质的任意混合物)形成的固体都被称为“冰”，因为它们在来源和性质上都具有相似性。这意味着，为了避免模棱两可，行星科学家们在提到水结的冰时，必须特别指明是“水冰”，这么复杂的情况对地球上的人来说并不常见，因为地球上的温度太高，比水更容易挥发的化合物无法自然结冰。

凝结是这样一个过程：靠近太阳的硅酸盐和离太阳远一些的冰(还有那些剩余的硅酸盐)组成了第一代尘埃颗粒。它们没有凝结成更为致密坚硬的微粒，而是有着复杂的“蓬松”形状。所以当它们相互碰撞时，往往会粘在一起，而不是弹开来。在凝结开始后仅仅1万年，这些微粒通过碰撞，持续凝结和吸积(粘在一起)，成长为直径约1厘米的球状体。再过10万年后，太阳系将由一群直径大约10千米的天体组成，这些天体被称为“星子”。它们都以相同的顺行方向围绕太阳旋转，并被包围在由剩余气体和尘埃构成的弥漫薄雾中。

最早期的一些微观颗粒藏身在陨石内部，它们得以被保持原样，所以我们知道凝结是在多久以前发生的。通过测量这些颗粒内部经历放射性衰变的产物，我们可以计算出它们的年龄。最早期的微观颗粒的年龄是一个特别好记的数字：45.67亿岁。 最“原始”的陨石是从未经受加热或蚀变的星子碎片，被称为“碳质球粒陨石”，是我们研究早期太阳系环境的最直接证据。

到目前为止，天体间的碰撞基本上是一个偶然事件，可一旦星子的大小达到约10千米——很明显更大的星子会有更大的引力——就容易遭受更频繁的碰撞，它们的生长速度也因此超过了其他星子。这之后再过几万年，最大星子的直径就已达到1000千米左右，在这个过程中，它吞噬了大部分其他较小的星子。

这些巨大的星子被冠以一个新名字——“行星胚胎”。可能有几百个行星胚胎是在内太阳系形成的。它们的质量大到足以凭借自身的引力把它们拉成球形。行星胚胎内部的温度可能很高，足以让物质熔化，使铁内陷，形成一个明显的内核，很大程度上这并不重要，因为接下来还要发生一些别的事情。

行星胚胎是类地行星形成的基础。在这个阶段，大部分小颗粒都不见了。只有两个胚胎撞在一起时，行星胚胎才会有显著的生长。这样的碰撞被称为“巨大撞击”，它释放出的热量足够熔化碰撞形成的融合体。想象一个熔岩球，它表面都发着炽热的红光，周围零散漂着一些已经冷却的渣块。在球体深处，液滴状的“铁雨”穿过硅酸盐岩浆，向内沉陷，聚拢到中央核心。你的头脑中要有上述这张图片，它描绘了在巨大撞击后，一个行星胚胎的状态。

这个过程假设了撞击不会把两个行星胚胎都撞成碎片，会有一定数量的碎片作为碰撞的抛射物被抛向太空，这是一个必要的前提。大约需要5000万年的时间，才能通过行星胚胎之间一系列的巨大撞击，形成一颗地球大小的行星。由于碰撞的随机性，由此而来的天体间“族谱”非常复杂。在早期碰撞过程中，将任何单个行星胚胎视为“原始地球”或“原始金星”都是毫无意义的。

在火星轨道之外，年轻木星的引力作用太强大，会把岩质星子搅入偏心率更大的轨道，在这里，往往因为行星胚胎的相互碰撞过于剧烈，导致胚胎无法通过吸积来实现增长。相反，分裂是一个常见的结果，巨大的行星胚胎无法在这里生长，它们本来可能会通过碰撞产生第五颗类地行星。如今在该区域，我们发现的大多数小行星都只占曾经行星胚胎质量的一小部分。木星将大部分小行星甩到了明显偏心的轨道上，因此，大多数小行星最终会与木星或另一颗巨行星相撞，或被完全逐出太阳系。

这些形成巨行星的天体当中含有很高比例的冰和岩石。在“冰线”之外，生长中的行星可以利用的物质更多。我们不确定胚胎—胚胎碰撞在这里扮演了什么角色，同样也不能确定巨行星如何能获得如此多的气体。有这样一种理论：当行星胚胎的质量超过10或15个地球质量后，其引力就足以清除残留在星云中的大量气体，从而使得它们的岩质核和冰质核被厚厚的气体外壳包裹；另一种观点认为，星云中的引力不稳定，这导致每颗巨行星都在一个密度特别大的结中生长，在这个结中的气体自然地被限制在生长中行星的周围。

关于此类问题的意见分歧有很多，其中一个是关于内外太阳系行星相对生长速度的。目前还不清楚木星是在地球和金星形成之前还是之后形成的，如果土星、天王星和海王星是通过胚胎—胚胎碰撞成长起来的话，那么它们一定比木星生长得慢，这是因为随着与太阳的相对距离增加，胚胎-胚胎碰撞的频率应该会降低。

当太阳进入它的“金牛T”阶段时，从星云中清除气体的工作就终止了。“金牛T”阶段是以今天正在经历这一过程的金牛T型恒星命名的。在大约1000万年的时间里，来自处于“金牛T”阶段恒星的强烈气体外流会吹走所有剩余的气体和尘埃，这种强烈的气体外流被称为“ 金牛T星风”。与其他巨行星相比，天王星和海王星的气体比例较少的一个可能原因是：它们生长比较慢，在金牛T星风这一过程结束之前，有动力收集气体的时间比较短。

迁移的行星

人们争论的另一个问题是，随着时间的推移，行星的轨道之间，尤其是巨行星的轨道之间会发生怎样的变化，这种变化会到什么程度。在太阳星云被驱散之前，星云物质和大型轨道天体之间的引力相互作用会逐渐减小行星胚胎和年轻行星的轨道半径，导致行星胚胎和年轻行星向内迁移。在星云扩散之后，行星和较小天体之间的引力相互作用可能会发挥更大的功能。一些人认为，在大约5亿年间，最外层的巨行星会使外围的冰质星子轨道向内偏转。最终，这些冰质星子可能会通过与下一个巨行星碰撞等方式继续向内迁移，直到它们离木星足够近，再让木星把它们向外抛。这些被抛出的冰质星子可能是如今的奥尔特云的起源。木星每向外抛掷一个天体，就会更靠近太阳一些。不过反过来说，当一颗巨行星向内抛掷一块冰时，其他巨行星也会被向外推。在这个描述中，木星会向内迁移，而土星、天王星和海王星则向外迁移；天王星和海王星甚至有可能互换位置(为天王星的轴倾角达到目前的状态提供了机会)。如今的海外行星，是指那些海王星向外行进时，在扫过的区域之外幸存下来的行星。

不过，请不要产生行星的轨道能够快速或急剧变化的印象。那些声称金星或火星在圣经时代曾靠近地球，引发各种神话和自然灾害的言论，是完全站不住脚的。我所描述的外行星迁移过程极其缓慢，并且是它们与星云气体以及大量已不再存在的小天体间的相互作用累积的结果。

然而，行星及其间引力的相互作用在不断地改变着它们的结构。因此，混沌理论认为，我们不能预测几百万年后行星的位置。不过我们可以肯定，太阳系是足够稳定的，在未来的几十亿年内，没有任何行星会发生碰撞或被抛射。至少在未来50亿年内，我们大概率是安全的，而在50亿年后，天文学家们预计太阳将膨胀成一颗红巨星。届时，火星漫游将是遥远未来的地球人面临的最不重要的问题。

为什么是所有的卫星

到目前为止，对于卫星到底是随行星一起生长，还是后来被捕获的问题，还没有一个确切的答案，你对此也不该感到惊讶。巨行星的顺行大卫星是最容易解释的，它们被认为是在巨行星成长过程中，由巨行星周围的气体云和尘埃组成的，就像一个微型版的太阳星云。那些只有几千米大小的，在靠近巨行星的轨道上运动的“顺行”微型卫星，则可能是较大卫星的碎片，这些较大卫星因为距离巨行星太近而被撕碎。巨行星的外层卫星大多处于逆行轨道，它们可能是被捕获的小行星、海外天体或彗星核。

从理论上讲，一颗行星不太可能将一个路过的“访客”天体俘获到自身的轨道上。由于引力作用，一颗较小的天体会与行星擦肩而过，但不大可能减速到足以被行星俘获进入轨道的程度。但是，如果这个“访客”是一个双天体，当其中一个天体将动量传递给另一个天体后，它自己会被俘获，而另一个天体在遇到行星后会更快地离开。对于海王星的逆行大卫星海卫一，目前流行的一种解释是：海卫一原来是一个双海外天体的一半。这似乎是可信的，因为有几个已知的海外天体都是孪生体。请注意，这里留下了一个尚未解决的疑问：为什么这么多的海外天体(包括小行星)从一开始就有卫星？

我们对地球的卫星(月亮)则有不同的解释。月球似乎是由地球在成长过程中最后一次胚胎-胚胎碰撞所产生的碎片凝聚而成的。火星的两颗小卫星(火卫一和火卫二)曾经是小行星，它们被俘获进入近圆形轨道的原因尚不清楚。

碰撞和陨击时标

虽然大规模天体之间的碰撞在如今极为罕见，但仍有非常多的小天体最终可能与行星相撞。在39亿年以前那个被称为“晚期重轰击”的时期，小行星和彗星撞击行星的速度要远远高于今天。尽管在“晚期重轰击”时期后，月球上的陨石坑一直在以较慢的速度形成，但月球上“晚期重轰击”时期的陨石坑仍保存得很好(图2)。当物体以每秒几十千米的速度撞击固体时，撞击点发出的冲击波会将物体击碎，在固体上留下一个陨石坑。陨石坑通常是圆形的，只有在这种极少数情况下，如撞击天体以掠射角度到达固体时，陨石坑才不是圆形的。

根据陨石坑的直径，可以很好地理解它们的形态层次，并且可以在实验和计算机模型中重现这一切。在月球上，直径仅有15千米的微小陨石坑呈简单的碗状。直径长达140千米的陨石坑并不会比它更深，而是有着平坦的底部，通常在被冲击波挖掘后会立即反弹形成一个中心峰，在图2顶部附近有一个很好的例子。更大的陨石坑可能会有一组中心峰，且直径大于350千米的陨石坑会以两个或两个以上同心环的形式出现。在重力较强天体上，陨石坑从一种类型到另一种类型的过渡时，直径间的分界线较小。

地球的陨石坑记录保存得很差，因为它是一个活跃的星球。在地球上，清除或掩埋陨石坑的过程几乎与陨石坑形成的速度相同。幸运的是，多亏了阿波罗载人登月计划返回地球后带来了可确定日期的样本，再加上苏联的几次无人驾驶样本返回任务，月球上现存的大片古代地形使我们能够计算出月球表面已知年代的陨击坑的密度。通过这种方法，我们知道了晚期重轰击的日期，以及自那以后月球被撞击的平均速度。地球一定受到了和它的卫星同样的撞击流，并且我们有充分的理由相信，对水星、金星和火星来说，这一近似结果也是适用的。因此，计算陨石坑数量是我们估算行星表面年龄的最好方法。即使对陨石坑的绝对年龄存在疑问，我们通常也可以有把握地假设，陨石坑密度较低的地表比陨石坑密度较高的地表更年轻。

图2　月球表面一个470千米宽的区域的照片。这个区域布了陨石坑。这些陨石坑大多是在39亿年前形成的，冲掉了所有较老的陨石坑。每个陨石坑都是由一个比它小2~030倍的物体撞击形成的。地球的某些部分曾经看起和这个区域很相似

如今，地球每年会被大约1万颗1公斤以上的陨石撞击，但其中大多数陨石会因体积太小而无法通过大气层，它们在大气层中会被摩擦加热并被损耗。每年约有1000公斤的陨石会撞击地球，但最终只有10公斤左右的陨石能通过大气层。直径150米的陨石撞击地球会产生直径约2千米的陨石坑，其撞击地球的平均间隔约为5000年。大约每20万年会随机发生一次直径约1千米的陨石撞击，这样的陨石穿透地球大气层时视若无物，它会以匀速撞击地面，形成一个直径约20千米的陨石坑。更大、更具破坏性的陨石撞击鲜有发生。

碰撞影响着太阳系中的每一个天体，但陨石坑只存在于有固体表面且其他活动不足以抹去撞击记录的天体上。1994年7月，天文观测者发现了一系列碎片，这些碎片来自一颗被潮汐破坏的彗星。观测者幸运地在碎片即将与木星相撞前发现了它们，从而目睹了几次碎片与木星的撞击，发现每次撞击都在这颗巨行星的大气层中留下了褐色的疤痕，并持续了数周之久。2009年7月，一次未观测到的撞击也留下了这样一道疤痕。

行星是生命的居所

如果地球和太阳不是处于一个恰当的距离上，你就不会读到这本书，因为生命可能还没有形成——即使有生命，我们也不可能进化到这种程度。科学家们认为每颗恒星周围都有一个“宜居带”，在这个距离上，行星表面的温度对生命来说既不太热也不太冷。与金发姑娘(Goldilocks)偏爱熊宝宝的粥(粥的温度“刚刚好”)类似
[2]

，此宜居带有时也被称为“金发姑娘地带”。在这种情况下，“宜居”意味着某个地方可以维持任何类型的生命，即使只是简单的微生物，但这并不意味着该环境适合人类居住。

我们的生命活动需要水，所以宜居带通常等于这样一个与恒星的距离：在这个距离下，行星表面的温度可以使水以液态的形式存在。行星大气的密度和组成会影响行星的表面温度，但表面温度的主要控制因素是来自行星对恒星的热量吸收情况。据估计，太阳周围的宜居带为从距太阳大约0.95~1.5 AU的区域。这个估算结果表明，金星(0.72 AU)位于宜居带内边缘之外，火星(1.52 AU)位于宜居带外边缘的外侧。自行星形成以来，太阳的热量输出可能略有增加，所以随着时间的推移，宜居带将向外推。因此，火星虽然似乎不太适合生命居住，

但也不是没有希望。

由行星表面温度定义的宜居带一直被批评过于狭窄。在某些情况下，尽管表面看起来不适宜居住，但行星内部产生的热量可能会为生命提供一个适合生存的生态环境。即使在地球上，我们也知道存在着生活在0℃以下或100℃以上的“极端微生物”。因此，即使所有的生命都像地球上的生命那样，基于碳链分子并依赖水作为溶剂，太阳系中也有好几个地方可能会存在生命(尽管目前我们只知道地球上存在着生命)，并且在银河系的其他地方也存在着至少数百万个适合居住的地方。我将在本书的结尾再回到这个主题。

太空探索

望远镜是非常有用的，例如，我们可以用它来测量行星表面和大气层的温度及组成。早在1781年，威廉·赫歇尔就用望远镜准确地识别了火星上的极地冰盖。木星足够大，距离地球足够近，即使用相当普通的望远镜也能观测到它云层中的风暴。但如果不是太空探索的出现，这本书会变得更加枯燥，会有更多内容是凭空推测。半个世纪以来，地球上的太空探测器造访了太阳系的每一颗行星。1959年，苏联探测器到达月球；1969年至1972年期间，有12名美国宇航员在月球表面行走；20世纪60年代，美国国家航天局(NASA)的无人驾驶号(Unmanned)和苏联的无人探测器飞向了金星和火星，并在70年代到达各自的预定轨道，实现了软着陆。第一次飞向木星和土星的太空探索发生在20世纪70年代，而飞向其他巨行星的太空探索是在20世纪80年代。自1990年以来，越来越多的轨道飞行器探索了类地行星，机器人漫游者在火星表面爬行，木星和土星的复杂轨道之旅也得以实现。

这些任务中最著名的包括：1976年登陆火星的海盗1号
和2号
；1990年至1994年期间，麦哲伦号用雷达绘制了金星的表面；旅行者1号
和2号
在1979年至1989年间飞过了巨行星；1995年至2003年期间绕木星运行的伽利略号
；卡西尼号
于2004年开始绕土星轨道运行，并于2005年向土卫六表面发射了惠更斯号
探测器。

而未来几年太空探索的亮点则包括：从火星、小行星和彗星上收集样本并返回地球，以及人类在月球上的重现。美国和俄罗斯不再是仅有的太空强国。欧洲航天局(European Space Agency， ESA)已经有单独前往火星和金星的探测器，也有与美国宇航局联合前往土星的探测器，不久还将有与日本合作一起前往水星的探测器。日本已经向月球和小行星发射了探测器，中国和印度也都有探测器到达过月球。从科学上讲，各国间已经有了很多合作，大多数探测器携带的仪器都是由多个国家提供的，但不可否认的是，除了长期战略和商业利益的考量，

在太空探索领域中，国家自豪感也处在紧要位置。

[1]
原文为75年，现代常用的轨道周期为~796年。

[2]
这是一首英国童谣。

02 岩质行星 Rocky Planets

本章里，我会聊聊我们居住的行星——地球，还有与地球类似的天体——水星、金星和火星这三颗类地行星，以及月球。对国际天文学联合会(IAU)的天文学家来说，月球只是一颗卫星，但从地质学家或地球物理学家的角度来看，月球的成分和内部结构使其能与类地行星相提并论。图3是相同比例下的这五个天体，相关数据在表3里。在这一组天体中，水星和月球其实没有大气层。金星的体积、质量和密度只比地球小一点点，所以金星的表面重力也只比地球小一点点，但是大气密度比地球要大得多。火星的体积比水星大，密度比水星小，由此产生的两种效应相互抵消，所以火星和水星的表面引力非常接近，不过由于火星更冷，所以它能够保持稀薄却像样的大气层。月球的表面重力为地球的六分之一，是这些天体中表面重力最低的，这是月球漫步者会以奇怪的方式四处走动的原因。表中的平均表面温度略去了这五个天体的地表温度随纬度的巨大变化，在某些情况下，还略去了昼夜之间地表温度的变化。例如在白天，水星的最高温度超过400℃，而漫长的水星之夜后，水星黎明的温度低于-180℃。

表3　类地行星的基本数

图3　上图：以相同的比例从左到右展示——水星、金星、地球、月球和火星。下图：更大的巨行星、木星、土星、天王星和海王星，还有和它们同样比例的类地行星

核

类地行星的特点是外表有很多岩石，主要是硅酸盐矿物类。但它的密度很大，里面不可能全部都是岩石，所以我们认为类地行星中心有一个富含铁的内核。没有一颗行星的核可以被直接看到或取样，但有几条彼此独立的证据链可以证明类地行星有一个富含铁的内核。其中之一是密度，即使考虑到类地行星内部会在高压下压缩，类地行星内部的密度也必须比岩石大。并且，轨道飞行器的轨道分析结果证明，沿着指向行星中心的各个方向，密度对称地增加。模拟岩质行星内部可能状况的化学模型表明，岩质行星内部深处的氧不足以使所有铁被氧化结合在硅酸盐矿物中。因此，如果行星的内部曾经熔融，金属铁因为比岩石密度更大，将向中心下沉。这是一种分化过程。

地球和水星的富铁核外侧一定是熔融状态的，证据是这两颗行星现在都有很强的磁场。地球和水星的磁场显然是由导电流体的发电机运动产生的。对于如此小的行星来说，水星的密度非常高，所以它的核一定非常大，估计占据了水星体积的40%和质量的75%。金星、月球和火星内部没有产生磁场，所以它们的核可能是完全凝固的。

研究地球时，我们通过研究地震波如何穿过地球，获得了很多关于地核的证据。地震波是由地震(或地下核试验)引发的振动，它证实了地球有一个半径为1215千米的固态内核和一个半径为3470千米的液态外核，这两者的成分似乎都主要是含有5%~10%镍的铁合金，但地球的密度参考值说明地核含有密度小于铁的物质，它只占地球外核的6%~10%，内核的2%~5%。对此最可能的解释是地核里混进了氧、硅和硫。

总的来说，地核约占地球体积的16%。金星和火星的核分别约占各自体积的12%和9%，这两个数值主要是根据两颗行星的平均密度估算出来的。另外关于月球有限的地震数据来自阿波罗计划，它们暗示着月球有一个相对较小的核，半径在220~450千米之间(不到月球总体积的4%)。大约每20颗陨石中就有1颗成分是含4.5%~18%镍的铁合金，这与小行星带中小行星的核一样，这些核在碰撞分解前就已经在内部分化了。

幔和壳

类地行星核周围的硅酸盐部分被称为幔。幔占据了类地行星的大部分体积和大部分质量(除了水星)。壳是覆盖在幔上相对较小的部分，也是由各种硅酸盐组成的，不过在成分上与幔略有不同。

行星目前的幔是由熔化的岩石演化来的，这些岩石曾在最终的巨大撞击时覆盖整个行星，地质学家称之为“岩浆海洋”。在岩浆海洋冷却的过程中，它的表面会向太空辐射热量，使其冷却成坚硬的外壳。然而，由于来自下层的湍流和上层的撞击，这层外壳会不断地反复破裂然后被搅动。岩浆海洋会持续冷却，但不像水球会最终冻结，类地行星上没有使整个岩浆海洋变成固体的特定凝结温度。熔融硅酸盐物质的性质就是这样，各种成分的矿物会在不同的温度和压力下结晶。行星科学家们还不确定岩浆海洋的分层结晶程度，也不确定密度高的矿物是否能够下沉，密度较低的矿物是否能够上浮，或许它们还会粘在一起形成巨大的“岩石冰山”，能使其自身更有效地浮起。

这些聚集的漂浮物质在化学成分上与其下方的岩浆海洋不同，它们形成了月球最早的真正意义上的壳。如今，聚集的漂浮物质在月球上以高地(月球表面的苍白区域)的形式存在。在更大的类地行星上，最古老的地壳的性质还没有被确定，部分原因是最古老的地壳很多被后来的壳所取代(至少被覆盖了)。要想知道这是如何发生的，我们必须把注意力转回幔。当一颗年轻的行星冷却下来时，它的幔会完全凝固，硅酸盐物质的两个重要特性随之开始作用。其中之一是：足够热的硅酸盐固体既不是完全不动的，也不是完全定型的。行星内部的热岩石能够以每年几厘米的速度(和指甲生长的速度一样)流动，就像一块沥青会随着时间变形一样。对一个坚固的幔来说，如果存在驱动力，在固体地幔中会发生缓慢的，但在地质学上来说是实实在在的移动。在行星内部，推动幔的动力来自热量。深层幔，其密度将略低于较冷的上部地幔，因此它们有交换位置的趋势。这种运动被称为对流，你可以在加热的汤锅中观察到它，但在行星内部，“固态对流”要慢得多。

想象一条由热幔形成的“饰带”或“羽流”在向上流动，并将较冷的幔向下置换。离地表越近，上升幔所经受的压力就越小，这就用上了硅酸盐的第二个相关特征。随着压力下降，硅酸盐开始熔化，这一过程被称为“部分熔融”，因为只有部分固体会熔化。这样形成的岩浆里二氧化硅的含量会略高于形成岩浆的固体。由此产生的岩浆密度也比固体低，浮力会把岩浆向表面挤压，尤其在覆盖在岩浆上的岩石受张力或已经断裂形成通道时。除非岩浆成为侵入物滞留在地下，否则它会通过火山向外喷发。

以这种方式形成的岩石被称为火成岩。岩浆活动所产生的壳可以通过渗透或覆盖的方式取代行星原有的壳。月球上的黑斑，也就是月球上的“月海”——是低洼地带，那里颜色较浅的原始地壳被以这种方式产生的熔岩流掩埋了。现在地球上壳的来源一个是地幔部分熔融形成的海洋地壳，还有多代海洋地壳熔融、再循环形成的大陆地壳。地球的海洋地壳厚6~11千米，而大陆地壳的厚度可以从较薄拉伸地带的25千米左右上升到主要山脉下面90千米。总的来说，地壳只占地球总体积约1%。月球的壳的平均厚度约为70千米(占月球体积的13%)，范围包括高地地区大于100千米到某些主要撞击盆地下的20千米。

总之，在化学成分上，壳与下面的幔类似，不同之处在壳从幔中提取的方式。壳的密度较低，一般来说二氧化硅含量比幔高。壳比幔更多样化，壳中有岩石，它能与任何大气或液态水发生化学反应。这些岩石被分解或溶解，被重力、风、水或冰带走，沉积在其他地方。这些沉积物叫作沉积岩。埋藏、变形和加热可导致沉积岩或火成岩再结晶，通过这种过程形成的岩石被称为变质岩。

内部热量

行星的内部很热，部分原因是吸积过程留下了热量。对更大的行星来说，这种“原始热量”现存的比例会更大。因为含热量与行星体积有关，行星体积取决于半径的立方，热流失受表面积的限制，表面积只取决于半径的平方。

行星内部也会因为放射性同位素的衰变产生热量。会衰变的放射性同位素有很多，但只有四种会产生明显的热量：钾-40、铀-238、铀-235和钍-232。由于它们的化学特征，这些元素在岩石壳中的含量比在幔中更为丰富。在地球上，地壳所产生的辐射热(放射性衰变)与体积比地壳大得多的地幔所产生的辐射热大致相同。

类地行星产热元素的总量取决于它的质量(也取决于体积)。就像原始热量一样，在更大的行星上，放射热会被更有效地保留下来。以地球为例，现今散发到地表的热量仅有一半左右是原始热量，其余几乎都是放射热。

岩石圈

在壳和幔交界以下到达一定深度之后，物质通常会发生由冷而硬到热而流动的转变，壳和最上层幔构成了一个均一的力学层——一层坚硬的外壳。它被称为“岩石圈”，我们用希腊单词lithos （岩
石
)来表示这层岩石具有普通岩石的力学特性。岩石圈下面是幔，虽然幔的成分也是岩石，但它足够热，足够脆弱，可以产生对流。这个区域有时也被称为软流圈
(asthenosphere，包含希腊语a-sthenos表示，意思是“没有力量”)。

地球的岩石圈大约有100千米厚，被分成了许多板块。由于底层软流圈特别脆弱，这些板块会被“冲散”。作为“板块构造”过程的一部分，岩石圈在板块被拉开的地方(通常是海洋深处，我们看不到)形成，然后会在一个板块被拉到另一个板块下方之后(也就是海沟标记的俯冲带)被破坏。大多数地震是由一个板块被邻近板块碾压所引起的。如果有人告诉你地球板块构造是“地壳在地幔上滑动”，那他们就错了，他们犯了许多学校教科书和考试大纲上常见的错误。事实上，地球板块是由地壳和与其连接的最上层坚硬地幔组成的，它们一起滑过更深、但不那么坚硬的软流圈地幔。

岩石圈是脆弱的，当一块岩石碾过另一块岩石时，就会发生断层。断层在地球上很常见，尤其是在两个板块相遇的区域。我们在其他行星上也发现了断层(图4)。

图4　500千米宽水星局部图。太阳光来自右边。影子标出一个千米级的陡坡，它的一侧有一个开放的字母M的形状。这是一个名叫猎犬悬崖的古老逆冲断层，它标志着右边(东边)的地面被推到左边(西边)的地面之上。图中一些陨石坑比这个断层更古老，而另一些则比这个断层更年轻

板块构造似乎是地球特有的。水星、月球和火星是更容易冷却的较小天体，它们的岩石圈也更厚，这无疑是仅在地球有板块构造的原因之一。但另一个更重要的因素在于，要使板块具有可移动性，软流圈的顶部需要足够脆弱。在地球内部，岩石当中含有少量水，这不仅让它们更脆弱，还形成了少量能润滑颗粒边界的熔化物。金星没有水分，所以它的软流圈是干燥的，岩石圈板块无法在其上自由滑动。

行星的软流圈或是干燥或是非常深厚，这对行星表面产生了两个主要影响：第一个是影响山脉的高度和盆地的深度。如果山脉和盆地的落差太大，软流圈就会使覆盖在上面的岩石圈流动并弯折，将地形反差度降到足以仅靠岩石圈的强度来支撑。第二个是影响软流圈带来的大冲击导致的裂纹。直径几十千米的冲击物以排山倒海之势冲击岩石圈，将其破坏，形成了盆地状的陨石坑，并带有同心裂缝环这一特征。在较薄的岩石圈中，这些同心裂缝环往往更加致密，因此可以用一些多环碰撞盆地来估计软流圈形成时的深度。当一颗行星慢慢冷却时，其岩石圈会逐渐变厚。

火山活动

岩浆是熔岩爆发前的名字，它主要有三个产生原因。热量可以直接作为岩浆的第一个成因，但也是最不重要的一个。行星岩石圈以下的热量积累缓慢，这可能导致大量的火山活动，行星内部强烈变化的潮汐应力又会造成星体内部的摩擦，导致“潮汐加热”，形成岩浆。压力的突然降低也有可能导致熔融，这可能是岩浆的第二个成因，这一情况只发生在大型撞击盆地所在的幔上。幔的上升区压力降低会导致熔岩部分熔化(例如，导致地球海洋地壳的形成)。岩浆形成的第三个原因是将水引入地幔或地壳，下层水会降低硅酸盐熔化的初始温度。地球俯冲带的上方有一串火山，因为被向下拖拽的俯冲板块的岩石中含有水，这些水向上渗入了俯冲板块上的覆盖板块底部。覆盖板块底部的温度没有热到足以使熔岩直接熔化，但即使温度没有上升，只要引入水，熔岩就会开始熔化。

月球

自从人们通过望远镜看到月球上的火山口，就开始推测月球火山活动。但他们错了，因为我们现在相当肯定，月球上几乎所有的环形山都是由撞击造成的。事实上，月球上主要的火山区域是那些曾被认为是干涸海床的黑色区域，尽管它们的名字仍然是mare
(发音为mah-ray
)，意思是“海”。黑色区域的名字的复数是“maria
”(发音为mah-ri-a
)。火山区覆盖了约17%的月球表面，大部分位于月球离我们近的那面，也就是一直面向地球的那个半球。在这里，与陆地玄武岩成分相似的熔岩已经淹没了大多数多环碰撞盆地。

月海玄武岩的具体喷发口很难确定(图5)。这些喷发口很明显不是圆锥形火山，很有可能是裂缝。最有可能的是，炽热的熔岩通过裂缝被膨胀的火山气体喷射到高度超过1千米的地方。熔岩掉到地面的过程中，仍然炽热得足以摊开，蜿蜒流下数百千米。随着喷发速度的减弱，大部分裂缝的喷发口自动封闭，或者被后来的火山喷发所掩埋。

图5　200 千米宽的视野下，月海的东南边缘。右边的崎岖地形是盆地边缘部分隆起的高原地壳。左上方较暗、较光滑的区域是月海玄武岩，它淹没了地势较低的地区。一条名为哈德利沟纹（Hadley Rille）的1千米宽的海沟从南到北穿过视野中心。我们认为这是一条通道，熔岩从一个几乎被阴影遮蔽的源头流出后，流经这里。阿波罗
15号
在接近图像的中间、靠近哈德利沟纹的地方着陆

阿波罗的六次登月计划 (1969—1972年)中，有四次是在月海上登陆的，因为那里地势平坦，比高地更安全。阿波罗号带回了可供分析的月海玄武岩样品，通过其中的放射性物质的衰变情况(放射性年代测定法)，我们进行了高精度年代测定。该样品展示了年龄在39亿年到31亿年之间的月海，这样长时间的火山作用可以对月海做最简单的火山解释——盆地形成直接引发了火山作用。此外，2000年后的研究已经测定了一些重叠陨石坑足够少的月海，这些月海的年龄都小于12亿年。但在2007年，地球上发现了一片被认定为陨石的月球碎片。这个碎片是作为陨石撞击的抛射物被抛出月球的，里面含有已经存在43.5亿年的玄武岩碎片，比晚期重轰击的结束时间提早了5亿年。如此高龄的月海被随后形成盆地的抛射物掩埋，已经看不见了。所以如今我们知道，月球上的火山活动开始得早，结束得晚。

水星

水星的知名度远不如月球。不到一半的水星图片是由美国国家航天局(NASA)的水手10号在1974年至1975年间拍摄的。此后，再没有探测器到达过水星。直到2008年，美国宇航局的信使号探测器开始一系列的多重掠行后，水星才再次被探访。信使号探测器揭示的细节足以消除大多数人对水星上火山活跃程度的怀疑。如图4中右下角光滑的地形和正上方直径为120千米的盆地现在被认定为火山。水星缺乏浅色高地和深色熔岩之间反照率(反射亮度)的对比，人们先前最怀疑的就在这儿。浅色高地和深色熔岩使月球上的月海十分明显，这似乎是因为水星熔岩矿物质里的铁含量比月球(和地球陆地)玄武岩里的铁含量要少得多。熔岩形成的平原可能占了大部分水星表面，其中一些年龄大到可以追溯到晚期重轰击时代，还有密集的陨石坑。另一些熔岩形成的平原年龄比较小，上面的陨石坑较少。

信使号拍摄了一些火山口的照片，还拍摄了一些奇怪的10千米大的斑点。这些斑点有些明亮，有些黑暗，可能是特别年轻的爆炸性喷发点。在宇宙飞船进入水星轨道更系统、详细地记录水星图像之前，水星火山活动的持续时间很可能还无法确定。确认水星火山活动的持续时间的第一个机会将是2011年
[1]

信使号进入水星轨道的时刻。如果信使号仍然没有解决这个问题，那么水星火山活动的持续时间将由欧洲航天局的贝比科隆博(BepiColombo)水星探测计划来解决，该任务计划2020年抵达水星。但可以肯定地说，水星的大面积熔岩至少是在30~40亿年前形成的，但很可能在过去10亿年内还有熔岩形成。水星上有如此长时间的火山活动是人们没有预料到的，这可能是由同一个神秘热源加热，并且这个热源还使水星的核心至今仍有部分熔融。

金星

金星比水星大得多。它的大小和质量表明，金星产生的热辐射几乎和地球一样多，因此金星上火山活动的频次也和地球差不多。但由于金星没有板块构造，两者火山活动的形式大相径庭。

金星有一个浓密的、永远多云的大气层，这使得我们能用雷达来研究金星之前，它的表面一直是个谜。图6显示了美国国家航天局(NASA)的麦哲
伦号探测器获得的部分金星雷达图像。该探测器在1990年至1994年间几乎绘制出了整个金星的地图。通过向地面连续发射一连串雷达脉冲，再对反弹回来的波进行复杂分析、组合，形成了雷达图像。在大多数情况下，你可以像看黑白光学图像一样看雷达图像，但事实上，行星每个特征的亮度主要取决于行星局部表面的粗糙程度，而不是它对可见光的反射率。

图6展现了金星表面的大部分特征，多个从西向东的熔岩流穿过图中，一些更粗糙(更亮)，一些更平滑(更暗)。单个熔岩流的叶状模式与地球和火星上的熔岩流非常相似，但这种模式在月球和水星上却很难辨别，因为月球和水星上的熔岩流边缘已经被撞击分解了。

图6　麦哲伦号
拍摄的500千米宽的部分金星图像。该地区部分是熔岩，源自图像中心以西300千米处。但图像东南角是一些崎岖的地形，代表金星上现存的最古老的地壳。图像的西部，从北到南是一个被熔岩流破坏的带脊和断裂地形的山区

除了大约覆盖了表面一半的熔岩流，金星上还有许多清晰可辨的火山。图7显示了一个例子，该图片的背景是一座5千米高的火山，侧翼呈缓坡状。这种火山在地球上被称为“盾状火山”，是玄武岩通过一个火山口反复喷发形成的。在火山的侧面可以看到单个熔岩流。没有人知道这座火山或其他类似火山的上一次喷发是在多久以前。金星近期或现今的火山活动，是否都存在这种形式？对于这些问题，有一些有趣的线索，但都没有证据。因为这些火山活动太小了，无法提供计算陨石坑的可靠统计数据。这座特殊的火山建立在一个较古老的地域上，这个地域更为平坦，上面有许多裂缝。图7前景中的陨石坑可能与它左边明亮的熔岩流无关。

金星上有超过300个被称为“冕”(coronae)的同心环状或椭圆形裂缝。我们认为这些裂缝的起源与月球和水星的多球撞击盆地不同。它们的直径从200米到2000多千米不等，通常与某种形式的火山活动有关。也许每一个冕都标志着一个地点，即软流圈中上升的地幔柱顶住岩石圈的底部。地幔柱仍在这里的冠状抬升为非常宽的圆顶，而较早的冠状区因为缺少地幔柱的支撑，会渐渐塌陷。这种下陷解释了同心断裂。

图7　计算机生成的金星上玛阿特火山（Maat Mons）的三维透视图。该图是通过在雷达测高仪获得的地形模型上覆盖雷达图像来实现的，火山的垂直尺度被放大了10 倍。这两组数据都是由麦哲伦号
探测器收集的。右前部分的陨石坑直径23千米

金星上的陨石坑比地球上要多，但远比月球和水星上的少(在图6中你不会发现任何陨石坑)。这其中两个因素在起作用。在金星上是看不到直径小于3千米的陨石坑的，它稠密的大气层保护了其表面不受小撞击。但有一些较大型的陨石坑，因为携带过多能量的物体不受金星大气的影响。较大陨石坑的数量少，可能是因为这平均年龄只有5~7亿年的年轻金星表面。金星地表年龄比较平均，没有特别古老或特别年轻的大片地形。

在20世纪90年代，对这一现象的标准解释是：几乎整个金星的地表都是在一场5~7亿年前，持续不超过几千万年的火山活动中重新塑造的。这与金星缺乏板块构造的原因一致。因为缺乏板块构造，在大部分上层软流圈熔化之前，深层幔的大部分热量都被困在岩石圈盖之下。最终，冷而致密的岩石圈崩塌，而困于岩石圈下面的岩浆将会喷发。自金星形成以来，类似的事情可能已经发生了六次，在接下来的1亿年内可能还会再次发生。

最近，这种让金星有全球灾难性火山爆发的模型遭到了质疑，因为陨石坑的统计数据并不能排除这个塑造过程是在一个更长的时期内发生的，比如在过去的5亿年里，不定时被熔岩覆盖的随机区域越来越小。

地球

在地球上，内部热量的收支是由火山活动和板块构造共同调节的，从而不能使用金星上的软流层温度偏移的假设。在地球岩石圈以下产生的热量中，只有大约三分之一是通过传导发散出去了。其余大部分热量通过大洋中脊的喷发被传递到岩石圈顶部(在大洋中脊，新的物质被添加到分离的板块之间)。此外，在岩石圈以下产生的小部分热量则是通过俯冲带上的火山爆发和地幔柱上的各种“热点”被传递到岩石圈顶部。在俯冲带，岩石圈板块旧的、冷的部分回流融入软流圈，使得它重新冷却。

我们最接近金星火山灾难的是：每隔几千万年，就有一个直径达1000千米的区域会被多达10立方千米的玄武岩熔岩所掩埋，这就是所谓的“洪流玄武岩”。印度西北部的“德干陷阱”(6600万年前)、英国-北极泛滥玄武岩(格陵兰岛和不列颠群岛西北部，5700万年前)、哥伦比亚河洪流玄武岩(美国西北部，1600万年前)都是比较著名的例子。这些重大且罕见的事件可能会向大气中注入大量火山气体，尤其是二氧化硫，以及被称为“火山灰”的火山岩碎片，这会严重影响全球气候。图8显示了地球上熔岩流的一个例子，可以与其他行星的图像进行比较。

图8　这张70千米宽的太空照片显示了美国爱达荷州的“月球火山口”熔岩场。熔岩流的来源是西北部崎岖高地边缘附近的一系列裂缝。可将熔岩流的叶状形态与图6 中的金星流进行比较

地球上的火山活动与其他行星最大的不同之处在于，地球岩浆中气体不断上升、膨胀，往往会使相当大一部分火山喷发具有爆炸性。原因有二：其一是循环水、二氧化碳和二氧化硫会从俯冲带上方逸出，大大增加了原始气体深层的内部泄漏，因此地球上有更多的气体会驱动火山爆发；二是大陆地壳的存在有利于形成硅含量高于玄武岩的岩浆。这些富含二氧化硅的岩浆比玄武岩更黏稠，也更容易破碎。日本富士山(Mount Fuji)这种经典的“画册”式尖顶锥形火山在地球之外的行星上很少见，因为它们是相对富含硅的火山爆发的结果，而且部分尖顶锥形火山的喷发是爆炸性的。

火星

与地球和金星相比，火星上的火山较少，但规模往往很大。大型玄武岩盾状火山主要分布在塔尔西斯地区(大部分位于图9中)和埃律西昂地区。奥林匹斯山是塔尔西斯最大的火山，直径约600千米，从山顶到山底的距离高达24千米，是整个太阳系最大的火山。

火星有这么大的火山的原因有两个。首先，火星是一个“单板块行星”，其岩石圈是一个完整的外壳，即一个单一的板块。相对于底层地幔软流圈，火星的岩石圈实际上是静止的；而在地球上，板块相对于地幔柱四处漂移，因此，仅仅几百万年，由地幔柱补给的火山就会漂走，火山的岩浆供应也就被切断了。与地球不同的是，只要地幔柱保持活跃，火星上的地幔柱就会一直向岩石圈的同一地点提供岩浆。奥林匹斯山可能在10亿多年前就开始成形了，确切日期无从得知，因为我们只能通过陨石坑计数来确定如今火星地表事物的年代，而无法看到更古老的、被埋在地下的火山内部。奥林匹斯山顶有几个相互重叠的火山喷发口，其历史可以追溯到1亿~2亿年前，但其侧翼最年轻的熔岩流大约只有200万年的历史，它可能有一天会再次喷发。塔尔西斯高地的其他火山肯定更古老，但如今可能都已经是死火山了。

图9　这幅3000千米宽的拼接图像显示了火星上几个巨盾状火山。左边是奥林匹斯山，太阳系中最大的火山。图像右边的边缘是塔尔西斯火山。从南部边缘的中心向东北延伸，分布着三座山：帕弗尼斯山、艾斯克雷尔斯山和什洛尼尔斯山

火星上有这么大的火山的第二个原因是“它可以”。火星有一个寒冷而坚硬的岩石圈，约为地球岩石圈的两倍厚。如果你把奥林匹斯山移到地球或金星上，它们的岩石圈就会因为相对较薄而在负荷之下凹陷下来，这座火山也就失去了高度。

高分辨率图像显示了大型火山之间的平原和火星其他几个地区的熔岩流的细节。然而，这些熔岩流因其具有的一些特征，也被认为是火山，这引起了相当大的争议。图10显示了一个值得注意的示例。

图10　这张图片展示了50 千米宽的火星的争议区域，由欧洲航天局的火星快车轨道飞行器拍摄。有人认为这个板块的表面是熔岩流，有着断裂冷却的壳。另一些人则认为这是冰冻海面上破碎的浮冰，现在被灰尘覆盖。两个陨石坑的年龄都超过了板块表面的年龄，它们的边缘足够高，可以防止内部被水淹没。陨石坑实际上是圆形的，但在这张斜视图中被压扁了

地球上曾经收集到30多个火星陨石。陨石要么是玄武岩熔岩，它们是火星的撞击物碎片；要么是更粗糙的晶体侵入的等价物，其结晶年龄的跨度从45亿年到1.6亿年不等。由此，我们可以推断，尽管火星表面的大片区域覆盖着各种各样的沉积物，但火成岩在深处构成了火星地壳的大部分区域。

表面过程

风化层和空间风化

火山活动是由行星内部活动驱动的，但行星的地貌可以通过其表面活动来塑造。对一个没有空气，也没有大气层保护的行星来说，直接作用于其表面的过程主要是陨石和微陨石的轰击。从陨石坑中抛出的碎片状物质，即“抛射物”，覆盖了行星地表，深达数米。在这种行星的地表上，有坚实基岩的地方非常罕见(图11)。月球土壤被称为“风化层”，阿波罗号宇航员在其上留下的脚印主要由几毫米大小的颗粒组成，包括晶体碎片、微小的岩石碎片和玻璃球。这些玻璃球是冰冻的液滴，由撞击产生的热量生成。通过火山口挖掘和抛射物扩散，风化层在各种尺度上不断地重新排列，这一过程被称为“冲击成壤”。在撞击速度更快的水星上，风化层的颗粒大小约为月球风化层的三分之一。

图11　阿波罗号宇航员戴夫·斯科特拍摄的哈德利沟纹的远摄照片。左边2米厚的水平层是一个罕见的基岩实例——可能是熔岩流构成的，它暴露在了陡峭的斜坡上。哈德利沟纹的其他地方都被风化层覆盖，风化层的颗粒大小不一，从巨砾到灰尘都有

如果行星没有大气，太阳紫外线就可以直达表面，随着时间的推移，紫外线可能会破坏化学键。如果有微陨石撞击，又或者行星没有磁场，来自太阳风的带电粒子也会影响行星表面的化学性质。这样，无大气的行星会经历一系列被统称为“太空风化”的过程，这些过程会慢慢改变其表面成分。例如，连接铁和氧原子的键可能被破坏，释放出氧气，留下被称为“纳米铁”的亚微观纯金属颗粒。

若一颗行星有大气层，那么只有特别大的罕见撞击物才能以高速到达表面。例如，在地球的大气层中，尺寸小于150米的石质小行星可能会发生解体，由此产生的碎片足够小，会通过摩擦减速。因此，它们到达地面时，几乎已经失去了所有的初始速度，所以不能形成陨石坑。微陨星尘，主要是微陨石，也可能是较大陨石摩擦脱落的碎片，以每百万年0.1~1毫米的平均积累速度沉降到行星地面。这种尘埃对总沉积速率的贡献很小，除了远离陆地的深海海底，微陨星尘通常会完全被其他沉淀物所淹没。

侵蚀和运输

除了对景观产生影响，风、流水和移动的冰(冰川)也会磨损岩石，并将岩石碎片带走。在化学风化过程中，水也能溶解岩石。水中溶解的元素可能会重新出现在其他地方，并在新的矿物质中沉淀。这尤其适用于盐沉积，也适用于许多形式的碳酸盐岩。但是在地球上，大多数石灰石，即碳酸钙，是由海洋生物外壳的碎片形成的，这证明了将溶解的碳酸盐(或溶解的二氧化碳气体)转变成可以变成岩石的固体物质需要一个重要的生物转化步骤。

火星上的沙尘暴很有名，它在1809年首次被望远镜观测到。当火星在近日点时，接收到的太阳能比远日点多40%，火星上速度超过每秒20米的风可以将极其多的尘埃吹到空中，以至于大部分火星表面会持续数周被遮蔽。有时，除了奥林匹斯山的峰顶，几乎看不到火星表面有什么凸出的东西。由于经常有云聚集在奥林匹斯山，它的峰顶通常看起来是白色的，也因此它以前的名字是奥林匹斯之雪(Nix Olympica)，意思是奥林匹斯山上的雪。但这个名字在航天器传回的图像显示这里真正发生了什么以后就被修改了。

从轨道上或地面上都可以看到火星上有许多风的活动迹象(图12)，它们以较小的风波纹的形式出现在沙丘和表面尘埃中。火星上的一些沙丘正在被风不断雕凿，但另外一些的形状可能已经有数百万年没有改变了。风成沙
[2]

是火星上有侵蚀存在的一个有力证据。大气的低密度意味着火星上能够输送沙粒的风速必须比地球上的风快得多，由于这种磨蚀，一些裸露在外的岩层形成了奇特的形状。

图12　一些沙丘，只缺些等比例的骆驼或棕榈树就像地球了。事实上，这张照片是由美国宇航局的机遇号
火星车在火星表面拍摄的，它从火山口的边缘斜拍到火山口底部的沙丘。可见区域大约有100米宽

金星的大气密度比地球大得多，其地面气压是地球的92倍，因此，即使是缓慢的风也能使沙粒四处移动。金星上也有几处沙丘，然而在这里，当风吹起的颗粒撞击基岩时，侵蚀力十分有限，部分原因是因为稠密空气的冲击速度较慢且具有缓冲作用，还有部分原因则是480℃的地表高温会使材料塑性变形，而不是以易碎的方式磨损。

对地球人来说，流动的水通常是最常见的泥沙运输媒介——比如河流中的水，或者海滩上的波浪。在太阳系中，除了地球，目前没有任何天体的表面条件能让水稳定地保持在液态。金星太热了。火星的正午温度尽管远高于0℃，但它的大气层非常稀薄，表面的冰会直接变成蒸汽，而不是融化成水。有大量的证据表明，火星表面曾经有大量的水流动(图13)。火星至少经历了与地球相同的极端气候，并且在数十亿年前，它的大气密度和湿度足以导致降雨和灾难性的洪水。太阳系最大的峡谷系统是火星水手谷(Valles Marineris，水手9号探测器在1971年传回的图像中发现了这个峡谷，并以探测器的名字给峡谷命了名)。这是一个4000千米长的裂谷系统，始于地壳的破裂。当水流经水手谷时，由于侵蚀作用，水手谷会变宽。它最深的地方到了地面边缘以下的7千米处(亚利桑那州的大峡谷只有2千米深)。水手谷还非常宽，以至于如果你站在峡谷的一边朝对面看时，会发现另一边消失在地平线之外。

图13　一系列东西向的裂缝证明了火星上水手谷复合体的构造起源。在这幅视野为800 千米宽的图中，水手谷只有一小部分被露出。请注意蜿蜒深切的河道从南面进入，这显示了流动的水在拓宽主峡谷中发挥的作用

尽管水手谷广阔无垠，却一直没有被前太空时代的望远镜观测人员发现过。1877年，意大利人乔范尼·夏帕雷利(Giovanni Schiaparelli)绘制了臭名昭著的火星“运河”地图，随后得到了美国人珀西瓦尔·洛厄尔(Percival Lowell)的支持。洛厄尔于1916年去世，他一生都认为这些运河是聪明的火星人设计的巨大工程。事实上，这些运河与火星上许多真实存在的河道没有任何关系，其中补充支流分支网络的水可能是由降雨提供的，包括图13中所示的许多长得多的河道。流经其他地方的水可能是永久冻土融化的时候，从地下漏出来的。河道注入平原形成的流线型“岛屿”，表明它们曾被巨大的洪水冲刷过。在这些地方降落的机器人着陆器(1976年的海盗1号
和1997年的火星探路者号
)发现了大量洪水冲刷之后留下的岩石。

火星上主要的山谷无一例外都有许多撞击坑，所以很明显，它们一定是古老的，并且最后一次流动发生在10多亿年前。在最后一次流动之后，许多山谷的侧壁都发生了山体滑坡，谷底如今布满了由寒风吹成的火星沙丘。在20世纪70年代和80年代，大多数科学家会告诉你，尽管火星在遥远的过去曾经历过至少一个潮湿的时期，但现在除了两极有小水冰覆盖外，其他地方都很干燥。想象一下，在1999年，当一架名为“火星轨道相机”的高分辨率成像仪开始在火星的几个陡坡上发现那些只有几米宽、几百米长的沟壑时，人们会有多么惊讶。这些沟壑缺少重叠的陨石坑，经过观察，其中许多沟壑下游的碎片堆积扇已经开始掩埋沙丘。这些特征表明这些沟壑一定是年轻的，但年轻到什么程度，在“火星轨道相机”发现沟壑不久之后，新的图像开始变化，这证明了一些沟壑在今天仍然是活跃的(图14)。

图14　1999 年8 月（左）和2005 年9 月（右）拍摄的两张照片，展示的是一个1.5 千米宽的区域，这个区域展示了直径6 千米的火星陨石坑内壁。陨石坑边缘穿过左上方，斜向画面右下方。边坡内壁上有许多侵蚀沟壑，其中一条沟壑在这两个日期之间似乎是流动的，一些苍白的碎屑流到了较低的斜坡上

争论的重点已经从质疑火星最年轻的沟壑的年龄转移到关注火星沟壑是如何被开凿上。有一种理论认为，水是开凿沟壑的“罪魁祸首”。在火星地下土中，可能有承压的液态地下水储集层存在。当斜坡(如图14中的火山口壁)在地下水位以下破裂时，土壤中的冰屏障(永久冻土)通常会阻止水逃逸。然而，如果屏障被暂时拆除，水就会涌出来。这种液体是稳定的——它在流动时既沸腾又冻结——但它可以在完全蒸发之前穿过这些沟壑的其中之一。持怀疑态度的人认为，沟壑的开凿并不需要液体，可以被解释为干燥岩石崩裂的结果。

一些火星科学家发现了火星表面有冰川存在的证据，特别是在高原边缘的侵蚀地带。现在，火星表面除了两极外没有其他可见冰层，但从轨道上拍摄的高分辨率图像显示，火星表面布满地面的岩石可能是覆盖(和隔离)地下冰的碎片。从火星轨道获得的探地雷达数据证实了这一点，这也是为什么我更愿意把图10中显示的区域视作被灰尘覆盖的冰冻海洋，而不是熔岩流的原因之一。

月球上的河道，如哈德利沟纹(图5)，是熔岩通道。这些河道不是被水冲刷出来的，月球上唯一的水是两极附近风化层中的少量冰。在金星上，人们已经标记了200多条蜿蜒的河道，其中一条长达6800千米。金星不太可能经历过足够极端的气候变化，能让足够近期存在的液态水侵蚀出这些通道，所以这些河道可能也是被熔岩冲刷而成的。

表面特征的命名

我已经多次使用过其他行星地形地物的名称：奥林匹斯山、水手谷、哈德利沟纹等。如果没有这些名字，我就只能说它们是“火星上最大的火山”“火星上巨大的峡谷系统”和“阿波罗15号
着陆处附近的那条大沟”。除非使用一个完全无法记住的坐标系，否则对不那么引人注目的那些地物，我将更难描述。

没有人在这些行星上住过，那么谁来制定行星地物的名字？这些名字正式吗？当天文学家们第一次开始用望远镜标记这些行星的地图的时候，有些人思想足够独立，给这些地表特征创造了独特的名字，并且他们通常不会考虑任何前人成果。成立于1919年的国际天文学联合会的早期任务就是整理混乱的行星地表名称，为被多重命名的地表特征制定唯一的官方名称，并为未来的命名建立标准和惯例。这些标准和惯例会被运用到新发现的天体和行星表面的特征上。这里的行星表面特征可能是人们想命名的特征，也可能是由于成像技术的改进而变得可见的特征。最初，成像技术的改进仅仅是指更大更好的望远镜。国际天文学联合会的创始人没有意识到，他们已经建立了一种方法，可以对由宇宙飞行器揭示的行星表面特征的命名进行监督。

一些人会批评国际天文学联合会对冥王星重新分类的处理，但我知道，没有人会对国际天文学联合会管理下，行星表面特征的命名的基本原则有负面意见。这是公平的，非政治性的，并试图体现世界上所有的文化，不只对单一个体，而对整个太阳系保持中立。

国际天文学联合会的命名法以对月球的表面特征的命名作为惯例。给环形山一个“不称职”的名字，但给其他大多数行星地表特征的命名都是一个名词加上一个拉丁描述词，用来表示它的类别。比如，“奥林匹斯山(Olympus Mons)”的意思是“奥林匹斯山(Olympus Mountain)”，这个名字可以立即告诉你，这个地表特征是一个名为奥林匹斯的山。虽然没有人怀疑奥林匹斯山是一座火山，但我们看到描述词并没有这样说。描述词会避免可能是错误的解释，只纯粹地进行描述。

你可能会遇到的常见描述词有：裂谷(一种深深的、细长的、陡峭的洼地)、起伏(一种流状特征)、堑沟(长、窄、浅的凹陷)，平原低地(低洼平原)、平原高地(高平原或高原)、峭壁(悬崖)和谷(分支谷)。在月球上，还有mare(复数maria)，翻译过来就是“海”。这个名称已经根深蒂固，无法用一个更贴切的词来替代。

每个星球上的名字都有主题。月球上的环形山是以已故的著名科学家、学者和艺术家的名字命名的，月球上的海则用描述各种气象条件的拉丁语来命名。除了月球，火星是唯一一个在国际天文学联合会参与之前就有大量名称流传的地方。这些名字来自乔范尼·夏帕雷利和欧仁·安东尼亚第(Eugenios Antoniadi)在19世纪晚期的望远镜测绘，后来加上了现代描述词。主要包括一些广阔的区域，如塔尔西斯地区和埃律西昂地区。火星上的每一个大山谷都以不同国家语言中的“火星”命名，小山谷则以地球上的河流命名。在金星上，几乎所有的名字都和女性有关：陨石坑是以历史上著名的女性命名的，其他大部分特征都是以女神命名的。在水星上，陨石坑是以死去的艺术家、音乐家、画家和作家的名字命名的，峭壁(悬崖)则是以科学探险队或船只的名字命名的。比如猎犬悬崖
(图4)就取自英国皇家海军的猎犬号，查尔斯·达尔文也乘坐过这艘船。他在航行的过程中收集了大量启发进化论的观察资料。

类似的命名原理也适用于小行星和其他行星的卫星。例如，木星的卫星木卫二上有以凯尔特神和英雄命名的环形山，木卫二其他大部分特征的名字都取自古典神话。

大气

每颗类地行星诞生后，其内部气体都会从岩浆海洋中逸出，类地行星必定都有过大气层。尽管从火山逸出的气体能显示大气曾经的样子，但是这些原始的大气层如今已经不复存在。月球和水星的引力太小，不能抓住大气这张“毯子”。你有时可以看到月球和水星的“大气”加了引号，因为其“大气”压力小到只有地球大气压力的十亿分之一，它们主要由微陨石和宇宙射线撞击表面产生的游离原子组成。这些原子是如此稀少，以至于每个原子都更可能飘向太空，而不是与另一个原子相撞。这种状态形成了行星的“外逸层”，它原本是大多数其他行星的大气中最外层的稀薄地带，却是月球和水星所能聚集的全部大气。

质量更大的类地行星的引力更强，这使它们能够更有效地留住气体，即使这些行星大气的密度和化学成分已经在无数的演化过程中变得面目全非。早期更活跃的太阳风可能带走了大部分原始大气，但这些大气会通过火山活动进行补充。一个重要的、正在进行的过程是短波长的太阳紫外线可以把水蒸气分子分解成氢和氧。氢非常轻，可以逃逸到太空，这使得水的光解成为一个不可逆的过程。金星和火星都以这种方式失去了大部分原本的水分。表4总结了如今金星、地球和火星大气的组成。

表4　如今类地行星的大气

*表中展示了六种最常见气体的丰度，以分子总数的百分比(地球大气中的水变化很大)、表面压力以相对地球的倍数形式表示

由于被紫外光分解，大气分子可以通过一系列被称为“光化学”的反应与其他分子结合。这一现象在距地表约100千米的“热层”中尤为明显。之所以将这个区域命名为“热层”，是因为这一层被太阳紫外线能量加热，这种能量要么用于分解分子，要么用于剥离电子，后者被称为电离。离子(主要是地球上的氧和金星、火星上的二氧化碳)在热层的外层中非常常见，它们形成了一个被称为“电离层”的导电层。当太阳风暴将等离子体从太阳带到地球时，这些等离子体会扭曲地球磁场，导致地球电离层中产生异常电流，严重干扰无线电通信，甚至导致电力故障。

大气层较深处，也就是紫外线无法穿透的地方，不受光化学的影响。这里的空气主要是通过与地面的接触变暖，而地面是由太阳加热的。所以在大气层最低的一层对流层中，随着高度的上升大气温度反而下降。大气压力和密度也是同理，这意味着对流层包含了大气的大部分质量。由于空气和岩石之间的化学反应，对流层的成分会变化，这是风化作用的必然结果。再加上生命活动，地球上对流层的成分会演化。植物和原始的单细胞生物仅在这里利用太阳能和大气中的二氧化碳来建造身体，释放出原始大气中极为罕见的气态氧。没有植物，像人类这样靠氧气生存的动物就不能生存，地球对流层的温度也会不同，我稍后会解释这一点。

当对流层底部附近的空气受热时，它们会膨胀，从而有了浮力。于是底部附近的空气上升，取而代之的是来自上方的冷空气。另一个对流的例子就是之前在一颗行星的地幔中。空气对流驱动着地球、金星和火星上的天气变化。但每颗行星对流的环流模式是不一样的，因为对流还取决于行星的自转速度(金星的自转速度缓慢)、大气的旋转速度(金星对流层上部的旋转速度远远超过金星本身的旋转速度)和昼夜温差(火星的昼夜温差大、金星的昼夜温差小)等因素。图15显示了金星南极上方的典型环流。相反，地球大气中的螺旋风暴系统往往始于热带附近。

地球复杂的大气层与它邻居们的不同。在金星和火星处，温度随对流层高度的上升迅速下降，在被称为中间层(非对流层)的地方，温度随高度上升缓慢下降，之后在热层，由于吸收了紫外线，温度再度随高度的上升而上升。但地球在类地行星中是独特的。在地球对流层和中间层之间有一段高度约10~50千米的区域，在这里，温度随高度的增加而增加，这就是平流层。平流层变暖的原因是臭氧分子会吸收230~350纳米波长的紫外光子(热层和中间层对紫外光子是透明的)。臭氧是三个氧原子结合在一个分子(O3)中，而不是两个氧原子结合在一个分子(O_2
)中。臭氧是由大气中含量较高的氧通过光化学反应组装而成的。两个氧原子(O_2
)通常是指“氧”。

图15　间隔24 小时拍摄的，金星上直径2000 千米的南极旋涡的“眼睛”。这个点表示南极。这些用中红外线拍摄的图像显示的是距离金星地表约60 千米的云顶。“眼睛”的中心更温暖，看起来更明亮，表明这里的云被向下拉到了更温暖、更深的大气层

温室效应和臭氧层空洞

很多人都知道“臭氧层空洞”和“温室效应”，但他们往往把“臭氧层空洞”和“温室效应”混为一谈，认为它们是气候变化的双生子。但是，这两者是截然不同的。

臭氧层(仅)存在于地球的平流层，是吸收230~350纳米紫外线的地方，这对我们和其他生活在地表的生物来说非常重要，因为230~350纳米的紫外线辐射会导致皮肤癌和基因损伤。令人惊讶的是，只需要很少的臭氧就能为地球上的生物提供一个有效的屏障。如果你把平流层中分散的臭氧全部收集起来，在海平面上铺开，只会形成一层3毫米厚的脆弱面纱。因此，在20世纪70年代和80年代，当人们发现南极洲上空的平流层失去了大约一半的臭氧时，人们非常担心，并开始谈论“臭氧层上的空洞”。臭氧丢失的主要原因是它会与一种叫作氯氟碳化合物(CFCs)的工业化学物质反应。这些化学物质现在已被禁止用于气溶胶喷雾剂和制冷剂，以免它们泄漏到大气中。南极的臭氧层空洞和北极上空较小的臭氧层空洞现在已经稳定下来。在极地以外的地区，臭氧只损耗了百分之几，尤其在热带地区根本探测不到。

臭氧浓度与全球平均温度之间没有直接联系。臭氧层被严重损耗会让生活变得不愉快，但这与气候变化或全球变暖几乎没有关系。行星对流层的温度是由低层大气吸收红外辐射的效率来控制的，因为可见光会使地面变暖，而变暖的地面会发出红外线辐射。大气的温度取决于两个因素：(1)它与地面接触时吸收的热量；(2)它能吸收地面反射的红外辐射的量。

大多数气体对红外辐射来说是透明的，但由两种或两种以上不同元素组成的分子吸收红外辐射的能力相当强。因此，氮(N_2
)、氧(O_2
)和氩(Ar)不吸收红外线，而水蒸气(H_2
O)、二氧化碳(CO_2
)、二氧化硫(SO_2
)和甲烷(CH4)则相反。行星大气对红外辐射的吸收就好比把热量困在温室里一样，被称为“温室效应”。在金星、地球和火星的大气层中存在着一种自然的温室效应。金星的大气温室效应使其表面温度保持在惊人的500℃以上，这主要是由于金星含有大量的二氧化碳。水蒸气和二氧化碳将地球温度加热至大约30℃。火星的大气层稀薄，富含二氧化碳，其温室效应仅到6℃左右。

地球的温室效应使地球的温度保持在一定范围内，以满足在这里生命进化的需要。在生命的调节下，地球温室效应的强度发生了变化，使地球的温度保持在合适的范围内。40亿年前，太阳的亮度只有今天的70%，所以如果那时地球的大气层和今天一样的话，地球会冷得多。但是，在40亿年前，地球的大气层的主要成分可能是二氧化碳，密度是今天的100倍，所以温室效应会更强。由于原始藻类的存在，地球大气层现在的二氧化碳含量下降到了大约5亿年前的十分之一左右，温室效应肯定也在下降。游离氧(O_2
)最早出现在22~27亿年前，在2~2.5亿年前达到峰值，浓度约为目前的170%。显然，地球上的生命不仅受大气成分变化的影响，而且还从中受益。

自工业时代以来，人类就以各种方式影响着大气：臭氧损耗、工业烟雾等。但是，我们最应该担心的是我们向大气释放的二氧化碳，或者更确切地说，我们向大气返还的二氧化碳，因为其中的大部分二氧化碳是在以前，由生物体从大气中提取出来，并以煤或石油的形式封存起来的。自1960年以来的50年间，大气中二氧化碳的含量增加了约20%(比任何自然过程都要快)，并且仍在增加。这种“人为温室效应”将不可避免地导致全球气候变暖。气温只需上升几度就会影响生态系统，也会使局部天气(包括短期气温波动)更加极端。气温上升的另一个后果将是全球海平面上升，这主要是因为水会随着气候变暖而膨胀。因此，虽然大气中的自然温室效应是一件好事，但人类引起的温室效应的迅速增强可能会对我们的文明带来潜在的灾难性后果。

自然温室效应逐步降低抵消了太阳光度的缓慢增强。在自然温室效应普遍逐渐减弱的背景下，地球的气候发生了几次变化，冰河时代是其中最著名的例子。在冰河时代，大部分(甚至全部)的地表水都被冻结了。这些气候的变化与其说是由大气控制的，不如说是由地球轴倾角和轨道偏心的变化控制的，类似的效应可能解释了火星表面湿度随时间的剧烈变化。

云

云层具有很强的反射率，所以云层越厚，直接反射回太空的太阳能就越多。但是，多云的天空也增加了大气对阳光照射到地面的热量的吸收能力，因此云层对全球气温的影响是复杂的。金星上连绵不断的云层并没有使它的表面免受温室效应的加热影响。

当温度和压力使大气的某些成分凝结成液滴或冰粒时，云就形成了。就类地行星而言，形成云的相关成分通常是水。虽然水只占金星大气层的一小部分，但在距金星表面45~65千米的对流层顶部，有足够的水来形成一层连续的云。在那里，水蒸气凝结成直径约2微米的水滴，它们保持悬浮，因为太小无法下落，又被称为气溶胶。金星大气中的二氧化硫溶解在其中，这些水滴就变成了硫酸。但是，如果有人试图告诉你这是“在金星上下硫酸雨”，那他们就错了。无论这些水滴被大气环流拉到45千米以下的什么地方，热量都会使它们再次蒸发，而且它们永远没有机会变成大到足以落向地面的雨滴。

在地球的地表以上大约6千米处，云主要是由微小的冰粒子组成，而在这个高度以下，云的成分主要是水滴。雨云其实不是灰色的，只是看起来像罢了，这是因为雨云足够厚，可以遮挡许多的光。在火星上，云层相对稀少。在火星对流层的大多数地方，云层是由水冰构成的，但在对流层/中间层边界附近约80千米处，我们观察到的是二氧化碳粒子云。

极冠和海洋

除了凝结成云，大气成分也可能在行星表面凝结成冰或液体。地球是目前唯一拥有海洋的类地行星，而海洋当然是由水构成的。在行星的两极附近，水会被冻结形成极冠。年轻的金星可能曾经历过海洋覆盖星球的短暂纪元，在这之后，蒸发的水蒸气加剧了迅速增长的温室效应，导致了目前的干旱。这些水蒸气蒸发后会因为光解作用而消失。

但火星是不同的。有种说法是大约38亿年前，一个巨大的“北欧大洋”(Oceanus Borealis)占据了火星上整个地势较低的北方平原，这在20世纪90年代风靡一时。目前虽存在争议，但许多人接受火星上可能有湖泊的观点。这些湖泊的面积如果足够大，比如在河道流动时期(图13)，就被称为“海洋”，一些冰冻的遗迹甚至能保存下来，只是被灰尘覆盖(图10)。但毫无疑问的是，火星如今的极冠表面有冰存在(图16)。这些冰包括“永久”的水冰和随季节生长和收缩的二氧化碳冰霜。

图16　在早春（左）和盛夏（右）时，1500 千米宽的火星北极冠照片。在夏天，大部分二氧化碳冰霜已经升华（从冰变成蒸汽），只留下残留的“永久”水冰冠

地球和火星的极冠会与大气相互作用。实际上，它们的极冠是大气中“冻结”的气体沉积物，要么以雪的形式从云层中落下，要么直接凝结在地面上。当温度升高时，极地冰冠中的物质会以先融化然后蒸发(地球上的水或过去火星上的水)，或直接从冰升华为蒸汽(如今火星上的二氧化碳和水)返回大气中。

这样的循环不可能发生在像月球和水星这样没有大气的天体上，所以我们也不会指望在月球和水星上出现极地冰冠。但是在20世纪90年代，人们注意到从这两个天体两极附近的陨石坑内部的永久阴影区域反射出来的雷达信号强度不同寻常，与将水冰作为颗粒分散在风化层中反射的雷达信号一致。对此，一种可能的解释是：这些陨石坑的底部很寒冷，以至于任何游离的水分子都倾向于附着在它表面。

极冠的水不一定是这些天体自带的，它可能来自后来的彗星撞击。如果要在月球上建立一个人类殖民地，甚至只是一个永久使用的基地，能否在月球上找到水源至关重要。显然极地是寻找水源的最好选择。2009年，一艘宇宙飞船撞进了一直被阴影笼罩的一个极地陨石坑，抛射出的羽状物证实了月球上有水存在。其他航天器获得的红外光谱也显示出，水和水合矿物分散在月球上很多地区的风化层中，虽然浓度很小，但这让人们发现月球可能没有那么完全不适合居住。

循环

行星内部、表面和大气之间的相互作用，以及它们之间成分的循环是极其重要的。地球的“水文循环”是最常见的例子，它不是一个单一的循环，而是一系列相互连接的循环组合。从本质上说，海洋中的水蒸发形成云，然后凝结成雨或雪的形式，最终通过河流或季节性出现的极冠回到海洋中。水可以被吸入地球内部，通过地面的渗透进入俯冲带深处或浅一些的地方，并通过火山重新出现。水还可以与岩石发生化学反应(风化)，并储存在矿物中。地球还有一个重要的“碳循环”，大气中的二氧化碳、活的动植物、溶解的二氧化碳、海洋石灰岩、碳氢化合物沉积物、火山气体等参与，它们之间形成了循环。

火星上肯定也会有类似的循环，尽管这些循环表现得更为零星，发生在不同的时间尺度上，且每个循环的相对重要性也不同。金星上可能还有更慢的二氧化碳和二氧化硫的循环。在这个循环中，大气会风化金星表面的岩石，这些岩石最终会被熔岩流埋到深处，在那里，气体再次被释放出来，并通过火山口逃回大气。在我们探索并记录下这些多循环和相互关联周期的复杂性与时间尺度之前，我们对每颗行星“运行机理”的理解仍然是不成熟的。

[1]
本书成书于2010年。

[2]
指风力作用形成、搬运、堆积的沙粒及沙丘。

03 巨行星 Giant Planets

巨行星是主宰太阳系的天体——假如你愿意忽略太阳，并且认为天体的大小很重要。图3的第二行展示了太阳系的四颗巨行星的尺寸。当我们将这四颗巨行星与等比例缩放的类地行星进行比较时，很明显，巨行星的尺寸遥遥领先。在图3中，天王星的图像是由环绕在地球轨道上的哈勃太空望远镜拍摄的，其他三颗巨行星的图像则是由到访这些行星的宇宙飞船拍摄的。巨行星的密度比类地行星要小，因此质量对它们的影响并没有那么重要。木星的密度只有地球的24%，土星的密度则更小，小到假如它落到一个足够大的水桶中，甚至能漂浮起来。这些巨行星在其赤道面上都有行星环，但只有土星和天王星的行星环足够明显，能在图3中看到。这些行星环看起来坚固，其实是由无数极其微小的轨道粒子组成的。在下一章中，我们将讨论这些行星环，以及巨行星的卫星。

按照惯例，一颗巨行星的大小，要从它的云层顶部开始测量。这种云层存在于对流层中。对流层上方是基本透明的、密度逐渐降低的大气层，此大气层的分类方法与地球相同。但定义或探测巨行星的对流层底部是很难的，即使对离地球最近的巨行星——木星——也是如此。1995年，伽利略号
释放的再入探测器探测了木星的云层。在高压(22个大气压)和高温(153℃)摧毁它之前，探测器只到达了木星云层下方160千米处。或许，在温度和压力如此高的情况下，每个巨行星的气态对流层与液态区域之间没有明显的界线，属于逐渐过渡。可以确定的是，这些巨行星没有足以让人站立的坚实表面。巨行星的基本数据展示在表5中。由于巨行星在快速地旋转(见表2)，它们的形状会变平，因此这里的极直径比赤道直径要小。木星的极直径比赤道直径小6.5%，土星的极直径比赤道直径小10%，而对于气体含量较低、自转速度较慢的天王星和海王星来说，这一差异仅在2%左右(对于类地行星来说，这一差异不到1%)。

内部结构

我们没有办法直接研究巨行星的内部，但我们可以利用巨行星的大气成分(99%的氢和氦)和我们对太阳系构成成分的常识，构造一个与测量密度一致的模型，由此推算出的内部压力也会一致。在大气层之下，每颗巨行星都必须有一个主要由氢分子(H2)和氦原子(He)组成的区域，我们最好称其为“流体”而不是“液体”或“气体”。在巨行星的中心，可能都有一个岩石内核——木星和土星内部有一个大概是3倍地球质量的岩石内核，而天王星和海王星内部则有一个大概与地球质量相等的岩石内核；在内核周围，应该有一个由未知比例的水、氨和甲烷组成的“冰”的外核——木星的外核质量大约是地球质量的2倍，土星的外核质量大约是地球质量的6倍，天王星大约是12倍，海王星大约是15倍。即使我们可以估算巨行星中心的压强(木星中心的压强达到了惊人的5000万个大气压)，但我们并不知道巨行星内部的成分，并且对其内部的温度也只有一个模糊的概念(木星中心的温度超过15 000℃，海王星核的外边缘处温度大约是2200℃)。因此，我们无法知道这些外核和内核是处于熔融态还是固态。对于在这种极端条件下的物质会如何表现，我们并不完全理解。比如金属铁是否能从岩石中区分出来，向中心下沉，形成内核中的内核。甚至天王星和海王星的内核是不是冰和岩石的混合物。

表5　巨行星的基本数据

*请注意，表中的质量单位是表3中类地行星的1000倍

在天王星和海王星的核周围有个氢和氦组成的壳，仅相当于1个地球质量，却有大约6000千米厚；而“气态巨行星”木星和土星的核周围有更厚的氢和氦包层，分别超过300个和80个地球质量。相比冰或岩石，氢模型更容易建立。科学家们非常自信地宣称，超过200万个大气压的压强下，氢原子会被挤压得十分紧密，电子将不再被限制在特定的原子中。在这时，氢原子会变成一片类似熔化的金属海洋，电子就在其中漫游，这种电子的自由运动使“金属氢”成为一种优良的导电体。木星核周围的金属氢壳层(其中含有一些氦)可能有260个地球质量(占木星总质量的80%)，而土星核周围的金属氢壳层可能只有41个地球质量(占土星总质量的40%多一点)。图17显示了木星的完整内部结构。

巨行星的内部结构有可能依然在演化，这是因为除了天王星之外，它们向太空辐射的热量都超过了从太阳接收到的热量。木星是如此大，以至于可能仍在释放自它形成以来就困住的大量原始热量，但土星和海王星不一样，这种过剩的热量表明有热量正在被生成。这些热量差大到不可能是辐射热，因此这些巨行星的内部分化可能仍在进行：密度更大的物质向内部沉降(使内壳层生长，周围的壳层变得更薄但更纯净)，其重力势能转化为热能。这种热量可能来自核(或内核)的持续增长。以土星为例，这还可能来自它的金属氢壳层中的氦滴向内沉降。

图17　截面图显示了木星内部的假想内层。主要标记了对流层云顶区(亮)和带(暗)

大气

成分

我们研究巨行星内部主要是通过合理的猜测，但对其大气的研究可以更多地依赖观察和测量。巨行星的云和其覆盖层的成分可以用光谱学来研究。光谱学研究的是不同波长的阳光在大气不同深度的吸收情况，而巨行星大气中每一深度处的平均分子质量，可由从巨行星后方的航天器发射的无线电信号的折射量来确定。另外，伽利略号
探测器在进入木星下降过程中对木星大气层也进行了多种测量。表6比较了这四颗巨行星大气层的化学成分。除了列出的化学成分，每个巨行星的大气都含有少量的乙炔(C_2
H_2
)；木星的大气含有乙烯(C_2
H_4
)，并且它和土星的大气都含有磷化氢(PH_3
)、一氧化碳(CO)和锗烷(GeH_4
)。

天王星和海王星大气最上层的连续云由甲烷冰粒子组成。由于木星和土星的大气温度过高，甲烷无法凝结，取而代之的是氨冰颗粒凝结成了最上层的云。这些顶部云层的厚度大约为10千米，在它们的下方，“空气”可能会再次变得纯净。计算表明，在木星最上端云层下方大约30千米处，应该有由硫化氢铵(NH_4
HS)组成的第二层云；在第二层云下方大约20千米处，应该有由水(顶部是冰，下面是液滴)组成的第三层云。伽利略号
探测器在合适的深度发现了可能的硫化氢铵云，但没有发现任何水冰云。有人说这是因为模型本身有误，也有人说，这是因为水冰云是不连续的，探测器刚好从水冰云的缝隙中穿了过去，因此没观测到水冰云。同样的分层也可能出现在土星上，但由于土星的重力较小，云层之间的距离大约是木星云层的3倍。在天王星和海王星的甲烷云之下，也可能有含氨云。

表6　巨行星大气中检测到的气体

*显示了每种气体在不同巨行星大气中所占的比例

木星氨云顶部的大气压力是地球海平面大气压力的2~3倍。在其他巨行星上，云层顶部的压力接近地球海平面的大气压力。

大气环流

即使只是通过小型望远镜，我们也能在木星上看到平行于赤道的全球云带。在其他巨行星上，这一特征不那么明显。来自太阳的热量一定在这种大气环流中扮演着某种角色，影响了气态巨行星大气的可见部分。但木星的大气环流似乎主要是由内部热驱动的，并且是由木星的快速旋转控制的。

传统上，暗带被称为“带(belt)”，中间的亮带则被称为“区(zone)”。图17显示了木星上主要带和区的名称。由于我们没有固体表面作为参照系，所以在测量巨行星上的风速时，要参照巨行星自身的平均自转速度。在木星上，云层顶部的风以每秒130米的速度向东吹过大部分赤道带。北赤道带和南赤道带与赤道区的相邻边缘都有这种运动，但风速随着与赤道之间距离的增大而减小，并最终发生逆转，直到到达热带地区，风向在热带地区再次发生逆转。以此类推，每条带和区之间的风向反复逆转，直到极地地区。

在木星的很多区，大气主要是上升的，这会导致氨云在高处凝结，使那里显得很明亮。相反，在木星的带，大部分大气在下沉，这会把云顶拉得更低，使它们看起来更暗。但在木星上已经发现了这种模式的局部例外，并且上升的区和下沉的带的一般规律在其他巨行星上几乎不存在，因为其他巨行星上的大气环流更难理解。影响区和带能见度的一个复杂因素是，人们对会给云层添加颜色的微量化合物的性质和丰富程度知之甚少。这些微量化合物被预测是光化学反应的结果。木星大气的各种黄色和红色可能是由硫(S，从硫化氢或氨硫化氢中光化学释放)、磷(P，从亚磷酸中释放)或肼(N_2
H_4
，从氨中光化学释放)造成的。

土星大气颜色的变化不那么明显，区和带的模式也不那么明显。但是，土星大气的风速更高，向东吹的风的速度超过每秒400米，在赤道两侧10纬度的区域内非常盛行。

木星和土星上的旋转风暴系统是众所周知的，最著名的例子是木星大红斑。可以从图3中看到它——一个椭圆形地貌，横跨南赤道带和南热带区的边界，从东到西绵延26 000千米，呈螺旋状结构，逆时针旋转的周期大约为6天。至少从1830年起，从望远镜的观测中就可以清楚地看到木星的大红斑。在木星(在图17中沿着南温带观测)和土星上都可以看到不同尺度的小风暴。大约每隔30年，在夏季的北半球，土星大气图案就会被一个巨大的土星风暴系统毁损一次。该风暴系统会从赤道附近的一个白点开始，在1个月内扩散至环绕整个土星，然后逐渐从视野中消失。

木星和土星呈淡黄色，天王星和海王星呈蓝绿色，这是因为我们是通过一定深度的甲烷气体覆盖层来看它们的云顶的。甲烷气体会优先吸收较长波长的光，即红色的光。

天王星82.1°的轴倾角导致了极端的天王星季节变化。例如当旅行者2号
——唯一造访天王星的宇宙飞船——在1986年飞过天王星时，天王星的南极阳光充足，而北半球的大部分地区正经历着长达数十年的黑暗。在旅行者号
拍摄的图像上，天王星的南半球看起来平淡无奇，令人失望，但随着天王星年的推移，太阳开始在更宽的纬度范围内升起和落下，天王星也开始越来越像其他巨行星(图18)。2007年，天王星经过它的春分点，其南极以及南半球的其他部分随后开始逐渐进入漫长的黑暗，并且南半球的仲冬将在2028年达到顶峰。

1989年，旅行者2号
飞越海王星，揭示其中的详情。那时的海王星看起来就像蓝色版本的木星，在赤道以南有一个巨型风暴系统，以黑斑的形式存在。这个风暴系统被命名为“大暗斑”，以致敬其在木星上的著名“表亲”。然而，“大暗斑”的寿命较短，到1994年就消失了。与木星和土星不同的是，海王星上的赤道风是向西吹的(与行星的自转方向相反)，在图18中可以看出这一点，大黑点相对较小的、更偏南的黑点在西移。

图18　上图：1998 年8 月（左）和2006年7月（右），哈勃太空望远镜观测到的天王星。参照大气环带图案来看，天王星的自转轴相对于太阳的方向变化是明显的。1998 年，南极周围的地区仍然处于阳光之下，但到2006 年，行星轴几乎与太阳平行。在1998 年拍摄的照片中，天王星的北极附近可以看到明亮的高云，同时也可以看到光环和一些内侧卫星。但到了2006 年，光环是侧面对着镜头，看不见了。取而代之的是，可以看到一颗规则卫星天卫一（Ariel）和它的影子

下图：旅行者2 号在1989 年接近海王星时所拍摄的两张海王星图片。这两张照片几乎完全记录了一个行星的自转。大暗斑和伴生的高亮度十分突出。请注意海王星的带状结构，和一个更南的小暗点

磁层

每颗巨行星都有很强的磁场。“磁偶极矩
[1]

”常用于测量行星磁场。海王星的“磁偶极矩”是地球磁场的25倍，天王星的“磁偶极矩”是地球的38倍，土星的“磁偶极矩”是地球的582倍，木星的“磁偶极矩”是地球的1949倍。为了产生这些磁场，每颗行星必须包含一个在进行某种对流运动的导电流体区域。在有磁场的两颗类地行星(水星和地球)中，对导电流体区域的解释是它们的铁核形成了一个流体外壳。木星和土星的磁场可能是在金属氢层中产生的，由行星相对快速的自旋所激发。但天王星和海王星的金属氢压力太低了，所以它们的磁场成因很难解释，可能是由它们外核的导电“冰”的内部运动造成的。

行星磁场(同样适用于水星和地球)的一个重要影响是，它会将行星包裹在一个太阳磁场线无法穿透的区域内，这个区域被称为行星的“磁层”。太阳风中的带电粒子(主要是质子和电子)的路径是受太阳磁场控制的，除非它们撞击到行星磁层的“弓形激波”，“弓形激波”会使带电粒子偏离行星。

带电粒子有时也能通过行星的磁层，尤其是会通过行星背向太阳的长长的磁尾泄漏回来。在两极附近，带电粒子可以沿着磁场线被引导到大气层的顶部。在那里，带电粒子的到来会在天空中发出被称为极光的光芒。极光在地球上广为人知，在木星和土星上也能被观测到。

[1]
人们最早认为磁体是由无数小的磁偶极子组成。后来认识到物质的磁性乃是由分子电流定向排列而产生，于是重新设定了计算方法，但仍保留了等效的“磁偶极矩”的概念。

04 巨行星的卫星和光环 Giant Planets' Satellites and Rings

具有光环和一大群卫星，是四颗巨行星的共同特征。虽然这两点在重要程度和规模上存在差异，但每个环-卫星系统之间的相似之处比差异多。

环-卫星系统

巨行星的大多数外侧卫星都在偏心轨道上运行，通常与行星的自转方向相反。此外，许多外侧卫星的轨道相对它们的行星的赤道的倾角大于30°。这些天体因为引力太小，无法把自己拉成球形，再加上典型的轨道偏心、逆行和倾斜性质，于是被统称为“不规则卫星”。这些不规则卫星最大的有100千米宽，普通的只有几千米宽，是数量最多的一类卫星。据最新统计，木星有55颗不规则卫星，轨道半长轴从105到400个木星半径不等；土星有38颗不规则卫星，轨道半长轴从184到417个土星半径不等；天王星有9颗不规则卫星，轨道半长轴从167到818个天王星半径不等；海王星有6颗不规则卫星，轨道半长轴从223到1954个海王星半径不等。

而“规则卫星”是指那些在近圆形顺行轨道上的大型卫星。“规则卫星”离它们的行星要近得多，轨道相对其行星的赤道倾角很小。木星有4个“规则卫星”(伽利略发现的那些)，它们的轨道半长轴从5.9到26.3个木星半径不等。尽管规则卫星不符合国际天文学联合会对行星的定义，但它们都是实实在在的，在地质学上与类地行星有许多共同之处。土星有8颗规则卫星，除了一颗，其余的都比木星的规则卫星小得多。土星的8颗规则卫星的轨道半长轴分别从3到59个土星半径不等。天王星有5颗规则卫星，轨道半长轴分别从5到23个天王星半径不等。海王星有一颗大卫星——海卫一(Triton)，在半长轴为14个海王星半径的轨道上运行。尽管海卫一的轨道是逆行的，但它被认为是“规则的”。所有规则卫星(包括海卫一)都具有一个重要特征：潮汐力
[1]

对它们的控制很强，以至于它们处于同步旋转的状态，每公转一圈就自转一次，因此，就像地球的月球一样，规则卫星总是用同一面对着自己的行星。

我们在更近一些的地方发现了不规则形状的碎片块，于是很方便地将其分为“内侧超小卫星”。它们有圆形的、顺行的赤道轨道，组成行星环的微粒也是如此。考虑到一些内侧超小卫星的轨道位于环内，一个大的光环粒子和一个小的内侧超小卫星之间可能没有根本的区别。木星只有4颗已知的内侧超小卫星，但土星有14颗，其中7颗的轨道位于土星最内侧的规则卫星轨道之中。天王星有13颗内侧超小卫星，海王星有6颗。

行星环的宽度和数量因行星而异，土星环是迄今为止最壮观的行星环，但总的来说土星环的厚度不超过几十千米。大多数情况下，行星环与行星的距离比“洛希极限”(Roche limit)还要近。“洛希极限”是一个边界，在它的内侧的任何大型天体都会被潮汐力撕裂。我们认为大多数行星环是卫星或彗星离行星太近时被潮汐破坏遗留下来的碎片。但一些不那么坚固的环显然是由附近卫星活动排入太空的粒子或某些撞击产生的粒子形成。

土星环是由冰构成的，会反射80%的阳光。尽管土星环的外表很突出(图3)，但如果把它们集中在一起，环中的物质只能形成一个直径约100千米的物体。虽然还没有拍摄到单个光环粒子，但当行星的阴影落在土星环上时，土星环冷却的速度表明它主要由直径在1厘米到5米之间的微粒构成。相比之下，木星环的粒子要小得多，主要是微米大小，并且这些粒子的反射能力也比土星环中明亮的冰团要弱得多。天王星和海王星的环状物质反射太阳光的能力很差，和木星一样；但天王星和海王星的大部分光环粒子的直径都在厘米到米之间 ，和土星一样。

图19　卡西尼号于2009 年7 月27 日拍摄的5000 千米宽的部分土星环照片。在这个尺度下，土星环的曲率（在右边的视野之外）几乎不显现。在粒子密度最大的地方，光环反射的阳光最多，黑色的部分显示出无粒子的缝隙。土卫十八（Pan）是一颗直径为28 千米的牧羊犬卫星，图中可以看到它在土星环最宽的缝隙中运行。土卫十八除了会将这个环间隙清扫干净，还会影响间隙内其他狭窄且不连续的卫星环。这张照片是在太阳非常靠近土星环所在平面的时候拍摄的，土卫十八的影子在土星环上特别长

轨道共振导致环与环内小卫星之间存在复杂的引力相互作用(图19)。这些环内小卫星通常被称为“牧羊犬卫星”，因为其中一些环内小卫星会将环间隙清扫干净，另一些环内小卫星形成时会产生一些窄小的环，且这些环的轨道刚好在它们的内侧或外部。一般来说，环与它们的行星的距离要小于环与规则卫星的距离。但土星是个例外，因为它有一个由暗的尘埃物质组成的外环。这个弥散的外环围绕着土卫九的轨道。土卫九是土星最内侧的不规则卫星。

值得注意的卫星

曾经有一段时间，几乎所有人都认为，即使那个外行星最大的卫星，也只是枯燥的天体。它们只是古老的冰球，被撞击弄得坑坑洼洼，记录着外太阳系的轰击历史。如果你不想研究共同轨道演化，外行星卫星就没有什么意义了。这种观点一直持续到了1979年3月，直到加州大学的斯坦顿·皮尔与两位同事发表的一篇论文指出，木星最内层的伽利略卫星，木卫一(Io)和木卫二(Europa)之间精确的2∶1轨道共振会导致木卫一的形状发生潮汐变形，因此，木卫一内部应该是熔融的。通过对木卫一和木卫二的密度估计和表面光谱分析，我们已经知道木卫一有岩石外壳，不像其他卫星外壳主要是冰。因为岩石体内部的熔化温度要高得多，所以提出岩石体有一个熔融内部是特别大胆的猜想。还好旅行者1号在论文发表的几天后飞过木卫一，传送回喷发的火山图片，里面显示木卫一火山顶部是300千米高的喷射羽状物，不然很少有人会相信这种说法。

虽然木卫一的潮汐加热是迄今发现的卫星中最强的，但这样的过程也影响着各种其他卫星，它们中的许多都有古代潮汐加热的痕迹。潮汐加热使这些卫星千差万别，这也引起了地质学家的兴趣。大多数有潮汐加热的卫星只有核是岩石，地质学家对此并不介意。这些卫星被一层厚厚的冰覆盖，表面一层可能在化学组成上截然不同。外太阳系天体普遍表面温度低(木星卫星的表面温度为-140℃，海王星卫星的表面温度为-235℃)，在这里，冰的力学性质和融化行为与内太阳系的岩石非常相似。换句话说，这些天体具有和类地行星类似的行为和结构，只是其核心是岩石而不是铁，壳和幔是冰而不是岩石。

但木卫一是一个例外。它没有冰，却有岩石构成的外壳和被幔包围着的铁核，如果它是围绕太阳而不是木星运行的，将被归类为类地行星。木卫二是一种混合结构，类似于把木卫一深埋在100~150千米冰层下。接下来，我将描述这两颗卫星以及其他一些最吸引我的卫星，把重点放在更典型的例子上。尽管这些卫星是坑坑洼洼的冰球，它们也比我们之前想象的沉闷球体更有趣。

木卫一

木卫一的直径只有3642千米，略大于我们的月球，密度也更大，但两者却截然不同。木星的引力会使偶发的抛射体向内聚焦，这意味着木卫一比木星其他同样布满陨石坑的卫星——木卫三和木卫四——更容易受到撞击。但木卫一的地形被火山过程重新改造过，且改造速度很快，以至于木卫一表面没有留下陨石坑。木卫三和木卫四的轨道在木卫二之外。1979年，在研究旅行者1号拍摄的木卫一的第一张彩色特写照片时，它的黄色色调让许多人猜测——木卫一表面清晰可见的叶状熔岩流是由硫构成的。然而人们现在普遍认为木卫一的火山是由熔融硅酸盐物质构成的，也就是真正的“岩石”。在木卫一表面，尽管火山活动区域以外的地方非常寒冷，但喷发的火山口中心温度远远超过了1000℃。图20所示的喷发气体里主要有二氧化硫，而在地球上火山的喷发气体主要是水蒸气。硫和二氧化硫在木卫一表面凝结成“霜”，赋予了木卫一颜色。

木卫一位于木星磁场俘获的带电粒子带内。带电粒子带内的辐射很强烈，以至于NASA的伽利略
号探测器无法让航天器对木卫一进行多次近距离飞行，因此，木卫一只有一小部分表面的成像质量足够好，可以显示出几百米以下的细节。木卫一最清晰的图像像素只有10米宽，即使如此，我们也没有从其中发现陨石坑。

如果木卫一的火山活动速度长期以来都没变，那么木卫一的整个壳和幔一定已经循环了许多次。熔岩流和从喷发羽流掉落的物质覆盖着较老的地表，这相当于以平均每年几厘米的速度掩埋着木卫一全球的地表。木卫一表面火山活动很快掩盖了陨石坑，让它们无迹可寻。同时因为木卫一的引力太弱，无法抓住水蒸气或其他轻气体，所以即使木卫一曾经有过冰层，火山活动也早就已经将它蒸发，使其消失在太空中。对火山学家来说，木卫一是一个多么美妙的地方啊!要是严酷的辐射环境没有彻底地阻碍人类对木卫一表面的探索就好了。

图20　上图：2007 年3 月，飞向冥王星的新视野号
（NewHorizons）在飞越木星时，拍摄到的木卫一的新月形图像。在一个叫作特瓦史塔（Tvashtar） 火山喷口的地方，夜间的火山喷射羽流高达300 千米，所以它的上部是在阳光下的。在其源头可以看到白炽的光，羽流下方的阴影里的部分被来自木星的反射光微弱地照亮

下图：这张250 千米宽的特瓦史塔全景图是八年前伽
利略号
探测器拍摄的。阳光是从左边来的。最暗的物质是近期的熔岩流，左上方东西方向的明亮条纹是从火山裂缝中喷发出来的炽热熔岩

木卫二

木卫二的直径为3130千米，它是我的最爱。旅行者号在1980年和1981年探测飞行时拍摄的照片显示，木卫二的表面看起来像一个裂开的蛋壳，几乎看不到陨石坑。很明显，这是因为潮汐加热以某种方式重塑了木卫二冰冷的外层，虽然速度没有木卫一那么快。伽利略号
的高分辨率成像任务揭示了木卫二复杂的地表历史，并引发了一场异常激烈的争论。众所周知，木卫二的表面主要是水冰，其总体密度表明这层冰壳有100~150千米厚，覆盖着密度更大的内部岩石。但是，密度参数并不能区分固态冰和液态水。由于温度较低，木卫二表面的冰坚硬而易碎。关于木卫二，争议的焦点是地表下“冰”的状态：它是一路冻结到与岩石接触的区域，还是底部是液体，而顶部是漂浮的冰壳？

关于争议中的这两个观点，后者需要更快的内部潮汐加热速度，以及加入冰下是液态水的全球海洋这一奇特概念。我个人认为，图21这类图像中得到的表面特征很清楚，这样的冰通常很薄，只有几千米厚，所以一定是漂浮在水面上的。然而，在伽利略号
环绕木星系统运行的数年时间里，成像团队中一个强大的游说团体坚持不懈地试图用由厚冰层中固态对流驱动的过程来解释木卫二的表面特征。

现在被普遍接受的木卫二的地质结构可以用图21来解释。这张图片显示了许多由100米高的悬崖围成的高大的“冰筏”。冰筏的表面特征是一系列的山脊和沟槽，且朝不同的方向运动。冰筏之间的纹理比较杂乱，图像模糊。在这个区域之外，木卫二有大片没有被分解成冰筏的区域，那里的表面图像是不间断的山脊和沟槽，图21中的冰筏显然是这种支离破碎的碎片。裂隙的开闭导致了山脊和沟槽图像的出现，并且裂隙开闭的潮汐周期可能与木卫二3.6天这一公转周期一致。在整个木卫二上，任何时候都只有少数裂隙是活跃的。当一个活跃的裂隙被打开时，它的宽度可能只有1米，水会从下面被抽上来，暂时暴露在顶部。这些处在寒冷真空中的水会在瞬间沸腾并冻结，接着很快被泥浆覆盖。当裂隙闭合时，一些泥浆被挤压到表面，在闭合的裂隙上方形成一个山脊。下次裂隙打开时，山脊开裂，再次闭合时，又有更多的泥浆加入其中。裂隙几年的开合就足够在中心沟槽周围形成我们看到的这种大小的山脊。最终，每条裂隙都会永久封死，但新的裂隙又会在其他地方开始作用，于是图像就形成了，这使得覆盖木卫二大部分地区的山脊和沟槽地形呈现出一种类似于毛线团的外观。

图21　木卫二康纳马拉混沌区（Conamara Chaos region）的特写镜头，画面有42 千米宽。来自下层海洋的“融解”使得冰筏在该地区重新结冰之前能够漂移开来。阳光来自右边

图21中的“线团”地形会被另一个影响木卫二的剧烈过程破坏。这个过程叫作“融解”，它会导致破碎的冰筏混杂在一起，形成“混沌”。可能是由于海底的硅酸盐火山爆发，在未来的混沌区域之下海洋会变得异常温暖，表面冰壳的底部会逐渐融化，冰就变得更薄了。最终，冰层表面融化，浮冰筏(或浮冰)从冰架裸露的边缘断裂，漂流到裸露的海洋中。任何暴露在水面上的水都会很快重新结冰，也许我们最好将它想象成这样：几千米厚的冰筏缓缓驶入被冰雪覆盖的海洋，就像地球夏季北冰洋融化的浮冰那样，而不是进入了真正开放的水域。在图21的西北部分，你可以看到许多原本合在一起的冰筏，因为它们没有漂流很远，并且它们的“线团”纹理可以匹配。

短暂的热量过剩消失后，海洋会重新结冰，冰筏停止漂流，重新冻结的海面和筏下的冰又开始变厚了。当再次冻结的区域足够厚、足够脆时，可能会出现新的裂隙，新一代的“线团”纹理会开始覆盖整个区域。图21中有一条穿过对角线的“年轻”的裂隙，它两边各有一条狭窄的山脊。裂隙穿过冰筏的地方看起来并不引人注目，但你可以看出它一定很年轻，因为它穿过了冰筏之间重新结冰的海洋。

如果这个描述哪怕对一点点，那么它就蕴含着一些非常值得思索的东西。虽然木卫二上最丰富的溶解盐可能是硫酸镁，而不是地球海洋中的氯化钠，但是海水与海底岩石的化学反应也会使海洋含盐。任何这样覆盖着有潮汐加热岩石的海洋都为生命提供了一个栖息地，就像人们认为地球上生命开始的地方。缺乏阳光并不是生命诞生的障碍，因为处于食物链底部的“初级生产者”将从海底温泉(热液喷口)供应给海洋的化学物质中获得能量。这种生命是依赖化学合成的生命，而不是光合作用的生命。在地球的海底，最热的喷口被称为“黑烟囱”，因为喷发口的液体混合到海水中时，会形成金属硫化物颗粒的烟羽。令人惊讶的是，这些喷发口是生命的绿洲，那里的生物群落包括一些像虾蟹这样的高级生物，以化学合成的微生物为食。这些微生物通过将二氧化碳转化为甲烷来获取能量。如果地球上的生命就是在这样的环境中开始的，那么木卫二上为什么不能产生生命呢？

可是要在几千米厚的冰层下找到生命是极具挑战性的，这需要木卫二着陆器在冰层上钻或融化出一个洞，然后发射一枚能探测到“黑烟囱”的水下探测器。但如果年轻裂隙两侧的山脊是由从海洋中挤出来的泥浆形成的，那么这样雄心勃勃的任务可能就没有必要了。因为当裂隙打开时，它可以为植物或(更合理的)海洋藻类等光合生物提供一个生态位。就像地球上的生命一样，木卫二上的生命可能是由化学生物这一祖先进化而来的。辐射会使暴露在外的水柱顶部几厘米区域不适宜居住。但在以下几米的区域里，有足够的阳光可以让生命进行光合作用。如果有初级生产者依靠阳光生存，如植物、藻类，那么就可能有动物以它们为食。为了找到答案，我们第一步要做的就是研究从裂隙中挤出来的山脊样本。

美国国家航天局和欧洲航天局在太阳系外侧探索领域的下一个大型合作项目很可能是前往木星系统，主要目的是通过探冰雷达和对潮汐运动的幅度进行测量，来验证木卫二上是否存在海洋。木卫二的潮差在基岩的厚冰壳上大约只有1米，但对漂浮在海洋上的“薄”冰壳来说大约有30米。遗憾的是，此探测任务的着陆器还没能被设计出来，但至少会用高分辨率的轨道光谱仪来寻找山脊物质中的生物分子。

土卫二

如果木卫二的冰能够在不深入地表的情况下被取样，那么寻找木卫二的生物标志物就会容易得多。土星的一颗卫星，土卫二提供了这样一个寻找生物标志物的机会。土卫二的直径只有504千米，而且它的密度太低，容不下很多岩石。旅行者号
显示土卫二是一个奇怪的小世界，它的部分地区布满了陨石坑，但另外一些地方却没有。卡西尼号
于2004年开始对土星系统进行轨道勘测，其传送的高分辨率图像显示，土卫二有一个被许多有规律的裂隙切割的表面，但这个表面和木卫二的“线团”区域不像。卡西尼号还发现了土卫二南极附近的裂隙向太空喷射冰晶(图22)。幸运的是，卡西尼号
携带了一台用于研究离子和中性粒子的质谱仪，科学家们因此调整了飞船的轨道，使其能够穿过喷射的羽状物并获取了一些样本。样本中含有水、甲烷、氨、一氧化碳和二氧化碳，可能也有一些简单的有机分子。有机分子是一个化学术语，表示连接在一起的碳原子，但并不意味着生命起源。如果这些羽状物早些被发现，卡西尼号就可能会装上更适合检测生物标志物的仪器。

图22　卡西尼号拍摄的两张土卫二图像。左图：过曝的月牙形视图，显示了延伸到地表以上100 千米的羽状物。右图：土卫二的部分斜视图，由几个规律的裂隙切割而成，就像那些已知羽状物的起源地。这里有一些小型陨石坑（小到旅行者号拍不到），表明这一特定区域可能已经不再活跃

我们几乎可以肯定的是，土卫二和土卫四存在2∶1的轨道共振。这个轨道共振驱动了土卫二上的潮汐加热，从而推动裂隙的形成，并为羽流提供了动力。但是，没有人预料到土卫二会如此活跃。尤其令人困惑的是与土卫二大小相仿的邻居——土卫一是一个布满陨石坑的典型冰球，没有任何活动历史。土卫二的表面下不太可能隐藏着一个全球性的海洋，但是在羽流起点处下面可能有液态水。液态水对生命是有好处的，但土卫二内部的营养物质供应有限，比不上木卫二这样的大型天体，因此它似乎也不是一个很有希望的生命栖息地。

土卫六

土卫六直径为5150千米，是土星唯一在规模上能与木星的伽利略卫星相匹敌的卫星。旅行者号
拍到的土卫六只是一个模糊的橘黄色球体，因为它是唯一有稠密大气层的卫星。土卫六的大气中97%是氮，但甲烷及其光化学衍生物使土卫六的大气浑浊，还将平流层变成了不透明的烟雾。土卫六有一个由冰(大部分是水冰)构成的外壳和幔，占其半径的三分之一，其下覆盖着一个岩石内核。土卫六可能有一个铁内核，但在这种情况下，为了平衡全球平均密度，冰幔必须更厚。土卫六的自转周期受季风的影响，这表明土卫六的岩石圈一定与其内部分离，很可能是被内部海洋分离的。土卫六的内部海洋可能是水或水氨混合物。和水相比，氨在低得多的温度下仍然是液体。大多数模型都将土卫六的内部海洋视作冰幔中的一层，没有直接把内部海洋置于内部岩石的顶部。

卡西尼号用三种办法探测了土卫六的表面，并解决了这个问题：(1)卡西尼号
从对烟雾透明度最高的近红外光谱的一些窄波段当中，获得了模糊但有用的地表图像；(2)卡西尼号
使用像麦哲伦金星轨道飞行器那样的成像雷达来观察土卫六的地面，这不受云层的影响；(3)卡西尼号
搭载着一艘名为惠更斯(Huygens)的登陆器，登陆器在降落到地面的过程中拍摄了土卫六云层下的图像。惠更斯号
降落在土卫六赤道附近一片布满卵石的沙地上。这片沙地看起来像火星，不过这里的沙子和鹅卵石都是冰做的。沙子可能是被风吹来的，在土卫六的其他区域，雷达图像显示了大片的风吹沙丘。而鹅卵石一定是通过流动的液体运输的。考虑到土卫六的大气成分和表面温度，这些液体一定是甲烷(CH_4
)或乙烷(C_2
H_6
)。在下降过程中，惠更斯号
看到了靠近着陆点的水系通道分布，并且惠更斯号的雷达成像显示了许多其他地区的复杂山谷系统，从冰壳“基岩” 裸露的高地开始，流向沉积物堆积的低地盆地。更妙的是，惠更斯号在两极附近都发现了被乙醇污染的液态甲烷湖(图23)。一些湖床是干的，另一些湖床里有浅水或“沼泽”，它们很可能会随季节而变化。显然，土卫六在地质上很活跃。我们已经确认土卫六上有一些被严重侵蚀的陨石坑，并且有一些被怀疑是“冰火山”的地点，在那里喷发出类似于地球熔岩流的冰冷的“岩浆”。

图23　范围1100千米的卡西尼号雷达拼接图，展示了土卫六北极附近的图像。黑暗区域是湖泊，最大的一个面积超过10 万平方千米，比北美的苏必利尔湖大20%。我们可以看到树枝状的水系通道为湖泊提供了水源。图片上添加了经度线。空白区域未成像

尚不清楚冰火山和构造作用在多大程度上雕刻和重塑了土卫六表面。但很明显，在基岩被侵蚀之后(土卫六上的当然是被冰侵蚀的)，紧跟着的是泥沙的搬运和沉积，这是影响土卫六表面的主要因素。土卫六上的降雨一定是甲烷液滴，但就像地球上的降雨一样，这些甲烷液滴可以在地面上流动，形成泉水，流入溪流和河流。甲烷与结冰的“基岩”发生化学反应的情况、它的侵蚀能力、它蒸发回大气的速度，以及再次下雨前，它在大气停留的时间，这些都是不确定的。所有这些都是土卫六的甲烷循环与地球水文循环相似的因素。火星在很久以前也有降雨、河流和湖泊，但土卫六是太阳系内除地球外唯一现在还有降雨、河流和湖泊的地方。总有一天，我们会发射另一个探测器更彻底地探索土卫六，也许会包括一个飘浮在烟雾下的气球。它的浮力是可变的，这样它就可以在有趣的地方着陆，对湖水进行采样，并在完全陌生的海岸上获得海浪拍击海岸的照片。

天卫五和天卫一

我们还在争论土卫六上是否有冰火山活动，但在天王星的五颗常规卫星中的两颗存在古老的冰火山活动，这是不容置疑的。这两颗卫星是天卫五和天卫一，它们的表面温度为-200℃。古老的冰火山活动的影响可以从旅行者2号
传回的图片上看到。旅行者2号
已于1986年1月飞越天王星系统。

天卫一是两个卫星中较大的一个，直径1158千米，表面地质形态复杂。在它最古老的遍布陨石坑的地形上，存在大量断层，断层上岩块高耸。大多数断层都符合术语“裂谷”的定义，谷底地势平坦。然而，大部分峡谷并没有保存着断裂前的表面，而是被光滑的物质覆盖着，至少在旅行者号1
千米分辨率下看起来是光滑的。

可能在超过20亿年前的遥远过去，潮汐加热导致了天卫一的表面破裂，冰火山熔岩流出，覆盖了裂谷的地面。在天卫一表面的一些地方可以看到冰火山熔岩的延伸，它掩埋了一些较老的陨石坑。由于天王星与太阳的距离，我们认为天卫一上的冰是比在木星卫星上发现的略含盐的冰更复杂的混合物，其液体最可能是通过部分熔融产生的水和氨的2∶1混合物。这种液体在-100℃下仍是液态，比融化水冰所需的热量少得多。

在天王星最小的常规卫星——天卫五上也能看到独特的“熔岩”流。天卫五的直径不过472千米，对于这样小的天体来说，它的表面非常多样化，甚至可能超过土卫二。天卫五上重叠撞击坑的数量表明，“熔岩”流的最后一次活动的时间可能是在数十亿年前。旅行者2号
只看到了天卫五的半个球体，其成像区域的一半布满了陨石坑。不同寻常的是，大多数较老的陨石坑都有平滑的外观，就好像它们是被从天而降的东西覆盖着一样，只有较年轻的陨石坑是原始的。成像区域的另一半里面三个尖锐的地形单元，被称为冠状体。每一个冠状体都是不同的，但都包含复杂的脊状地形或规律地形，包括被确定为冰火山熔岩流的特征(可能是水氨熔岩，就像天卫一上的那样)，以及由原始的陨石坑形成的凹痕。这里的凹痕和那些布满坑洞地形上的一样。

一种关于天卫五的早期理论认为，每个冕都代表着一次灾难性全球分裂里的碎片，并且我们低估了再吸积作用。但更有可能冕是冰火山作用的场所，冰火山作用只有在衰退期才会留下可辨认的流状痕迹。覆盖在冕之外较老的陨石坑表明可能有爆炸性喷发，冰火山向太空喷射冰粒，其中一些像雪一样沉降下来，改变了原有地形的特征。但我们不知道这是什么时候发生的，为什么会发生。在本世纪中叶之前，不太可能有另一个飞行器到天王星进行探测，因此，我们也不太可能得到这个问题的答案。

海卫一

海卫一是海王星最大的卫星，直径为2706千米。它的外壳布满冰，但密度又很大，证明内部有一个坚实的岩石核心。旅行者2号
在1989年飞过海卫一时，发现了海卫一冻结的氮冰极冠。以前在地球上用光谱法也探测到过这个氮冰极冠。就像火星极地冰冠中的二氧化碳一样，这些冰冠在夏天可能会因为升华(而不是融化)而收缩，从而将其中的氮添加到海卫一稀薄但还算可观的大气中。海卫一的大气主要由氮构成。形成其地壳稳定的“基岩”冰似乎是甲烷、二氧化碳和水的混合物，也有可能有氨，但氨在光谱探测中几乎是不可见的。

海卫一的最佳图像分辨率约为每像素400米，它们揭示了极地冰冠之外复杂的地质表面，包括了可能是由冰火山形成的各种地貌(图24)。在海卫一的表面，陨石坑随处可见，但数量并不多，而且很有可能大部分表面陨石坑的历史都不到10亿年。海卫一另一个引人注目之处是，它拥有从极地冰冠喷发出来的间歇泉，能够喷出高约8千米的黑色粒子。海卫一有些由氮晶体组成的高空云，类似于我们大气层中的卷云。

旅行者2号
只能看到海卫一南极的冰冠，因为在旅行者2号
飞过海卫一时，其北半球的大部分地区处于黑暗之中。海卫一上的季节很奇特，这是海王星29.6°的自转轴倾角加上海卫一21°的轨道倾角共同作用的结果。此外，海卫一的轨道平面围绕海王星的轴进动，因此，海卫一的一个完整季节周期并不等于海王星164年的轨道周期。海卫一的一个完整季节周期为688年，其中包含164年的子周期。在整个季节周期中，海卫一上的太阳可以垂直照射的纬度范围在北纬50°到南纬50°之间。旅行者2号
飞越海卫一时，海卫一正巧接近南极的夏至，太阳垂直照射南纬50°。因此海卫一北半球大部分地区正处于黑暗之中，无法被观测到。旅行者号观测到，在阳光照射下，海卫一的南极冰冠正在消退。1997年从地球上的观测证实了海卫一南极冰冠会升华为气体的事实，表明自旅行者号与海卫一相遇以来，海卫一的大气压力在八年内增加了一倍。与此同时，看不见的北极冰盖可能正在生长，因为大气中的氮凝结在北极寒冷的表面上。

图24　旅行者号
拍摄的拼接图像覆盖了海卫一上2000千的区域。上方是南，阳光从右上方照射过来。南极冰冠参差不齐的边缘斜穿过图像的顶部。长而窄的弯曲脊(沟)可能是冰火山的冰岩浆喷发的裂隙。左下角平坦的平原和盆地可能是广阔的冰火山熔岩。中间和右下角的涟漪区域被称为“哈密瓜地形”，视觉上类似于甜瓜的表皮，但成因尚不清楚

[1]
潮汐力会引起潮汐变形(见132页)，指当一个位于另一个天体的引力场时，这个天体会因为受到潮汐力而扭曲。

05 小行星 Asteroids

一本关于行星的书如果不讨论小行星，那它将是不完整的，因为小行星是内太阳系会撞击行星的最常见物体(小行星撞击比彗星撞击常见10倍)。此外，最大的小行星谷神星已被正式归类为矮行星。

形状、尺寸和成分

谷神星是美国宇航局黎明号
宇宙飞船的目标，它将在2015年环绕谷神星运行5个月
[1]

。在那之前，黎明号已经在灶神星度过了从2011年7月开始的一年。灶神星是第二大小行星。一些较小的小行星已被宇宙飞船访问过，并由宇宙飞船提供的图像(图25)证实了它们的形状是不规则的。

每50颗小行星中大约就有1颗可能拥有自己的卫星。幸运的是，当伽利略号
在1993年飞过第二颗小行星艾达(Ida)时，发现艾达就有。这是第一颗被证实有卫星的小行星。随后，通过先进的望远镜技术，如可以补偿地球大气闪烁的自适应光学望远镜，人们又发现了更多拥有卫星的小行星。小行星卫星的大小从相对较小到与主星相似都有。事实上，名为休神星(Antiope)的小行星似乎是由两颗相互环绕的天体组成。它们的大小难以分辨，都在110千米左右，但中心距离只有170千米。迄今已知两颗小行星各有两颗小卫星。一些小行星的卫星可能是碰撞出的碎片，另一些则可能是被捕获的物体，但这两种说法都有些勉强，因为很难解释为什么这些“卫星”绕小行星的轨道运行而不飞散。

图25　不同规模的小行星的图片。上部：艾达，一颗直径为54 千米的主带小行星，它的小卫星艾卫（Dactyl）在它的右边。左下：爱神星（Eros），一颗直径为33 千米的近地小行星。右下角：丝川（Itokawa），一颗直径为0.5 千米的越地小行星。艾达和爱神星上有许多可见的陨石坑，小得多的丝川上则布满了石块

测量出小行星的密度在1.2~3.0 g/cm^3
之间。石质陨石显然是小行星的碎片，但其密度约为3.5 g/cm^3
，石质铁陨石的密度更是接近5.0 g/cm^3
，由此可知，所有被测量的小行星都不可能是完整的固体，它们一定是多孔的碎石堆。一些测量过的小行星，如2005年日本探测器隼鸟号(Hayabusa)造访的丝川(图25)，以及其他由隼鸟号
雷达确定出形状的卫星，似乎是由两个主要的团块通过狭窄的腰部连接而成的“相接双星”(contact binaries)。然而丝川表面众多的巨石表明，这两个主要的团块本身也由许多分块组成。

小行星的颜色并不鲜艳，但还是可以根据它们的反射光谱对其进行分类，并主要可将其分为三种类型。S型小行星具有硅酸盐岩石的特征，与石质陨石具有明显的同源性。轨道与太阳距离在2.0~2.6 AU之间的小行星大多数是S型小行星。而在距太阳2.6~3.4 AU之间，最为常见的是具有碳质球粒陨石特征的C型小行星。轨道距太阳超过3.4 AU的小行星趋向于暗红色，这些小行星被称为D型小行星。D型小行星可能是长期暴露于太阳辐射(空间风化)期间，被含碳物质形成的焦油状表面残留物着色。这些焦油状的物质通常被称为“托林(tholins)”，是美国天文学家卡尔·萨根(Carl Sagan， 1934—1996)从古希腊单词“mud”中创造出来的一个术语。

散布在各处的小行星似乎主要是金属的(M型)，它们显然与铁陨石有关。少数小行星表面似乎有玄武岩，特别是灶神星。这些小行星是V型小行星。这些小行星或者其现在支离破碎的母体，可能曾经有足够的温度来进行内部熔化和火山爆发。

小行星的轨道

大多数已知小行星的质量相当于月球质量的4%，它们的轨道位于火星和木星轨道之间，也就是所谓的“小行星带”。超过3000颗主带小行星已被记录在案。主带小行星一半以上的质量集中于四颗最大的小行星：谷神星、灶神星、智神星(Pallas)和健神星(Hygeia)，它们的直径分别为950千米、530千米、540千米和430千米。灶神星的密度比智神星大，所以虽然它的体积略小，但质量更大。未被发现的小行星的大小从单个岩石块大小到尘埃颗粒大小都有。然而，小行星带实际上是一个空空荡荡的空间，你不要认为它充满了相互碰撞的岩石。所有通过小行星带发射的太空探测器都安然无恙，甚至必须细心操作才能与任意一颗小行星接近，以便经过时能对小行星进行研究。

木星的引力会对主带小行星的轨道产生相当大的影响。值得注意的是，木星的引力可以防止小行星进入会与木星自身周期产生共振的轨道，因此，几乎没有任何小行星的轨道周期与木星的轨道周期是简单的4∶1、3∶1、5∶2或2∶1的关系，这些关系分别对应与太阳的平均距离(轨道半长轴)为2.06AU、2.50AU、2.82AU、3.28 AU的区域。这些区域中没有小行星存在，因此被称为“柯克伍德缝隙(Kirkwood gap)”，以1886年发现并解释这一现象的美国天文学家丹尼尔·柯克伍德(Daniel Kirkwood)的名字命名。然而，并不是所有的共振轨道都是不稳定的小行星轨道，事实上有一小部分小行星的轨道周期是木星的三分之二(3∶2的轨道共振)。

与木星轨道周期相同的小行星有很多。在这群小行星中，直径超过1千米的可能有100多万颗，总质量约占主小行星带的五分之一。发生这些情况的区域只分布在木星自身轨道前60°和后60°的范围内。这些地方很特殊，小天体可以在太阳和木星的引力下稳定地绕轨道运行，这里被称为前拉格朗日点和后拉格朗日点。按照惯例，这些轨道上的小行星以特洛伊战争英雄的名字命名(轨道在木星自身轨道前60°区域的小行星以希腊名字命名，轨道在木星自身轨道后60°区域的小行星以特洛伊战争英雄名字命名)，但统称为“特洛伊型小行星”。

末日降临

已经知道有一些小行星与火星有类似木星的“特洛伊”关系(小行星的轨道周期与火星轨道周期相同)，但地球没有特洛伊伴侣。有一些小行星的轨道与我们的轨道相交，被称为越地小行星。你可能会担心，越地小行星或许会与地球发生有些吓人的碰撞，但其实小行星的轨道往往与黄道有交角，所以当它们穿过我们的轨道时，它们几乎总是“高于”或“低于”我们。只有其中一部分越地小行星被视为潜在威胁小行星(Potentially Hazardous Asteroids，PHAs
)。这些小行星以小于0.05 AU的距离通过地球(这个范围太近了，如果有第三个天体引起的摄动，可能最后会引发小行星和地球的碰撞)，并且有着150米以上的直径(足够大，能不减速地通过大气层)。到2009年底，我们大约记录了1100颗潜在威胁小行星，以及不到100颗有潜在危险的彗星。

通过计算得到的最接近潜在威胁小行星的是毁神星(半径为350米)，它将在2029年4月13日(星期五)非常接近地球。在它于2004年被发现后不久，毁神星的轨道还鲜为人知(其与地球发生碰撞的概率被估算为2.7%)，但随后一系列更长时间的观测表明，毁神星将安全地在离地球地面约3万千米的地方通过。毁神星将在2036年4月13日再次返回，但由于我们不知道它在2029年经过地球时与地球的距离，所以我们也不知道它的轨道在这次相遇中受到地球引力的影响有多大。然而，毁神星与地球在2036年发生碰撞的可能性还是微乎其微。

如果有小行星不减速地穿透地球大气层，那将是非常危险的。小行星一旦撞击海洋，就可能引发海啸；一旦撞击陆地，就会撞出一个比自身大得多的坑，并摧毁周围地区。近日，在太平洋最南端的别林斯高晋海海底(the Bellingshausen Sea)发现了一个距今220万年，长130千米的陨石坑，名为埃尔塔宁陨石坑(Eltanin)。这个陨石坑显然是由直径几千米的小行星造成的。在撞击海床之前，这颗小行星的速度几乎没被海洋减缓，更不用说大气层了。计算机模型显示，这颗小行星撞击贝林豪森海底引发的海啸会摧毁智利南部海拔300米的海岸和新西兰海拔60米的海岸。此次撞击向大气排放的水和尘埃数量之大甚至可能触发气候变化，这也导致了我们的祖先——直立人
[2]

，大约在这个时期离开了非洲。另一次碰撞发生在地球和一颗10千米长的“恐龙杀手”小行星之间。碰撞发生在6500万年前，形成了直径200千米的奇克苏鲁伯陨石坑(Chicxulub crater)。这个陨石坑现在被埋在墨西哥尤卡坦半岛(the Yucatan peninsula of Mexico)的沉积物下面。这次碰撞引发了一场全球环境剧变。人们普遍认为这是导致“大规模灭绝事件”的原因，当时地球上约有75%的物种灭绝。

幸运的是，这种规模的灾难非常罕见，但统计数据显示，小行星撞击与火山爆发、地震和极端天气事件一样，都是潜在的“末日”原因。直径1千米的小行星平均每20万年撞击一次海洋，能摧毁距撞击点3000千米的海岸。直径为200米的小行星撞击大约每1万年会发生一次，但其引发的海啸半径要小得多。

为了对每一颗潜在威胁小行星所造成的危害进行分类，天文学家们使用了一个名为“都灵风险标度(the Torino Scale)”的数值系统。这个系统是在都灵的一次会议上达成一致，并因此得名的。这个数值系统将小行星传递的能量和与地球碰撞的可能性整合在一起，对潜在威胁小行星会造成的危害进行分类，用从0~10的单一数字表示。0表示发生碰撞的可能性微乎其微，而且(或者)小行星穿透大气层的可能性低到可以忽略。10代表这是会导致全球灾难的“恐龙杀手” 小行星。大多数直径超过150米的潜在威胁小行星在被发现时，其“都灵风险标度”数值为0或1，但当充分研究过它们的轨道之后，1通常被降级为0。毁神星曾短暂拥有过“都灵风险标度”的最高纪录——4级。4级代表“近距离接触”，值得天文学家们注意；大于1%或更大的碰撞机会，可造成区域破坏。但在2006年，毁神星的“都灵风险标度”被降至0级。

一个被称为“太空卫士”的半正式的天文台网站承担了定位和分类所有潜在威胁小行星的任务。这一点很重要，因为对大多数的自然灾害来说，我们所能做的只是减轻影响，但是我们有可能防止潜在的小行星碰撞威胁。为了达到这个目的，我们有必要改变潜在威胁小行星的速度或它的运动方向，这件事的完成时间越提前，所需的动作就越小。有很多种方法可以做到这一点：可以简单粗暴地给潜在威胁小行星装备火箭发动机；也可以用更微妙的策略，在潜在威胁小行星的一面涂上一层反射物质，让太阳辐射压为我们工作。用核弹炸开进入地球大气层的潜在威胁小行星并不是一个明智的选择，因为除非能保证所有的碎片都很小，无法穿透大气层，否则这样可能会造成多重影响，使问题变得更糟。

小行星矿业

虽然希望很小，但有人认为小行星可能是宝贵的原材料来源。一颗直径为1千米的M型小行星所含的镍和铁的量超过整个地球一年的消耗量。最典型的例子是灵神星(Psyche)，其所含的镍和铁的量足以满足地球上数百万年的消耗。小行星，尤其是M型小行星，也含有铂等贵金属。

开采第一颗小行星的初期投资会非常大，但潜在的回报也是巨大的。小行星的主要价值到底是为地球提供原材料还是为太空工业提供原材料，这还有待观察。一些近地天体很可能是已停止运转的彗星，它们的尘埃表面下残留着水冰。这些水冰可以用作推进剂、辐射屏蔽以及饮用水。

名称和暂定名称

到1891年，人们已经发现了332颗肉眼可见的小行星，摄影技术的提升又使这一数字在10年内增至464颗。现在，已知的不同类型的小行星的数量已经超过100 000颗，并且每一颗都需要以某种方式进行标识。国际天文学联合会有一个监督每一项新发现的临时命名体系。临时命名的规则是发现年份加上双字母代码以及数字下标，与发现日期和序列相对应。第一个字母(A-Y，没有I)代表了小行星是在哪个半月内被发现的，A为1月1日至15日，B为1月16日至31日，以此类推，直到Y， Y为12月16日至31日。第二个字母代表小行星被发现的顺序，从A到Z，没有I，有25个选项。不够用时加数字下标会增加一个周期为25的循环。因此，2011BA意为2011年1月16日至31日期间发现的第一个天体，2011BB是第二个，2011BA_1
是第26个，以此类推。要精确测定一颗小行星的轨道可能需要几年的时间，但轨道被准确测定之后，这颗小行星就可以被授予一个永久性的名称，代替临时名称。例如，毁神星最初被临时命名为2004 MN_4
，表示它是在2004年6月16日至30日期间，被发现的第113颗小行星。

发现团队有着对小行星永久命名的特权。一些自动化巡天设备发现了如此多的新的小行星，以至于它们的管理者们乐于接受命名建议。永久名称前要加上一个数字，这个数字在添加每个新名称时按顺序加入。因此，形式上我们有(1)谷神星、(4)灶神星、(99942)毁神星，等等。对于所有这些小行星来说，可用的神话名称太少了，理论上几乎任何名称都是允许的，但这个名称不能是贬义的，并且与近期的政治或军事活动无关。我认识几个有小行星以他们的名字命名的天文学家(是同事用他们的名字来给小行星命名的，你不能用自己的名字给小行星命名)。有一颗小行星名叫(5460)Tsenaat'a'i，在纳瓦霍语中是“飞石”的意思。我参与命名的唯一小行星是(57424)Caelumnoctu，是拉丁文“Caelum Noctu”，意为“夜晚星空”。这颗小行星在2007年被命名，是为了纪念英国广播公司(BBC)长期播出的电视节目《夜空》(The Sky at Night)播出50周年。我们从列表中选择这个名字是因为这颗小行星的编号对应了《夜空》第一次播出的日期——1957年4月24日(57/4/24)。

[1]
本书成书于2010年，2015年黎明号如期抵星，并传回了谷神星表面图片。

[2]
疑似原文有误，普遍认为人类祖先为智人。

06 海外天体 Trans-Neptunian Objects

木星和海王星之间存在数量相对稀少的小行星群——半人马小行星。一些半人马小行星是暗红色的，类似于涂了焦油的D型小行星，另一些则是蓝色的，这表明它们的大部分表面可能是刚刚暴露出来的冰。由于半人马小行星的轨道与巨行星的轨道交叉或接近，所以并不稳定，寿命不超过1000万年。半人马小行星可能是因为与海王星的近距离接触而被拉回海王星轨道内侧的海外天体。与巨行星的进一步相互作用可能会将半人马小行星推入太阳系的内部，直到它们变成短周期彗星，在太阳系内通过近日点。在那里，半人马小行星会被太阳加热，失去挥发性物质，这种变化有时会形成引人注目的尾巴。

在海王星的L4拉格朗日点附近发现了六个特洛伊天体。动力学论证表明，两个拉格朗日点都有数量巨大的特洛伊天体在等待着被发现，并且海王星的特洛伊型小行星的数量可能是木星的10倍。

在海王星之外，我们将看到柯伊伯带和所有其他的海外天体。柯伊伯带的一组天体与海王星的轨道共振为3∶2。这个类别的成员被非正式地称为“冥族小天体”，也包括冥王星。注意不要把“冥族小天体(plutino)”和“类冥天体(Plutoid)”混淆。类冥天体是国际天文学联合会的官方术语，指任何大到足以被列为矮行星的海外天体。类冥天体可以是冥王星、经典柯伊伯带天体(缺少海王星的轨道共振)，也可以是主带以外的黄道离散天体(Scattered Disk objects)。经典的柯伊伯带天体也被称为“QB1-os”，因为在冥王星之后发现的第一个柯伊伯带天体被临时命名为1992QB1。

冥王星和冥卫一

大多数海外天体的性质鲜为人知。冥王星和它的卫星冥卫一(Charon)足够大，与地球的距离足够近，所以几十年来，人们一直通过望远镜对其进行研究。在冥王星的光谱上已经探测到冰冻的氮、甲烷和二氧化碳。最清晰的望远镜图像显示，冥王星上的暗斑可能是富含托林
[1]

的残留物。冥王星的密度表明，岩石必须占其总质量的70%左右，所以冥王星的内部很有可能有一个岩石内核。而这些岩石很可能分化出了一个富含铁的坚硬内核，其上覆盖着一层主要由水冰构成的幔，再上面覆盖着一层挥发性更强的壳。

冥王星位于近日点附近时(最近一次位于近日点附近发生在1989年)会有一个富含氮的大气层，密度可能比海卫一的大气层还要大。冥王星的引力是非常弱的，假想它有一个包裹着99%大气的外壳，这个外壳会延伸到其表面上方300千米处；对地球来说，这样的大气延伸的等效高度只有40千米。冥王星将在2113年到达远日点。在其与太阳的距离从近日点的45亿千米增加到远日点的74亿千米的过程中，冥王星的大部分大气预计会凝结到其表面上。遗憾的是，我们错过了在近日点近距离研究冥王星的机会。美国国家航空航天局的新“地平线”号(Horizon)探测器将于2015年飞越冥王星，届时，大部分冥王星大气层可能已经凝结，并将其表面“永久”隐藏在季节性氮冰之下
[2]

。

冥王星的自转周期为6.4天，与它最大的卫星冥卫一的公转周期相同，与此同时，冥卫一也在同步自转。这种关系是强潮汐的结果，意味着冥王星和冥卫一永远以同样的一面面向对方。冥卫一在大小和质量上与冥王星比例接近，比其他任何行星或矮行星与自己最大卫星的比例都要大。冥卫一的质量大约是冥王星的12%，它的轨道距离冥王星中心只有17个冥王星半径。相比之下，月球的质量仅为地球的1.2%，轨道半径为60个地球半径。冥卫一离冥王星很近，这解释了为什么它直到1978年才被发现。冥王星的两颗较小的卫星冥卫二(Nix)和冥卫三(Hydra)是在2005年被发现的，它们的轨道在冥王星的轨道平面上，与冥卫一形成接近4∶1和6∶1的轨道共振。

在冥王星表面看到的冥卫一的大小，等于在地球上看到的月球的大小的8倍。由于冥王星和冥卫一的相对质量非常接近，它们的共同质心(“重心”)不在冥王星内部，而在两个天体之间的空间点上。尽管已经知道了像(90)休神星这样的双小行星，还有像2001QW332(直径为200千米的双生子)这样的双柯伊伯带天体，但是冥王星和冥卫一依然是大到足以算作行星或矮行星的天体中，体量最为接近的一对。

冥卫一的表面主要是水冰和微量的氨。它的密度比冥王星小，但仍然足以形成一个坚固的岩石内核。冥卫一可能是一个相对平淡的、布满陨石坑的星球，而冥王星可能会像其表面物质多样性所显示的那样，通过地质活动给我们留下深刻的印象。

可能还有一点能让冥卫一比冥王星更引人注目，那就是冥王星的轴倾角是119.6°(大于90°意味着它的自转是逆行的)，而冥卫一的轨道正好在冥王星的赤道平面上，因此，相对于它们围绕太阳的联合轨道而言，冥卫一的轨道有很大的倾斜度。冥卫一受到的来自太阳和冥王星的竞争性潮汐拉力足够强大，可能在冥卫一冰幔内的某处引发融化。如果是这样的话，未来就有趣了。冥卫一有一个类似于木卫二的表面，在冥卫一表面之下甚至还有一个潜在的孕育生命的海洋。迄今为止，我们取得的最好的提示来自2007年获得的红外光谱。通过这些红外光谱，我们发现，冥卫一表面的水冰仍处于原始的水晶体形式，而不是冰的无定形亚微观状态，这种状态暴露在太阳紫外线辐射和宇宙射线轰击下的时间已经超过数万年。冥卫一的间歇泉能对此作出最简单的解释。像土卫二上的羽状物那样，冥卫一的间歇泉会从内部喷射出新鲜的冰。

其余的海外天体

表7列出了在撰写本文时，冥王星和其他10大海外天体的排名。其中阋神星(Eris)、鸟神星(Makemake)和妊神星(Haumea)被正式认定为矮行星。妊神星是扁平的，这要么是因为它的自转周期只有4小时，非常快，要么是因为碰撞。表7中的天体都是经典的柯伊伯带天体，除了阋神星、2007OR10(黄道离散天体)、2002TC302(与海王星的轨道共振为5∶2)、伊克西翁(Ixion，冥族小天体)和塞德娜(Sedna)。塞德娜以一种奇特的方式位于黄道离散天体之外，它有一个高度椭圆的轨道，远日点在距离太阳975 AU处。

表7　最大的海外天体

续表

除冥王星外，人们对表中天体的大小知之甚少(即使是表中给出近似数值的天体)。这些海外天体的尺寸是基于对反照率(天体反射入射光的百分比)的假设估算出来的。如果海外天体的反照率比假设的要小，那么它们一定会更大，但如果它们反照率比假设的要大，那么它们一定会更小。对海外天体尺寸的估计可以通过测量其表面的热辐射来改进，但是因为海外天体太冷了(表面温度只有零下230℃或更低)，所以只能利用在地球大气层上方的太空望远镜才能做到这一点。鉴于这些不确定性，表中的海外天体不太可能全都进入未来的“十大海外天体”名单。

海外天体的颜色范围分布为从红色(表面可能广泛分布着托林)到蓝灰(表面有暴露的冰或无定形碳)。妊神星是蓝灰色的，其质量(从其卫星轨道导出)表明，妊神星的密度比冥王星大，因此它必须有相对较高比例的非冰成分。已经在创神星的光谱中检测到的结晶冰和氨水合物，这表明创神星的表面是最近重塑的(所使用的论据与那些为冥卫一提出的论据类似)。这意味着需要地质活动或重大撞击事件，以产生足够广泛的喷射物来主导光谱。

有2%~3%的海外天体拥有卫星，与拥有卫星的小行星比例相当。在较大的海外天体中，这一比例更高，这给解释海外天体的卫星的起源造成了一些困扰。

如果美国宇航局的“新地平线”
任务在2015年飞越冥王星-冥卫三之后仍然保持健康，它将被导向一个更遥远的海外天体。该目标尚未确定，但理想情况下将是一个蓝灰色的海外天体，与冥王星的红色性质形成对比。

一颗海外行星？

大多数天文学家认为，我们已经发现了所有隶属太阳系的大型天体。当然，柯伊伯带中不可能隐藏任何行星大小的天体，因为如果存在这样一个天体，柯伊伯带将是不稳定的。然而，对于一颗尚未完全逃离太阳系的外围行星(俗称“X行星”)来说，仍然存在两种可能性。第一种可能性是，在距太阳80~170 AU处的倾斜偏心轨道上，有一个质量与地球质量相当的天体。如此巨大的天体(可能是由于与海王星的近距离接触而被向外抛射的)的存在可以解释为什么在距太阳48AU之外的柯伊伯带，我们观测到的天体数量突然减少。这个现象被称为“柯伊伯悬崖”。这可能也解释了塞德娜等天体的极端轨道散布现象。

外围行星存在的第二种可能性出自长周期彗星往往来自天空的一个特定区域，而不是某个随机方向。有人认为，这些长周期彗星是从奥尔特云中被驱逐出来的，这种天体与木星质量相当，距太阳约32 000AU。这样的天体很难用望远镜探测到，但并非不可能。如此遥远的一颗“行星”不会受到太阳引力的束缚，它可能只是一个从另一颗恒星的行星系统中偶然逃脱的星际空间漫游者。

[1]
一种存在于远离母恒星的寒冷星体上的物质，是一类共聚物分子，由最初的甲烷、乙烷等简单结构有机化合物在紫外线照射下形成，它并不是单一的纯净物，并没有确定的化学分子或明确的混合物与之对应。托林在颜色上通常呈浅红色或棕色。托林无法在今日的地球自然环境下形成，但在外太阳系以冰为主的天体表面占有极大的含量，也见158页。

[2]
新地平线号在2015年夏天飞越冥王星时，其表面凝结。

07 系外行星 Exoplanets

毫无疑问，有行星的恒星十分常见，这已经不再是一种猜测。到2010年，已有超过400颗恒星被证实至少有一颗行星在绕着它们运动。这些高难度的探测结果表明，大多数类日恒星一定会有行星相伴。为了避免混淆，专业人士通常称它们为“太阳系外行星”或“系外行星”。系外行星不包括质量超过13个木星质量(氘发生核聚变的阈值)的系外暗天体。这些系外暗天体被认为是类恒星而不是类行星，并被称为“褐矮星”。

检测方法

20世纪70年代末以来积累的证据表明，大多数年轻的类日恒星周围都有一圈尘埃。类日恒星周围有尘埃的最初线索是尘埃对恒星候选体红外光谱的影响，之后的线索来自20世纪80年代开始获得的尘埃盘图像。不管这些盘状物是行星形成前的太阳星云，还是恒星柯伊伯带的残余尘埃，盘状物的存在本身就表明尘埃盘中应该有大量行星。1995年，第一个系外行星被确认，这之后，发现系外行星的速度越来越快。

径向速度

发现第一颗系外行星的方法，同时也是之后发现大多数系外行星的方法，是探测恒星径向速度的微小变化。2010年至少有超过300颗系外行星是通过这种方法被发现的。径向速度是一颗恒星向着或远离地球运动的速度，不受视线范围内任何运动的影响。通过测量恒星光谱特定波长的特征吸收线，可以确定其径向速度的变化，精度高达1米/秒。当恒星向我们移动时，特征吸收线会向短波端移动，称为“蓝移”；当恒星远离我们时，特征吸收线会向长波端移动，称为“红移”，这种现象被称为多普勒效应。长期以来，径向速度变化一直被用来测量双星的轨道速度，从而推断双星的质量。但如果要测量质量小得多的系外行星对质量大得多的恒星的微小影响，就需要非常灵敏的现代仪器。在考虑由系外行星所引起的恒星径向速度的微小变化越来越明显之前，必须先考虑到地球自身轨道运动所引起的径向速度变化。

恒星和系外行星之间的引力取决于它们的质量之和。幸运的是，对于类太阳恒星来说，恒星的光谱类型和其质量之间有着众所周知的关系。知道了这一点，我们就可以利用恒星径向速度变化的周期和幅度来确定引起恒星前后运动的系外行星的质量。一般来说，能独立测量系外行星轨道平面方向的方法是不存在的。因此，我们假设系外行星的轨道平面与我们的视线方向平行，以此来估计系外行星的质量。但是，除非系外行星的轨道平面恰好与我们的视线方向平行，不然恒星真实的径向速度变化一定会大于我们所探测到的速度变化。不过，基于假设，对随机定向轨道平面的统计表明，大多数系外行星的质量不会超过我们估计结果的两倍。

径向速度法适用于离恒星较近的大行星，因为行星的大质量和近距离都会导致恒星径向速度的变化达到最大。因此并不奇怪，第一批被探测到的系外行星往往比木星更大，并且其轨道距离恒星只有一个天文单位，我们称之为“热木星”。

“热木星”的发现曾引起相当大的轰动，因为这些“热木星”位于恒星的冰霜线之内，并且不可能形成于它们现今所处的位置。人们已经接受了“热木星”会进一步演化，然后向内迁移的观点。这重新引发了关于我们太阳系早期行星迁移范围的争论。如果木星继续向内迁移，它将依次摧毁或驱散每一颗类地行星。有一段时间，对“热木星”的研究开启了这样一个前景：“热木星” 摧毁或驱散每一颗类地行星的行为是正常的，而像我们太阳系这样存在类地行星的系统则是非常罕见的。然而，改进的系外行星探测技术以及新出现的系外行星探测技术已经开始发现岩质行星，这表明早期“热木星”的发现，仅仅是由于“热木星”更容易被发现而已。

凌日

第二种常用的搜寻系外行星的方法是寻找“凌日”，这种方法的使用频率可能很快就会超过径向速度法。一颗系外行星挡在它的恒星之前，使恒星光线的一小部分被阻断，这种现象就叫“凌日”。大多数凌日现象可利用自动望远镜对可能存在行星的恒星进行反复扫描发现。这些自动望远镜最初是地面上的望远镜，但现在也有太空专用望远镜。

只有当系外行星的轨道平面几乎完全平行于我们的视线方向时，凌日才可能发生。从统计学上讲，这大约只适用于0.5%的系外行星系统。在凌日过程中，星光一般只是轻微变暗。但是对最大的系外行星来说，星光变暗的幅度也最大。此外，对运动轨道靠近恒星的系外行星来说，凌日发生的频率也更高。因此，运动轨道靠近恒星的最大系外行星更有可能被探测到。于是，“热木星”被发现的概率再一次多于任何其他类型的行星。恒星与行星的相对大小可以通过恒星光线变暗幅度的精确值来推断，而凌日持续的时间可以为我们提供轨道速度和轨道半径的线索。因为凌日现象表明系外行星的轨道平面在我们的视线方向上，所以对后续的径向速度测量就可以帮我们更好地描述该系统。在这种情况下，我们用径向速度法得到的行星质量是真实值，而不是最小估计值。

影像法及其他方法

系外行星的成像极具挑战性，因为它们比恒星暗淡得多。只有少数恒星的系外行星有个体成像。如你所料，这些成像的系外行星都是木星大小或者比木星大，大部分在距离其恒星数十甚至数百个天文单位的轨道上运行。2008年，夏威夷的红外望远镜获得的一幅自适应光学图像显示，有三颗系外行星围绕着编号为hr8799的年轻类太阳恒星运行，它们的轨道与该类太阳恒星的距离分别为24AU、38AU和68AU。在这三颗系外行星之外，距该类太阳恒星大约75AU处，有一个尘埃盘。

另一种探测系外行星的方法称为“天体测量学”。这种方法在未来有很大的潜力，它依赖于对恒星位置的精确测定。任何看不见的“轨道伴星”都会引起恒星的摆动。天体测量学试图检测这种恒星位置的变化，而不是视线方向上恒星径向速度的变化。由大轨道上的一颗大质量行星引起的这种恒星位置的变化是最大的，所以这种方法可以与对小轨道更敏感的方法互补。2002年，哈勃太空望远镜记录了编号为Gliese 876的恒星的横向摆动，首次证实了天体测量学法的成功。这使我们对一颗质量为2.6个木星质量，轨道距其恒星0.2AU，已经被径向速度法探测到的系外行星有了更进一步的了解。2009年，一颗编号为VB10的红矮星被发现其位置偏离源自一颗质量为6个木星质量的系外行星，这是用天体测量学法首次发现的不为人知的系外行星。

另一种截然不同的方法是利用前景星和背景星之间永远不会重复的随机精确对齐。前景星就像一个“微引力透镜”，放大了来自背景星的光。被探测到的背景星的亮度在几周的时间内上升然后下降。如果前景星碰巧有一颗系外行星，便会导致一个持续数小时或数天的短暂的亮度高峰，叠加在一个缓慢上升再下降的亮度变化区间上。直到2010年，这种微引力透镜方法已经发现了10颗系外行星。

系外行星的命名

系外行星没有名字。我们通过在其恒星的名称或星表名称后面添加小写字母来识别系外行星。在一类恒星系统中，第一个被发现的系外行星是b，第二个是c，以此类推(不使用a)。因此，Gliese 876的第一颗系外行星是Gliese 876 b，随后在同一系统中发现的两颗系外行星是Gliese 876 c和Gliese 876 d。这个惯例会导致混乱，因为这些字母与多系外行星系统中的行星的位置没有关系。然而，这种方式是有效的。也许我们不强制使用这种命名方式是明智的，当地人可能已经为他们的家园起了很好的名字。

多系外行星系统

已知有近50颗恒星有多颗系外行星绕着其运行，使用组合检测技术有时可以提供这一信息，但其实这项工作仅用径向速度法就可以完成：这不过是一个逐步揭示更微妙的周期性变化的过程。表8列出了一些较大的多系外行星系统，其中，Gliese 581系统尤其值得注意。Gliese 581是一颗距地球20.5光年的红矮星。Gliese 581系统包含着已知的质量最小的系外行星Gliese 581 e。这颗系外行星的质量可能只有1.9个地球质量，可以确定一定不超过4个地球质量。Gliese 581系统同时也包含着一颗可能被海洋覆盖的类地行星Gliese 581 d，它的质量超过7个地球质量。Gliese 581 e因温度太高而无法产生生命，甚至无法保留大气层。但Gliese 581 d似乎位于其恒星的宜居带。

表8　一些多系外行星系统

* 引用的一些质量是最小估计值。MJ = 木星质量

在已知拥有系外行星的恒星中，距离我们最近的是波江座ε(Epsilon Eridani)，距离地球只有10.5光年。波江座ε b(Epsilon Eridani b)由径向速度法发现，它是一颗巨行星，其质量与木星质量相近，位于距其恒星3.4 AU的轨道上。红外望远镜显示，波江座ε周围有着以其为中心的，距其约3 AU和20 AU的岩石碎片带——小行星带，外加一个从距其35 AU处延伸到距其100 AU处的外尘埃盘。尘埃盘的结构已经被用来作为一颗未经证实的行星存在的证据。这颗行星名为波江座ε c(Epsilon Eridani c)，质量约为木星质量的十分之一，距离波江座ε大约40 AU。

研究

对于任何系外行星，我们都只有极少的直接信息。如果通过径向速度法或天体测量学确定了系外行星的质量，我们就可以假设一个可能的密度来推断该行星的大小。系外行星的大小可以由凌日法来揭示，也可以通过成像法来确定(基于亮度和假定反照率)。利用行星的大小，我们也可以假定一个可能的密度来推断它的质量。系外行星与恒星的距离使我们可以得出行星表面温度或大气温度的合理取值，但行星表面温度或大气温度也取决于反照率和大气中温室气体的混合物，因此误差空间也很大。

研究系外行星的下一个重大突破可能会随着我们分析系外行星大气成分能力的提高而到来。这最好由太空望远镜来完成，因为它能够分离并分析单个系外行星的可见光和红外光谱——最重要的是类地行星的可见光和红外光谱。可以根据气体的吸收特性来确定行星大气中一些含量丰富的气体的种类。探测到不应该在简单化学条件下共存的一对气体，比如氧和甲烷，可能是我们获得的第一个生命会影响系外行星大气层的证据。正如地球上的生命使地球大气层发生了根本性的变化一样，系外行星的大气层也会受其生命的影响。

系外行星上的生命

在我们的银河系中，大约有100亿颗类似太阳的恒星，约占所有恒星的十分之一。系外行星一定很多，因为已经被充分研究过的类太阳恒星中，有一半都有行星绕其运行。到目前为止发现的大多数系外行星都是巨行星，因为它们最容易被探测到。但目前还没有证据表明类地行星是普遍存在的。系外行星系统显然是多种多样的，不过，在像ψ和b这样的“热木星”向内迁移的过程中，没有任何一颗类地行星能幸存下来。这样的“热木星” 的轨道目前距离恒星不到0.06 AU(表8)。我们已经开始寻找的类地行星很可能存在于很大一部分系外行星系统中。

究竟有多少系外行星可能存在生命，这是一个令人烦恼的问题。让我们来做一个非常保守的估计，只有1%的类日恒星有一颗类地行星长时间在宜居带中运行。以此推算，我们的银河系会有1亿颗可供居住的类地行星。此外，围绕着系外行星运行的可居住卫星的数量可能至少与此相当。

但是，逻辑链的下一步就不那么确定了。考虑到生命所需的条件，生命开始的可能性有多大？生命的基本构成要素并不是生命开始的必要因素。我们知道，太空中充满了有机分子，水也很丰富，所以处在宜居带的大多数系外行星将都有碳基生命所需的所有必要成分。这意味着《星际迷航》
[1]

(Star Trek)中关于“我们所知的生命(life as we know it)”的说法并不是对依赖外来化学物质的其他生命形式的推测，它只是一派胡言而已。

生命自然出现的过程是否容易，我们还不能确定。许多人，包括我自己，都认为系外行星的海洋中存在着无数的有机分子，而且已经有数百万年可以去发展生命，因此，系外行星上不可避免会开始形成生命。一旦生命传播开来，就很难被完全根除。即使生命被彻底根除了，它同样容易重新开始。

我们知道，地球上的生命用了不到5亿年的时间就建立起支持生命存在的永久基础。在我们找到系外行星上存在生命的迹象之前，银河系(以及银河系外的宇宙)中是否存在丰富的生命还有待证实。即使我们在火星、木卫二或土卫二上发现了现在或过去存在的生命，我们也不能贸然下结论说生命是从那里孤立开始的，因为太阳系中的天体并不是完全相互孤立的。微生物可以从一个撞击抛射物的碎片转移到另一个撞击抛射物的碎片中存活下来，木卫二的生命可能来自地球。我们也可以想象，地球上的生命是从火星上的一颗陨石开始的。

有人在吗

如果其他恒星上有生命，那么会不会存在智慧生命呢？让我们理性地推测。据我们所知，智能生物需要多细胞生命。如果微生物生命开始了，随后进化产生多细胞生物的可能性有多大？你可以对这个问题发表你的意见。在地球上，从微生物生命开始到进化产生多细胞生物经历了几十亿年。

多细胞生物出现后，其他星球上的生存竞争会像在地球上那样，推动达尔文式的进化吗？智力是会为生存竞争带来优势的一个因素，那么，智力在生存竞争中有多不可或缺呢？

即使按照我保守估算的数字，银河系中有1亿颗宜居的类地行星，如果再加上一种悲观的观点，生命开始的概率只有1%，那么仍有100万个天体会有生命存在，地球就是其中之一。如果地球是所有行星中的唯一或第一颗拥有智慧的行星，那将是很奇怪同时也令人敬畏的事。但如果生命是如此丰富，而智慧是生命的一个普通产物，那么智慧生命都在哪里呢？除非智慧极少出现，或者持续时间不长，例如，我们自己的文明就可能屈服于战争、自然灾害或者自找的气候变化，否则银河系应该充满智慧。

智慧生命并不一定是我们发现它的地方所特有的。虽然恒星之间的距离很大，但在它们之间旅行是完全可能的。你不需要比光速还快的旅行，你所需要的只是决心和耐心。想象一艘足够容纳数百人的宇宙飞船，它需要100年的时间才能到达10光年外的一颗宜居的系外行星。我们可以使用可预见的未来几十年的技术，自己建造这样一艘船。然而除非使用某种休眠的方式，否则一到两代船员将在飞行途中经历生死，所以，这将是一次绝对单程的旅行。如果我们把这些殖民者送到附近所有可居住的系外行星上，不久之后，成功被殖民的地方有能力发射自己的殖民地飞船。我们希望在本世纪末对这些可居住的系外行星进行识别和描述。银河系有10万光年辽阔，所以，即使殖民浪潮到达10光年外要1000年的时间，那么只需1000万年就可以完成整个星系的殖民。毁灭单个殖民地的灾难，或个别殖民地船只的失败，都不足以使殖民进程偏离轨道。

银河系已经有超过100亿年的历史了。假设智慧生命是丰富的，那么应该有无数物种有足够的时间来殖民银河系。这就是费米悖论，以1950年美国物理学家恩里科·费米(Enrico Fermi)的名字命名。应该有众多外星文明存在，但没有外星文明存在的迹象：尽管地外文明探索(Search for Extra-Terrestrial Intelligence， SETI)旗下工作的团队对天空进行了扫描，但并没有探测到太空中的人造信号，也没有探测到伟大的天文工程作品存在的迹象以及可靠的地球外星访客记录。到底是智慧生命稀少，还是我们太愚蠢，找不到证据？我希望有一天我们能找到答案。

全书完

[1]
语出科幻影视系列作品《星际迷航》第一季第2集，斯波克(Spock)说：“我们所知的生命都是碳化合物组成的，但如果生命是基于另一种元素呢？例如硅。”

索引

A

accretion 吸积

ammonia clouds 氨云

Antiope 休神星

Antoniadi, Eugenios 欧仁·安东尼亚第

aphelion 远日点

Apollo 阿波罗

Apophis 毁神星

Ariel 天卫一

asteroid belt 小行星带

asteroid mining 小行星矿业

asteroid, Trojan 特洛伊型小行星

asthenosphere 软流层

astronomical unit 天文单位（AU）

B

Beagle Rupes 猎犬悬崖

BepiColombo 贝比科隆博

brown dwarfs 褐矮星

C

carbon 碳

carbon cycle 碳循环

carbon dioxide 二氧化碳

carbon monoxide 一氧化碳

carbonaceous chondrites 碳质球粒陨石

carbonate rock 碳酸盐岩

Cassini（spacecraft） 卡西尼号（探测器）

Centaurs 半人马小行星

Ceres 谷神星

Charon 冥卫一

comet 彗星

condensation 凝结

Copernicus, Nicolaus
[1]

尼古拉斯·哥白尼

crater　环形山

crust　地壳

cryovolcanism　冰火山

cubewanos　经典柯伊伯带天体

D

Dawn(spacecraft)　黎明号(宇宙飞船)

Deimos　火卫二

differentiation　分化

E

Earth-crossing Asteroid　越地小行星

eccentricity(orbital)　(轨道的)偏心率

eclipses　日食

ecliptic　黄道

Edgeworth, Kenneth　肯尼斯·埃奇沃思

Enceladus　土卫二

Eris　阋神星

Eros　爱神星

erosion　侵蚀

eruption plumes　喷射的羽状物；羽流

ESA　欧洲航天局

Europa　木卫二

exoplanets　系外行星

exosphere　外逸层

F

Fermi Paradox　费米悖论

G

Galilean satellites　伽利略卫星

Galileo(spacecraft)　伽利略号(探测器)

greenhouse effect　温室效应

H

habitable zone　宜居带

Hadley Rille　哈德利沟纹

Haumea　妊神星

heliocentric theory　日心说

Herschel, William　威廉·赫歇尔

hot Jupiter　热木星

Hubble Space Telescope　哈勃太空望远镜

Huygens(spacecraft)　惠更斯号(土星探测器)

hydrologic cycle　水文循环

Hygeia
[2]

健神星

I

IAU(International　国际天文学联合会

Astronomical Union)

ice line　冰线

Ida　艾达

Inner moonlets　内侧超小卫星

Io　木卫一

ionosphere　电离层

irregular satellites　不规则卫星

Itokawa　丝川

J

Jupiter　木星

Jupiter Great Red Spot　木星大红斑

K

Kepler, Johannes　约翰内斯·开普勒

Kepler's laws　开普勒定律

Kirkwood gaps　柯克伍德缝隙

Kuiper belt　柯伊伯带

Kuiper cliff　柯伊伯悬崖

Kuiper, Gerard　杰拉德·柯伊伯

L

liquid water　液态水

lithosphere　岩石圈

Lowell, Percival　珀西瓦尔·洛厄尔

M

Magellan（spacecraft） 麦哲伦号（金星探测器）

magma ocean 岩浆海洋

magnesium 镁

magnetic field 磁场

magnetospheres 磁层

Makemake 鸟神星

mantle 幔

maria 月海

Mars 火星

Mars canals 火星运河

Mars core 火星核

Mars dust storms 火星沙尘暴

Mars gullies 火星沟壑

Mars meteorites 火星陨石

Mars polar caps 火星极冠

Mars sand dunes 火星沙丘

martian 火星人

Mercury 水星

Mercury core 水星核

Mercury magnetic field 水星磁场

MESSENGER（spacecraft） 信使号（探测器）

meteorites 陨石

methane 甲烷

methane clouds 甲烷云

micrometeorites 微陨石

Miranda 天卫五

Moon 月球

N

NASA 美国国家航天局

Neptune 海王星

Neptune Great Dark Spot 大暗斑

New Horizons（spacecraft） 新视野号（探测器）

Newton, Isaac 艾萨克·牛顿

nickel 镍

nuclear fusion 核聚变

O

Olympus Mons 奥林匹斯山

Oort Cloud 奥尔特云

orbital period 轨道周期

orbital resonance 轨道共振

orbits 轨道

oxygen 氧

ozone 臭氧

P

Pallas 智神星

Pan 土卫十八

Peale, Stanton 斯坦顿·皮尔

perihelion 近日点

Phobos 火卫一

Phoebe 土卫九

phosphorus 磷

photochemistry 光化学

photodissociation 光解

planet 行星

planet, dwarf 矮行星

planet, gas giant 气态巨行星

planet, giant 巨行星

planetary embryo 行星胚胎

planetesimals 星子

plumes 羽流

plutino 冥族小天体

Pluto 冥王星

Plutoid 类冥天体

potentially hazardous asteroid 潜在危胁小行星

prograde 顺行

Psyche 灵神星

Q

Quaoar 创神星

R

radial velocity 径向速度

regolith 月球风化层

regolith 风化层

regular satellites 规则卫星

retrograde 逆行

S

Sagan, Carl 卡尔·萨根

satellites 卫星

satellites of asteroids 小行星卫星

satellites of planets 行星卫星

satellites of TNOs 海外天体的卫星

Saturn 土星

Saturn storms 土星风暴

Scattered Disk objects 黄道离散天体

Schiaparelli, Giovanni 乔范尼·夏帕雷利

Sedna 塞德娜

shepherd satellites 牧羊犬卫星

silicates 硅酸盐

solar magnetic field 太阳磁场

solar nebula 太阳星云

Solar System 太阳系

space exploration 太空探索

Spaceguard 太空卫士

spectroscopy 光谱学

spectroscopy, infrared 红外光谱

spectroscopy, optical 光谱学

stony 石质陨石

stony-iron 石质铁陨石

sulfur 硫

sulfur dioxide 二氧化硫

sulfuric acid 硫酸

Sun 太阳

surface temperature 行星表面温度

T

telescopes 望远镜

terrestrial planet 类地行星

thermosphere 热层

tholins 托林

Titan 土卫六

transits 凌

trans-Neptunian objects 海外天体（TNOs）

Triton 海卫一

troposphere 对流层

U

Uranus 天王星

Uranus seasonal variations 天王星季节变化

V

Valles Marineris 水手谷

vapour 蒸气

Venus 金星

Vesta 灶神星

Viking（spacecraft） 海盗号（探测器）

volcanism 火山活动

Voyager（spacecraft） 旅行者号（探测器）

W

water 水

water ice 水冰

weathering 风化作用

weathering, chemical 化学风化

weathering, space 太空风化

Contents

Introduction

1　The Solar System

2　Rocky planets

3　Giant planets

4　Giant planets' satellites and rings

5　Asteroids

6　Trans-Neptunian objects

7　Exoplanets

Further reading

Index

Introduction

In a sonnet of 1816 refl ecting upon his experience of reading a new translation of the works of Homer, the young English poet John Keats wrote of ‘breathing the pure serene’ in ‘realms of gold’, and continued:

Then felt I like some watcher of the skies

When a new planet swims into his ken;

Or like stout Cortez when with eagle eyes

He star’d at the Pacifi c-and all his men

Look’d at each other with a wild surmiseSilent, upon a peak in Darien.

Keats’s new planet metaphor was either inspired by Sir William Herschel’s sighting of Uranus in 1781, or by discoveries of the fi rst four asteroids (1801–7). Being more recent, the latter would have been fresher in people’s memories. A layman such as Keats would have thought of them as new ‘planets’, although today they are regarded as too small to qualify.

I still travel in ‘realms of gold’ when I see Saturn with my own eyes through even a small telescope, though the novelty has somewhat faded when it comes to seeing a newly discovered remote ice-ball as a single pixel in a digital image, or a hint of a Jupiter-sized companion to another star expressed as a minute wobble in the star’s position.

However, for me, the true ‘Cortez experience’ recurs whenever I see a new planetary landscape (in some cases, a cloudscape)unfold before me on images sent back from a visiting spacecraft.Exploration of our Solar System has reached a stage that allows us to appreciate other planets and their large satellites as worlds,endowed with geographies, geologies, and meteorologies as complex and fascinating as those of our own planet, Earth. Many of them are places that you and I could, in principle, visit. They are not generally suitable for a picnic, but we could at least jump up and down, scoop up handfuls of dirt, climb a hill, or slither down into a valley. Some are even places where life might be found.

In this book, I will share with you what is known of the origin,evolution, and especially the present-day condition of the planets in our Solar System. Here, astronomers now offi cially recognize only eight planets (Pluto has been demoted, as I will describe), but there are plenty of other bodies big enough to behave like planets so far as geologists like myself are concerned. These are fascinating, so I will not ignore them, though they are too numerous to treat individually.

Finally, I will turn to ‘exoplanets’, which are planets orbiting other stars. The fi rst was discovered as recently as 1995, and by now several hundred have been documented. We cannot see them in any detail, but we do have enough information to make some comparisons between the layouts of those exoplanetary systems and the Sun’s family.

Chapter 1　The Solar System

Planets in history

Before the curses of light pollution and smog, people were more familiar with the night sky than they tend to be today. Planets in the sky were recognized as special by ancient cultures, because they are ‘wandering stars’ that migrate against the background of the ‘fi xed’ stars. Five planets have been known since antiquity:Mercury, Venus, Mars, Jupiter, and Saturn – which are the only ones bright enough to come to the attention of the unaided eye.Of course, the Sun and Moon were obvious too, but the ‘planets’appear as wandering points of light, whereas the Sun and Moon show disks and tended to be regarded differently. Throughout most of humankind’s existence, the Earth was imagined to be the centre of creation, unrelated to objects in the sky, so it was not thought of as a planet.

The intellectual leaps that recognized that the Earth is a ball of rock going round the Sun, that the planets do likewise, and that the Earth is just one of their number were a long time coming. The process was slow, and there were many false dawns. During the 5th century BC, the ancient Greek philosopher Anaxagoras correctly surmised that the Moon is a spherical body refl ecting the light of the Sun, and he was sent into exile on account of his beliefs. In the succeeding centuries, various Chinese astronomers developed similar ideas, but the idea of the Moon as a globe probably did not embed itself into popular consciousness until its appearance through a telescope became known during the 17th century.

As for the planets, they were generally regarded as points of light going round the Earth, until the counterintuitive ‘heliocentric’ view with the Sun as the centre of motion became accepted. The earliest written suggestions that the Earth goes round the Sun occur in Indian texts dating from the 9th century BC, but despite this and subsequent independent suggestions, notably by Hellenic and Islamic sages and eventually by Nikolas Copernicus in 1543, the concept did not achieve ascendancy until the 18th century. Partly on account of his advocacy of the heliocentric theory, Galileo Galilei (who through his telescope had seen mountains on the Moon, the phases of Venus, and four tiny moons orbiting Jupiter)was held under house arrest from 1633 until his death in 1642.

Simply by revealing the planets as tiny but discernible discs,whereas the stars remained as points of light, use of the telescope from the start of the 17th century onwards marked planets as fundamentally different to stars, and eased the path to regarding them as worlds comparable to our own. Incidentally, we now know that stars are much bigger than planets, but (except for the Sun) they are so very much more distant that only in a few cases can even the most sophisticated of modern telescopes show any surface details (on photographs, bright stars look bigger than faint stars, but that is just an optical effect – the brightness is being smeared out).

Kepler’s laws of planetary motion

The planets slotted into their rightful place in human comprehension thanks to Johannes Kepler’s (1609) realization that the planets (including the Earth) travel round the Sun in paths (orbits) that are ellipses rather than perfect circles, coupled with Isaac Newton’s (1687) insight into gravity that explained this motion. Then their distances and sizes relative to the Earth could begin to be deduced.

An ellipse is what you might think of as an ‘oval’. Mathematically, it is defi ned as a closed curve drawn about two points (the foci of the ellipse) such that the sum of the distances from each focus to any point on the curve is identical. A circle is a special kind of ellipse in which the two foci coincide, at the circle’s centre. The further apart the foci, the more elongated, or ‘eccentric’, the ellipse. Kepler deduced that planets follow elliptical orbits, with the Sun at one focus of each ellipse (the other focus being empty). The point on an orbit closest to the Sun is called ‘perihelion’ (Greek for ‘closest to the Sun’), and the point furthest away is called ‘aphelion’ (Greek for‘furthest from the Sun’). Planets’ orbits are not strongly eccentric,and if you see them drawn in plan view they look very much like circles. For example, when Mars is at aphelion its distance from the Sun is less than 21% greater than when it is at perihelion, and for the Earth the difference is only 4%.

Kepler is justly famous for his three laws of planetary motion.Kepler’s First Law is simply the statement that each planet moves in an elliptical orbit, with the Sun at one focus. The Second Law describes how the speed of a planet varies around its orbit: a planet moves faster the closer it is to the Sun (for reasons subsequently explained by Newton’s theory of gravity) such that an imaginary line linking the planet to the Sun sweeps out an equal area in equal time. Kepler’s Third Law relates a planet’s orbital period (how long it takes to complete a circuit round the Sun) to its average distance from the Sun: the cube of the orbital period is proportional to the square of the average distance. The average distance from planet to Sun turns out to be equal to half the length of the orbital ellipse’s long axis (its ‘semi-major axis’) or, if you prefer, half the straightline distance between perihelion and aphelion.

Kepler’s laws of planetary motion enabled precise calculation of the sizes of the orbits of other planets, with an accuracy limited almost entirely by the uncertainty in how well the size of the Earth’s orbit could be measured. Even as long ago as 1672,simultaneous observations of Mars from widespread locations enabled the Earth–Sun distance to be measured as about140 million kilometres, remarkably close to the correct value of149,597,871 kilometres. Observations of the transit of Venus across the Sun’s disc in 1761 and 1769 (the latter requiring Captain Cook to station himself in Tahiti) produced a revised estimate of153 ± 1 million kilometres. Despite these and other scientifi c advances, which continued to strengthen a fully self-consistent and elegant model of the Solar System’s scale and nature, a papal ban on printing ‘heliocentric’ books in Rome remained unrevoked until 1822.

You would be excused for thinking that once the distance to a planet has been established, working out its size would be trivial.However, the smallness of a planetary disc through even a large telescope, coupled with the shimmering of the Earth’s atmosphere,leads to signifi cant uncertainty in measuring the angular size of the planet (in other words, how big it appears). For example, when he discovered Uranus in 1781, William Herschel’s measurement of its disc was 8% too large. Rather than trying to measure how big a planet looks, the most precise telescopic way to determine its size is to time how long it takes to pass in front of a star. Such‘occultations’ are rare events, but by the close of the 19th century the sizes of the planets had been determined with considerable accuracy ( Table 1 ).

Herschel discovered Uranus by accident, but Neptune was located in 1846 as a result of a deliberate search, guided by slight perturbations in the orbit of Uranus (distorting it from a perfect ellipse) that could be best explained by the gravitational infl uence of an unseen outer planet. When it had been documented for long enough, the orbit of Neptune in turn seemed to show perturbations pointing to a further undiscovered planet. This triggered a search that found Pluto in 1930. At fi rst, astronomers assumed that this newly hailed ninth planet must be similar in size and mass to Uranus and Neptune. However, by 1955 it had been shown that Pluto could be no larger than the Earth; in 1971the estimate was revised downwards to the size of Mars; and in1978 its surface was found to be dominated by highly refl ective frozen methane which meant that its physical size had to be even smaller to remain consistent with its total brightness. We now know that Pluto’s diameter is only 2,390 kilometres, so its size is smaller (and, in fact, its mass is much smaller) even than Mercury.The apparent perturbations in Neptune’s orbit that, rather fortunately, inspired the search for Pluto are now attributed to observational inaccuracies.

Table 1　The sizes of the planets (equatorial diameters)

* C. Flammarion,Popular Astronomy (Chatto and Windus,Piccadilly)

Pluto lost its status as an offi cially recognized planet in 2006.That was a contentious move, though in my opinion the right one.Before describing how this came about, I will review the nature of the Solar System as it is now understood.

A review of the Solar System

The Sun

In the centre of the Solar System is the Sun, which is a fairly ordinary star, powered by the conversion of hydrogen into helium by nuclear fusion in its core. The Sun’s diameter is 109 times and its mass is nearly 333,000 times greater than the Earth’s. It contains about 740 times more mass than everything else in the Solar System put together. Consequently, the Sun’s gravity is so dominant that objects in the Solar System orbit the Sun in almost the perfect ellipses recognized by Kepler. Perturbations to a planet’s orbit caused by other planets are tiny, though they can be measured.

The planets

Table 2 summarizes some basic properties of the planets, quoted relative to the Earth to avoid very large numbers. Distance from the Sun is quoted in ‘Astronomical Units’, abbreviated as AU,defi ned as the average Earth–Sun distance. This is fairly simple to remember as (near enough) 150 million kilometres. A planet’s orbital period is how long it takes to complete one circuit round the Sun, which is of course its own ‘year’. The orbital periods and distances from the Sun in this table are related to each other by Kepler’s Third Law. Conveniently, this means that the square of any planet’s orbital period (in Earth-years) is equal to the cube of its average distance from the Sun (in AU). The Earth’s mass is very nearly 6 million billion billion kilograms (or 6 thousand billion billion tonnes), hence the convenience of comparing other planets to the Earth rather than quoting standard scientifi c units such as kilograms, seconds, and metres.

Rotation period is how long it takes a planet to spin once on its axis. For a rapidly spinning planet, this is almost the same as the time from one sunrise to the next (the planet’s own ‘day length’),but the relationship is not exact because a planet’s orbital motion continuously changes the direction between planet and Sun. The Earth’s rotation period is 23 hours and 56 minutes, but it takes exactly 24 hours to rotate far enough to bring the Sun back to the same point in the sky. From a planet’s perspective, the Sun migrates completely round the sky during the course of a single orbit, in addition to the changing direction towards the Sun from any point of the planet’s surface caused by the planet’s rotation.A planet whose rotation had become tidally locked so that it rotated exactly once per orbit (synchronous rotation) would keep one face permanently towards the Sun. Mercury does not quite do this, but rotates exactly three times during the course of two orbits,as a result of which it turns relative to the Sun once per two orbits,so its day is twice as long as its year.

Table 2　Some properties of the planets compared. Distance from the Sun refers to average distance. Years and days are Earth-years and Earth-days. See Table 1 for sizes

There is a change in character between the four inner planets and the four outer ones. The inner planets (Mercury, Venus, Earth, and Mars) are relatively small and low in mass compared to the outer four (Jupiter, Saturn, Uranus, and Neptune). There is also a contrast in their densities, the inner planets being denser than the outer ones.The inner planets are called the ‘terrestrial planets’, signifying that they are all ‘Earth-like’. The outer four are the ‘giant planets’. Some call them ‘gas giants’ to refl ect the fact that they have so much hydrogen and helium. Others reserve that particular term for just Jupiter and Saturn, which are more gassy than the other two, though even those each contain more than one Earth-mass of gas.

Figure 1 is a map of the Solar System, showing orbits to scale,except that the orbits of Venus and Mercury are too small to include. Part of Pluto’s orbit is shown, to help with discussion later. Something that I have not yet mentioned, but without which such a map could not be drawn, is that planetary orbits all lie approximately in the same plane. Relative to the Earth’s orbit,which makes a convenient reference plane known as the ‘ecliptic’,Pluto’s orbit is inclined at 17.1°, Mercury’s at 7.0°, Venus’s at 3.4°,and all the others at less than 3°.

1.Map of the Solar System, showing planetary orbits at the correctrelative sizes. Orbits are only slightly eccentric, so look virtuallyindistinguishable from circles. The unlabelled circle inside Mars’sorbit is the Earth’s orbit, not the Sun! The orbits of Venus and Mercuryare too small to include. Pluto is not a planet, but its orbit is shownbecause it is representative of a large number of small bodies beyondNeptune’s orbit

When Pluto is near perihelion, it is inside the orbit of Neptune,but there is no prospect of them colliding. Their differing orbital inclinations prevent their paths from intersecting, and moreover Neptune is always on the opposite side of the Sun whenever Pluto passes inside Neptune’s orbit. This is possible because for every three orbits completed by Neptune, Pluto completes exactly two.Such a relationship is referred to as 3:2 orbital resonance.

As well as their orbits being nearly coplanar, every planet goes the same way round the Sun: they travel anticlockwise as seen from an imaginary vantage point far above the Earth’s north pole.Anticlockwise motion is also manifested in the direction in which each planet except Venus and Uranus rotates on its axis. Because anticlockwise motion is so common, it is called ‘prograde’.Clockwise orbital motion or rotation is regarded as backwards and is referred to as ‘retrograde’.

With the exception of Uranus, the axis about which each planet rotates is less than 30° away from being at right angles to its orbital plane. Mercury is nearly ‘perfect’, with a tilt of only 0.1°,whereas Earth’s axis is tilted at 23.5°. The direction in which a planet’s axis points and the amount of tilt both vary when measured over tens of thousands of years, but they are effectively constant on the timescale of a single orbit. Axial tilt is why planets have seasons; on Earth, summer occurs in the northern hemisphere during that part of the orbit when the north end of the Earth’s axis is tilted towards the Sun, and northern winter is six months later when the Earth is on the other side of the Sun, so that the north end of the axis is tilted away from the Sun. Of the two planets that don’t conform, Venus’s axis is tilted at only 2.7°but it rotates very slowly in the retrograde direction (giving it a day length of 116.7 Earth-days), whereas Uranus’s axis is tilted by82.1° with rapid retrograde rotation. Uranus probably suffered a catastrophe that knocked it over, having started with prograde rotation that became tipped over by 97.9° (97.9° being 180° minus82.1°). This would result in the present situation without calling on a separate event to reverse its direction of spin.

Satellites of planets

All planets except Mercury and Venus have satellites, or ‘moons’.These are smaller bodies close enough to orbit the planet rather than the Sun. Strictly speaking, a planet and its satellite each orbit their common centre of mass (or ‘barycentre’). However, planets are so much more massive than their satellites that their barycentre is inside the planet, and it is usually perfectly adequate to regard satellites as going round their planet. Most satellites’orbits lie close to their planet’s equatorial plane and almost all the large ones have prograde orbits, which is defi ned as orbiting in the same direction as the planet’s spin.

The Earth’s satellite is, of course, the Moon (with a capital M).This is exceptional in being relatively large in comparison to its planet, having a diameter 27% and a mass 1.2% of the Earth’s. By coincidence, the Moon’s size and distance from Earth are such that it appears almost the same as the Sun, which is much larger but correspondingly further away. When the Moon passes exactly between the Earth and the Sun, it hides the Sun’s disk, causing a solar eclipse. If the Moon’s orbit round the Earth were exactly coplanar with the Earth’s orbit, there would be an eclipse every lunar orbit (that is, every month). However, the Moon’s orbit is inclined at 5.2° to the ecliptic, so eclipses are rare, occurring only when the Moon happens to pass between the Earth and the Sun at one of the two points where its orbit crosses the ecliptic.Unravelling the cyclic nature of these events and predicting when eclipses would occur (though without fully understanding the reasons) was one of the great achievements of Babylonian astronomers about 2,600 years ago. Lunar eclipses, when the Moon passes into the Earth’s shadow, are controlled by the same cycle, but are more common because the Earth’s shadow is considerably bigger than the Moon.

Mars has two tiny satellites. Jupiter has four exceeding 3,000kilometres in diameter (which are those that Galileo discovered),plus at the last count 59 others less than 200 kilometres (most less than 4 kilometres) across. Saturn has a similar total number of known satellites, though only one of them rivals Jupiter’s largest. Uranus has fi ve satellites between 400 and 1,600kilometres across and 22 known smaller ones, and Neptune has one large satellite and a dozen known small ones. Most of the small (few kilometres across) outer satellites of Jupiter and Saturn were discovered using telescopes (rather than by visiting spacecraft), and more tiny satellites of the giant planets surely remain to be found, especially at Uranus and Neptune, where detection by telescope is especially hard for two reasons: they are further from the Sun and so are less brightly lit, and they are further from the Earth and so would look fainter even if they were equally well lit.

The larger satellites are geologically very interesting and I say more about them later, but all satellites are useful for the planetary scientist because they enable their planet to be weighed.The orbital period of a satellite depends only on its average distance from the planet’s centre and their combined mass (which can be calculated using Newton’s gravitational elaboration of Kepler’s Third Law). Because satellites are so much smaller, the mass of the planet dominates almost entirely, in the same way that planets’ orbits round the Sun depend on distance and solar mass.

Asteroids, trans-Neptunian objects, and comets

This book is about planets, rather than the whole Solar System,but it is worth noting that objects of other types vastly outnumber the planets and their satellites combined, although admittedly these are small and their total mass is relatively insignifi cant.Although planetary scientists have come to realize that the boundaries are somewhat blurred, these ‘junk’ objects can be divided into three broad classes: asteroids, trans-Neptunian objects, and comets.

Asteroids range downwards in size from 950 kilometres across(the diameter of Ceres, the largest example), with no lower limit.Asteroids only a few tens of metres across have been detected as they pass close by the Earth, and the remains of smaller ones that fall to the ground can be found as meteorites. Formerly assumed to be fragments of a destroyed planet, we now think that asteroids never belonged to a planet-sized object. The total mass of all the asteroids is probably less than a thousandth of the Earth’s mass.Some have clearly experienced mutual collisions, as attested by their irregular shapes.

Without exception, asteroid orbital motion is prograde. Most have orbital inclinations of less than 20°, but eccentricity is typically greater than for planets. The orbits of most asteroids lie between those of Mars and Jupiter (the so-called ‘asteroid belt’), but some come much closer to the Sun, passing inwards of the Earth and even (in a handful of examples) inwards of Mercury. A few asteroids are known orbiting beyond Saturn. Like the meteorites derived from them, most asteroids are stony or carbonaceous in composition, but some are made of iron and nickel. So far as we can tell, asteroid composition tends to be less stony and more carbonaceous and eventually icier with distance from the Sun.

Beyond the orbit of Neptune, between about 30 and 55 AU from the Sun, small icy bodies become common, and there are several that exceed the largest asteroids in size. This region is usually called the ‘Kuiper belt’, named after the Dutch-American Gerard Kuiper who predicted it in 1951 as a zone where icy lumps should be left over from the birth of the Solar System. An Irishman,Kenneth Edgeworth, said much the same in a more obscure journal in 1943, so some prefer to call this the ‘Edgeworth-Kuiper belt’. The fi rst Kuiper belt object to be discovered and recognized as such was found in 1992, but now many hundreds of them have been catalogued, and it has become clear that Pluto should be numbered among them. Similar objects with perihelion not far beyond Neptune’s orbit but reaching about 100 AU at aphelion are counted as ‘Scattered Disk’ objects. Together with the Kuiper belt,these make up a family called ‘trans-Neptunian objects’, or TNOs,all in prograde orbits. The total mass of TNOs is probably around200 times that of the asteroid belt (one-fi fth of an Earth-mass),and in total there may be nearly 100,000 bodies more than 100kilometres in size. One ‘Scattered Disk’ object discovered in 2005and subsequently named Eris seems to be marginally bigger than Pluto. We can be more confi dent about their masses because they both have satellites with well-documented orbits, showing that the mass of Eris is 28% greater than that of Pluto.

Comets have been known since antiquity because a comet can briefl y look very spectacular, thanks to the development of a tail of gas and dust that can stretch across the sky when the comet passes close to the Sun. However, the solid part of a comet is just a chunk of dusty ice (famously described as a ‘dirty snowball’), only a few kilometres across in most cases. A comet spends most of the time far from the Sun, and develops a tail only when it passes close enough for the Sun to warm it. This happens rarely because comets have extremely eccentric orbits with perihelion usually inside the Earth’s orbit but aphelion near or well beyond Jupiter’s orbit. Some come from so far beyond that their orbits look like parabolas (infi nitely long ellipses), and make only one passage close to the Sun throughout recorded history. Those are ‘long-period’ comets,and appear to have been dislodged from an ill-defi ned shell surrounding the Sun at about 50,000 AU known as the Oort Cloud. In contrast, ‘short-period’ comets probably originated as Scattered Disk objects that were perturbed into an eccentric orbit with a small perihelion distance by a close encounter with a fellow object. Those with orbital periods of hundreds of years still have their aphelion in the Scattered Disk, but aphelion can be nudged closer to the Sun as a result of a close encounter with a giant planet. For example, Halley’s comet has aphelion near Neptune’s orbit, and an orbital period of 75 years, whereas Encke’s comet has aphelion near Jupiter’s orbit and a period of only 3.3 years. Comets lose mass by degassing every time the Sun’s heat warms them, so after fewer than a thousand perihelion passages a comet is probably reduced to an inert aggregate of ice-free rock and dust, hard to distinguish from an asteroid.As you might expect, given their source, the orbits of ‘short-period’comets are prograde and tend to be close to the ecliptic. However,no such restriction applies to long-period comets whose orbits can be highly inclined or even retrograde.

What is a planet? How Pluto came to be thrown out of the club

The fi rst TNO to be discovered was Pluto, in 1930. Even after Pluto’s small size became apparent (and subsequently, thanks to the discovery of its largest satellite in 1978, its small mass), people tended to think of Pluto as the ninth planet. However, when the known population of the Kuiper belt blossomed into hundreds of objects, several of which rivalled Pluto in size, it became increasingly anomalous to classify Pluto as a planet and yet other Kuiper belt objects as something different. When Eris was confi rmed to be more massive and probably larger than Pluto,then logically either all the large TNOs had to be called planets, or none of them. However, many people argued to retain Pluto as a planet on sentimental or historical grounds.

Decision-making was hampered by the fact that the term ‘planet’had never been fully defi ned. Eventually, at a meeting of the International Astronomical Union held in Prague in 2006, during which passions ran high, delegates voted to accept some defi nitions that have largely settled the issue. Two criteria for planethood were non-controversial: the IAU ruled that, fi rstly, a planet must have suffi cient mass for its self-gravity to overcome ‘rigid body forces’ so that it assumes a hydrostatic equilibrium (nearly round) shape, and secondly that it must be in orbit about the Sun. This second criterion rules out large satellites such as our own Moon.

A third criterion was the crucial one. It states that to be counted as a planet, a body must have ‘cleared the neighbourhood around its orbit’ of everything except much smaller objects. This is the test that Pluto fails. Pluto has not cleared its neighbourhood, because it shares it with many bodies of similar size and indeed also with the vastly more massive Neptune. On the other hand, Neptune does pass the test, because it is many thousands of times more massive than anything else in the same orbital region (such as Pluto).

Having taken the bold but entirely logical step to expel Pluto from the planetary club, the IAU seems immediately to have regretted it, and invented not one but two new classes for it to belong to. At the 2006 Prague meeting, the newly coined term‘dwarf planet’ was defi ned as ‘a celestial body that is in orbit round the Sun, has suffi cient mass for its own gravity to pull it into a nearly round shape, has not cleared the neighbourhood of its orbit, and is not a satellite’. Determining whether or not shape is ‘nearly round’ is diffi cult to do remotely, and controversial to defi ne, but in adopting this defi nition the IAU gave Pluto, Eris, and Ceres (the largest asteroid) the consolation prize of being called ‘dwarf planets’. At the time, it was acknowledged that other large TNOs would be ranked as dwarf planets when they had been adequately measured, and sure enough in 2008 a Kuiper belt object named Makemake(pronounced as four syllables), estimated to be about two-thirds the size of Pluto, was judged to pass the shape test and was admitted as a fourth dwarf planet, closely followed by a fi fth called Haumea.

The IAU seemingly came to regret having lumped Pluto-like objects in the same category as Ceres, and in 2008 invented a new term, ‘Plutoid’, to denote trans-Neptunian dwarf planets. Ceres is thus the only dwarf planet that is not a Plutoid, and there is surely no undiscovered asteroid large enough ever to join it in that category. However, there are probably numerous undiscovered or inadequately documented large TNOs that will join Pluto, Eris,Makemake, and Haumea as both Plutoids and dwarf planets.Incidentally, Eris is named (appropriately, considering the controversy that it caused) after a classical Greek goddess of discord, whereas Makemake and Haumea are named after Pacifi c island fertility deities.

How it all happened

Growing planets

Until recently, it would have been possible to argue that planets are rare in the cosmos, but it now seems clear that planets are a usual by-product of star formation. The existence of our Solar System is thus a consequence of the origin of the Sun itself.

A star is believed to form when a vast interstellar cloud made mostly of hydrogen, but mixed with a few other gases and tiny solid particles referred to as dust, contracts under the infl uence of its own gravity. As the cloud contracts, most of the matter becomes concentrated into the centre, in a body that becomes increasingly hot because of the gravitational energy converted to heat by the process of infall. Eventually, the central pressure and temperature rise so high that hydrogen nuclei begin to fuse together to make helium, at which stage the central body can be called a star. The planets grow from some of the material left behind during the fi nal stages. Conservation of angular momentum causes any slight initial rotation of the cloud to speed up during contraction, and matter not incorporated into the star becomes concentrated into a disk in the star’s equatorial plane,rotating in the same direction as the star.

This rotating disk is where planets form. The one that gave birth to our Solar System is referred to as the solar nebula, ‘nebula’being Latin for ‘cloud’ and used by astronomers to denote any large mass of gas and/or dust in space. There are strong reasons for believing that the solar nebula’s composition was about 71%hydrogen, 27% helium, 1% oxygen, 0.3% carbon, and 0.1% each of nitrogen, neon, magnesium, silicon, and iron. Almost all the original dust in the solar nebula was probably vaporized by heat from the young Sun, but soon conditions in the nebula became cool enough for new dust grains to condense, not as individual elements but as compounds produced by chemical combination.Helium does not combine into chemical compounds, so the most abundant compounds that could condense involve either hydrogen or oxygen.

Thanks to the available elements and the local temperature and pressure, oxygen was able to bond with silicon and various metals to form a range of compounds called silicates in the inner part of the nebula. These are common minerals on Earth that crystallize when molten rock cools, but in the solar nebula they grew directly from gas. Hydrogen was incorporated into solid particles only where the temperature was low enough for hydrogen-bearing compounds to form, and for most purposes this seems to have been beyond about 5 AU from the Sun. At and beyond this so-called ‘ice line’, water (made of hydrogen plus oxygen) could condense as specks of ice. Further from the Sun, more volatile compounds formed where hydrogen bonded with carbon to make methane and with nitrogen to make ammonia, and carbon with oxygen to form either carbon monoxide or carbon dioxide. At about 30 AU, it was cold enough for nitrogen to condense as solid particles of pure nitrogen. By one of the quirks of planetary science vocabulary, any solid made of water, methane, ammonia,carbon monoxide, carbon dioxide, or nitrogen (or indeed any mixture of these) is referred to as ‘ice’, recognizing similarities in origin and properties. This means that, to avoid ambiguity,planetary scientists have to specify ‘water-ice’ when referring specifi cally to frozen water – a complication that rarely arises on Earth, where temperatures are too high for compounds more volatile than water to freeze naturally.

Condensation happened in such a way that the fi rst dust grains –microscopic specks made of silicates close to the Sun and ices(plus some leftover silicates) further from the Sun – did not grow as dense, rigid specks. Instead, they had intricate ‘fl uffy’ shapes,and when these bumped into each other, they tended to stick together rather than bouncing apart. Within as little as ten thousand years after the onset of condensation, the particles could have grown into globules about a centimetre across through the combined effects of continuing condensation and accretion (sticking together) when they collided. After perhaps100,000 years, the Solar System would have consisted of hordes of bodies about 10 kilometres across, dubbed ‘planetesimals’.These were all swirling round the Sun in the same, prograde,direction and enclosed in a diffuse haze made of the remaining gas and dust.

We know how long ago this happened, because some of the earliest grains survive unaltered inside meteorites. We can measure radioactive decay products within them to work out their age, which is a particularly memorable number: 4.567 billion years. The most ‘primitive’ meteorites, which are fragments of small planetesimals that never suffered heating or alteration, are called ‘carbonaceous chondrites’ and are our most direct evidence of conditions in the early Solar System.

Hitherto, collisions had been essentially a matter of chance, but once planetesimals reached about 10 kilometres in size, the greater gravitational pull of the largest ones was able to make itself felt. These suffered more frequent collisions, so their rate of growth outpaced that of the others. Within a few more tens of thousands of years, the largest planetesimals had grown to a thousand or so kilometres across, gobbling up most of the smaller ones in the process.

These large planetesimals are dignifi ed by a new name: ‘planetary embryos’. Maybe a few hundred were formed in the inner Solar System. They would have been massive enough for their own gravity to pull them into spherical shapes. They may have been hot enough internally for melting to occur, allowing iron to sink inwards to form a distinct core, but that is largely immaterial because of what happened next.

These planetary embryos were what the terrestrial planets formed from. Now that the majority of the small stuff was gone,signifi cant growth could happen only when two embryos smashed together. Such a collision is referred to as a ‘giant impact’, and liberates enough heat to largely melt the merged body formed by the collision. Imagine a sphere of molten rock, glowing red hot except for a few rafts of chilled clinker on its surface, with deep inside a ‘rain’ of iron droplets settling inwards through the silicate magma to accrete onto the central core, and you should have a picture in your mind that conveys the state of a planetary embryo in the aftermath of a giant impact.

This assumes that the impact doesn’t smash both bodies to smithereens, but inevitably a certain amount of debris will be thrown out to space as ejecta from the collision. It probably took about 50 million years to build up an Earth-sized planet by serial giant impacts between planetary embryos. Because of the randomness of the collisions and the complex ‘family tree’ of giant impact collisions between bodies that themselves had been formed by giant impacts, it is meaningless to regard any single embryo early in the process as ‘the proto-Earth’ or ‘the proto-Venus’.

Beyond the orbit of Mars, the gravitational effect of the young Jupiter was strong enough to stir the rocky planetesimals into more eccentric orbits, so that mutual collisions were often too violent to allow growth by accretion. Instead, fragmentation was a common outcome, so large planetary embryos that might have eventually collided to produce a fi fth terrestrial planet were unable to grow here. Today, in that region, we fi nd most of the asteroids, representing only a tiny fraction of the mass that once existed there. Jupiter scattered the majority into markedly eccentric orbits, so that eventually most collided with Jupiter or another giant planet, or were ejected from the Solar System entirely.

The bodies from which the giant planets formed had a high proportion of ice as well as rock within them. There, beyond the‘ice line’, the growing planets had much more material to draw upon. The role of embryo–embryo collisions is uncertain, and so is the mechanism by which they acquired so much gas. One theory is that after they had exceeded 10 or 15 Earth-masses, their gravitational pull was suffi cient to scavenge huge quantities of whatever gas survived in the remaining nebula, and so their rocky and icy kernels became encased within deep gassy envelopes.Another school of thought holds that gravitational instabilities in the nebula caused each giant planet to grow inside a particularly dense knot, where the gas was naturally confi ned about the growing planet.

Opinion is also divided over the relative rates of planetary growth in the inner and outer parts of the Solar System, and it is unclear whether Jupiter formed before or after the Earth and Venus.However, if they grew by embryo–embryo collisions, Saturn,Uranus, and Neptune must have grown more slowly than Jupiter because collisions should be less frequent with increasing distance from the Sun.

Scavenging of gas from the nebula was terminated when the Sun entered its ‘T Tauri’ phase, named after the star T Tauri which is undergoing this process today. For perhaps 10 million years, a strong outfl ow of gas from the star, called the ‘T Tauri wind’, blows away all the remaining gas and dust. A likely reason for Uranus and Neptune having proportionally less gas than the other giant planets is that they took longer to grow, leaving less time to collect gas before the T Tauri wind put an end to the process.

Migrating planets

A further matter of debate concerns ways in which orbits can change over time and the extent to which this happened,particularly among the giant planets. Until the solar nebula was dispersed, gravitational interactions between nebular material and large orbiting bodies would tend gradually to decrease the radius of their orbits, causing embryos and young planets to migrate inwards. After nebular dispersal, gravitational interactions between planets and smaller bodies could have played an even more dramatic role. Some suggest a period of half a billion years or so when the outermost giant planet was defl ecting the orbits of outlying icy planetesimals inwards, where they would be likely eventually to be nudged further inwards by interaction with the next giant planet, and so on until they passed close enough to Jupiter for Jupiter to fl ing them outwards. These out-fl ung icy planetesimals could be the origin of today’s Oort Cloud. Jupiter must have moved fractionally closer to the Sun each time it fl ung a body outwards, but conversely the other giant planets would have been nudged outwards each time one of them swung a lump of ice inwards.This story has Jupiter migrating inwards, while Saturn, Uranus,and Neptune migrated outwards. It is even possible that Uranus and Neptune swapped places (providing an opportunity for Uranus’s axis to become tipped over into its present state).Today’s TNOs are those that survived beyond the zone swept clear during Neptune’s outward march.

Please do not form the impression that the orbit of a planet is capable of changing either rapidly or dramatically. Claims that Venus and/or Mars passed close to the Earth during biblical times,triggering various myths and natural disasters, are completely untenable. The outer planet migrations I have described happened extremely slowly, and as a result of cumulative interactions with nebular gas and with vast numbers of small bodies that are no longer available.

Nevertheless, the planets and their mutual gravitational pulls are continuously changing confi guration. Chaos theory says it is therefore impossible to predict planetary positions more than a few million years ahead. However, it can be shown that the Solar System is suffi ciently stable that no planet is likely to collide or be ejected in the next few billion years. We are probably safe for at least 5 billion years, which is when astronomers expect the Sun to swell up into a red giant, whereupon the wanderings of Mars will be the least of the problems faced by any far future Earthlings.

Why all the satellites?

By now, you should not be surprised that there is no straightforward answer to the question of whether satellites somehow grew alongside their planets or were acquired later.The large prograde satellites of the giant planets are the easiest to explain. They are thought to have formed within a cloud of gas and dust surrounding each giant planet as it grew, rather like a miniature version of the solar nebula. Tiny prograde satellites only a few kilometres in size orbiting close to giant planets are probably fragments of larger satellites that came too close and broke apart. The outer satellites of giant planets are mostly in retrograde orbits, and these are probably captured bodies that began as asteroids, TNOs, or comet nuclei.

Theoretically, it is almost impossible for a planet to capture a passing visitor into orbit about itself. An incoming smaller body will be swung past a planet by the pull of its gravity, but it can’t easily be slowed down enough to be captured into orbit. However,if the visitor is a double object, one of the pair can be captured by transfer of momentum to the other member, which will scoot away even faster after the encounter. A currently favoured explanation for Neptune’s large retrograde satellite, Triton, is that Triton was formerly half of a double TNO that strayed close to Neptune. This seems plausible, because several TNOs are known to be twin bodies. Mind you, it leaves unresolved the issue of why so many TNOs (and indeed asteroids too) have satellites in the fi rst place.

The Earth’s Moon has a different explanation, and seems to have condensed from debris thrown into orbit about the Earth by the fi nal embryo–embryo collision of the series by which the Earth grew. The two tiny satellites of Mars (Phobos and Deimos) are asteroids, whose capture into close circular orbits is not understood.

Collisions and the cratering timescale

Although collisions between substantial objects are now extremely rare, there is still a large number of small objects that could eventually collide with a planet. Until about 3.9 billion years ago(an epoch called the ‘late heavy bombardment’), the rate at which asteroids and comets were hitting planets was much higher than today. Impact craters of that age are well preserved on the Moon( Figure 2 ), though cratering has continued at a slower rate ever since. An impact crater forms on a solid body when something hits it at a few tens of kilometres per second, and is excavated by shockwaves that radiate from the point of impact. Craters are circular, except for rare examples when the impacting body arrives at a grazing angle.

There is a well-understood hierarchy of crater morphologies depending on diameter, and which can be reproduced experimentally and in computer models. On the Moon, craters from microscopic size up to 15 kilometres across have simple bowl shapes.Then up to about 140 kilometres diameter, craters do not become deeper but have fl at fl oors, and usually a central peak formed by rebound immediately after excavation. There is a nice example near the top of Figure 2 . Larger craters may have a group of central peaks,and then craters bigger than 350 kilometres take the form of two or more concentric rings. The transitions from one type to another occur at slightly smaller diameters on bodies with stronger gravity.

Earth’s cratering record is poorly preserved, because it is an active planet where processes that erase or bury craters almost keep pace with the rate at which craters are formed. Fortunately, the vast tracts of ancient terrain surviving on the Moon allow us to count the density of impact craters on surfaces whose ages are known,thanks to datable samples returned to Earth by the Apollo programme of manned lunar landings, supplemented by a few Soviet unmanned sample-return missions. By this means, we know the date of the late heavy bombardment and also the average rate at which cratering has affected the Moon ever since.The Earth must have been exposed to the same fl ux of impactors as its satellite, and there are good reasons for believing that this is also a reasonable approximation for Mercury, Venus, and Mars.Counting craters is thus the best way we have to estimate ages on planetary surfaces. Even if the absolute age is in doubt, it is usually safe to assume that a surface with a lower crater density is younger than one with a higher crater density.

2.A 470-kilometre-wide view of a heavily cratered region of the Moon.Most of these craters date from about 3.9 billion years ago, obliteratingany older craters. Each crater was formed by the impact of a bodyabout 20 to 30 times smaller than the crater itself. Parts of the Earthwould once have looked similar

At present, the Earth is hit annually by about 10,000 meteorites greater than 1 kilogram, but most of those are too small to survive passage through the atmosphere, where they are heated and worn away by friction. The yearly supply of 1,000-kilogram meteorites is only about 10, and the average interval between impacts by150-metre-diameter objects (which would produce a crater some 2kilometres across) is about 5,000 years. Impactors about1 kilometre in diameter arrive at random about once every200,000 years, boring through the atmosphere as if it were not there, hitting the ground with undiminished speed, and forming a crater perhaps 20 kilometres across. Larger, and more devastating,impacts are even less frequent.

Collisions affect each body in the Solar System, but craters survive only where there is a solid surface and insuffi cient other activity to erase the record. Observers were fortunate to discover a string of fragments of a tidally disrupted comet shortly before they collided with Jupiter in July 1994. Several of the collisions were witnessed,and each left a brown scar in the giant planet’s atmosphere that lingered for several weeks, as did a scar found in July 2009 made by an unobserved single impact.

Planets as abodes of life

If Earth were not at a comfortable distance from the Sun, you would not be reading this book, because life may not have become established and we could not have evolved here even if it had.Scientists talk of a ‘habitable zone’ around every star, at a distance where the surface temperature on a planet would be neither too hot nor too cold for life. By analogy with Goldilocks’ preference for baby bear’s porridge (whose temperature was ‘just right’), the habitable zone is sometimes called the ‘Goldilocks zone’. In this context, ‘habitable’ means somewhere that could sustain life of any kind, even just simple microbes. It does not imply that the environment would be inhabitable by humans.

Because our kind of life requires water, the habitable zone is usually equated with the distance from a star at which the surface temperature of a planet would enable water to exist in liquid state.The density and composition of a planet’s atmosphere infl uences the surface temperature, but the main control is heat received from the star. The habitable zone around the Sun is estimated to extend from about 0.95 to about 1.5 AU. These estimates put Venus (0.72 AU) well inward of the inner edge of the habitable zone, and Mars (1.52 AU) at its outer fringe. The Sun’s output has probably increased slightly since the planets were formed,nudging the habitable zone outwards over time, so Mars would seem to be a poor candidate for life, but it is not a hopeless case.

The idea of a habitable zone defi ned by planetary surface temperature has been criticized as too narrow. There are circumstances where heat generated within a planet may provide an environmental niche suitable for life, although the surface may seem inhospitable. Even on Earth, we know of ‘extremophile’organisms living below 0 °C or above 100 °C. Thus, even if all life is, like that on Earth, based on chains of carbon molecules and dependent on water as a solvent, there are several places in the Solar System where it could exist (though only one, the Earth,where it is known to exist) and at least many millions of habitable places elsewhere in the galaxy. I shall return to that theme near the end of the book.

Space exploration

Telescopes are very useful, for example to measure the temperature and composition of a planet’s surface and atmosphere. The polar ice caps on Mars were correctly identifi ed by William Herschel as long ago as 1781. Jupiter is suffi ciently large and close that storms among its clouds can be monitored even with fairly modest telescopes. However, this book would be duller and more speculative were it not for half a century of space exploration when space probes from Earth have visited every planet in the Solar System. Soviet probes reached the Moon in1959, and twelve American astronauts walked on its surface between 1969 and 1972. Unmanned American (NASA) and Soviet probes fl ew past Venus and Mars in the 1960s, and achieved orbit and soft landings during the 1970s. The fi rst Jupiter and Saturn fl y-bys were in the 1970s, and the other giant planets were visited in the 1980s. Since 1990, the terrestrial planets have been explored by increasingly capable orbiters, robotic rovers have crawled across the Martian surface, and complex orbital tours of both Jupiter and Saturn have been achieved.

The most famous missions include Vikings 1 and 2 that landed on Mars in 1976; Magellan that mapped the surface of Venus by radar 1990–4; Voyagers 1 and 2 that fl ew past the giant planets between 1979 and 1989; Galileo that orbited Jupiter between1995 and 2003; and Cassini that began an orbital tour of Saturn in 2004 and sent a probe named Huygens to the surface of Titan in 2005.

Highlights in the years ahead include return to Earth of samples collected from Mars, asteroids, and comets, and a renewal of human presence on the Moon. The USA and Russia are no longer the only space powers. The European Space Agency has gone solo to Mars and Venus, to Saturn jointly with NASA, and will soon go to Mercury with Japan. The Japanese have sent probes to the Moon and to an asteroid, and China and India have each reached the Moon. Scientifi cally, there has been much cooperation (and most probes carry instruments contributed by several nations),but it is undeniable that there is also national pride at stake,together with long-term strategic and commercial interests.

Chapter 2　Rocky planets

Here,I will discuss the planet that we live on and other bodies like it, namely the three other terrestrial planets Mercury,Venus, and Mars, and also the Moon. To the astronomers of the IAU, the Moon is just a satellite, but its composition and internal structure place it among the terrestrial planets from the perspective of a geologist or geophysicist. Figure 3 shows these five at the same scale, and Table 3 lists some relevant data. Within this group, Mercury and the Moon have effectively no atmosphere. Venus has only slightly lower size, mass, and density than the Earth, so gravity at its surface is only slightly less than on the Earth. However, its atmosphere is considerably denser. Mars is larger than Mercury but less dense. These two effects offset each other so that their surface gravities are very similar, but being colder, Mars has been able to hold on to a thin but respectable atmosphere. The Moon has the lowest surface gravity of all – about one-sixth of the Earth’s – which is why Moon-walkers bound around so strangely. Mean surface temperatures obscure wide variations with latitude and, in some cases, between day and night. For example, the hottest daytime temperature on Mercury exceeds 400 °C, whereas at dawn after a long Mercurian night the temperature is below –180 °C.

Table 3　Basic data for the terrestrial planets

3.Top: from left to right, Mercury, Venus, Earth, Moon, and Mars,shown at the same scale. Bottom: the much larger giant planetsJupiter, Saturn, Uranus, and Neptune, with the terrestrial planetsinserted to the same scale

Cores

Terrestrial planets are distinguished by having rocky exteriors,made largely of silicate minerals. However, their densities are too great for them to be rocky throughout, and it is believed that each has an iron-rich core at its centre. No planet’s core can be seen or sampled directly, but there are several independent lines of evidence. Density is one, showing that the interior must be denser than rock even allowing for internal compression at high pressure,and analyses of the trajectories of orbiting spacecraft show that density increases symmetrically about each planet’s centre.Chemical models for what is likely to happen inside a rocky planet suggest that there is insuffi cient oxygen for all the iron to be oxidized and bound up in silicate minerals. Thus, if the interior had ever been molten this would have allowed metallic iron,which is denser than rock, to sink towards the centre. This is an example of a processes called differentiation.

The outer parts of the iron-rich cores of the Earth and Mercury must be molten today, because those two planets have strong magnetic fi elds, apparently generated by dynamo motion in an electrically conducting fl uid. For such a small planet, Mercury’s density is very high, so its core must be exceptionally large,occupying about 40% of its volume and accounting for nearly 75%of its mass. Magnetic fi elds are not being generated inside Venus,the Moon, and Mars, so their cores are probably entirely solid.

In the case of the Earth, we have additional evidence about the core from studying how seismic waves, which are vibrations triggered by earthquakes (or underground nuclear tests!), travel through the planet. This confi rms a solid inner core 1,215 kilometres in radius and a fl uid outer core 3,470 kilometres in radius. Both seem to be mainly iron alloyed with 5%–10% nickel, but density arguments require something less dense than iron too, making up 6%–10% of the outer core and 2%–5% of the inner core. The likeliest explanation is some mix of oxygen, silicon, and sulfur.

In total, the Earth’s core occupies about 16% of the planet’s volume. Comparable values for Venus and Mars, which are estimates based largely on their average densities, are about 12%and 9%, respectively. There are some very limited seismic data from the Moon (from the Apollo programme), hinting at a relatively small core between about 220 and 450 kilometres in radius (less than 4% of the Moon’s total volume). About 1 in every20 meteorites is made of an alloy of iron with 4.5%–18% nickel,corresponding to the cores of planetesimals from the asteroid belt that had differentiated internally before being broken up by collisions.

Mantles and crusts

The silicate part of a terrestrial planet surrounding its core is called the mantle. This makes up the majority of the total volume of each terrestrial planet, and most of their mass except for

Mercury. The crust is a relatively minor unit overlying the mantle.It is also of silicate, though slightly different in composition to the mantle.

A planet’s present mantle evolved from the molten rock that would have covered the globe after the fi nal giant impact collision,known to geologists as a ‘magma ocean’. While a magma ocean cools, its surface must radiate heat to space, causing it to chill to a solid skin. However, this skin would continually be broken and stirred back in, thanks to turbulence below and impacts from above. The magma ocean would continue to cool, but, unlike the freezing of a ball of water, there is no discrete temperature at which the whole of it would become solid. The nature of molten silicate material is such that minerals of various compositions crystallize out at different temperatures and pressures. Planetary scientists are unsure of the extent to which magma oceans crystallized in layers, or whether minerals denser than the melt were able to sink while less-dense minerals were able to rise,perhaps sticking together to form massive ‘rock bergs’ that could force their way up more effectively.

Aggregations of this flotation material, chemically different to the underlying magma ocean, formed the earliest true crust on the Moon, where it survives today as the lunar highlands (the pale areas on the Moon’s face). On the larger terrestrial planets, the nature of the oldest crust has not been determined, partly because it has largely been replaced (or, at least, covered over) by later kinds of crust. To see how this might happen, we have to turn our attention back to the mantle. As a young planet cools, eventually its mantle becomes fully solid. Two important characteristics of silicate materials now become relevant. The fi rst is that suffi ciently hot solids are neither completely immobile nor undeformable. Hot rock in a planet’s interior is capable of fl owing at speeds of a few centimetres per year (the rate at which your fi ngernails grow), in much the same way as a block of pitch will deform over time. Within a solid mantle, motion will occur at a slow but geologically effective pace if there are any forces capable of driving it. Inside a planet, the necessary impetus comes from heat. Hotter mantle from deep down will be slightly less dense than the cooler mantle above, so there is a tendency to swap places. Motion of this sort is called convection, and is what you can observe in a pan of soup heated on a hob, except that within a planet it is much slower ‘solid state convection’.

Imagine a streamer or ‘plume’ of hot mantle welling upwards and displacing colder mantle downwards. As it gets closer to the surface, the pressure experienced by the rising mantle decreases,which brings into play the second relevant characteristic. As pressure falls, silicates begin to melt. The process is called ‘partial melting’, because only part of the solid melts, and the magma that forms is slightly richer in silica than the solid from which it was extracted. The resulting magma is also less dense than the solid,so buoyancy forces will squeeze it upwards towards the surface,especially if there are pathways where the overlying rock is under tension or fractured. Unless it stalls below ground as an intrusion,the magma will be erupted through volcanoes.

Rock formed in this way is described as igneous, and crust produced by igneous activity can replace the original crust of a planet by infi ltration or burial. The dark patches on the Moon, the lunar ‘maria’, are low-lying regions where the paler primary crust has been buried by lava fl ows produced in this way. The presentday crust of the Earth results from partial melting of the mantle to make oceanic crust, and from melting and recycling of many generations of oceanic crust to make continental crust. The Earth’s oceanic crust is 6–11 kilometres thick, whereas continental crust varies from about 25 kilometres in thin, stretched regions to90 kilometres below major mountain ranges. In total, crust occupies only about 1% of the Earth’s total volume. The Moon’s crust averages about 70 kilometres in thickness (13% of the Moon’s volume), ranging from 〉100 kilometres in some highland regions to 〈20 kilometres below some major impact basins.

In summary, crust is chemically related to the underlying mantle, but differs in ways depending on how it was extracted from it. Crust is lower in density and its average composition is richer in silica than the mantle. Crust is more varied than mantle, and includes rock that has reacted chemically with any atmosphere or liquid water, and that has been broken apart or dissolved, transported (by gravity, wind, water, or ice), and deposited elsewhere. Such deposits constitute sedimentary rock.Burial, deformation, and heating can cause sedimentary or igneous rock to recrystallize, in which case it is known as metamorphic rock.

Internal heat

Planets are hot inside partly because of heat left over from their accretion. For a bigger planet, the fraction of this ‘primordial heat’remaining today is greater. This is because heat content is related to planetary volume, which depends on the cube of the radius,whereas heat leakage is limited by surface area, which depends only on the square of the radius.

Heat is also generated inside a planet, by decay of radioactive isotopes. There are many of these, but only four whose decay produces signifi cant heating: potassium-40, uranium-238,uranium-235, and thorium-232. Because of their geochemical affi nities, these elements are more abundant in crustal rocks than in the mantle. In the Earth, approximately the same amount of heat is generated radiogenially (that is, by radioactive decay) in the crust as in the whole of the volumetrically much larger mantle.

A terrestrial planet’s total content of heat-producing elements depends on its mass (and hence its volume). Just like primordial heat, radiogenic heat is retained more effectively in larger planets.In the case of the Earth, about half the heat leaking to the surface today is primordial, and almost all the rest is radiogenic.

Lithospheres

The transition in properties from cold and rigid to warm and convective generally occurs at some depth below the boundary between crust and mantle. Thus the crust and the uppermost mantle constitute a single mechanical layer, forming a rigid outer shell. This shell is called the ‘lithosphere’, using the Greek word lithos (‘rock’) to indicate that the layer has the mechanical properties of everyday rock. Below the lithosphere is where the mantle, although rocky in composition, is hot enough and weak enough to convect. This zone is sometimes called the asthenosphere (using Greek a-sthenos meaning ‘without strength’).

The Earth’s lithosphere is about 100 kilometres thick and is fractured into a number of plates, which are able to be shunted around thanks to the special weakness of the underlying asthenosphere. As part of a process known as ‘plate tectonics’, new lithosphere is created where plates pull apart (usually hidden from view below the ocean) and destroyed where one plate is drawn below another, at subduction zones marked by trenches on the ocean fl oor. The grinding of one plate against its neighbour is the cause of most earthquakes. If anyone tells you that the Earth’s plates are ‘crust sliding over the mantle’, they are wrong, repeating a persistent fallacy that appears in many school textbooks and examination syllabuses. The truth is that a plate consists of crust and the conjoined rigid uppermost mantle, which together slide across the deeper, less rigid, asthenospheric mantle.

The lithosphere, being brittle, is the layer where faults can occur,as one mass of rock grinds past another. Faults are common on the Earth, especially in the zones where two plates meet, and can be identifi ed on other planets too ( Figure 4 ).

Plate tectonics seems to be unique to the Earth. Greater lithospheric thickness in the more easily cooled smaller bodies of Mercury, the Moon, and Mars undoubtedly contribute to this, but a more important factor is that for plates to be mobile, the top of the asthenosphere needs to be especially weak. Within the Earth, this is accomplished because of a small amount of water within the rock, which weakens it and encourages the formation of a small amount of melt that lubricates grain boundaries. Venus has lost its water, so its asthenosphere is dry and lithospheric plates cannot slide freely across it.

4.A 500-kilometre-wide view of part of Mercury. Solar illuminationis from the right. Shadow picks out a kilometre-high scarp with theshape of an open letter M on its side. This is an ancient thrust faultnamed Beagle Rupes, marking where the terrain on the right (east) hasbeen pushed westwards over the terrain on the left (west). Some of thecraters are older and others younger than this fault

A planetary asthenosphere that is dry, or very deep, is manifested principally by two effects at the surface. One is the height of mountains and depth of basins. If these are too great, the asthenosphere will fl ow and fl ex the overlying lithosphere, thereby reducing the topographic contrast until it is small enough to be supported by the strength of the lithosphere alone. The second is the pattern of fracturing caused by large impacts. An impactor several tens of kilometres in diameter arrives with suffi cient force for the resulting crater-forming shockwaves to disrupt the lithosphere, and the crater will take the form of a basin marked by concentric rings of fractures. In a thinner lithosphere, the rings tend to be closer together, so these multi-ringed impact basins can be used to estimate the depth to the asthenosphere at the time of their formation. As a planet slowly cools, its lithosphere becomes gradually thicker.

Volcanism

Magma, the name given to molten rock before it erupts, can be generated inside a planet essentially by three different causes.Direct application of heat is only one of these, and is often the least important: slow build-up of heat trapped below a planet’s lithosphere may account for some episodes of widespread volcanism, and strongly varying tidal stresses inside a planetary body work against internal friction, leading to ‘tidal heating’.Alternatively, decreasing pressure in an upwelling zone in the mantle can cause partial melting (for example, leading to the generation of Earth’s oceanic crust). Also, it is possible that sudden reduction in pressure, as must happen to the mantle below where a major impact basin is excavated, could trigger a melting event. The third mechanism is to introduce water into the mantle or lower crust. Water reduces the temperature at which silicates begin to melt. The Earth has chains of volcanoes above subduction zones, because water that has been dragged down within the rocks of the subducting plate escapes upwards into the base of the over-riding plate. Here conditions are not hot enough for melting when dry, but partial melting will begin as soon as water is introduced even though there has been no rise in temperature.

The Moon

People began to speculate about volcanism on the Moon almost as soon as craters were seen through telescopes. They were on a false trail because, as we are now quite certain, almost all the craters on the Moon were made by impacts. In fact, the major volcanic areas of the Moon are the dark patches that were once thought to be dried-up sea beds. That is not the case, though they still bear the name ‘mare’ (pronounced mah-ray), which is Latin for ‘sea’. The plural is ‘maria’ (pronounced mah-ri-a). These cover about 17% of the Moon’s surface, mostly on the near side, which is the hemisphere that permanently faces the Earth. Here, lava with a composition similar to terrestrial basalt has fl ooded the major multi-ringed impact basins.

Specifi c vents where the mare basalts were erupted are hard to identify ( Figure 5 ). Clearly, they did not take the form of conical volcanoes. Most likely, they were fi ssures through which fountains of incandescent molten lava were expelled by the force of expanding volcanic gas to heights well in excess of a kilometre. On falling to the ground, the lava was still hot enough to spread out,fl owing downhill for hundreds of kilometres. Most of the fi ssure vents sealed themselves over as their rate of eruption waned, or were buried by later eruptions.

Four of the six Apollo Moon landings (1969–72) were on maria,which are fl atter and so safer places to land than the highlands.Samples of mare basalt brought back for analysis can be dated with high precision by measuring radioactive decay products within them (radiometric dating), and the Apollo samples show a range of mare ages from 3.9 to 3.1 billion years. This long duration of volcanism put paid to the simplest volcanic explanation for the maria, which was that the volcanism was a direct product of the basin-forming impacts. Furthermore, work since the year 2000has identifi ed some patches of mare bearing suffi ciently few superimposed impact craters that they must be younger than about 1.2 billion years. Conversely, in 2007 a fragment of lunar material found on Earth as meteorite (having previously been fl ung off the Moon as ejecta from an impact crater) was found to contain fragments of basalt dated at 4.35 billion years, half a billion years before the late heavy bombardment ended. No maria of such great age remain visible, having been buried by ejecta from subsequent basin-forming impacts. So now we know that lunar volcanism began early as well as fi nishing late.

5.A 200-kilometre-wide view of the south-east edge of Mare Imbrium.The rugged terrain on the right is highland crust uplifted in part of thebasin rim. The darker, smoother area in the upper left is mare basaltsthat have fl ooded the lower-lying ground. A 1-kilometre-wide trenchnamed Hadley Rille winds from south to north across the centre of theview, and this is believed to be a pathway along which lava fl owed froma source largely obscured by shadow. Apollo 15 landed close to HadleyRille, near the middle of the image

Mercury

Mercury is much less well known than the Moon. Under half of it was imaged by NASA’s Mariner 10 in 1974–5, and the planet then remained unvisited until NASA’s MESSENGER probe began a series of fl y-bys in 2008. This revealed details suffi cient to overcome most people’s scepticism over the extent of volcanism on Mercury. For example, in Figure 4 the smooth terrain in the lower right and fi lling the 120-kilometre-diameter basin just above right of centre is now accepted as volcanic.Previous doubts were heightened by the fact that Mercury lacks the contrast in albedo (refl ected brightness) between paler highlands and darker lavas that makes the maria so obvious on the Moon. This seems to be because the minerals making up Mercury’s lavas contain much less iron than is typical of lunar(and terrestrial) basalts. Plains formed by lava probably constitute the majority of Mercury’s surface. Some of them are old enough to date back to the era of the late heavy bombardment and are densely cratered, others are younger and have fewer craters superimposed on them.

MESSENGER imaged a few volcanic vents and also curious10-kilometre-sized blotches – some bright, some dark – that may be sites of particularly young explosive eruptions. How long Mercury stayed volcanically active is likely to remain unresolved until a spacecraft achieves orbit about Mercury and records images systematically and in better detail. The fi rst chance will be when MESSENGER begins the orbital phase of its mission in2011, and if the issue remains unresolved it should be settled by the European Space Agency’s BepiColombo mission that is due to arrive at Mercury in 2020. At present, it is safe to say that extensive areas of lava were emplaced during a period covering at least 4 to 3 billion years ago, and possibly extending to within the past billion years. Such a long duration of volcanic activity on Mercury was not anticipated, and may result from the same mysterious heat source that keeps part of its core molten.

Venus

Venus is much bigger than Mercury. Its size and mass would suggest almost as much radiogenic heat production as the Earth,and hence a similar level of volcanic activity. However, because Venus lacks plate tectonics, its volcanism operates rather differently.

Venus has a dense, permanently cloudy atmosphere, which kept the surface a total mystery until it became possible to study it by means of radar. Figure 6 shows a radar image of part of Venus obtained by NASA’s Magellan probe, which mapped almost the entire planet between 1990 and 1994. Radar images are assembled by complex analysis of the echoes bounced back in response to a continual string of radar pulses beamed at the surface. For most purposes, you can treat radar images like the black-and-white optical images that they resemble, though in fact the brightness of each feature is controlled mainly by how rough the local surface is, rather than its albedo in visible light.

Figure 6 typifi es much of Venus. It shows numerous individual lava fl ows – some rougher (brighter) and some smoother(darker) – that fl owed from west to east across the image. The lobate pattern of the individual fl ows closely resembles that of lava fl ows on Earth and Mars, but which is hard to discern on the Moon and Mercury where the fl ow margins have become degraded by impacts.

As well as lava fl ows covering about half its surface, Venus has many clearly identifi able volcanoes. Figure 7 shows an example. In the background is a 5-kilometre-high volcano with gently sloping fl anks of the kind known on Earth as a ‘shield volcano’ that results from repeated eruption of basalt through a single vent. Some individual lava fl ows can be made out on the fl anks. No one is sure how long ago this volcano and others like it last erupted. There have been intriguing hints but no proof of recent or present-day activity on volcanoes such as this, and they are rather too small for reliable crater-counting statistics. This particular volcano is built upon an older terrain unit that is smoother, except for numerous fractures upon it. The impact crater in the foreground is probably unrelated to radar-bright lava fl ows immediately to its left.

6.A 500-kilometre-wide Magellan image of part of Venus. The area ismostly lava, fed from a source 300 kilometres west of the image, but inthe south-east corner is some rugged terrain representing the oldestsurviving crust on Venus. Running from north to south in the west ofthe image is a mountain belt of ridged and fractured terrain that isbreached by the lava fl ows

Circular or elliptical patterns of concentric fractures termed‘coronae’, of which more than 300 have been identifi ed on Venus,are not thought to share a common origin with the multi-ringed impact basins of the Moon and Mercury. They can be anything from 200 metres to over 2,000 kilometres across, and are usually associated with some form of volcanism. Probably each corona marks a site where an upwelling plume in the asthenospheric mantle impinged on the base of the lithosphere. Coronae where the plume is still present are uplifted as very broad domes, whereas older ones, no longer supported by a mantle plume, have sagged. The sagging, in particular, explains the concentric fractures.

7. Computer-generated three-dimensional perspective view showing the volcano Maat Mons on Venus. This was made by draping a radar image over a model of the topography obtained by radar altimetry. Vertical scale is exaggerated tenfold. Both sets of data were collected by the　Magellan orbiter. The impact crater in the right foreground is 23 kilometres across

Impact craters on Venus are more common than on the Earth, but considerably less abundant than on the Moon and Mercury (you will not fi nd any in　Figure　6 ). There are two factors at play here. Craters less than about 3 kilometres across are entirely absent from Venus, because its dense atmosphere shields the surface from small impactors. However, larger craters are formed by objects carrying too much energy to be affected by the atmosphere. Their lack of abundance has to be explained by the young age of the surface, which works out on average to be between about 500 million and 700 million years. There are no large tracts of terrain that seem to be very much older or very much younger than the global average.

The standard explanation for this in the 1990s was that pretty much the whole planet was resurfaced in an orgy of volcanism that began 500–700 million years ago, and lasted no more than a few tens of millions of years. This would be consistent with Venus’s lack of plate tectonics leading to most heat from the deeper mantle being trapped below the lithospheric lid, until much of the uppermost asthenosphere had melted. Eventually, the cold, dense lithosphere would founder, and the buoyant magma from below would erupt. Something similar could have occurred half a dozen times since Venus was formed, and maybe it could happen again within the next 100 million years.

This model calling for catastrophic global volcanism has recently been challenged, on the grounds that the cratering statistics do not rule out a more gradual process. Progressively smaller areas could have been resurfaced by lavas at random intervals throughout the past half billion years.

Earth

On Earth, volcanism and plate tectonics combine to regulate the internal heat budget and thus prevent major asthenospheric temperature excursions of the kind postulated for Venus. Only about one-third of the heat generated below the lithosphere leaks out by conduction. Most of the heat is conveyed to the top of the lithosphere by eruption at mid-ocean ridges (where new material is added to diverging plates) and, to a smaller extent, by eruptions at volcanoes above subduction zones and at various ‘hot spots’ above mantle plumes. The asthenosphere is cooled by the reincorporation into it of the old, cold parts of lithospheric plates at subduction zones.

The closest we get to a Venus-like volcanic catastrophe is when, every few tens of million years, a region maybe a thousand kilometres across is buried by the eruption of up to ten cubic kilometres of basalt lava. This is known as a ‘fl ood basalt’. The ‘Deccan Traps’ of northwest India (66 million years), the Brito-Arctic fl ood basalts(Greenland and the north-western British Isles, 57 million years),and the Colombia River fl ood basalts (north-western USA, 16 million years) are among the better-known examples. These major but rare events could be capable of injecting so much volcanic gas, notably sulfur dioxide, plus fi ne fragments of volcanic rock known as ‘ash’,into the atmosphere that global climate could be severely affected.Figure 8 shows an example of lava fl ows on the Earth, for comparison with the images from other planets.

The way in which volcanism on the Earth probably differs most from the other planets is that expansion of gas within rising magma tends to make a substantial proportion of eruptions explosive in nature. This is for two reasons. The first is that recycled water, carbon dioxide, and sulfur dioxide escaping upwards above subduction zones adds greatly to the leakage from the deeper interior of primordial gases, so the Earth has more gas available to drive eruptions explosively. The second is that the existence of continental crust facilitates generation of magma with a higher silica content than basalt. These silicarich magmas are more viscous than basalt, so they fragment more easily. Classic ‘picture-book’ steeply conical volcanoes such as Mount Fuji in Japan are rare except on Earth, because they are symptomatic of relatively silica-rich and partly explosive eruptions.

8.A 70-kilometre-wide view from space showing the ‘Craters of theMoon’ lava fi eld in Idaho, USA. The source of the fl ows was a series offi ssures near the edge of the rugged highlands in the north-west.Compare the lobate form of the lava fl ows with the fl ows on Venus inFigure 6

Mars

Compared to the Earth and Venus, Mars has relatively few volcanoes. However, their small numbers are compensated by large size. Major groupings of large basaltic shield volcanoes occur in the Tharsis region (much of which is included in Figure9 ) and the Elysium region. Olympus Mons is the largest Tharsis volcano, measuring about 600 kilometres across its base and 24kilometres from top to bottom, which makes it the largest volcano in the entire Solar System. There are two reasons why Mars has such big volcanoes. The fi rst is that Mars is a ‘one plate planet’. Its lithosphere is an intact shell (a single plate)effectively stationary with respect to the underlying mantle asthenosphere. Unlike the Earth, where plates drift around relative to mantle plumes so that plume-fed volcanoes are carried away and cut off from their magma supply after only a few million years, a mantle plume on Mars supplies magma to the same spot in the lithosphere for as long as the plume remains active. Olympus Mons may have begun to be constructed more than a billion years ago. We have no way to tell, because we can only date (by crater counting) what is exposed at the surface today, and can’t see the older, buried,interior of the edifi ce. There are several overlapping calderas at its summit, whose fl oors are dated at around 100 to 200 million years, but the youngest lava fl ows on the fl anks appear to be only about 2 million years old, and it is likely that Olympus Mons will erupt again one day. Other volcanoes in the Tharsis region are defi nitely older, and are probably now extinct.

9.A 3,000-kilometre-wide mosaic of images showing severalenormous shield volcanoes on Mars. On the left is Olympus Mons, theSolar System’s largest volcano. On the right-hand edge is TharsisTholus, and running north-east from the centre of the southern edge,a line of three: Pavonis Mons, Ascraeus Mons, and Ceraunius Tholus

The second reason why Mars has such big volcanoes is ‘because it can’. It has a cold, strong lithosphere, about twice as thick as the Earth’s. If you transplanted Olympus Mons to the Earth or Venus,their relatively thin lithospheres would sag beneath the load, and the volcano would lose height.

High-resolution images reveal details of lava fl ows on the plains between the large volcanoes and in several other regions of Mars.However, there are also features regarded by some as volcanic that have aroused considerable controversy. Figure 10 shows a notable example.Over 30 fragments of impact ejecta from Mars have been collected on Earth as meteorites. They are all either basaltic lava or more coarsely crystalline intrusive equivalents, spanning a range of crystallization ages extending from 4.5 billion years to as young as160 million years. We can infer that igneous rock makes up the bulk of the Martian crust at depth, even though large tracts of surface have a veneer of sediment of various kinds.

10.A 50-kilometre-wide image of a controversial area of Marsobtained by ESA’s Mars Express orbiter. Some say the platy surface isa lava fl ow with a fractured cooling crust. Others see this as brokenpack ice (now dust-covered) on the surface of a frozen sea. The twoimpact craters are older than the platy surface, and their rims werehigh enough to prevent their interiors from fl ooding. The craters areactually circular in outline, but are foreshortened in this oblique view

Surface processes

Regolith and space weathering

Volcanism is driven from inside a planet, but planetary landscapes can be sculpted just as much by processes that occur essentially at the surface. On a body that is airless and therefore unprotected from space, by far the dominant process acting directly on the surface is bombardment by meteorites and micrometeorites. Fragmented material (‘ejecta’) thrown out from craters blankets the surface to a depth of several metres, and sites where solid bedrock is visible at the surface are rare ( Figure 11 ). The lunar soil, known as ‘regolith’, in which the Apollo astronauts left their footprints is composed of grains mostly a fraction of a millimetre in size, comprising fragments of crystal, tiny bits of rock, and glassy spherules that are frozen droplets of melt generated by the heat of the impact. Regolith is continually rearranged on a variety of scales by excavation of craters and dispersal of ejecta, a process known as ‘impact gardening’. On Mercury, where impact speeds are faster, regolith grain-size is expected to be about one-third that of lunar regolith.If there is no atmosphere, solar ultraviolet light can reach the surface, where it may, over time, break chemical bonds.Micrometeorite impacts and (if there is no magnetic fi eld) charged particles from the solar wind can also affect surface chemistry, so airless bodies experience a suite of processes, collectively described as ‘space weathering’, that slowly alter the composition of the surface. For example, the bonds linking iron to oxygen atoms can be broken, allowing oxygen to escape and leaving submicroscopic grains of pure metal, called ‘nanophase iron’.

11.Telephoto view looking across Hadley Rille, taken by Apolloastronaut Dave Scott. The 2-metre-thick horizontal layer runningacross from the left is a rare example of bedrock (probably a lava fl ow),here exposed on a steep slope. Everywhere else is covered by regolithranging in size from boulders down to dust

When a planet has an atmosphere, only the largest, and infrequent, impactors can reach the surface at high speed. For example, in the Earth’s atmosphere, stony asteroids less than about 150 metres in size are likely to be sheared apart. The resulting fragments are small enough to be slowed down by friction, so by the time they reach the ground they have lost almost all their initial velocity, and do not form craters. Meteoritic dust, which is mostly micrometeorites but also fragments frictionally ablated from larger meteorites, settles to the ground at an average accumulation rate of 0.1–1 mm per million years. This dust makes such a tiny contribution to the total rate of sedimentation that it is totally swamped by other sediment, except on deep ocean fl oor far from land.

Erosion and transport

Impact gardening aside, processes that can wear away rock and transport the resulting fragments are wind, fl owing water, and moving ice (glaciers). Water can also dissolve rocks, during chemical weathering. Elements carried in solution by water may reappear elsewhere, being precipitated in new minerals. This applies especially to salt deposits, and also to many forms of carbonate rocks. However, on Earth most limestone (calcium carbonate) is formed from fragments of the shells of marine organisms, demonstrating an important biological step in turning dissolved carbonate (or dissolved carbon dioxide gas) into solid material that can become rock.

The dust storms on Mars are famous, having been fi rst noted by telescope in 1809. At perihelion, when Mars receives 40% more solar energy than at aphelion, winds in excess of 20 metres per second can lift so much dust high into the sky that most of the surface is obscured for several weeks. Sometimes little can be seen poking through other than the summit of Olympus Mons. Because of the clouds that often congregate there, this often looks white,hence its former name of Nyx Olympica (Snows of Olympus),which was revised when images from spacecraft showed what was really going on.Many signs of the action of wind on Mars can be seen from orbit or on the ground ( Figure 12 ) in the form of sand dunes and also smaller wind-ripples in the surface dust. Some of the dunes on Mars are being actively sculpted by the wind, but others have probably not changed their form for millions of years. Wind-blown sand is a powerful agent of erosion on Mars. The low atmospheric density means that a wind capable of transporting sand grains has to be blowing much faster than on Earth, and some exposed layers of rock have become curiously sculpted by abrasion.

12.Some sand dunes, needing only camels or a palm tree for scale. Infact, this picture was taken by NASA’s Opportunity rover on the surfaceof Mars, looking obliquely down from the rim of a crater onto a fi eld ofdunes on the crater fl oor. The visible area is about 100 metres across

Venus has a much denser atmosphere than Earth, with 92 times greater ground-level atmospheric pressure. Even sluggish winds can shift sand particles around, and Venus has several fi elds of sand dunes. However, here when a wind-blown grain strikes an exposure of bedrock its erosive power is limited, partly because of the slow speed and cushioning of the blow by the dense air, and partly because the high surface temperature of 480°C makes material deform plastically rather than abrading in a brittle fashion.

For Earthlings, fl owing water is usually the most familiar agent for transporting sediment – in a river, or as waves on a beach. In the Solar System, nowhere other than Earth currently has surface conditions allowing liquid water to be stable. Venus is far too hot,and although the noontime temperature on Mars can creep well above 0 °C, its atmosphere is so tenuous that ice at the surface turns directly to vapour rather than melting. However, there is abundant evidence that water once fl owed in prodigious volumes across the surface of Mars ( Figure 13 ). Mars has suffered extremes of climate at least the equal of Earth’s, and billions of years ago its atmosphere was suffi ciently dense and wet to permit rainfall and catastrophic fl ooding. The largest canyon system in the Solar System, Valles Marineris (‘the Valleys of the Mariner’, named after being discovered on images returned by the probe Mariner 9 in1971), is a 4,000-kilometre-long rift system initiated by fracturing of the crust, but widened by erosion when water fl owed through it.

13.A series of east–west fractures attests to the tectonic origin ofMars’s Valles Marineris canyon complex, of which only a fraction iscovered by this 800-kilometre-wide view. Note the winding and deeplyincised channels feeding into it from the south, which show the roleplayed by fl owing water in widening the main canyon

At its deepest point, the fl oor is 7 kilometres below the rim(Earth’s Grand Canyon in Arizona is only 2 kilometres deep), and it is so wide that if you stood on one rim, the opposite side would be out of sight beyond the horizon.

Despite its vastness, Valles Marineris was not recognized by pre-Space Age telescopic observers. The notorious ‘canals’ of Mars mapped by the Italian Giovanni Schiaparelli in 1877, and subsequently championed by the American Percival Lowell who until his death in 1916 thought they were giant works of engineering by intelligent Martians, are illusory. They bear no relation to any of the many genuine channels on Mars. Of these,examples fed by a branching network of tributaries (including many much longer versions of those shown in Figure 13 ) are likely to have been supplied by rainfall. The water fl owing along others probably leaked out of the ground, possibly when permafrost melted. The streamlined shapes of the ‘islands’ where channels debouch onto the plains show them to have been scoured by catastrophic fl oods. Robotic landers ( Viking 1 in 1976 and Mars Pathfi nder in 1997) that touched down in such places found an abundance of rocks dumped there by fl oodwaters.

All the major valleys on Mars have numerous impact craters superimposed upon them, so clearly they must be ancient, having last fl owed well over a billion years ago. Since then, many have suffered landslips from their walls, and their fl oors now bear trains of sand dunes formed by the cold wind howling along their length. In the 1970s and 1980s, most scientists would have told you that although Mars experienced at least one wet epoch in its distant past, it is now extremely dry except at the poles where there are small caps of water-ice. Imagine everyone’s surprise when in 1999 a high-resolution imager called the Mars Orbiter Camera began to reveal gullies only a few metres wide and a few hundred metres long on steep slopes in several places on Mars.The lack of superimposed craters and the observation that in many cases debris fans at their downstream ends had begun to bury sand dunes showed they must be young features, but how young? Proof was not long in coming that some are still active today, when repeat images began to reveal changes ( Figure 14 ).

The debate has now moved on from questioning the age of the youngest gullies, and now focuses on how they are cut. One theory is that water is responsible. There could be reservoirs of liquid groundwater under pressure in the Martian subsoil. Where a slope,such as the crater wall in Figure 14 , cuts below the water table, a barrier of ice within the soil (‘permafrost’) would normally prevent its escape. However, if the barrier were temporarily to give way,water could come gushing out. The liquid would not be stable – it would be both boiling and freezing as it fl owed – but it could traverse the length of one of these gullies before completely evaporating. Sceptics argue that liquid fl ow is not necessary to carve the gullies, and that they can be explained as a result of dry rock avalanches.

14.Two views of the same 1.5-kilometre-wide area covering the innerwall of a 6-kilometre-diameter Martian crater, recorded in August 1999(left) and September 2005 (right). The rim cuts across the top left, andthe fl oor is towards the lower right. There are many gullies eroded intothe slope of inner wall, one of which seems to have fl owed betweenthese two dates, carrying some pale debris onto the lower slope

Some Mars scientists see evidence for glaciers, especially at the eroded edges of highland plateaus. There is no ice exposed at the surface today (except that at the poles), but the rock-strewn ground revealed in high-resolution images from orbit could be debris covering (and insulating) underlying ice. Ground-penetrating radar data obtained from Mars orbit lend credence to this, which is one of the reasons why I am happier to accept the region shown in Figure 10 as a dust-covered frozen sea rather than as a lava fl ow.

Channels on the Moon such as Hadley Rille ( Figure 5 ) were lava pathways and were certainly not cut by water, and the only lunar water is small quantities of ice in the regolith near the poles. More than 200 sinuous channels have been mapped on Venus, one of which is 6,800 kilometres long. It is very unlikely that Venus experienced suffi ciently extreme climate change for liquid water to have existed recently enough to erode these channels, so they too were probably cut by lava.

Naming surface features

I have used names of surface features on other planets several times already: Olympus Mons, Valles Marineris, Hadley Rille, and so on. Without such names, I would be reduced to referring to them as ‘the biggest volcano on Mars’, ‘Mars’s giant canyon system’, and ‘that big trench near where Apollo 15 landed’. Less notable features would be even harder to describe, unless by a totally unmemorable coordinate system.

But nobody lives there, so who allocates names and how offi cial are they? When astronomers fi rst started to draw maps through their telescopes, some were suffi ciently independently minded to invent their own names, often regardless of any previous work.An early task of the IAU (founded in 1919) was to sort out the mess, arrive at single offi cial names for multiply named features,and to establish standards and conventions for allocating future names. This applied to the names of newly discovered bodies and also features on the surfaces of planetary bodies that it might become desirable to name or that would become visible thanks to improved imaging techniques. Originally, the latter meant simply bigger and better telescopes, and few founders of the IAU can have realized that they had established a means for supervising the nomenclature of features revealed by visiting spacecraft.

Some have castigated the IAU’s handling of Pluto’s reclassifi cation,but I know of no one who thinks badly of the basis for the IAU-administered naming process. This is fair, non-political, and seeks to represent all the world’s cultures – not necessarily on any single body, but balanced across the whole Solar System.

Building on what had already become common practice for lunar features, IAU nomenclature assigns a single unqualifi ed name to craters, whereas most other features are given a name plus a Latin descriptor term that denotes what kind of a feature it is. Thus‘Olympus Mons’ means ‘Olympus Mountain’, telling you immediately that this feature is a mountain named Olympus. Note that although no one doubts that Olympus Mons is a volcano, the descriptor term does not say this. Descriptor terms intentionally avoid interpretation (which may turn out to be wrong) and stick to description .

Common descriptor terms that you may meet are: chasma (a deep, elongated, steep-sided depression), fl uctus (a fl ow-like feature), fossa (long, narrow, shallow depression), mensa (fl attopped prominence with cliff-like edges), planitia (low-lying plain), planum (high plain or plateau), rupes (scarp), and vallis(branching valley). On the Moon, there is also mare (plural maria)which translates as ‘sea’ but had become too entrenched to be replaced by a more apt term.

There are also themes for names on each planet. Lunar craters are named after famous deceased scientists, scholars, and artists,whereas maria take Latin terms describing various weather conditions. Mars is the only place other than the Moon with signifi cant heritage of names from before the IAU became involved. These, with modern descriptor terms added, come from telescopic mapping by Giovanni Schiaparelli and Eugenios Antoniadi in the late 19th century, and mostly refer to broad regions such as Tharsis and Elysium. Each large valley is given the name for Mars in a different language, whereas small valleys are named after rivers on Earth. On Venus, almost all names are female: craters are named after famous historical women and most other features after goddesses. On Mercury, craters are named after dead artists, musicians, painters, and authors,whereas scarps (rupes) are named after scientifi c expeditions or the ships that carried them. Beagle Rupes ( Figure 4 ) is named after HMS Beagle on which Charles Darwin voyaged while amassing the observations that inspired his theory of evolution.

Similar principles apply to names of asteroids and the satellites of other planets. For example, Jupiter’s satellite Europa has craters named after Celtic gods and heroes, and most other features have names taken from the classical myth about Europa.

Atmospheres

After its birth, each terrestrial planet must have developed an atmosphere when internal gases leaked out via the magma ocean.These primitive atmospheres do not survive today, though the gases escaping from volcanoes show what they may have been like.The Moon and Mercury have too little gravity to hang on to a gas blanket, and the ‘atmospheres’ that you can sometimes fi nd quoted for them, with pressures much less than a billionth of the Earth’s atmospheric pressure, consist largely of stray atoms knocked of the surface by micrometeorite and cosmic ray impact.So sparse are these atoms that each is more likely to drift off into space rather than collide with another atom. This condition defi nes the ‘exosphere’ of a planet. It is merely the tenuous outermost zone of most atmospheres, but is all that the Moon and Mercury can muster.

The stronger gravity of the more massive terrestrial planets enables them to hang on to gas more effectively, although the density and chemical composition have evolved out of all recognition as a result of numerous processes. In the early days,the more active solar wind may have stripped away most of each original atmosphere, but these would be replenished by volcanism. An important ongoing process is that shortwavelength solar ultraviolet light can split molecules of water vapour into hydrogen and oxygen. Hydrogen is very light, and can escape to space, which makes this ‘photodissociation’ of water an irreversible process. Venus and Mars have both lost much of their original water in this way. The compositions of the present-day atmospheres of Venus, Earth, and Mars are summarized in Table 4 .

Having been split by ultraviolet light, atmospheric molecules can combine with others, by series of reactions described as‘photochemistry’. This occurs especially in a planet’s‘thermosphere’ which begins about 100 kilometres above the surface, so named because this layer is heated by the solar ultraviolet energy used in either splitting molecules apart or stripping them of some of their electrons. The latter process is called ionization, and ions (mainly of oxygen for the Earth and carbon dioxide for Venus and Mars) can be suffi ciently common in the outer reaches of a thermosphere to make an electrically conducting layer referred to as the ‘ionosphere’. When a solar storm brings plasma from the Sun to the Earth, this distorts the magnetic fi eld and causes unusual currents to fl ow in the ionosphere that can badly disrupt radio communications and even cause power failures.

Table 4　The present-day atmospheres of terrestrial planets,showing the abundances of the six most common gasesexpressed as a percentage of the total number of molecules(water is very variable in Earth’s atmosphere), and the surfacepressure relative to Earth

Deeper layers of an atmosphere, where the short-wavelength ultraviolet does not penetrate, are immune from photochemistry.Here the air is warmed mostly by contact with the ground (which is warmed directly by the Sun), and so in the lowest layer, called the troposphere, atmospheric temperature decreases upwards.Atmospheric pressure and density also decrease upwards, which means that the troposphere contains most of the mass of the atmosphere. In the troposphere, composition can evolve because of chemical reactions between air and rock (this is a corollary of chemical weathering) and especially (perhaps only) in the case of the Earth because of life. Here plants and primitive single-celled organisms use solar energy and atmospheric carbon dioxide to build their bodies, releasing gaseous oxygen that was vanishingly rare in the original atmosphere. Without plants, oxygenbreathing animals (like us) could not exist. The temperature would also be different, as I will explain shortly.

When air near the base of the troposphere is heated, it must expand, which makes it buoyant. It will then rise, to be replaced by colder air displaced from above. This is another example of convection (which you previously met within a planet’s mantle),and is what drives the weather on the Earth, Venus, and Mars.The pattern of circulation is different in each case because it also depends on such factors as the planet’s rate of rotation(slow for Venus), the rate of rotation of the atmosphere (much faster than that of the planet itself in the case of Venus’s upper troposphere), and the day–night temperature difference (high for Mars, small for Venus). Figure 15 shows the characteristic circulation above Venus’s south pole. In contrast, spiral storm systems in the Earth’s atmosphere tend to begin near the tropics.

The Earth’s atmosphere also differs from its neighbours in the complexity of its layering. At Venus and Mars, temperature decreases rapidly with altitude in the troposphere, then decreases more slowly with altitude in a (non-convecting) layer called the mesosphere, and then rises with altitude in the thermosphere because of the ultraviolet absorption. The Earth is unique among terrestrial planets in having a layer extending from about 10 to 50 kilometres altitude, between its troposphere and mesosphere, where temperature increases with altitude. This is the stratosphere, which is warmed by the absorption of 230–350-nanometre-wavelength ultraviolet photons (to which the thermosphere and mesosphere are transparent) by ozone molecules. Ozone is three oxygen atoms bound in a molecule (O 3 ), as opposed to two oxygen atoms (O 2 )which is what is usually meant when referring to ‘oxygen’, and is assembled from oxygen by photochemical reactions higher in the atmosphere.

15.The ‘eye’ of Venus’s 2,000-kilometre-diameter south polar vortex,imaged 24 hours apart. The dot indicates the south pole. These images,recorded in the mid-infrared, see the cloud-tops about 60 kilometresabove the surface. The centre of the ‘eye’ is warmer (appearingbrighter), showing that here the clouds are drawn downwards towarmer, deeper levels

Greenhouse effects and the hole in the ozone layer

Many people are aware of the ‘hole in the ozone layer’ and the‘greenhouse effect’, but tend to confl ate them as twin culprits of climate change. However, the two are very different.The ozone layer occurs (only) in the Earth’s stratosphere, and is where 230–350-nanometre ultraviolet light is absorbed. This is very important for ourselves and other surface-dwelling life,because if it is not blocked out such radiation can cause skin cancers and genetic damage. It takes surprisingly little ozone to be an effective screen. If you gathered all the ozone that is dispersed in the stratosphere into a single layer at sea-level it would be only about 3 millimetres thick. This is a fragile veil, so when in the 1970s and 1980s it became apparent that over Antarctica the stratosphere had lost perhaps half its ozone, there was considerable concern, and talk of a ‘hole in the ozone layer’.The main cause was traced to reactions involving industrial chemicals called chlorofl uorocarbons (CFCs) which, as a consequence, have now been banned from their former use in aerosol sprays and refrigerants so they cannot leak into the atmosphere. The Antarctic ‘ozone hole’ and a lesser one over the Arctic have now stabilized. Depletion of ozone is only a few per cent outside of the polar regions, and is undetectable over the tropics.

There is no simple link between ozone concentration and mean global temperature. A badly depleted ozone layer would make life unpleasant, but has little to do with climate change or global warming. The tropospheric temperature of a planet is controlled by how effectively the lower atmosphere absorbs infrared radiation. This is because visible sunlight warms the ground, and the warmed ground emits infrared radiation. The temperature of the atmosphere depends on two factors: the heat it picks up from contact with the ground, and how much of the outgoing infrared radiation it can absorb.

Most gas species are transparent to infrared radiation, but molecules consisting of two or more different elements absorb infrared quite strongly. Thus nitrogen (N 2 ), oxygen (O 2 ), and argon (Ar) do not absorb infrared, but water vapour (H 2 O),carbon dioxide (CO 2 ), sulfur dioxide (SO 2 ), and methane (CH 4 ) do.By analogy with trapping warmth inside a greenhouse, this is called the ‘greenhouse effect’. There is a natural greenhouse effect in the atmospheres of Venus, Earth, and Mars. Thanks mostly to its enormous load of carbon dioxide, the atmospheric greenhouse effect on Venus maintains its surface temperature an impressive500 °C above what it would otherwise be. Water vapour and carbon dioxide warm the Earth by about 30 °C, and greenhouse warming of Mars, which has a tenuous carbon dioxide-rich atmosphere, is only about 6 °C.

Earth’s greenhouse effect keeps the temperature within a range to suit the life that has evolved here. Mediated by life itself, the strength of the greenhouse effect has changed to keep the temperature in the right range. Four billion years ago, the Sun was only about 70% as brilliant as it is today, so the Earth would have been very much colder, had its atmosphere been the same as today’s. However, before 4 billion years ago, it was probably mostly carbon dioxide, and 100 times denser than today, so the greenhouse effect would have been stronger. Thanks to primitive algae, the carbon dioxide content had decreased to about 10 times its present value by about half a billion years ago, so of course the greenhouse effect must have declined too. Free oxygen (O 2 ) fi rst appeared some time between about 2.7 and 2.2 billon years ago,and peaked at about 170% of its present concentration between250 and 200 million years ago. Clearly, life on Earth has both infl uenced and benefi ted from changes in the composition of the atmosphere.

Since the beginning of the industrial era, human activity has affected the atmosphere in various ways: ozone depletion, industrial smog, and so on. However, what should concern us most is our release of carbon dioxide into the atmosphere, or, rather, back into the atmosphere, for most of this is carbon dioxide previously extracted from the atmosphere by organisms and sequestered as coal or oil. The amount of atmospheric carbon dioxide increased by about 20% in the 50 years since 1960 (faster than any natural process), and is still increasing. This ‘anthropogenic greenhouse effect’ will inevitably lead to warming of the global climate. A few degrees’ rise in temperature will affect ecosystems and will also tend to make local weather (including short-term temperature fl uctuations) more extreme. Another consequence will be a rise in global sea-level, chiefl y because water expands as it warms. So,although the natural greenhouse effect in our atmosphere is a good thing, human-induced rapid increases in the effect could have potentially disastrous consequences for our civilization.

Against a background of general gradual decrease in the natural greenhouse effect, which counterbalanced the slow waxing of the Sun’s luminosity, there have been several excursions in the Earth’s climate. Ice Ages, when much (in extreme cases all) of the surface water was frozen, are the best-known example. These are controlled not so much by the atmosphere as by variations in the tilt of the axis and the eccentricity of the orbit. Similar effects probably explain the drastic changes in the wetness of Mars’s surface over time.

Clouds

Clouds are highly refl ective, so the cloudier an atmosphere, the more solar energy is refl ected directly back into space. However, a cloudy sky increases the ability of an atmosphere to trap heat from the sunlight that does reach the ground, so the effect of clouds on global temperature is complex. The unbroken clouds of Venus have not saved its surface from being thoroughly cooked by the greenhouse effect.

Clouds form when the temperature and pressure make it favourable for some constituent of the atmosphere to condense as liquid droplets or ice particles. In the case of the terrestrial planets, the relevant constituent is usually water. Although water is only a small fraction of Venus’s atmosphere, there is enough to form a continuous layer of cloud at the top of its troposphere, between about 45 and 65 kilometres above the surface. There, water vapour condenses as droplets about2 micrometres across. These remain suspended, being too small to fall, and are described as aerosol droplets.Atmospheric sulfur dioxide dissolves in them, so they turn into sulfuric acid. However, if anyone tries to tell you that it ‘rains sulfuric acid on Venus’, they are wrong. Wherever the droplets are drawn down below about 45 kilometres by atmospheric circulation, the heat causes them to evaporate again, and they never have the chance to become raindrops large enough to fall groundwards.

Above about 6 kilometres, Earth’s clouds consist mostly of tiny ice particles, and below that altitude they are mostly droplets of water. Rainclouds are not really grey, they just look that way because they are thick enough to blot out so much light. On Mars,clouds are comparatively rare. In most of its troposphere, they are made of water-ice, whereas around 80 kilometres, near the troposphere/mesosphere boundary, clouds of carbon dioxide particles have been observed.

Polar caps and oceans

As well as condensing to form clouds, atmospheric constituents may condense as either ice or liquid at the surface. The Earth is the only terrestrial planet to have oceans today, which of course are made of water. Near the poles, water is frozen to form polar caps.The young planet Venus may have enjoyed a brief epoch when oceans covered the globe, before the evaporated water vapour(subsequently lost by photodissociation) added to a burgeoning greenhouse effect leading to the current parched situation.

However, Mars is different. A vast ‘Oceanus Borealis’ occupying the whole of the low-lying northern plains about 3.8 billion years ago was in vogue in the 1990s. Although that remains contentious,many would accept the likelihood of lakes on Mars extensive enough to be called ‘seas’ at the time when channels such as those in Figure 13 were fl owing, and some frozen relics may even survive, buried by dust ( Figure 10 ). However, there is no doubt that ice exists at the surface today in Mars’s polar caps ( Figure 16 ).These consist of ‘permanent’ water-ice with a fringe of carbon dioxide frost that grows and contracts seasonally.

16.1,500-kilometre-wide images of Mars’s northern polar cap in earlyspring (left) and high summer (right). In summer, most of the carbondioxide frost has sublimed (turned from ice to vapour), leaving onlythe residual, ‘permanent’ cap of water-ice

Earth’s and Mars’s polar caps interact with the atmosphere. They are, in effect, deposits of gases that have ‘frozen out’ of the atmosphere, either falling from the clouds as snow or condensing directly onto the ground. When the temperature rises, material from the polar caps is returned to the atmosphere, either by melting and then evaporation (for water on Earth, and probably Mars in the past) or by subliming directly from ice to vapour (on Mars, for carbon dioxide and water today).

Equilibria like these cannot occur on airless bodies like the Moon and Mercury, and so polar caps are not to be expected. However,during the 1990s it was noted that radar signals are refl ected with unusual strength from permanently shadowed regions inside craters near the poles of both bodies. This would be consistent with water-ice dispersed as grains within the regolith. A possible explanation is that the fl oors of these craters are so cold that any stray water molecules that wander into them tend to adhere to the surface in ‘cold traps’. This water need not be part of these bodies’original inventory, it could have been supplied later by impacting comets. Finding a supply of water on the Moon is of great importance if a human colony, or even just a permanently occupied base, is ever to be established there. The poles are clearly the best bet, and in 2009 water was confi rmed in an ejecta plume created when a spacecraft was crashed into a permanently shadowed polar crater. Infrared spectra obtained by other spacecraft revealed water and hydrated minerals dispersed in the regolith across broader regions, in minute concentrations but raising hopes that the Moon might not be so wholly inhospitable as formerly believed.

Cycles

Interplay between interior, surface, and atmosphere, and the cycling of components between them, is extremely important. The Earth’s ‘hydrologic cycle’ is the most familiar example. It is not a single cycle, but an array of interconnected loops. In essence,water in the oceans evaporates to form clouds, and later precipitates out as rain or snow that eventually fi nds its way back into the oceans (via rivers or seasonal polar caps). Water can be drawn into the interior (deeply at subduction zones or more shallowly by infi ltration of the ground) and re-emerge via volcanoes. It can also react chemically with rock (chemical weathering) and be stored within minerals. There is also an important ‘carbon cycle’ with loops passing between atmospheric carbon dioxide, living plants and animals, dissolved carbon dioxide, marine limestones, hydrocarbon deposits, volcanic gases,and so on.

Mars is sure to have similar cycles, though acting more sporadically and over different timescales, and with different relative importances for each loop. There are probably even slower cycles involving carbon dioxide and sulfur dioxide on Venus, in which the atmosphere weathers the surface rocks, which eventually become buried by lava fl ows to depths at which the gases are liberated once more and escape back to the atmosphere through volcanic vents. Until we have explored and documented the complexities and timescales of these multi-looped and inter-related cycles, our understanding of what makes each planet‘tick’ will remain naive.

Chapter 3　Giant planets

These are the bodies that dominate the Solar System – provided you think it is size that matters, and are willing to overlook the Sun itself. The four giant planets are illustrated to scale in the lower half of Figure 3, showing how comprehensively their size overshadows the terrestrial planets. The view of Uranus is from the Hubble Space Telescope in orbit about the Earth, whereas the other giant planets are as seen by visiting spacecraft. Their domination by mass is not quite so overwhelming, because they are less dense than the terrestrial planets. Jupiter’s density is only24% of the Earth’s, and Saturn is even less dense and would fl oat if dropped into a suffi ciently large (and purely hypothetical)bucket of water. All of them have rings in their equatorial plane,though only those of Saturn and Uranus are suffi ciently prominent to be visible in Figure 3. Although the rings look solid, they are made of myriads of orbiting particles and are extremely insubstantial. They are discussed, along with the giant planets’satellites, in the next chapter.

By convention, the size of a giant planet is measured from the top of its clouds. These occur in the planet’s troposphere, above which are largely transparent and progressively less dense layers classifi able in the same way as for the Earth’s atmosphere. The base of a giant planet’s troposphere is hard to defi ne and has never been explored even in the case of Jupiter, where in 1995 an entry probe released by the Galileo spacecraft reached a depth of 160kilometres below the cloud-tops before pressure (22 atmospheres)and temperature (153 °C) put paid to it. Probably, the troposphere of each giant planet merges seamlessly into a fl uid interior at temperatures and pressures so high that there is no distinction between gas and liquid. Certainly, there is no solid surface that a human could ever stand upon.

Basic data for the giant planets are given in Table 5 . The polar diameters quoted there are less than equatorial diameters,because rapid rate of rotation (see Table 2) fl attens their shapes.Jupiter’s polar diameter is 6.5% less, and Saturn’s 10% less, than its polar diameter. The difference is only about 2% for the less gassy and more slowly rotating Uranus and Neptune (and is less than 1% for each terrestrial planet).

Interiors

There is no simple way to study the interior of a giant planet, but we can use atmospheric composition (99% hydrogen and helium)and our general knowledge of what the Solar System as a whole is made of to construct a model that is consistent with its measured density, and with the interior pressures that we can infer from this. Below the atmosphere, each giant planet must have a zone consisting mostly of hydrogen molecules (H 2 ) and helium atoms(He), in a state that it is better to call ‘fl uid’ rather than either‘liquid’ or ‘gaseous’. At the very centre, there is probably a rocky inner core, of about three Earth-masses inside Jupiter and Saturn,and about one Earth-mass inside Uranus and Neptune.Surrounding the inner core, there ought to be an outer core of ‘ice’composed of unknown proportions of water, ammonia, and methane, amounting to about twice the mass of the Earth inside Jupiter, maybe six Earth-masses inside Saturn, twelve inside Uranus, and fi fteen inside Neptune. We do not know whether these outer and inner cores are molten or solid, because although we can estimate the pressure (a staggering 50 million atmospheres in the centre of Jupiter), we do not know the composition and have only a vague idea of the likely temperature(ranging from in excess of 15,000 °C in the centre of Jupiter to about 2,200 °C at the outer edge of Neptune’s core). Our understanding of how materials behave under such extreme conditions is sketchy, including whether metallic iron could differentiate from the rock and sink towards the centre to form an inner-inner core. The cores of Uranus and Neptune might even be undifferentiated mixtures of ice and rock.

Table 5　Basic data for the giant planets. Note that the mass units are a thousand times bigger than for theterrestrial planets in Table 3

Accounting for the cores leaves little more than one Earth-mass for the hydrogen and helium exteriors of Uranus and Neptune,comprising shells about 6,000 kilometres thick. However, the‘gas giants’ Jupiter and Saturn have much deeper envelopes of hydrogen and helium surrounding their cores, in excess of 300and 80 Earth-masses, respectively. Hydrogen is easier to model than ice or rock, and scientists are pretty confi dent that at pressures greater than about 2 million atmospheres, hydrogen atoms are squeezed so tightly together that electrons are no longer confi ned about specifi c atoms. Instead, they are able to wander through a sea of hydrogen that behaves like a molten metal. This freedom of electron movement makes ‘metallic hydrogen’ an excellent conductor of electricity. A shell of metallic hydrogen (with some helium dissolved in it) surrounding Jupiter’s core probably accounts for about 260 Earth-masses(80% of Jupiter’s total mass), whereas around Saturn’s core it is thought to comprise a more modest 41 Earth-masses (just over40% of Saturn’s total mass). Figure 17 illustrates the full internal structure of Jupiter.

The internal structure of the giant planets may still be evolving because, with the possible exception of Uranus, they all radiate more heat to space than they receive from the Sun. Jupiter is so massive that it could still be leaking out a signifi cant amount of primordial heat trapped within since its formation, but for Saturn and Neptune this heat excess shows that heat must actually be being generated within. The discrepancy is too large to be radiogenic heat, so internal differentiation may still be occurring.The settling of denser than average material inwards (allowing an inner shell to grow while the surrounding shell becomes thinner but purer) would convert gravitational potential energy into heat.Such heat could come from continuing growth of cores (or inner cores) or, for Saturn only, from inward settling of helium droplets inside its metallic hydrogen layer.

17.Cut-away diagram showing the proposed internal layers withinJupiter. The principal tropospheric cloud-top zones (bright) and belts(dark) are labelled

Atmospheres

Composition

In contrast to the reasoned speculation about giant planet interiors, understanding of their atmospheres can draw more on observation and measurement. The composition of clouds and the overlying layers can be measured by optical spectroscopy, which is the study of how sunlight of different wavelengths is absorbed at various depths within the atmosphere. In addition, the average molecular mass at each depth can be determined by the amount of refraction experienced by radio signals transmitted by a spacecraft while it disappears from view behind the planet. Also, the Galileo entry probe made various measurements inside Jupiter’s atmosphere during its descent. Table 6 compares the chemical composition of the four giant planets’ atmospheres. In addition to the species listed there, each contains smaller traces of ethyne(C 2 H 2 ), Jupiter has ethene (C 2 H 4 ), and Jupiter and Saturn both have phosphine (PH 3 ), carbon monoxide (CO), and germane(GeH 4 ).

The topmost layer of continuous clouds on Uranus and Neptune is of methane-ice particles. It is too warm for methane condensation at Jupiter and Saturn, where instead ammonia-ice particles condense to form the topmost clouds. These top cloud layers are about 10 kilometres thick, below which the ‘air’ probably becomes clear again. Calculations suggest that in the case of Jupiter, there should be a second layer of clouds made of ammonium hydrosulfi de (NH 4 HS) about 30 kilometres below, and a third cloud layer, this time of water (ice at the top, liquid water droplets below) about 20 kilometres lower still. The Galileo entry probe found probable ammonium hydrosulfi de clouds at about the right depth but did not fi nd any water-ice clouds. Some say the models are wrong; others say that the probe penetrated into a gap between discontinuous water-ice clouds. The same cloud layers are expected at Saturn, but spaced about three times further apart because of Saturn’s lower gravity. Ammonia-bearing clouds are expected below the methane clouds of Uranus and Neptune.

Table 6　Gases detected in the atmospheres of the giantplanets, showing the measured proportion made up by each

The atmospheric pressure at the top of Jupiter’s ammonia clouds is a factor of two or three less than the sea-level atmospheric pressure on Earth, whereas on the other giant planets the cloud-top pressure is close to Earth’s sea-level pressure.

Circulation

A global pattern of cloud bands running parallel to the equator is visible on Jupiter even through a small telescope. A similar pattern is repeated less dramatically on the other giant planets.Solar heating must play some role in the circulation of this, visible,part of their atmospheres, but it appears to be powered mostly by internal heat and to be controlled by their rapid rotation.

Traditionally, the dark bands are referred to as ‘belts’ and the intervening bright bands as ‘zones’. The names given to the main belts and zones on Jupiter are indicated on Figure 17 . Because there is no solid surface to act as a frame of reference, wind speeds on giant planets are measured relative to the planet’s average rate of rotation. On Jupiter, the cloud-top wind blows to the east at up to 130 metres per second across most of the Equatorial Zone. The adjacent edges of the North and South Equatorial Belts share this motion, but the wind speed decreases and ultimately reverses with distance away from the equator across each belt until the Tropical Zones are reached, where the wind direction reverses again, and so on with repeated reversals across each belt and zone until the polar regions.

In Jupiter’s zones, the atmosphere is mostly rising, leading to condensation of ammonia clouds high up, where they naturally appear bright. Conversely, in the belts the atmosphere is mostly sinking, drawing the cloud-tops lower, so to a depth where they look darker. Local exceptions to this pattern have been identifi ed on Jupiter, and the general rule of rising zones and sinking belts scarcely seems to hold at all on the other giant planets, whose atmospheric circulation is harder to fathom. A complicating factor infl uencing the visibility of zones and belts is the poorly understood nature and abundance of whatever trace compounds add colour to the clouds, and which are expected to result from photochemical reactions. Jupiter’s various hues of yellow and red could be caused by sulfur (released photochemically from either hydrogen sulfi de or ammonia hydrosulfi de), phosphorous (from phosphine), or hydrazine (N 2 H 4 , made photochemically from ammonia).

Colour variations are less pronounced in Saturn’s atmosphere, and the pattern of zones and belts is less prominent. However, wind speeds are higher, with eastward-blowing winds in excess of 400metres per second prevailing for 10° either side of the equator.

Rotating storm systems are well known on both Jupiter and Saturn. The most famous is Jupiter’s Great Red Spot. This can be seen in Figure 3, as an oval feature straddling the boundary between the South Equatorial Belt and the South Tropical Zone.It extends 26,000 kilometres from east to west, having a spiral structure and taking about six days to rotate anticlockwise. It has been apparent in telescopic observations since at least 1830.Smaller storms can be made out at a variety of scales on both Jupiter (look along the South Temperate Belt in Figure 17 ) and Saturn. About once every 30 years, during summer in its northern hemisphere, Saturn tends to be disfi gured by a giant storm system that begins as a white spot near the equator, but within a month can spread to encircle the globe before gradually fading from view.

Whereas Jupiter and Saturn have a yellowish cast, Uranus and Neptune appear bluey-green. This is because we see their cloud-tops through a depth of overlying methane gas, which preferentially absorbs the longer (red) wavelengths of light.

The 82.1 °Caxial tilt of Uranus makes for extreme seasonal variations. For example, when Voyager 2, the only spacecraft yet to have visited Uranus, fl ew past in 1986, the south pole was in full sunlight and most of the northern hemisphere was suffering decades of darkness. Its southern hemisphere looked disappointingly bland on the Voyager images, but as the Uranian year progressed and the Sun began to rise and set over a wider range of latitudes, the globe began more to resemble the other giant planets ( Figure 18 ). In 2007, Uranus passed through its equinox, and the south pole, followed gradually by the rest of the southern hemisphere, began to drift into long-term darkness,which will peak with southern midwinter in 2028.

When Neptune was revealed in detail during Voyager 2 ’s 1989fly-by, it resembled a blue version of Jupiter. There was even a giant storm system in the form of a dark spot just south of the equator, which was dubbed the ‘Great Dark Spot’ in tribute to its famous Jovian cousin. However, it proved to be shorter-lived, and had vanished by 1994. Unlike at Jupiter and Saturn, the equatorial wind stream on Neptune blows west (opposite to the planet’s rotation), as can be seen by the westward drift of the Great Dark Spot relative to the smaller, more southerly spot in Figure 18 .

Magnetospheres

Each of the giant planets has a strong magnetic fi eld. The‘magnetic dipole moment’ of Neptune, which is the conventional measure of a planetary magnetic fi eld, is 25 times greater than the Earth’s. Uranus’s is 38 times, Saturn’s is 582 times, and Jupiter’s is1,949 times greater. To generate these fi elds, each planet must contain a zone of electrically conducting fl uid undergoing some kind of convective motion. In the two terrestrial planets with magnetic fi elds (Mercury and Earth), the explanation is a fluid shell of their iron cores. The magnetic fi elds of Jupiter and Saturn are probably generated in the metallic hydrogen layer, stirred into motion by the planets’ relatively rapid rotation. Pressures are too low for metallic hydrogen in Uranus and Neptune, so their magnetic fi elds are harder to account for, but are probably caused by motion within electrically conducting ‘ice’ of their outer cores.

18.Top: Uranus seen by the Hubble Space Telescope in August 1998(left) and July 2006 (right). The change in orientation of the planet’saxis relative to the Sun is apparent from the pattern of the atmosphericbanding. The region around the south pole was still in sunlight in1998, but the axis had become nearly edge-on to the Sun by 2006.High, bright clouds are apparent in the far north in the 1998 image,which also shows the rings and several of the inner satellites. The ringswere edge-on and invisible in 2006, but instead we can see one of theregular satellites (Ariel) and its shadow. Bottom: two images ofNeptune seen by Voyager 2 during its approach in 1989, recordedalmost exactly one planetary rotation apart. The Great Dark Spot andassociated wisps of high, bright nitrogen cirrus clouds are prominent.Note also the general banded structure, and a smaller dark spotfurther south

An important consequence of a planet having a magnetic fi eld(which applies to Mercury and the Earth too) is that it cocoons the planet inside a zone into which magnetic fi eld lines from the Sun cannot usually penetrate. This zone is called the planet’s‘magnetosphere’. The paths of charged particles in the solar wind(chiefl y protons and electrons) are controlled by the Sun’s magnetic fi eld, until they hit the ‘bow shock’ of a planet’s magnetosphere, which diverts them past the planet.

Charged particles can get through sometimes, especially by leaking back up the long magnetotail, down-Sun from the planet.Near the poles, these can be channelled along fi eld lines towards the top of the atmosphere, where their arrival causes glows in the sky called aurorae, well known on Earth and observed also on Jupiter and Saturn.

Chapter 4　Giant planets’ satellites and rings

Rings and a large family of satellites are features common to all four giant planets. There are variations in emphasis and scale, but the similarities between each ring-satellite system outweigh their differences.

Ring-satellite systems

Most outer satellites of each giant planet travel in eccentric orbits,usually in the opposite direction to the spin on their planet.Furthermore, many of these orbits are inclined at 〉30° relative to their planet’s equator. The typically eccentric, retrograde, and inclined nature of their orbits earns these bodies the name‘irregular satellites’, quite apart from the fact that (being at most about 100 kilometres, and more often only a few kilometres,across) they have far too little gravity to pull themselves into spherical shapes. The irregular satellites are the most numerous class: at the last count, Jupiter had 55, with orbital semi-major axes ranging from 105 to 400 Jupiter radii; Saturn had 38, with orbits from 184 to 417 Saturn radii; Uranus had 9, 167–818Uranus radii; and Neptune had 6, 223–1,954 Neptune radii.The ‘regular satellites’ are the large ones in near-circular prograde orbits, much closer to their planets, and with very low inclinations. Jupiter has 4 (the ones discovered by Galileo) whose orbital semi-major axes range from 5.9 to 26.3 Jupiter radii.These are substantial worlds, and geologically have much in common with the terrestrial planets, though of course they do not satisfy the IAU defi nition of a planet. Saturn has 8 (all but one considerably smaller than Jupiter’s, and orbiting at 3–59 Saturn radii), and Uranus has 5 (at 5–23 Uranus radii). Neptune has one large satellite, Triton, orbiting at 14 Neptune radii, that would be regarded as ‘regular’, except for its retrograde orbit. An important characteristic, shared by all regular satellites (including Triton), is that tidal forces have such a grip on them that they are in synchronous rotation, rotating once per orbit, so that (like the Earth’s Moon) they keep the same face towards their planet.

Closer still, we fi nd irregular-shaped lumps of debris that it is convenient to distinguish as ‘inner moonlets’. These have circular,prograde, equatorial orbits. So do the particles that make up the rings, and, given that some inner moonlets’ orbits lie within the rings, there is probably no fundamental difference between a large ring particle and a small inner moonlet. Jupiter has only 4 known inner moonlets, but Saturn has 14, counting 7 whose orbits lie among those of its innermost regular satellites. Uranus has 13 and Neptune 6.

The width and number of rings varies from planet to planet,Saturn’s being by far the most spectacular, but in general their thickness is no more than a few tens of kilometres. Mostly, they are closer to their planet than a distance known as the ‘Roche limit’, a boundary within which any large body should be ripped apart by tidal forces. Most rings are regarded as debris left over from the tidal disruption of a satellite or comet that strayed too close to the planet, but some less substantial rings are demonstrably supplied from nearby satellites by particles vented actively into space or thrown up by impacts.

Saturn’s rings are made of ice and refl ect about 80% of the sunlight falling on them. Despite their prominent appearance(Figure 3), the material in them would suffi ce only to make a body about 100 kilometres in diameter if it could all be gathered together. Although individual ring particles have not been imaged directly, the rate at which the rings cool when the shadow of their planet falls across them shows that Saturn’s rings are mostly particles between about a centimetre and 5 metres in size. In contrast, Jupiter’s much less substantial rings are made largely of micrometre-sized particles that are also much less refl ective than the bright icy lumps in Saturn’s rings. The ring-material at Uranus and Neptune refl ects sunlight poorly (like Jupiter’s ring-material)but is mostly centimetres to metres in size (like Saturn’s ringmaterial).

19.A 5,000-kilometre-wide view of part of Saturn’s ring system,seen by Cassini on 27 July 2009. At this scale, the curvature of therings round the planet (out of view to the right) is scarcelydiscernible. The rings refl ect most sunlight where particles are mostdensely packed, and black space shows through in particle-free gaps.Pan, a 28-kilometre-diameter shepherd satellite, can be seenorbiting in the widest gap. As well as sweeping most of this gap clear,Pan infl uences narrow and discontinuous rings within the gap. Theexceptional length of Pan’s shadow on the rings to its right is becausethis image was recorded when the Sun lay very close to the plane ofthe rings

Orbital resonances lead to a complex gravitational interplay between rings and the inner moonlets that orbit among them( Figure 19 ). Those are often called ‘shepherd satellites’ because some sweep clear many of the gaps in the rings, and others form,deform, and maintain narrow rings with orbits just within or just beyond their own.

In general, rings occur closer to their planet than the regular satellites, but Saturn is an exception in that it also has a diffuse outer ring of dark, dusty material centred around the orbit of Phoebe, one of its innermost irregular satellites. The material in this ring, which was discovered in 2009 using a space-based infrared telescope, is presumably being supplied from Phoebe in some way yet to be understood.

Remarkable satellites

There was a time when pretty much everyone expected even the largest of the outer planets’ satellites to be dreary objects. Ancient ice-balls, heavily pock-marked by impacts, they would record the outer Solar System’s bombardment history, but would be of no further interest unless you wanted to study mutual orbital evolution. That was the standard view until 2 March 1979, when Stanton Peale, working at the University of California, published(with two colleagues) a paper pointing out that the exact 2:1orbital resonance between Jupiter’s innermost Galilean satellites,Io and Europa, ought to result in so much tidal distortion of Io’s shape that its interior should be molten. From estimates of density plus spectroscopic analysis of their surfaces, it was already known that Io has a rocky crust, unlike the other satellites that are predominantly ice. To suggest a molten interior inside a rocky body (where the melting temperature is so much higher) was a particularly bold step. Few might have believed this claim if Voyager 1 had not fl own past a few days later and transmitted pictures of explosively erupting volcanoes, topped by300-kilometre-high eruption plumes.

Although tidal heating of Io is by far the strongest, the same process affects various other satellites, and many more bear signs of ancient episodes of tidal heating. This makes them varied, and intriguing to geologists. They don’t mind that in most of them only the core is made of rock, surrounded by a thick mantle of ice,with perhaps a chemically distinct icy crust at the surface. Under the low surface temperatures prevailing in the outer Solar System(ranging from –140 °C for Jupiter’s satellites down to –235 °C for Neptune’s satellites), the mechanical properties and melting behaviour of the ice are very closely analogous to how rock behaves in the inner Solar System. In other words, those bodies have both the behaviour and structure of a terrestrial planet, with rock in place of iron in the core, and ice instead of rock in the crust and mantle.

Io is an exception in being ice-free with a rocky crust and mantle surrounding an iron core, and would be classifi able as a terrestrial planet if it was orbiting the Sun instead of Jupiter. Europa is a hybrid, having a structure like Io buried below 100–150kilometres of ice. Here I describe both of those and some of the other satellites that fascinate me most, concentrating on the more active examples, though even the crater-pocked ice-balls have turned out to be more interesting than the dull globes formerly imagined.

Io

Io is only slightly bigger (3,642 kilometres in diameter) and denser than our own Moon, but the two could hardly be more different. Io’s terrain is resurfaced so rapidly by volcanic processes that not a single impact crater is to be seen, despite the fact that the effect of Jupiter’s gravity in focusing stray projectiles inwards must mean that Io is struck more often than Jupiter’s heavily cratered satellites Ganymede and Callisto that orbit beyond Europa. When the fi rst Voyager 1 colour close-ups of Io were studied in 1979, its yellow hue led many to suppose that the lobate lava fl ows that could be recognized on its surface were made of sulfur. However, it is now accepted that Io’s volcanism is molten silicate material (true ‘rock’). The temperatures recorded in the heart of erupting volcanic vents are well in excess of 1,000 °C,despite the intense cold beyond the active areas. The gas that escapes to drive explosive eruptions such as those in Figure 20 is mostly sulfur dioxide (whereas on Earth, it would be mostly water vapour), and both sulfur and sulfur dioxide condense on the surface as ‘frost’ that imparts the colour to Io.

Io lies within a belt of charged particles confi ned by Jupiter’s magnetic fi eld. The radiation there is so intense that NASA’s Galileo mission controllers did not allow the spacecraft to make repeat close fl y-bys of Io, so only a small fraction of Io’s globe was imaged well enough to show details below a few hundred metres in size. On the most detailed images, the pixels are only10 metres across, and even on those no impact craters have been found.

If Io’s present-day rate of volcanism is representative of the long term, then its entire crust and mantle must have been recycled many times over. Covering of older surfaces by lava fl ows and fall-out from eruption plumes, amounting to a globally averaged burial rate of a couple of centimetres per year, obscures impact craters too rapidly for any to be apparent. If Io ever had an outer layer of ice, volcanic activity has long since vaporized it, allowing it to be lost to space, because Io’s gravity is too weak to hold on to water vapour or other light gas. What a fantastic place for a volcanologist to visit, if only the harsh radiation environment did not make Io’s surface so thoroughly inimical to human exploration.

20.Top: part of the crescent view of Io seen by the Pluto-bound NewHorizons mission passing Jupiter in March 2007. The plume from avolcanic vent at a site called Tvashtar caldera on the night-side rises300 kilometres so that its upper part is in sunlight. An incandescentglow can be seen at its source, and the shadowed lower part of theplume is faintly illuminated by light refl ected from Jupiter. Bottom:A 250-kilometre-wide view of Tvashtar seen eight years earlier by theGalileo orbiter. Sunlight is from the left. The darkest material is recentlava fl ows, and the east–west bright streak near the upper left isincandescent lava being erupted from a volcanic fi ssure

Europa

Europa (3,130 kilometres in diameter) is my favourite. Voyager images from fl y-bys in 1980 and 1981 showed its surface looking like a cracked eggshell, with very few impact craters to be seen.Clearly, tidal heating was somehow refashioning Europa’s icy outer layer, though not so rapidly as Io. Higher-resolution imaging by the Galileo mission revealed a complex surface history, and led to an unusually bitter controversy. It was already well known that Europa’s surface is predominantly water-ice, and the globe’s overall density shows that its icy carapace has to be about 100–150kilometres thick, overlying a denser, rocky interior. However,density arguments cannot distinguish between solid ice and liquid water. The surface ice is strong and brittle, thanks to its low temperature. The controversy that emerged was over the state of the ‘ice’ below the surface. Was it frozen all the way down to the rock or was the lower part liquid, capped by a fl oating ice shell?

The latter requires a greater rate of internal tidal heating coupled with the exotic concept of a global ocean of liquid water below the ice. So far as I am concerned, evidence from images such as Figure 21 makes it clear that the ice is generally thin, only a few kilometres, and so must be fl oating on water. However, for several years of Galileo ’s orbital tour of the Jupiter system, a powerful lobby group on the imaging team persisted in trying to explain the surface features as a result of processes driven by solid-state convection in the thick ice layer.

What is now the generally accepted basis of Europa’s geology is best explained by reference to Figure 21 . This shows numerous high-standing ‘rafts’ of ice, bounded by 100-metre cliffs. The surfaces of the rafts are characterized by a pattern of ridges and grooves, running in a variety of directions. Between the rafts, the texture is more jumbled, and lacks a clear pattern. There are large expanses of Europa (beyond this region) that have not been broken into rafts and where the surface pattern is uninterrupted ridges and grooves. The rafts in Figure 21 are clearly broken fragments of this sort of terrain. The ridge and groove pattern is caused by the opening and closing of cracks, probably on a tidal cycle coincident with Europa’s 3.6-day orbital period. Globally,only a few cracks would be active at any one time. When an active crack is opened (to a width of perhaps just a metre or so), water is drawn up from below. The water temporarily exposed to the cold vacuum of space at the top of the crack simultaneously boils and freezes, but pretty soon becomes covered by slush. When the crack closes, some slush is squeezed out onto the surface, forming a ridge above the closed crack. The next time the crack opens, the ridge is split, and is added to by more slush when the crack closes again. A few years of opening and closing would suffi ce to surround central grooves by ridges of the size we see. Eventually,each crack seals permanently, but a new crack will begin to operate somewhere else, and so the pattern is built up, giving the ridge and groove terrain covering much of Europa, an appearance that has been likened to that of a ball of string.

21.A 42-kilometre-wide close-up of part of the Conamara Chaosregion of Europa, where ‘melt-through’ from the underlying ocean hasallowed rafts of ice to drift apart before the area refroze. Sunlight isfrom the right

In Figure 21 , ‘ball of string’ terrain has been disrupted by the other great process that affects Europa. This is ‘melt-through’, and results in a jumbled mixture of broken ice rafts described as‘chaos’. Under a future chaos region, the ocean becomes unusually warm – maybe because of silicate volcanic eruptions on the ocean fl oor – and the base of the surface shell of ice gradually melts, so the ice becomes thinner. Eventually, melting reaches the surface,and rafts (or fl oes) of ice break away from the exposed edges of ice shelf and drift into the exposed ocean. Any exposed water would refreeze pretty quickly, and perhaps it is better to think of kilometre-thick ice rafts nudging their way into a sea covered by icy slush, rather than into truly open water like the summer thaw of pack ice in the Earth’s Arctic ocean. In the north-west part of Figure 21 , you can see the way many of the rafts originally fi tted together, because they have not drifted far apart and their ‘ball of string’ textures can be matched.

After the temporary heat excess dies away, the ocean refreezes and the rafts cease to drift. The ice of the refrozen sea surface and beneath the rafts begins to thicken again. When the refrozen area is suffi ciently thick and brittle, new cracks may open, and a new generation of ‘ball of string’ texture begins to overprint the whole region. In Figure 21 , there is a young crack, fl anked by a narrow ridge on either side, running diagonally across. It looks unremarkable where it crosses rafts, but you can tell that it must be young because it cuts the refrozen sea lying between the rafts.

If this story is even remotely correct, then there are some very thought-provoking implications. Chemical reactions with the underlying rock would make the ocean salty – though the most abundant dissolved salt might be magnesium sulfate rather than sodium chloride as in Earth’s oceans. Any such ocean overlying tidally heated rock provides a habitat for life equivalent to where life is believed to have begun on Earth. Lack of sunlight is no hindrance, because the ‘primary producers’ at the base of the local food chain would derive their energy from the chemical imbalance supplied to the ocean at submarine hot springs (hydrothermal vents). Such life is described as chemosynthetic, as opposed to photosynthetic. On Earth’s ocean fl oors, the hottest vents are called ‘black smokers’ because of the plume of metal sulfi de particles that forms when the vent fl uid mixes into the ocean water. These vents are surprising oases of life, where communities of organisms (including some as advanced as shrimps and crabs)feed on chemosynthetic microbes that gain their energy by converting carbon dioxide into methane. If life on Earth began in such a setting, why not also on Europa?

Life sealed below ice that is normally kilometres thick would be extremely challenging to fi nd, requiring Europa landers to drill or melt a hole through the ice in order to launch a robotic submarine probe that could home in on a ‘black smoker’ plume. However,such an ambitious mission may not be necessary if the ridges either side of a young crack are built of slush squeezed up from the ocean. While a crack is open, it could provide a niche for photosynthetic life such as plants or (more reasonably) marine algae. Like life on Earth, these could have evolved from chemosynthetic forebears. Radiation would render the top few centimetres of the exposed water column uninhabitable, but there would be enough sunlight for photosynthesis in the next few metres. If there are primary producers (plants, algae) living off sunlight, there could be animals feeding on them. To fi nd out, the fi rst step is to investigate a sample from the ridge squeezed out of a crack.

The next big NASA-ESA collaboration in outer Solar System exploration is likely to be a mission to the Jupiter system. Its primary goal will be to verify the existence of Europa’s ocean,using ice-penetrating radar and by measuring the amount of tidal fl exing (which would be only about a metre in the case of ‘thick’ice resting on bedrock, but about 30 metres for a ‘thin’ ice shell fl oating on an ocean). Sadly, a lander cannot be contemplated yet,but there will at least be high-resolution spectroscopy from orbit to look for biogenic molecules in the ridge material.

Enceladus

It would be much easier to fi nd biomarkers if Europan ice could be sampled without having to go down to the surface. Enceladus,a satellite of Saturn, offers just that opportunity. It is only 504kilometres in diameter and has too low a density to contain much rock. Voyager showed it to be a strange little world, heavily cratered in parts but elsewhere apparently lacking in craters. The higher-resolution images transmitted by Cassini , which began an orbital survey of the Saturn system in 2004, shows a surface cut by many families of cracks (though rather unlike the ‘ball of string’regions of Europa). It also discovered jets of icy crystals venting to space from cracks near the south pole ( Figure 22 ). Fortunately,Cassini carried a mass spectrometer intended for study of ions and neutral particles, so the spacecraft’s trajectory was adjusted to allow it to fl y through the plume and capture some samples. These were found to contain water, methane, ammonia, carbon monoxide, and carbon dioxide. There were also probably some simple organic molecules, though that is a chemical term denoting carbon atoms linked together and does not imply a biological origin. If the plumes had been known in advance, instruments better suited for detection of biomarkers might have been included in Cassini ’s payload.

22.Two Cassini images of Enceladus. Left: an overexposed crescentview, showing a plume extending at least 100 kilometres above thesurface. Right: an oblique view across part of Enceladus cut by severalfamilies of cracks, like those from which the plume is known tooriginate. A few small impact craters (too small for Voyager to see)show that this particular region is probably no longer active

Almost certainly, tidal heating (driven by 2:1 orbital resonance with Saturn’s next-but-one satellite Dione) drives the crack formation and provides the impetus for the plumes. However, no one expected Enceladus to be so active, and this is particularly baffl ing given that its similar-sized neighbour Mimas is an archetypical cratered ice-ball showing no history of activity. It is unlikely that Enceladus has a global ocean hidden below its surface, but there may be pods of liquid water beneath the plume sources. Liquid water is good for life, but the availability of nutrients within Enceladus is surely much more restricted than within a large body such as Europa, so Enceladus does not seem such a promising habitat.

Titan

Titan is Saturn’s only satellite that rivals Jupiter’s Galilean satellites in scale (5,150 kilometres in diameter). Voyager showed it only as a fuzzy orange ball, because – alone among satellites – it has a dense atmosphere. This is 97% nitrogen but is made opaque by methane and its photochemical derivatives that turn the stratosphere into an opaque smog. Titan has a crust and mantle made of ice (mostly water-ice) occupying the outer one-third of Titan’s radius and overlying a rocky core. There could be an iron inner core, in which case, to balance out the average global density, the base of the icy mantle would have to be deeper. Titan’s rotation period is affected by seasonal winds, showing us that the lithosphere must be decoupled from the interior, most likely by an internal ocean. This could be mostly water or a mixture of water and ammonia (which can remain liquid at a considerably lower temperature than pure water). Most models place it as a layer within the icy mantle, rather than situated immediately on top of the internal rock.

The Cassini mission tackled the problem of seeing through to Titan’s surface in three ways: it obtained blurred but usable images of the surface in some narrow bands of the near-infrared spectrum where the smog is least opaque, it used imaging radar like the Magellan Venus orbiter to see the ground irrespective of clouds, and it carried a landing craft, named Huygens , that provided images from below the clouds during parachute descent to the surface. Titan’s surface geological processes revealed by this array of imaging techniques are superb analogues to many of the processes that occur on Earth. The crust is dominantly water-ice, very rigid and rock-like in its behaviour in Titan’s –180 °C surface environment. Huygens came to rest near the equator on a sandy plain strewn with pebbles. It looked like Mars except that both sand and pebbles were made of ice. The sand could have been wind-blown, and indeed radar images reveal vast fi elds of wind-blown sand dunes in other parts of Titan. However, the pebbles must have been transported by fl owing liquid, which, given Titan’s atmospheric composition and surface temperature, must be methane (CH_4
) or ethane(C_2
H_6
). As it descended, Huygens saw branching drainage channels near to the landing site, and radar imaging reveals complex valley systems in many other regions, starting in highlands where the ‘bedrock’ of icy crust is exposed and draining into lowland basins where sediment accumulates.Better than that, it found lakes of ethane-tainted liquid methane near both poles ( Figure 23 ). Some lake-beds were dry, and others had shallow or marshy fringes, and it is likely that they vary seasonally. Titan is clearly geologically active. A few deeply eroded impact craters have been recognized, and there are some sites of suspected ‘cryovolcanism’, where icy ‘magma’ is erupted analogously to terrestrial lava flows.

23.A 1,100-kilometre-long mosaic of Cassini radar images, nearTitan’s north pole. The dark areas are lakes, the largest of whichexceeds 100,000 square kilometres, 20% bigger than Lake Superior inNorth America. Dendritic drainage channels can be seen feeding thelakes. Lines of longitude have been added; blank areas are unimaged

The extent to which cryovolcanism and tectonic processes contribute to the sculpting and resurfacing of Titan’s surface is unknown. However, it is clear that erosion of bedrock (in this case,ice, of course) followed by transport and deposition of sediment are major players. Rainfall on Titan must consist of droplets of methane that, like rainfall on Earth, infi ltrates the ground and feeds springs that supply streams and rivers. The capacity of methane to react chemically with the icy ‘bedrock’, its erosive power, the rate at which it evaporates back into the atmosphere,and how long it remains there before raining out again are uncertain. All these must be factors in a methanologic cycle that mimics Earth’s hydrologic cycle. Mars had rainfall, rivers, and lakes long ago, but Titan is the only other place where they occur today. One day, we will send another probe to explore Titan more thoroughly – perhaps including a balloon to drift below the smog,with variable buoyancy so it can touch down in interesting places.Such a mission could sample the lake fl uid, and obtain pictures of waves breaking on a thoroughly alien shore.

Miranda and Ariel

Although present-day cryovolcanism on Titan remains controversial, ancient cryovolcanism cannot be doubted on two of Uranus’s fi ve regular satellites, Ariel and Miranda, where the surface temperature is –200 °C. Its effects can be seen on images sent back by Voyager 2 , which fl ew through the Uranus system in January 1986.

Ariel is the larger of the two (1,158 kilometres in diameter). It is a complex globe, whose oldest cratered terrain is cut by numerous faults bounding high-standing blocks. Most of the faults defi ne fl at-fl oored valleys of the kind denoted by the descriptor term‘chasma’. However, rather than preserving down-dropped highland surface, the fl oors of most chasmata have been covered by smooth material, or at least by something that appears smooth at the 1-kilometre resolution of the Voyager images.

Probably in the distant past (more than 2 billion years ago), tidal heating led to fracturing of Ariel’s surface and the effusion of cryovolcanic lava. This covered the fl oors of the chasmata, and in places can be seen spreading beyond them to partly bury some older impact craters. At the distance of Uranus from the Sun, its ice is expected to be a more complex cocktail than the slightly salty ice found on Jupiter’s satellites. The most likely melt to be extracted by partial melting is a 2:1 mixture of water and ammonia. This is liquid at –100 °C and so can be generated by much more modest heating than would be required to melt pure water.

Individual ‘lava’ fl ows can also be seen on Miranda, which is Uranus’s smallest regular satellite (472 kilometres in diameter).For such a tiny body, it has a remarkably diverse surface, probably more varied even than Enceladus, although the number of superimposed impact craters shows that its last activity was probably billions of years ago. Voyager 2 saw only half the globe.Half of that is heavily cratered, but is unusual in that most craters(the older ones) have smooth profi les, as if they have been mantled by something falling from above, and only younger craters are pristine. The other half of the imaged area comprises three sharp-edged terrain units described as coronae. Each is different,but they all contain complex ridged or tonally patterned terrain,including features identifi ed as cryovolcanic lava fl ows (probably water-ammonia lava, as on Ariel), and pocked by pristine craters equivalent to those in the heavily cratered terrain.

An early theory about Miranda that each corona represents a fragment from catastrophic global break-up and re-accretion has been discounted. Most likely, the coronae are sites of cryovolcanism, of which only the waning phase has left recognizable fl ow-like traces. Mantling of the older craters in the terrain beyond the coronae may demonstrate explosive eruptions,spraying icy particles into space, some of which settled, snow-like,to subdue pre-existing topography. When and why this happened,we do not know. We are unlikely to fi nd out until there is another mission to Uranus, which is not likely before mid-century.

Triton

Triton is Neptune’slargest satellite (2,706 kilometres in diameter).Its outer part is icy, but it is dense enough to have a substantial rocky core. When Voyager 2 flew past in 1989, it found polar caps of frozen nitrogen ice (previously detected spectroscopically from Earth). Like the carbon dioxide in Mars’s polar caps, these probably shrink in summer, by sublimation rather than by melting, adding their content to Triton’s thin but respectable atmosphere which is made largely of nitrogen. The stable‘bedrock’ ice forming Triton’s crust appears to be a mixture of methane, carbon dioxide, carbon dioxide, and water. There may be ammonia too, which is almost invisible to optical spectroscopy.

The best images of Triton have a resolution of about 400 metres per pixel. They reveal a geologically complex surface beyond the polar cap, including various landforms that may have been created cryovolcanically ( Figure 24 ). Impact craters occur everywhere, but not in vast numbers, and it is possible that much of the surface is less than a billion years old. Triton is also remarkable for having geysers that erupt through the polar cap, lofting dark particles to a height of about 8 kilometres. There are a few high-altitude clouds made of nitrogen crystals, analogous to cirrus clouds in our own atmosphere.

Only the south polar cap was seen by Voyager 2 , because most of the northern hemisphere was in darkness. Triton’s seasons are peculiar, resulting from a combination of Neptune’s 29.6° axial tilt added to the 21° inclination of Triton’s orbit. Further to this,Trion’s orbital plane precesses about Neptune’s axis so that a full seasonal cycle on Triton equates not to Neptune’s 164-year orbital period, but to a 688-year cycle, with 164-year subcycles superimposed. During the full cycle, the subsolar latitude on Triton ranges between 50° north and 50° south. By chance, when Voyager 2 made its fl y-by, Triton was approaching extreme southern summer, with the Sun overhead at nearly 50° south, so a large part of the northern hemisphere was in darkness and could not be seen. The sunlit southern polar cap showed signs of being in retreat, and its sublimation to gas was verifi ed by observations from Earth in 1997 showing that atmospheric pressure had doubled in the eight years since the Voyager encounter.Meanwhile, the unseen north polar cap was probably growing, as atmospheric nitrogen condensed onto the frigid surface.

24.A mosaic of Voyager images covering a 2,000-kilometre-wideregion of Triton. South is towards the top, and sunlight is coming fromthe upper right. The ragged edge of the south polar cap runs diagonallyacross the top of the image. Long, narrow, curved ridges (sulci) may befi ssures where cryovolcanic icy magma was erupted. The smooth plainsand basins in the lower left are probably expanses of cryovolcanic lava.The dimpled area in the centre and lower right is called ‘canteloupeterrain’, by visual analogy to the skin of a melon, but its origin isunknown

Chapter 5　Asteroids

No book about planets would be complete without a discussion of asteroids, because these are the most common objects to hit planets in the inner Solar System (where asteroid impacts are about ten times more common than comet impacts). In addition, the largest asteroid, Ceres, is offi cially classifi ed as a dwarf planet.

Shapes, sizes, and compositions

Ceres is the goal for NASA's　Dawn spacecraft, which will spend fi ve months orbiting it in 2015, having already spent the year beginning in July 2011 at Vesta, the second most massive asteroid.

A few smaller asteroids have already been visited by spacecraft, providing images ( Figure　25 ) that confi rm their irregular shapes. Visualize a pock-marked potato scaled up to any size between tens of metres and a few hundred kilometres, and you should have a serviceable mental image of a typical asteroid. Telescopically observed periodic variations in asteroids'brightness show that mostly they take only a few hours to rotate. Generally, rotation is at right angles to their length, so they rotate like sausages twirled on a cocktail stick.

About 1 asteroid in 50 probably has its own satellite, and it was lucky that Ida, the second asteroid to be visited by a spacecraft when Galileo fl ew past in 1993, turned out to be one of these. That was the fi rst confi rmed discovery of an asteroid satellite, but subsequently many more have been found using advanced telescopic techniques, such as adaptive optics to compensate for the shimmering of the Earth’s atmosphere. Asteroid satellites range from the comparatively tiny up to sizes similar to the main asteroid. In fact, the asteroid named Antiope appears to consist of two mutually orbiting bodies of indistinguishable 110-kilometre size, whose centres are only about 170 kilometres apart. So far,there are two asteroids known to possess two small satellites each.Some asteroid satellites may be fragments from a collision, and others may be captured objects. Neither case is readily explicable,because it is hard to end up with objects orbiting rather than fl ying apart.

25.Images of asteroids at different scales. Top: Ida, a 54-kilometrelongmain belt asteroid, with its tiny satellite Dactyl to its right.Lower left: Eros, a 33-kilometre-long near-Earth asteroid. Lowerright: Itokawa, a 0.5-kilometre-long Earth-crossing asteroid. Thereare many impact craters visible on Ida and Eros, but the much smallerItokawa is boulder-strewn

Asteroid densities have been measured between 1.2 and 3.0 g/cm 3 .However, stony meteorites, which are clearly bits of asteroid, have densities of about 3.5 g/cm 3 and stony-iron meteorites have densities close to 5.0 g/cm 3 , so none of the measured asteroids can be an intact solid body. Rather, they must be porous rubble piles.Some, such as Itokawa, visited by the Japanese probe Hayabusa in 2005 ( Figure 25 ), and others whose shape has been determined by radar, appear to be ‘contact binaries’ consisting of two main masses joined at a narrow waist. However, the numerous boulders on much of Itokawa’s surface show that the two main masses are themselves composed of many pieces.

Asteroids are not strongly coloured, but can be grouped into several classes according to their refl ectance spectrum. There are three main types. S-types have the characteristics of silicate rock,and are evidently the same material as stony meteorites. They make up the majority of asteroids with orbits between about 2.0and 2.6 AU from the Sun, whereas from 2.6 to 3.4 AU, C-types,having the characteristics of carbonaceous chondrite meteorites,are the most common. Beyond 3.4 AU, asteroids tend to be dark and somewhat red in colour. These are dubbed D-type, and may be coloured by a tarry surface residue formed from carbonaceous material during prolonged exposure to solar radiation (space weathering). These tarry substances are usually referred to as‘tholins’, a term coined from the ancient Greek word for ‘mud’ by the American astronomer Carl Sagan (1934–96).

Scattered here and there are asteroids that appear largely metallic(M-type), clearly related to iron meteorites, and a few that appear to have basalt on their surface, notably Vesta, from which they take their designation V-type. These, or their now fragmented parent body, may have once been hot enough for internal melting and volcanic eruptions.

Asteroid orbits

Most known asteroids (equivalent to about 4% of the Moon’s mass)have orbits lying between the orbits of Mars and Jupiter, in the so-called ‘asteroid belt’. Over 3,000 main belt asteroids have been documented. More than half the total mass of these resides in the four largest examples, Ceres, Vesta, Pallas, and Hygeia, with diameters of 950, 530, 540, and 430 kilometres respectively (Vesta is denser than Pallas, so is more massive despite being slightly smaller).Undiscovered objects range down in size through individual lumps of rock to dust particles. Nevertheless, the asteroid belt is virtually empty space, and you should not think of it as replete with jostling rocks. All space probes that have been sent through the asteroid belt have survived without mishap, and even have to be steered carefully to come close enough to any asteroid to study it in passing.

Jupiter’s gravity has considerable infl uence on main belt asteroid orbits. Notably, it prevents asteroids settling into orbits whose periods would be in resonance with its own. There are virtually no asteroids whose orbital periods are simple 4:1, 3:1, 5:2, or 2:1 ratios of Jupiter’s. These correspond to average distances from the Sun(orbital semi-major axes) of 2.06, 2.50, 2.82, 3.28 AU,respectively,which are known as the Kirkwood gaps, after Daniel Kirkwood, an American astronomer who discovered and explained them in 1886.Not all orbital resonances are unstable with respect to asteroid orbits, and in fact there is a small family of asteroids whose orbital periods are two-thirds that of Jupiter (a 3:2 orbital resonance).

There are a great many more asteroids with the same orbital period as Jupiter. There may be more than a million of these greater than 1 kilometre in size, with a combined mass about one-fi fth that of the main belt. These occur only close to locations60° ahead of, and 60° behind, Jupiter in its orbit. Those are special places where the combined gravitational force from the Sun and Jupiter allows small objects to orbit stably, and are known as the leading and trailing Lagrangian points. Asteroids in these orbits are by convention given names of heroes from the Trojan War (Greek names 60° ahead of Jupiter and Trojan names60° behind), but are collectively referred to as ‘Trojan asteroids’.

We're all doomed!

A few asteroids are known in similar ‘trojan’ relationship to Mars,but Earth has no trojan companions. However, there are asteroids whose orbits cross ours, known as Earth-crossing asteroids. If you are worried about collisions, this may sound alarming, but asteroid orbits tend to be inclined to the ecliptic, so they almost always pass either ‘above’ or ‘below’ us when they cross our orbit.Only a subset of Earth-crossers are regarded as Potentially Hazardous Asteroids (PHAs), being those that can pass within0.05 AU of the Earth (a range suffi ciently close that perturbations caused by various third bodies could bring about a collision) and that are larger than about 150 metres in diameter (big enough to survive passage through the atmosphere with undiminished speed). By the end of 2009, about 1,100 PHAs had been documented, plus fewer than 100 Potentially Hazardous Comets.

The closest calculated approach by a PHA is by Apophis (350metres long) that will come very close on Friday 13 April 2029.Soon after its discovery, in 2004, its orbit was suffi ciently poorly known that there was a chance (estimated at 2.7%) of a collision,but subsequently a longer series of observations showed that it will pass safely about 30,000 kilometres above the surface. It will be back again on 13 April 2036, and because we do not know exactly how close it will pass in 2029, we do not know exactly how much its trajectory will be affected by the Earth’s gravity during that encounter. However, the chances of collision in 2036 are vanishingly small.

An asteroid that penetrates Earth’s atmosphere with undiminished speed is very dangerous. On hitting the ocean, it could cause a tsunami, and if it hits land, it excavates a crater much larger than itself and devastates the surrounding area.A 2.2-million-year-old, 130-kilometre crater named Eltanin has been discovered under the fl oor of the Bellinghausen Sea, in the southernmost Pacifi c ocean, apparently caused by an asteroid several kilometres in diameter. This would have barely been slowed by the ocean, let alone the atmosphere, before striking the sea bed. According to computer models, the resulting tsunami would have devastated the coast 300 metres above sea-level in southern Chile and 60 metres above sea-level in New Zealand.The quantity of water and dust thrown into the atmosphere might even have been the trigger for climate change leading to the migration of our ancestors, Home erectus , out of Africa, at about this date. The most recent collision between the Earth and a10-kilometre ‘dinosaur-killer’ asteroid happened 65 million years ago, creating the 200-kilometre-diameter Chicxulub crater, now buried beneath sediment in the Yucatan peninsula of Mexico. This caused a global environmental upheaval that is widely credited as the cause of a ‘mass extinction event’ when about 75% of species of life on Earth were wiped out.

Catastrophes of that magnitude are mercifully rare, but statistics show that asteroid impacts rank alongside volcanic eruptions,earthquakes, and extreme weather events as potential causes of death. A 1-kilometre asteroid able to devastate coasts 3,000kilometres from the point of impact strikes the ocean on average about every 200,000 years, whereas a 200-metre asteroid with a signifi cantly smaller tsunami danger radius might be expected about every 10,000 years.

To categorize the hazard posed by each PHA, astronomers use a numerical system called the Torino Scale (agreed at a meeting in Turin, hence the name). This combines the energy that would be delivered and the probability of collision into a single number from 0 to 10, where 0 means negligible chance of collision and/or too small to penetrate the atmosphere, and 10 is certain impact by a ‘dinosaur-killer’ causing global catastrophe. Most PHAs exceeding 150 metres in diameter are ranked either 0 or 1 when they are discovered, and the 1s are usually downgraded to 0 when their orbit has been more adequately determined. Apophis holds the record for having temporarily held a Torino rating as high as 4(‘Close encounter, meriting attention by astronomers; 〉1% or greater chance of collision capable of regional devastation’), but was downgraded to 0 in 2006.

A semi-formal linking of observatories known as Spaceguard has assumed the task of locating and categorizing all PHAs. This is important because, unlike most sorts of natural disaster when all we can do is mitigate the effects, it would be possible to prevent a collision by a PHA. To achieve this, it is necessary to change either the PHA’s speed or its direction of travel. The longer in advance this is done, the smaller the required change. There are various ways to do it, ranging from the brute-force method of equipping the PHA with a rocket motor, to the more subtle ploy of coating of one side in a refl ective substance so that solar radiation-pressure does the job for you. Using a nuclear bomb to blast apart an incoming PHA is not a smart idea, because unless you could guarantee that all the fragments would be too small to penetrate the atmosphere, you might make the problem worse by causing multiple impacts.

Asteroid mining

There is a silver lining, in that asteroids could be valuable sources of raw materials. A 1-kilometre M-type asteroid contains more nickel and iron than the world’s annual consumption, and the most massive example, Psyche, contains enough to last for millions of years. Asteroids, especially M-types, also contain precious metals like platinum.

The investment to begin mining the fi rst asteroid would be very great, but the potential returns are immense too. It remains to be seen whether the main value of asteroids turns out to be supply of raw materials to Earth or to space-based industries. Some near-Earth objects are probably defunct comets with remnant water-ice surviving beneath their dusty surfaces, which could be valuable as propellant and radiation shielding, as well as for drinking.

Names and provisional designations

By 1891,332 asteroids had been discovered visually, but photography had boosted the tally to 464 within 10 years. There are now over 100,000 known objects of all types, each of which needs to be identifi ed in some way. The IAU oversees a system of provisional designations given to each new discovery. This consists of the year of discovery plus a two-letter code coupled with numerical subscripts, corresponding to the date and sequence of discovery. The fi rst letter (A–Y, omitting I) specifi es which half-month the discovery was made in (A for January 1–15, B for January 16–31, and so on, up to Y for 16–31 December), the second letter (A–Z, omitting I, which gives 25 options) is awarded to each discovery in sequence, and a numbered subscript allows the cycle of 25 to be repeated as many times as necessary. Thus,2011 BA would be the fi rst body discovered in the period January16–31 2011; 2011 BB would be the 2nd; 2011 BA 1 would be the26th, and so on. When an object’s orbit has been well determined(which may take several years), it can be awarded a permanent name, which replaces the provisional designation. For example,Apophis originally had the provisional designation 2004 MN 4(signifying the 113th discovery during 16–30 June 2004).

The privilege of suggesting a permanent name is given to the discovery team, though some automated surveys reveal so many new objects that managers are glad of suggestions. Permanent names are a name preceded by a number, added in sequence as each new name is added. So formally we have (1) Ceres, (4) Vesta,(99942) Apophis, and so on. Available mythological names are too few for all these objects, and pretty much anything is allowed,except that names must be inoffensive and unconnected with recent political or military activity. I know several astronomers who have had asteroids named after them (by colleagues; you can’t name one after yourself ), and there is one called (5460)Tsenaat’a’i, which means ‘fl ying rock’ in the Navaho language. The only asteroid that I have had a hand in naming is (57424)Caelumnoctu, named in 2007 to commemorate the 50th anniversary of BBC television’s long-running programme The Sky at Night , which in Latin is Caelum Noctu . We picked it from a list because its number refl ects the date of the fi rst broadcast, which was 1957 April 24 (57/4/24).

Chapter 6　Trans-Neptunian objects

A relatively sparse population of asteroids, known as Centaurs,exists between Jupiter and Neptune. Some are dark and red,similar to the tarry (tholin-covered) D-type asteroids, but others are bluer, suggesting that much of their surfaces may be freshly exposed ice. Because their orbits cross or come close to the giant planets, they are not stable, persisting for no longer than about ten million years. Probably, Centaurs are TNOs that have been scattered inwards, perhaps by a close encounter with Neptune.Further interactions with giant planets probably nudge them inwards until they become short-period comets, spending perihelion in the inner Solar System, where they are heated by the Sun and lose their volatiles in sometimes spectacular tails.

Six trojan objects have been discovered close to Neptune’s leading Lagrangian point. Dynamical arguments suggest that vast numbers await discovery (in both Lagrangian points) and that Neptune trojans may be ten times more numerous than Jupiter’s.

Beyond Neptune, we reach the Kuiper belt and all the other TNOs. One family of Kuiper belt objects travel in 3:2 orbital resonance with Neptune. Members of the class, which includes Pluto, are known informally as ‘plutinos’, not to be confused with Plutoid, which is the offi cial IAU term for any TNO large enough to be ranked as a dwarf planet. Plutoids can be plutinos, classical Kuiper belt objects (lacking orbital resonance with Neptune), or Scattered Disk objects beyond the main belt. Classical Kuiper belt objects are known alternatively as ‘cubewanos’ (‘QB 1 -os’) because the first Kuiper belt object to be discovered after Pluto bore the provisional designation 1992 QB 1.

Pluto and Charon

The properties of most TNOs are poorly known. However, Pluto and its satellite Charon are suffi ciently large and nearby to have been studied telescopically for several decades. Frozen nitrogen,methane, and carbon dioxide have been detected spectroscopically on Pluto, and the sharpest telescope images reveal dark patches that are probably tholin-rich residues. Pluto’s density suggests that rock must be about 70% of its total mass, and most likely it is internally differentiated with a rocky core (and feasibly an iron-rich inner core) overlain by a mantle made mostly of water-ice topped by a more volatile-rich crust.

Near perihelion (which happened most recently in 1989), Pluto has a nitrogen-rich atmosphere possibly denser than Triton’s.Because Pluto’s gravity is so weak, an imaginary shell enclosing99% of its atmosphere would extend to 300 kilometres above the surface, whereas for the Earth the equivalent height is only40 kilometres. Much of Pluto’s atmosphere is expected to condense onto the surface while distance from the Sun increases from 4.5 billion kilometres at perihelion to 7.4 billion kilometres at aphelion in 2113. It is a pity that we missed the chance to study

Pluto from close range during perihelion. The fl y-past by NASA’s New Horizon mission to Pluto will occur in 2015, by which time much of the atmosphere may have condensed and hidden the‘permanent’ surface beneath a seasonal shroud of nitrogen-ice.Pluto’s 6.4-day rotation period is the same as the orbital period of its largest satellite, Charon, which also rotates synchronously. This relationship is a result of strong tides, and means that Pluto and Charon permanently keep the same faces towards each other.Pluto is more evenly matched in size and mass to Charon than any other planet or dwarf planet to its own largest satellite. Charon’s mass is about 12% of Pluto’s, and it orbits at a distance of only about 17 Pluto radii from Pluto’s centre. For comparison, the Moon’s mass is only 1.2% of Earth’s and its orbital radius is60 Earth radii. Charon’s proximity to Pluto explains why it remained undetected until 1978. Pluto’s two smaller satellites, Nix and Hydra, were discovered in 2005. These orbit in Pluto’s orbital plane in close to 4:1 and 6:1 orbital resonance with Charon.

Seen from Pluto’s surface, Charon would look eight times wider than the Moon does from Earth. Because their relative masses are so similar, their common centre of mass (their ‘barycentre’) is not inside Pluto but at a point in space between the two bodies.Although double asteroids such as (90) Antiope and double Kuiper belt objects such as 2001 QW 332 (200-kilometre diameter twins) are known, Pluto-Charon is the most evenly matched pair among bodies large enough to count as planets or dwarf planets.

Charon’s surface is dominated by water-ice with traces of ammonia. Its density is less than Pluto, but still suffi cient for a substantial rocky core. Charon may turn out to be a relatively passive, heavily cratered globe, whereas Pluto might impress us all by being geologically active, as the variety in its surface materials suggests.

On the other hand, there may be a reason for Charon to be more active than its larger cousin. This is because Pluto’s axial inclination is 119.6° (being greater than 90°, this means its rotation is retrograde). Charon’s orbit is exactly in Pluto’s equatorial plane, so shares the high inclination relative to their joint orbit about the Sun. Competing tidal pulls on Charon from the Sun and Pluto might feasibly be strong enough to cause melting somewhere within Charon’s icy mantle. If this is the case,then we are faced with the intriguing prospect of a Europa-like surface for Charon and even a potentially life-bearing ocean beneath it. The best hint we have so far comes from infrared spectra of Charon obtained in 2007 which found water-ice on Charon that is still in pristine crystalline form, in contrast to the amorphous submicroscopic state of ice that has been exposed to solar ultraviolet radiation and cosmic ray bombardment for more than a few tens of thousands of years. The simplest explanation for this is geysers, spraying out fresh ice from the interior, like the plumes on Enceladus.

The rest

Table 7 lists Pluto and the ten largest other TNOs as ranked at the time of writing. Of these, Eris, Makemake, and Haumea are offi cially recognized as dwarf planets. The latter is fl attened, either because of its rapid rotation (less than 4 hours) or resulting from collision. These are classical Kuiper belt objects, except Eris and2007 OR 10 (Scattered Disk objects), 2002 TC 302 (5:2 orbital resonance with Neptune), Ixion (plutino), and Sedna, which is an oddity way beyond the Scattered Disk, in a highly elliptical orbit with aphelion at 975 AU.

Table 7　The largest trans-Neptunian objects

Apart from Pluto, the sizes of these objects are poorly known(even those for which a single round number is given in the table).Their dimensions are estimates based on assumptions about their albedo (the percentage of the incident sunlight they refl ect). If they are less refl ective than assumed, they must be larger, but if they are more refl ective, then they must be smaller. Size estimates can be improved by measuring thermal radiation from their surfaces, but they are so cold (–230 °C or less) that this can be achieved only by telescopes in space, above the Earth’s atmosphere. Given the uncertainties, it is unlikely that all of these objects will survive into future ‘top ten’ lists.

TNOs range in colour from red (probably widespread tholins across their surfaces) to blue-grey (exposed ice or amorphous carbon). Haumea is one of the blue-grey ones, and its mass(derived from the orbits of its satellites) shows that its density is greater than Pluto’s, so it must have a relatively high non-ice content. On Quaoar, crystalline ice and ammonia hydrate have been detected spectroscopically, suggesting recent resurfacing(using arguments similar to those advanced for Charon). This would require either geological activity or a major impact event to generate ejecta suffi ciently widespread to dominate the spectrum.

Between 2% and 3% of TNOs are known to have satellites, which is similar to the abundance of asteroids with satellites. The proportion is higher among the larger TNOs and poses problems in trying to account for their origin.

If NASA’s New Horizon mission remains healthy after its 2015fl y-by of Pluto-Charon, it will be directed onwards to a more distant TNO. The target has yet to be determined, but ideally will be a blue-grey object to contrast with Pluto’s reddish nature.

A trans-Neptunian planet?

Most astronomers accept that we have discovered all the large objects belonging to our Solar System. Certainly, there can be nothing of planetary size hiding in the Kuiper belt. If such an object were present, then the Kuiper belt would be unstable.However, there remain two possibilities for an outlying planet(popularly dubbed ‘Planet X’) that have not yet quite gone away.One is that there is an Earth-mass object in an inclined and eccentric orbit between 80 and 170 AU from the Sun. The presence of such a large body (perhaps originally ejected outwards by a close encounter with Neptune) could explain an observed sudden drop-off in the population of the Kuiper belt beyond 48AU, known as the ‘Kuiper cliff ’. It might also account for the extreme scattering evidenced by objects such as Sedna.

The second possibility arises because long-period comets originate preferentially from a particular region of the sky, rather than coming in from random directions. It has been suggested that these were dislodged from the Oort Cloud by a Jupiter-mass body about 32,000 AU from the Sun. This would be hard, but not impossible, to detect by telescope. A ‘planet’ so far out need not be gravitationally bound to the Sun, but could be just a chance wanderer through interstellar space, possibly escaped from the planetary system of another star.

Chapter 7　Exoplanets

There is no longer any doubt that planets are common around other stars. Until comparatively recently, this was a matter for speculation,but by 2010 the number of stars proven to have at least one planet orbiting them had exceeded 400. Allowing for how diffi cult it is to make these detections, it is clear that the majority of Sun-like stars must be accompanied by planets. To avoid confusion, professionals usually refer to them as ‘extrasolar planets’ or ‘exoplanets’. The exoplanet tally excludes exotic dim objects exceeding 13 Jupitermasses,which is the threshold above which nuclear fusion of deuterium (heavy hydrogen) can occur. Those are called ‘brown dwarfs’ and are regarded as more star-like than planet-like.

Detection methods

Evidence that most young Sun-like stars have a surrounding ring of dust began to accumulate in the late 1970s. Initial clues came from the infl uence of dust on a candidate star’s infrared spectrum,then images of dust discs began to be obtained in the 1980s.Irrespective of whether these discs are like the solar nebula before planets formed or are remnant dust surviving in the equivalent of a star’s Kuiper belt, their mere existence showed that there ought to be plenty of planets out there too. The fi rst defi nite exoplanet discovery was made in 1995, after which discoveries gathered pace year by year.

Radial velocity

The fi rst discovery, and the majority ever since (more than 300 by2010), was made by detecting slight changes in a star’s radial velocity. This is the speed at which a star is travelling towards or away from the Earth, irrespective of any movement across the line of sight. Radial velocity changes can be determined to a remarkable precision of one metre per second by measuring shifts in the exact wavelength at which characteristic absorption lines appear in a star’s spectrum. These shift to shorter wavelengths (‘blue shift’) if the star is moving towards us and to longer wavelengths (‘red shift’)if the star is travelling away, in a phenomenon called the Doppler effect. Variations in radial velocity had long been used to measure orbital speeds (and hence to infer masses) of double stars, but the tiny infl uence of a much less massive exoplanet on a relatively much more massive star requires very sensitive modern instrumentation.Radial velocity changes caused by the Earth’s own orbital motion have to be accounted for before the more subtle changes attributable to the tug of the exoplanet on its star become apparent.

The gravitational attraction between star and exoplanet depends on the sum of their masses. Fortunately, for Sun-like stars there is a well-understood relationship between stellar spectral type and mass. Knowing this, we can use the period and magnitude of radial velocity changes to determine the mass of the exoplanet responsible for the forward and back motion of the star. Usually,there is no independent measure of the orientation of an exoplanet’s orbital plane, and unless the orbital plane is exactly edge-on to our line of sight, the true change in velocity must be greater than what we detect. However, statistical arguments(based on assuming randomly oriented orbital planes) show that the majority of masses can be no more than twice the estimate based on assuming that the orbit is edge-on to us.

The radial velocity method works best for large planets orbiting close to their star, because large mass and close proximity both lead to the greatest changes in the star’s radial velocity. Thus it should have been no surprise that the fi rst exoplanets to be detected tended to be more massive than Jupiter but orbiting only a fraction of an AU from their star.

Discovery of these so-called ‘hot Jupiters’ caused quite a stir,because they are well inside their stars’ ice line and cannot have formed where we now see them. It is now accepted that they grew further and then migrated inwards, and this has reopened the debate about the extent of planetary migration in our own Solar System’s early history. If Jupiter’s migration had continued inwards, it would have either destroyed or scattered each terrestrial planet in turn. For a while, ‘hot Jupiters’ opened the prospect that such an outcome was normal, and that planetary systems like our own are exceptionally rare. However, improved and additional techniques for exoplanet detection have begun to fi nd rocky planets, showing that the preponderance of ‘hot Jupiters’ in the early discoveries was merely a selection effect resulting from ease of discovery.

Transits

The second most prolifi c method for discovering exoplanets, likely soon to outpace the radial velocity method, is to search for ‘transits’,when a tiny fraction of a star’s light is cut off during passage of an exoplanet in front of it. Most transits are discovered by repeated scans of likely stars using automated telescopes, originally from the ground but now also by dedicated telescopes in space.

A transit can happen only if the exoplanet’s orbital plane lies almost exactly in our line of sight, which statistically should apply to only about half a per cent of all exoplanetary systems. The dimming of the starlight is slight, but is greatest for the largest exoplanets and occurs more often (and so is more likely to be detected) for exoplanets orbiting close to their star. Once again,discovery of ‘hot Jupiters’ is favoured over any other kind of planet. The exact amount by which the starlight dims can be used to deduce the size of the planet compared to its star. The duration of the transit gives us clues to orbital speed and orbital radius, but follow-up radial velocity measurements can better characterize the system. Because a transit demonstrates that the orbital plane lies in our line of sight, masses derived by the radial velocity method are true values rather than minimum estimates.

Imaging and other methods

Exoplanets are exceedingly challenging to image, because they are so much fainter than their stars. Single exoplanets have been imaged at only a handful of stars. As you might expect, these are all Jupiter-sized or larger, mostly orbiting at tens or even hundreds of AU. In 2008, an adaptive optics image obtained from infrared telescopes in Hawaii showed three exoplanets orbiting a young Sun-like star (catalogued as HR 8799) at 24, 38, and 68AU. Beyond them is a dust disc at about 75 AU.

Another method for exoplanet detection, called ‘astrometry’, has great potential for the future. This is based on very precise measurement of a star’s position in the sky. Any unseen orbiting companion will tug the star from side to side. Astrometry seeks to detect this, instead of radial velocity changes along the line of sight. The motion is greatest if caused by a massive planet in a large orbit, so is complementary to methods more sensitive to small orbits. The fi rst confi rmed success of the astrometric method was in 2002, when the Hubble Space Telescope documented sideways wobble of the star catalogued as Gliese876, refi ning what we knew about a 2.6 Jupiter-mass planet orbiting at 0.20 AU already detected by radial velocity changes.The fi rst astrometric discovery of a previously unknown exoplanet came in 2009, when a red dwarf star catalogued as VB10 was found to be dancing out of position because of a 6Jupiter-mass exoplanet.

A wholly different technique takes advantage of random (and never to be repeated) exact alignment between a foreground star and a background star. The foreground star acts as a ‘gravitational microlens’ that amplifi es the light from the background star. The detected brightness of the background star rises and then falls over a duration of several weeks. If the foreground star has a fortuitously placed exoplanet, this will cause a brief spike in the brightness (lasting a few hours or days) superimposed on the slower rise and fall. By 2010, microlensing had discovered a total of ten exoplanets.

Naming exoplanets

Names are not given to exoplanets. They are identifi ed by adding lower-case letters after the name or catalogue designation of their star. The fi rst to be discovered is b, the second is c, and so on (a is not used). Thus, the fi rst exoplanet of Gliese 876 is Gliese 876 b,and two subsequently discovered exoplanets in the same system are Gliese 876 c and Gliese 876 d. This convention is messy, with letters bearing no relationship to the positions of exoplanets in multiple systems. However, it works, and perhaps it is wise for us not to impose names. Maybe the natives already have perfectly good names for their homes.

Multiple exoplanet systems

Multiple exoplanets are known orbiting nearly 50 stars.Sometimes a combination of detection techniques provides this information, but radial velocity alone can do the job: it is just a matter of unravelling progressively more subtle periodic variations. Table 8 lists some of the larger multiple systems.Among these, the system of Gliese 581 (a red dwarf about 20.5light years away) is particularly noteworthy. It includes the least massive known exoplanet, Gliese 581 e, which could be only 1.9Earth-masses (and is almost certainly less than 4 Earthmasses),and also what is possibly a (large) ocean-covered terrestrial planet, Gliese 581 d, of more than 7 Earth-masses.Gliese 581 e is far too hot to support life, or even to retain an atmosphere, but Gliese 581 d appears to lie in its star’s habitable zone.

Table 8　Some multiple exoplanetary systems. Some of themasses quoted are minimum estimates. MJ
= Jupiter-mass

The nearest star known to have an exoplanet is epsilon Eridani,which is only 10.5 light years away. Epsilon Eridani b, discovered by the radial velocity method, is a Jupiter-mass giant in a 3.4 AU orbit. Infrared telescopes show that the star is accompanied by zones of rocky debris (asteroid belts) centred at about 3 AU and 20AU, plus an outer dust disc extending from 35 to 100 AU. Structure in the dust disc has been cited as evidence for an unconfi rmed one-tenth Jupiter-mass planet, epsilon Eridani c, at about 40 AU.

Study

We have little direct information about any exoplanet. If we determine mass (by radial velocity or astrometry), we can infer size by assuming a likely density. A transit will reveal size, which can also be deduced by imaging (based on brightness and assumed albedo). From size, we can deduce mass if we assume a density. Distance from its star gives us a fair idea of surface (or atmospheric) temperature, but this depends also on albedo and the mixture of greenhouse gases in any atmosphere, so there is a considerable margin for error.

The next major advance in the study of exoplanets will probably come as we improve our ability to analyse their atmospheric composition. This is best done by telescopes in space, capable of isolating and analysing the visible and infrared spectra of individual exoplanets – most importantly terrestrial ones. Several abundant atmospheric gas species can be identifi ed by their characteristic absorptions. Detection of a pair of gases that ought not to co-exist under conditions of simple chemistry, such as oxygen and methane, may be the fi rst evidence we obtain of life affecting an exoplanet’s atmosphere in the same way that the Earth’s atmosphere has been radically changed.

Life on exoplanets

There are about 10,000 million Sun-like stars in our galaxy (about1 in 10 of the total stars). Exoplanets must be abundant, having been found orbiting about half of the adequately studied Sun-like stars. Most discoveries so far have been giant planets, because those are the easiest to fi nd, and there is no proof yet that terrestrial planets are common. Planetary systems are clearly diverse, and no terrestrial planet is likely to have survived the inward migration of a ‘hot Jupiter’ such as ψ And b, currently orbiting less than 0.06 AU away from its star ( Table 8 ). However,because we are beginning to fi nd terrestrial planets, it is likely that they occur in a signifi cant proportion of exoplanetary systems.

The question of how many exoplanets might host life is a vexing one. Let’s take a very conservative estimate that on average only1% of Sun-like stars have a terrestrial planet orbiting in a long-duration habitable zone. That would give 100 million habitable terrestrial planets in our galaxy, and there are probably at least as many habitable satellites orbiting giant exoplanets.

The next step in the chain of logic is far less certain. Given the conditions required for life, how likely is it that life will begin? The building blocks for life are not a limiting factor. We know that space is awash with organic molecules, and that water is abundant too, so most exoplanets in a habitable zone will have all the necessary ingredients for carbon-based life. That means the Star Trek clichéof ‘life as we know it’, without delving into speculation about other forms of life that are reliant on exotic chemistries.

The ease or diffi culty with which life can spontaneously arise is a big gap in our understanding. Many (myself included) hold that with countless trillions of appropriate organic molecules in an exoplanet’s ocean, and with millions of years to play with, life will inevitably start. Once life has spread, it is hard to see how it can be completely eradicated, but if it was, it could presumably restart just as readily.

We know that it took life on Earth less than 500 million years to establish a permanent footing. The abundance of life in the galaxy(and, by implication, in the cosmos beyond) will remain unproven until we detect signs of life on exoplanets. Even if we were to fi nd current (or past) life on Mars, Europa, or Enceladus, we could not leap to the conclusion that life had begun there independently,because objects in the Solar System are not totally isolated from each other. Microbes could survive transport from one to another inside fragments of impact ejecta. Europan life could have come from Earth; it is conceivable that life on Earth arrived on a meteorite from Mars.

Is anybody out there?

If there is life around other stars, what about intelligent life? Let’s speculate rationally. So far as we know, biological intelligence requires multicellular life. If microbial life begins, how likely is it that subsequent evolution leads to multicellular organisms? You can take your pick on this issue. It took a couple of billion years to happen on Earth.

After multicellular life appears, will competition for survival drive Darwinian evolution as on Earth? Intelligence is one factor that confers an advantage, so how inevitable is intelligence?

Even on my conservative fi gure of 100 million habitable terrestrial planets in the galaxy, plus a pessimistic view that life has only a 1in 100 chance of starting, that still leaves a million worlds with life, of which the Earth is one. It would be strange (and aweinspiring)if Earth were the only or fi rst planet out of all that number ever to host intelligence. But if life is so abundant, and if intelligence is a common outcome of life, then where is everybody? Unless it arises exceedingly rarely, or does not last long (for example, our own civilization could succumb to wars,various natural disasters, or self-made climate change), then the galaxy ought to be teeming with intelligence.

Intelligent life would not have to be indigenous to where we fi nd it. Although the distances between stars are vast, it is perfectly feasible to travel between them. You do not need faster-than-light travel – all you need is determination and patience. Imagine a spaceship big enough to house hundreds of people, which would take 100 years to travel to a habitable exoplanet of a star 10 light years away. We could build such a ship ourselves, using technology foreseeable in the next few decades. One or two generations of the crew would live and die en route (unless some kind of suspended animation is used), and it would be very much a one-way trip. If we were to send such colonists to all the nearby habitable exoplanets (we expect to identify and characterize these by the end of the century), it would not be long before successful colonies had the capacity to launch their own colony ships, and so on. The galaxy is 100,000 light years across. Even if a wave of colonization takes 1,000 years to spread 10 light years, the entire galaxy could be colonized in only 10 million years. Catastrophes wiping out whole worlds or failures of individual colony ships would be insuffi cient to derail the process once it was underway.

The galaxy is more than 10 billion years old. If intelligent life is abundant, there has already been ample time for countless previous species to have colonized the galaxy. This is the Fermi Paradox, named after comments made by the American physicist Enrico Fermi in 1950. Extraterrestrial civilizations ought to be numerous, but there is no sign of them: no artifi cial signals detected from space (despite scans of the sky by teams working under the banner of SETI – Search for Extra-Terrestrial Intelligence), no sign of great works of astronomical engineering,and no credibly documented alien visitors to Earth. Is intelligent life rare, after all, or are we too stupid to see the evidence? One day, I hope we will fi nd out.

Further reading

There is a rich literature associated with astronomy and planetary science. The trouble is that, the longer or more specialized the book,the faster it goes out of date. On the other hand, some (not all!)websites are frequently updated. To help you discover more about planets, I suggest a few of the best books and several appropriate entry points to the internet.

General

J. K. Beatty, C. C. Peterson, and A. Chaikin (eds.), The New Solar System , 4th edn. (Sky Publishing Corporation and Cambridge University Press, 1999). This covers the lot. Each chapter is written by a specialist author. Badly dated in parts, but it remains a highly accessible classic.

I. Gilmour and M. A. Sephton (eds.), An Introduction to Astrobiology(Cambridge University Press, 2003). Updated in 2007, this is the second of two volumes based around an Open University course on planetary science, written at early undergraduate level. This one covers life, Mars, Europa, and Titan as potential habitats, and exoplanets. New edition expected 2011 .

N. McBride and I. Gilmour (eds.), An Introduction to the Solar System (Cambridge University Press, 2003). Updated in 2007,this is the fi rst of two volumes based around an Open University course on planetary science, written at early undergraduate level.It covers all the major components of the Solar System, except the Sun. New edition expected 2011.

S. A. Stern (ed.), Our Worlds: The Magnetism and Thrill of Planetary Exploration (Cambridge University Press, 1999). Easy but informative reading. Each chapter is a personal account by one of the leading practitioners.

D. A. Weintraub, Is Pluto a Planet? (Princeton University Press,2007). If you’ve read this far, then you already know the answer to the question posed by this book’s title. However, it covers much more than that, being an historical account of human perception of planets from ancient times right up to the recent squabbles over the classifi cation of TNOs.

Terrestrial planets

M. Hanlon, The Real Mars (Constable, 2004). A science writer’s perspective on Mars, simply written and beautifully illustrated.J. S. Kargel, Mars: A Warmer Wetter Planet (Springer Praxis, 2004).One leading scientist’s personal view of the role of hidden water on Mars.

R. M. C. Lopes and T. K. P. Gregg (eds.), Volcanic Worlds: Exploring the Solar System’s Volcanoes (Springer Praxis, 2004). A popular account, with chapters by specialist authors dealing with volcanism on each terrestrial planet, the Moon, Io, and icy satellites.R. G. Strom and A. L. Sprague, Exploring Mercury (Springer Praxis,2003). This is the best review of Mercury that I know, but written before MESSENGER began to study the planet.

Asteroids

J. Bell and J. Mitton (eds.), Asteroid Rendezvous: NEAR Shoemaker’s Adventures at Eros (Cambridge University Press, 2002). A wellillustrated and popular account of the fi ndings of the fi rst probe to orbit and then crash onto an asteroid.

Giant planets

F. Bagenal, T. Dowling, and W. McKinnon (eds.), Jupiter: The Planet,Satellites and Magnetosphere (Cambridge University Press, 2004).A fat volume with 26 chapters written by specialist authors. Will take you much further than the current book.E. D. Miner and R. R. Wessen, Neptune: The Planet, Rings and Satellites (Springer Praxis, 2002). A much slimmer and more simply written volume. Unlikely to date badly.

Satellites

R. Greenberg, Unmasking Europa (Springer, 2007). A clear and authoritative account of Europa, including some scathing passages about how Greenberg’s research team had to struggle against the establishment to gain acceptance for their thin ice interpretation.R. Lorenz and J. Mitton, Titan Unveiled (Princeton University Press,2008). The fi rst author is a key member of the Cassini-Huygens team that explored Titan, so this is an insightful account. However,it was written before Titan’s lakes were fully recognized.

D. A. Rothery, Satellites of the Outer Planets , 2nd edn. (Oxford Unversity Press, 1999). Written by myself, this is an account of large satellites from Jupiter to Neptune at a level that should suit if the current book has left you wanting more. It includes some Galileo fi ndings, but pre-dates the Cassini-Huygens mission to Saturn so is out of date in parts.

Exoplanets

H. Klahr and W. Brander (eds.), Planet Formation (Cambridge University Press, 2006). More technical than most others in this list, this volume is based on papers presented at a conference in2004. It looks at planet formation in the light of modern theories for our Solar System and discoveries of exoplanet systems.F. Casoli and T. Encrenaz, The New Worlds: Extrasolar Planets(Springer Praxis, 2007). The most up-to-date popular account of exoplanets that I could fi nd.

Websites

The following websites were accessed 4 July 2010.

General

www.nasa.gov

NASA’s home page. Click on the links here for news about missions or individual Solar System bodies.

Images

pds.jpl.nasa.gov/planets/NASA’s ‘Welcome to the Planets’ site, offering a simple introduction to each body and a small selection of images.

photojournal.jpl.nasa.gov/

A fuller archive of NASA images of Solar System bodies.

http://www.esa.int/esa-mmg/mmghome.pl

Multimedia gallery provided by the European Space Agency.

http://www.isas.ac.jp/e/index.shtml

Japan’s Institute of Space and Astronautical Science (ISAS), with links to images and movies from Japanese missions.

arc.iki.rssi.ru/eng/index.htm

The Russian Space Research Institute (IKI). Follow the link to Planetary Exploration for access to images and information from Russian (and former Soviet) missions.

hubblesite.org/gallery/

Gallery of images from the Hubble Space Telescope, searchable by name of planet.

Maps and nomenclature

http://www.mapaplanet.org/

A site where you can create your own maps of whatever region of a planet you choose, operated by the United States Geological Survey, Astrogeology Research Program.

planetarynames.wr.usgs.gov/

A gazetteer of nomenclature on planets, satellites, and asteroids.

Hosted by the United States Geological Survey, Astrogeology Research Program on behalf of the International Astronomical Union (IAU). Contains all you need to know about naming conventions, and up-to-date searchable lists of names of all kinds of features on each body.

News and data

http://nssdc.gsfc.nasa.gov/planetary/

Has links for each planet and other classes of body, taking you to fact sheets and much more.

http://www.minorplanetcenter.org/iau/mpc.html

Website of the IAU Minor Planet Center (at the Smithsonian Astrophysical Observatory). Especially good information on nearEarth objects.

www.boulder.swri.edu/ekonews/

Electronic newsletter about the Kuiper belt, plus various useful links.www.exoplanet.eu

The Extrasolar Planets Encyclopedia. Includes a frequently updated catalogue tracking the current tally of known objects, and also tutorials on the various methods of detecting exoplanets.

http://www.planetary.org/home/

The Planetary Society. An international (US-based) society promoting planetary exploration. A good source of relevant news and comment.

[1]
原书为Ni kolas，为尼古拉斯的希腊语拼法，

[2]
亦作Hygiea 或Hygieia，原意为司健康与卫生的女神。

Index

accretio n　20 ,　21 ,　36 ,　98

a m m onia　19 ,　72 ,　78 ,　94 ,　95 , 97—98 ,　112 ,　114

clouds　76—77

Antiope　102 ,　112

Antoniadi, Eugenios　59

aphelion　5

Apol l o　25 ,　33 ,　40—41 ,　51 ,　57

Apophis　105

Ariel　97

asteroid belt　14 ,　105

asteroids　13—14 ,　21 ,　101—109

Centaurs　110

composition　103

density　103

d iscovery　1 ,　108

Earth-crossing　105

impacts　101 ,　106—107

mining　107—108

names　108—109

orbits　14 ,　21 ,　104—105

potentially hazardous　105—107

satel lites　24 ,　101—103

Trojan　105

asthenosphere　37—39 ,　48

Astronomical Unit (AU)　8

atmosphere　6 ,　27 ,　28

circulation　62 ,　77—78

giant planets　71—2 ,　75—79

terrestria l pla nets　30 ,　36 ,　52 , 60—69

aurorae　81

BepiColombo (spacecraft)　42

brown dwarfs　116

ca rbon　18—19 ,　28 ,　94 ,　114 ,　123

cycle　69

dioxide　19 ,　48 ,　52 ,　61—62 ,　64—65 ,

67—70 ,　92 ,　94 ,　98 ,　111

monoxide　19 ,　76 ,　94

carbonate rocks　52 ,　69

Cassini (spacecraft)　29 ,　93—94 ,　95

Centaurs　110

Ceres　13 ,　17 ,　101 ,　104

Charon　112—113

clouds　43 ,　66—67 ,　75—77

comets　15—16 ,　27

orbits　16

condensation

in clouds　66—67 ,　76 ,　77 ,　87

in solar nebula　18—20

onto the grou nd　68 ,　100 ,　111

Copernicus, Nikolas　4

core (of a planet)　32—33

crater see impact crater

cratering timescale　25

crust　35—36

cryovolcanism　95—96 ,　97—98 ,　99

cubewanos　111

Dawn (spacecraft)　101

Deimos　24

differentiation　32—33 ,　74—75 ,　111

Earth

asthenopshere　38

atmosphere　47 ,　62—63

clouds　67

core　33

craters　25—26

crust　35 ,　48

greenhouse effect　66

lithosphere　37

magnetic fi eld　33 ,　81

ozone layer　63—64

plate tectonics　37—39 ,　46

stratosphere　62

volcanoes　39 ,　46—48

eccentricity (orbita l)　5 ,　14 ,　15 ,　21 , 66 ,　82 ,　115

ecl ipses　12

ecl iptic　10 ,　12

Edgeworth, Kenneth　14

Enceladus　93—94

Eris　15 ,　16 ,　17 ,　113

Eros　102

erosion　52

eru ptio n pl u m es　85 ,　87 ,　94 ,　113

ESA　29 ,　42 ,　50 ,　92

Europa　85 ,　89—93

names on　60

exoplanets　116—123

detection　116—119

life　122—123

multiple systems　120—121

naming　120

exosphere　60

Fermi Paradox　125

Ga l i leo (spacecraft)　29 ,　72 ,　76 ,　87 ,

89 ,　102

Ga l i l eo Ga l i lei　4 ,　83

greenhouse effect　65

habitable zone　27—28 ,　120 ,　123

Haumea　17 ,　113 ,　114

heat

differentiation　75

pri mo rd ia l　36 ,　74

rad iog en ic　36 ,　43 ,　75

tidal　39 ,　85—86 ,　89—90 ,　92—94 ,

97 ,　112

h el iocentric theory　4 ,　6

H erschel, Si r Wi l l ia m　1 ,　6 ,　28

h ot J u piters　118 ,　122

Hubble Space Telescope　71 ,　80 ,　119

Huygens (spacecraft)　29 ,　95

hyd rogen　7 ,　9 ,　18—19 ,　61 ,　72 ,　116

metallic　74—5 ,　81

mo l ecu la r　18 ,　72 ,　76

sulfi de　78

hydrologic cycle　69 ,　96

Hygeia　104

IAU (International Astronomical Union)　16—17 ,　30 ,　58—59 , 83 ,　108 ,　109

ice　15 ,　19 ,　21 ,　23 ,　28 ,　36 ,　50 ,　52 , 54 ,　56—57 ,　66—68 ,　72 ,　74 , 81 ,　84—98 ,　110 ,　114

a m m on ia　19 ,　72 ,　76 ,　97 ,　114

ca rbo n d ioxide　19 ,　68 ,　111

carbon monoxide　19

metha n e　7 , 19 ,　76 ,　111

n itrogen　19 ,　98 ,　111

water　19 ,　56 ,　68—69 ,　76—77 ,　89 , 94 ,　108 ,　111 ,　112—113

ice line　19 ,　22 ,　118

Ida　101—102

impact　27 ,　39 ,　40—41 ,　43 ,　51 ,　52 , 69 ,　83 ,　85 ,　86—87 ,　89 ,　93 , 97 ,　99 ,　101 ,　114

basin　35 ,　39 ,　44

crater　25—26 ,　44 ,　45 ,　50 ,　56 ,　106

ejecta　21 ,　41 ,　50 ,　51 ,　69 ,　114 , 123

gardening　51 ,　52

giant　21 ,　34

Io　85—88

ionosphere　61

iron　14 ,　18 ,　20—21 ,　32—33 ,　42 ,　52 ,

74 ,　81 ,　86 ,　94 ,　103 ,　107 , 111

Itokawa　102 ,　103

J u piter　21 ,　29

belts and zones　77—78

clouds　76—77

Great Red Spot　78

impacts　27

interior　72 ,　74

magnetic field　79 ,　81 ,　87

ri ngs　84

satel lites　4 ,　12 ,　85—94

storms　78

troposphere　71—72

Kepler, Johannes　4

Kepler's laws　4—5 ,　8 ,　13

Kirkwood gaps　104

Kuiper, Gerard　14

Ku iper belt　14 ,　16 ,　116

objects　14 ,　110—111

Kuiper cliff　115

life　2,27—28,62,64—65,92,94 , 106, 112,120 ,　122—123

colonization　124—125

intelligent　123—125

microbial　27 ,　92 ,　123—124

multicellular　124

origin　92 ,　123

lithosphere　37—39

Lowell, Perciva l　55

Magellan (spacecraft)　29 ,　43 ,　95

magma ocean　34

magnesium　18 ,　91

magnetospheres　79 ,　81

Makemake　17 ,　113

mantle　33—36

flow　34—35

plumes　46 ,　48

Mars　29 ,　30

atmosphere　54

canals　55

climate change　54 ,　56

clouds　53 ,　67

core　33

dust storms　53

greenhouse effect　65

gullies　56—57

ice　56—57

ionosphere　61

meteorites　50

names on　59

Olympus Mons　48—49 ,　53 ,　59

polar caps　68

sand dunes　53—54

satel l ites　12

seas　50

Valles Marineris　54—55

valleys and channels　54—56

volcanoes　48—49

water　54—57 ,　61 ,　67

wind　54

Mercury　30

atmosphere　60

Beagle Rupes　38 ,　60

core　33

magnetic fi eld　33 ,　81

names on　59—60

regolith　51

volcanism　42

MESSENGER (spacecraft)　42

meteorites　13 ,　14 ,　20 ,　26—27

carbonaceous chondrites　20 ,　103

iron　103

martian　50

stony　14 ,　103

stony-iron　103

methane　7 ,　19 ,　64 ,　72 ,　79 ,　92 ,

94—96 ,　98 ,　111 ,　122

clouds　76—77

micrometeorites　51 ,　52 ,　60

Miranda　97—98

Moon　12 ,　28 ,　29 ,　30

atmosphere　60

core　33

craters　40

crust　34 ,　35

Hadley Rille　41 ,　51 ,　57

maria　35 ,　40—41

nameson　59

origin　24

regolith　51 ,　68

volcanism　40—41

water　57—58 ,　68—69

NASA　29 ,　42 ,　43 ,　87 ,　92 ,　101 ,　111 , 114

Neptune　17 ,　115

clouds　77 ,　80

discovery　6

Great Dark Spot　79 ,　80

interior　72 ,　74

magnetic field　79

orbit　10—11

rings　84

satel lites　13 ,　98—100

Trojans　110

New Horizons (spacecraft)　88

Newton, I saac　4 ,　13

nickel　14 ,　33 ,　107

nuclear fusio n　7 ,　116

Oort Cloud　15 ,　23 ,　115

orbital resonance　11 ,　85 ,　94 ,　104

orbits　4—6 ,　9—11 ,　104

oxygen　18—19 ,　32—33 ,　52 ,　61—65 , 122

ozone　63—65

Pallas　104

Pan　84

Peale, Stanton　85

peri h el io n　6

Phobos　24

Phoebe　85

phosphorous　78

photochemistry　61 ,　62 ,　63 ,　78 ,　94

ph otodissociatio n　61 ,　67

planetary embryo　20—21

planetesimals　20—23 ,　33

planets

defi nition　16—17

distinguishing features3—4

dwarf　17

gasg iants　9

giant　9 ,　21—22 ,　23 ,　29 ,　71—81

known since antiquity　3

names of surface features　58—60

orbital migration　22—24

orbital period　5 ,　8

origin　18—21

other stars　see　exoplanets

rotation　8

sizes　6—7

surface temperature　28 ,　31

terrestrial　9 ,　20—21 ,　29 ,　30—70 ,　79 , 83 ,　86 ,　118 ,　120 ,　122—124

plutinos　110 ,　113

Pluto　15 ,　111—112

atmosphere　111

discovery　6

nota pla net　2 ,　7 ,　16—17

orbit　6 ,　10—11

satellites　111—112

Plutoid　17 ,　110—11

prograde　11

Psyche　107

Quaoar　114

radia l velocity　117—118 ,　120

regolith　51 ,　58 ,　68 ,　69

retrog ra d e　11 ,　83

rings　71 ,　82—85

Sagan, Carl　103

satel l ites

discovery　4 ,　13

Galilean　12 ,　85

inner moonlets　83

irregular　82

of asteroids　24 ,　101—103

of planets　4 ,　11—13 ,　24

of TNOs　24 ,　112 ,　114

reg ular　83

shepherd　84 ,　85

surface temperatures　86

Saturn　29

clouds　76—77

interio r　72 ,　74

magnetic field　79 ,　81

rings　83—85

satel lites　12 ,　93—96

storms　78

Scattered Disk objects　14—15 ,　111 ,

113

Schia parelli, Giovanni　53 ,　59

seasons　11 ,　100

Sedna　113—114

silicates　19 ,　21 ,　32 ,　33—36 ,　39 ,　87 , 91 ,　103

solar nebula　18—19 ,　22—23 ,　24 ,　116

Solar System　3—29

age　20

origin　18—22

space exploration　28—29

Spaceguard　107

spectroscopy　85 ,　93 ,　98 ,　111 ,　114

infra red　69 ,　95 ,　98 ,　113 ,　116

optica l　75 ,　103 ,　117

sulfur　33 ,　78 ,　87

sulfu rdioxide　47—48 ,　64 ,　67 ,　70 ,　87

sulfuric acid　67

Sun　7—8

magnetic field　81

telescopes　1 ,　4 ,　6 ,　13 ,　28 ,　40 ,　53 , 55 ,　58—59 ,　71 ,　77 ,　78 ,　80 , 85 ,　101—102 ,　111 ,　114 , 115 ,　118—119 ,　121—122

thermosphere　61 ,　62

tholins　103 ,　110 ,　111 ,　114

Titan　29 ,　94—96

tran sits　6 ,　118—119 ,　122

trans-Neptunian objects (TNOs) 14—15 ,　17 ,　110—115

Triton　83 ,　98—100

troposphere　62 ,　71—72

Uranus

clouds　77 ,　80

discovery　1 ,　6

interior　72 ,　74

magnetic field　79

orbit　6

rings　84

satellites　12—13 ,　97—98

seasonal variations　79

tilt　11 ,　79

Venus　29 ,　30

atmosphere　43 ,　45 ,　54 ,　62

clouds　66

coronae　44

core　33

craters　44 ,　45

greenhouse effect　65

ionosphere　61

names on　59

resurfacing　46

rotation　11

tran sits　6

volcanism　43 ,　46

water　61 ,　67

Vesta　101 ,　103 ,　104

Viking (s pacecraft)　29 ,　56

volcanism　39—50 ,　60 ,　86—88 ,　103

Voyager (spacecraft)　29 ,　79 , 86—87 ,　89 ,　93—94 ,　97—100

water　38 ,　39 ,　48 ,　57—58 ,　60—61 , 66 ,　69 ,　72 ,　97—98 ,　106 , 123

ice　19 ,　56 ,　67—68 ,　76—77 ,89 ,　94 ,　95 ,　108 ,　111—113

liquid　27—28 ,　36 ,　52 ,　54—56 ,　67 , 76 ,　89—93 ,　94

vapour　64—65 ,　67 ,　68 ,　87

weathering

chemical　52 ,　62 ,　69—70

space　52 ,　103

-----------------------------------------------------

Gravity: A Very Short Introduction

Copyright:© Timothy Clifton 2017

Gravity: A Very Short Introduction was originally published in English in 2017. This

translation is published by arrangement with Oxford University Press. Dook Media Group

Limited is solely responsible for this translation from the original work and Oxford University

Press shall have no liability for any errors, omissions or inaccuracies or ambiguities in such

translation or for any losses caused by reliance thereon

中文版权：©2020 读客文化股份有限公司

经授权，读客文化股份有限公司拥有本书的中文（简体）版权

版权所有，不得翻印

图字：30-2020-006号

图书在版编目（C I P）数据

牛津通识课. 引力 / [英] 蒂莫西·克利夫顿

(Timothy Clifton) 著 ; 颜子昂译. -- 海口 : 海南出

版社, 2020.4

书名原文：Gravity: A Very Short

Introduction

ISBN 978-7-5443-9273-0

Ⅰ. ①牛… Ⅱ. ①蒂… ②颜… Ⅲ. ①科学知识 - 普

及读物 ② 引力 - 普及读物 Ⅳ. ① Z228 ② O314-49

中国版本图书馆CIP数据核字 (2020) 第061526号

-----------------------------------------------------

目录

前言

01 从牛顿到爱因斯坦

02 太阳系内的引力

03 太阳系外的引力测验

04 引力波

05 宇宙学

06 引力物理前沿

后记

索引

Preface

Chapter 1 From Newton to Einstein

Chapter 2 Gravity in the Solar System

Chapter 3 Extrasolar tests of gravity

Chapter 4 Gravitational waves

Chapter 5 Cosmology

Chapter 6 Frontiers of gravitational physics

Epilogue

Further reading

Index

前言

这是一本关于引力(gravity)的书。引力就是使有质量的物质彼此靠拢的力。正是它导致苹果从树上落下，也是它让地球得以形成。引力是大自然所有基本力中最为人熟知的，但它的作用方式并不那么显而易见。现实中我们称为“引力”的现象，与时间和空间的本质深刻地联系在一起。这意味着现今人们对引力的理解，不仅能帮我们揭示出宇宙中万事万物运动的规律，同时也能使我们了解构建起宇宙的时间与空间的性质。

这本书的目的是向读者简要且全面地介绍引力。我们会从引力理论发展的历史开始讲起，然后再讨论今天的科学家们如何理解它。之后我们会考虑引力在地球、太阳系和整个宇宙中产生的效应。最后一章中，我会描述现在引力物理理论的研究前沿。

最后，我希望能够传达给读者的不仅限于引力是什么，还包括对引力的研究如何启发科学家们得到关于空间、时间和我们生活的宇宙的精彩结论。

01 从牛顿到爱因斯坦

在四大基本作用力——电磁力、强核力、弱核力与引力之中，引力是最弱的一个。但是，它主导了长距离下物体的相互作用。引力是仅有的只吸引不排斥的力，而且它不可能被屏蔽。因此大部分的大物体呈电中性，但不可能呈“引力中性”。有质量物体之间的引力从来都是使它们彼此靠近的，并且越靠近引力越强。

幸而有牛顿(Newton)和爱因斯坦(Einstein)这样的天才，我们才能对引力有所了解。但和其他力比起来，引力给科学家们提出了更多艰深的谜题。要想知道为什么会这样，我们就要从头说起，先来了解一下历史上引力理论是如何发展的。

引力的“上古史”

假设人类从一开始就知道(我们说是假设，但这几乎是可以确定的)，当我们把手里拿着的东西松开的时候，它总是会往下落。这样一来，就可以说人类一直都知晓引力的存在。而这种现象发生的原因，正是很多早期思想家关注的焦点。

亚里士多德(Aristotle)[他的著作《物理学》
(Physics)17世纪之前就在欧洲科学界发挥着举足轻重的作用]把引力解释为物体朝向它们“在宇宙中正确的位置”移动的趋势。他认为这一正确的位置取决于物质的组成成分，准确地说就是取决于物质中四大元素——土、水、空气和火——各自所占的比例。

亚里士多德提出，主要由土和水构成的物质应当朝着宇宙中心运动。对他来说，地球就是宇宙中心。因此当我们把由土构成的物体扔出去时，它就会落向地面。至于水，他认为由于土会沉入水底，所以水比土要轻，因此所有的水都存在于土的表面。同样，由于泡泡浮在水上，故空气比水轻，那么空气的正确位置在水上方，火则在空气上方。

基于当时人们对物质的构成元素的理解，这一体系从逻辑上给眼前的世界划分了层次。利用它，人们甚至可以描述物体下落时的加速度。亚里士多德提出：物体下落的加速度和它们的重量成正比，和它们下落时穿过的介质的密度成反比。也就是说，亚里士多德认为两千克的物质下落时加速度是一千克物质的两倍。

很遗憾，亚里士多德的理论并不正确。我们知道宇宙并不存在一个中心，好让物体落向那里。我们还可以通过实验证明物体在引力作用下的加速度并不与它们的质量成正比，而是无论物体质量如何都保持不变。这一发现是理解引力过程中的里程碑之一，因此我们也需要对它作更多说明。

所有物体在引力作用下的加速度都相等，这一事实并不直观。当我左手拿着一片羽毛，右手拿着铁块并同时松手，我不会期待它们同时着地：铁块应该先落地。那么“所有物体在引力作用下加速度都相等”是什么意思呢？为了理解这句话，我们需要考虑施加在这两个物体上所有的力。

当我松开羽毛时，除了引力之外，它还受到其他的力。当它开始下落，会受到周围空气产生的阻力。由于铁更重，空气阻力对羽毛的减速效果就比铁要强。一点小风对羽毛也会有很大的影响，而对铁块的干扰微乎其微。因此，上述理论并不适用于我们周围的环境。实际上，它描述的是物体在只受引力作用的情况下会发生什么。也就是说，如果除了引力外没有其他任何作用力，物体就会以相同的加速度下落。

对这一命题的验证通常归功于伽利略(Galileo)。传说1638年
[1]

，他将两个不同质量的炮弹从比萨斜塔上扔下，人们发现，无论这两个炮弹成分如何，它们都以相同的速度落地
[2]

。最近，阿波罗宇航员大卫·斯科特(David Scott)得出相同的结论。他站在月亮上，让一片羽毛和一把锤子同时落下，因为月亮上没有空气阻碍羽毛的运动，所以两个物体同时落在了月面上(见图1)。今天，我们把这一现象称为“自由落体的普遍性”(Universality of Free Fall)。接下来，我们将看到，它既是牛顿引力理论，又是爱因斯坦引力理论的关键。

图1　(a)伽利略从比萨斜塔扔下炮弹；(b)斯科特在月上同时松手让锤子和羽毛落下的画面

牛顿的引力理论

艾伊萨克·牛顿爵士(Sir Isaac Newton)的引力与运动的理论，最初于1687年集结成《自然哲学的数学原理》
(Principia Mathematica)书发表，它永久地改变了世界。这是关于引力的第一个真正的科学理论。和亚里士多德不同，牛顿并未尝试解释引力，他量化了引力的效应。由此，物体在地球上的运动、地球本身的运动和太阳系其他天体的运动的物理定律，都被推导出来了。

毫无疑问，牛顿理论是天才的成就，他开创了新的数学分支，并史无前例地提出：适用于人类、地球和天体的物理定律，都是相同的。亚里士多德曾试图解释的复杂运动都被归结于简单的定律。牛顿引力理论是辉煌的，在它被提出的两百年内，没有与之匹敌的理论。只通过一本《原理》，牛顿就在科学、工业和战争的世界里掀起了革命。此外，直到今日，他仍给我们的很多研究工作提供了框架。牛顿引力定律最基本的要素是绝对时间和绝对空间，它们作为所有运动的“背景”存在。万有引力瞬时地在宇宙中任意一对有质量的物体之间传递——仅此而已。

牛顿眼里的空间和我们日常生活中体会到的空间一样，仅仅是物体存在的永恒不变的舞台。我可以把一个物体X放在空间中的一点，然后用一把卷尺测出它和另一个物体Y之间的直线距离。在牛顿力学中，这一过程没有任何模棱两可之处。物体X和Y在空间中运动，但空间本身是静止的、不变的。

与之相似，牛顿的时间概念和我们与生俱来的对时间的直觉一样：一个瞬间接着另一个瞬间，不停息地向前流逝。在一段时间内，物体可以改变它们的位置，但时间本身是普适的，对万事万物都一视同仁。在牛顿的理论中，所有校准的时钟都以相同的方式测量时间，就像所有卷尺都以相同的方式测量两个物体之间的距离一样。

根据牛顿的理论，所有物体在没有外力作用的情况下都会以均匀的速度运动(这和亚里士多德的理解背道而驰)。如果有外力作用在物体上，这个力的效果会使物体加速。力越大，加速度越大；物体的质量越大，要得到相同加速度所需的力就越大。在这一理论体系下，引力不过是外力的一种，它的效果是把有质量的物体拉到一起。牛顿推断：两个物体之间的引力一定和它们的质量成正比，并和它们之间距离的平方成反比。也就是说，两个有质量物体之间的引力遵从如下方程：

其中M和m分别是两个物体的质量，r是它们之间的距离。这一简单的方程再加上牛顿运动定律，对估计大多数天体和地球上的物体的运动而言，就已经足够了。牛顿引力导致所有物体下落的加速度相同，这解释了伽利略的实验结果。现在将牛顿运动定律和牛顿引力结合起来考虑，就可以得出结论：加速度相同的情况下，物体质量越大，受到的引力越大。在牛顿的理论中，质量与引力刚好在加速度计算中相互抵消了。因此，一个物体在牛顿引力的作用下遵循牛顿运动定律运动时，它就一定会有一个和质量无关的固定的加速度。这并不意外：自由落体的普遍性从一开始就建立于牛顿的理论体系中了。

牛顿理论的第一个巨大成功，是可以用它来推导行星运动的规律。17世纪早期，约翰内斯·开普勒(Johannes Kepler)利用当时最先进的天文数据推导出了这些经验规律。开普勒定律表明：

·行星运动的轨迹是椭圆，太阳是该椭圆的其中一个焦点；

·时间间隔相等，行星和太阳的连线在行星绕太阳转时扫出的面积相等；

·行星绕太阳转一整圈的时间的平方，和行星轨道上最远的两点间距离(也就是椭圆的长轴)的三次方成正比。

图2　行星轨道示意图。行星在两段相同时间内扫出的阴影部分A和B的面积相等

图2表示了上诉三个定律涉及的物理量(轨道周期除外)。开普勒定律的优势在于它对当时所有已知行星都适用，即使开普勒提出定律的时候，人们还不知道它的物理基础是什么。但仅从表面来看，它们与观测数据非常吻合。牛顿知道开普勒定律，他在《原理》中解释了如何从万有引力定律推导出开普勒定律。这个推导是物理学历史上最伟大的成就之一。从先进的观测数据中推导出的经验定律首次被简单的数学公式证明了。牛顿告诉人们，描述从地球表面发射的炮弹的运动规律同样可以用来描述行星。我们今天熟知的很多物理学理论就是从这里开始的。

爱因斯坦的引力理论

牛顿理论发表两百年后，爱因斯坦的理论取代了它。如果说牛顿的理论简单而实用，那么爱因斯坦的理论就是优美且真正普适。爱因斯坦不只是改变了牛顿理论方程的形式，还直接颠覆了牛顿理论的根基——爱因斯坦改变了一切。

和很多物理理论发展的过程一样，爱因斯坦理论最初是为了解决一些已有的理论之间的不一致。牛顿提出了关于引力和运动的理论，但它和詹姆斯·克拉克·麦克斯韦(James Clerk Maxwell)在19世纪中期提出的关于光的理论不相容。麦克斯韦的光理论指出：宇宙中任何人测量到的光速都是一致的，并且这速度是一个略小于30万千米每秒的数字。乍一听似乎没什么关系，若是仔细想想，就能发现其中存在着问题。根据牛顿的理论，如果我坐在一辆以每小时100英里的速度运动的火车上，用每小时1000英里的速度发射一颗子弹，那么轨道附近的观察者将看到子弹以每小时1100英里的速度飞行。从数学的角度看，子弹速度和火车速度线性叠加了。现在，假设我们仍然坐在这辆火车上，点亮一把手电筒，那么在火车上的我看来，手电筒发出的光穿过车厢的速度就是光速(也就是30万千米秒)。再来考虑轨道附近的观察者。按照牛顿理论，这个人看到的光的速度应该是30万千米秒加上100英里小时(火车的速度)。但根据麦克斯韦的理论，结果却并非如此，麦克斯韦理论认为轨道旁边的人测量的光速和火车里的人测量的光速相等，也就是说，速度并不是线性叠加的。

上述矛盾意义深远。如果我们在速度如何叠加上意见不一致，那么我们根本就不能用物理学来计算物体的运动。牛顿和麦克斯韦的理论不可能都正确，至少有一个是错的。有少数科学家试图改写牛顿或者麦克斯韦的理论，但爱因斯坦没有这样做——他尽可能地谨慎处理这两个理论。爱因斯坦认识到，两个理论各自有其巨大优势，他用一种天才的手法化解了两者之间的矛盾。爱因斯坦假设：如果光速恒定定不变，那么时间和空间将不再是一个普遍的概念。正相反——他论证道——每个观察者对于时间和空间的概念都不同。根据爱因斯坦的新理论，在轨道附近的观察者眼中，坐在火车上的人手里的时钟比他自己手里的时钟走的要慢一些。与此相似，在火车上的人眼中，轨道附近观察者手里的时钟也比自己手里的要慢。

一开始，这个结论听上去相当奇怪，因为我们从很小的时候就已经被“时间是普遍的”这种想法“洗脑”了。爱因斯坦告诉我们，这一始于孩提时代的对时间的理解是错误的。时间并不是对所有人都以相同速度流逝，它不是一个普遍概念。时间是“私人物品”，它与我们相对运动的方式有关。相似地，空间也不像我们理解的那样是固定的舞台背景。我们脑子里的距离和物体的长度实际上都取决于我们如何运动。

这些想法非常惊人。起初，它们令人十分不安，因为我们理解世界的支柱好像突然间倒塌了。不过，我们不必去修复这些支柱，在爱因斯坦的理论中，有一个关于时间和空间的概念幸存了下来，并且依旧是独立于观察者存在的事物，这就是所谓的时空(space-time)。和牛顿的绝对时空观念不同，我们现在有了一个新的，可以同时囊括两者的构造。一个人或一个事物，比如你和我，在这个构造中沿着一条线运动，这条线就被称为我们的世界线(world-line)。每个人的时间都是按照自己的世界线测量出的，我的世界线可能和你的不同，但它们都存在于同一个时空(见图3)。

图3　同一个时空两个观者的世界线的例子。世界线相交之处，两个观者相遇

将时间和空间的概念进化为时空的概念，就能使牛顿力学和麦克斯韦理论相容。这是爱因斯坦在科学上的早期贡献之一，它就是现在人们熟知的狭义相对论(Special Theory of Relativity)的支柱。狭义相对论有许多深刻的结果，不少已经被实验证实。其中最著名的当属下面这个方程：

这个方程告诉我们，质量和能量是紧密地联系在一起的(当核武器面世时，这一事实变得无比明显且极具破坏力)。关于它的推导出的其他结论还包括不稳定粒子快速运动时它们的寿命会变长，以及任何物体的移动速度都不可能超过光速。

上述最后一条结论以及时空这个新概念，让爱因斯坦发展出了他的引力理论。紧接着，一个明显的矛盾推动了这个发现，牛顿理论又陷入了麻烦中。这回，矛盾产生于牛顿理论和狭义相对论之间。牛顿引力是瞬时存在于物体之间的，也就是说，如果太阳突然爆炸，根据牛顿的理论，在事情发生的那一刹那，我们立刻就能感受到引力的变化。爱因斯坦知道这是不可能的。首先，他发现没有任何物体的运动速度可以超过光速；其次，绝对普适的时间是不存在的，也就是说“两件事在不同地点同时发生”这种说法根本没有意义(如果在一个观察者眼中它们同时发生，那么在另一个运动状态不同的观察者眼中它们可能不同时发生)。所以，我们的理论中又存在一些错误需要修正。

爱因斯坦解决这个问题的手法更加精妙。他假设引力并不是把物体拉到一起的力，而是时空弯曲的结果。根据爱因斯坦的理论，有质量物体会相互靠近，只是因为它们在弯曲的时空中遵循最短路径运动。质量和能量导致时空弯曲，而时空弯曲折弯了物体移动的路径。这一想法的美妙之处是：我们不再需要把引力当成宇宙中存在的一种额外的力，有质量的物体之间的相互吸引仅仅源自时空本身(它本来就存在)。这就是广义相对论(General Theory of Relativity)的基本思路。

更加令人印象深刻的是，爱因斯坦解释了为何伽利略实验中的所有物体下落时加速度都一致。我们回想一下就会发现，牛顿理论并没有真正解释这一点，它仅仅被当成了一个事实，牛顿设计的理论和这一事实相容。爱因斯坦的理论在这方面做得更好。现在，在爱因斯坦的理论中已经不存在一个叫做引力的外力，所有物体的运动轨迹仅仅是时空弯曲的结果。由于所有物体都在同一个时空中运动，所以它们必须遵循相同的路径。换种说法就是：所有的物体都必须以相同的加速度下落。这正是伽利略观察到的现象。

这些想法可能会使人感到难以理解，所以我们来举一个例子。想象两个物体在没有受到力的作用时的运动轨迹。在平直空间中，它们会走直线，如图4所示。

如果空间弯曲了，那么它们将不再走直线。考虑最简单的弯曲空间：球面。球面上两点之间最短的线叫做大圆(great circle)(地球赤道就是大圆的一个例子)。如果两个物体在同一个球面上走不同的大圆，那么它们一开始会相互远离，然后再次靠近，如图5所示。

图4　两个粒子不受外力地在平直时空中运动的轨迹可能是这样两条直线

图5　两个粒子不受外力地在球面上运动的轨迹可能是这样两个大圆。它们不再相互平行，而是会相交

这就是爱因斯坦描绘的引力作用。他想象物体运动轨迹相交的真正原因是时空弯曲，而不是有某个外力作用其上，使它们朝左或朝右运动。时空的弯曲一般比球面的弯曲更加不规则，但基本原理是相同的。就引力的效应而言，爱因斯坦新理论中的主要效应和牛顿在两百多年前得出的定律非常相似。它们的区别在于，现在引力的定律伴随着对时间和空间的全新理解。同时，新的引力理论也预测了各种微小的、精细的效应(后面几章会详细讨论这些内容)。

现在，让我们来思考这些新理论在现实世界中意味着什么。假设一名跳伞运动员从飞机上跳下，自由下落的同时受到空气阻力。根据爱因斯坦的理论，这名跳伞运动员的轨迹是地球附近弯曲时空中的最直路线。从跳伞运动员的视角看来，这十分自然。如果不考虑空气持续作用在她身上的力，她应该和太空中的宇航员一样有失重感。我们认为跳伞运动员在加速运动，仅仅是由于我们习惯把地球表面当成参考系。如果放弃这个习惯，我们就没有理由认为她在加速。

现在，假设你站在地上观察这个正在下落的勇敢者，通常情况下你的直觉会认为你是静止的，但这是因为我们再次盲从于习惯，把地球当成了判决物体是运动还是静止的仲裁者。从这个圈子里跳出来吧!这样你就会意识到其实你正在加速。你会感到脚下有一个将你向上推的力，就像是站在加速上升的电梯里那样。在爱因斯坦理论的图像中，你站在地球上和你站在加速上升的电梯里没有区别
[3]

，因为两种情况中你都是在加速向上。后一种情况下是电梯导致你加速；前一种情况则是硬邦邦的地球把你从时空中“推上去”，让你偏离自由下落的轨迹。地球可以在维持自身形状的同时使其表面任何地点的物体加速上升，这是因为它周围的时空是弯曲的而非平直的。

当我们的观点发生转变后，引力的本质就很清楚了。跳伞运动员落向地球，是因为她身边的时空是弯曲的，而不是有什么力在拽她下去，这只是她在弯曲时空中的自然运动。另一方面，作为站在地上的人，你能感受到脚底的压力，正是因为坚硬的地球在把你向上推。并不存在什么外力把你拉向地球，只有使地球保持固态的静电力在你脚底作怪，

它阻止你做自然运动(也就是自由下落)。

如果我们不再拘泥于拿地球表面的相对运动做参考系定义我们的运动，我们就能意识到跳伞运动员并没有加速，相反，加速的是地球表面。回想一下伽利略的比萨斜塔实验，现在我们就能理解为什么他看到所有的炮弹都以相同的加速度下落了。并不是炮弹加速远离伽利略，而是伽利略自己在加速远离炮弹!如果我把很多个静止物体分开放置，然后自己加速远离它们，那么我也不会惊讶于远离它们的加速度都是一样的——伽利略和他的炮弹也是这个道理。

有些人会认为这种描述显然非常优美，另一些人则会由于爱因斯坦理论可以被实验证实而觉得它异常迷人。这些实验包括从行星运动的微扰到太阳周围的光线弯折等等。我们将在之后的几章里探索这些激动人心的现象。不过，我们要一直牢记：是时空的弯曲导致了这一切。

[1]
这一年份存疑。即使是传说，比萨斜塔实验也应该是1590年左右。

[2]
实际上，这个故事仅仅是传说，更合理的说法是：他利用铁球从斜面上滚下来得到了结论。

[3]
这一般被称为“等效原理”。

02 太阳系内的引力

太阳系——包括地球在内——是我们研究引力时触手可及的实验室。太阳系的引力场由比所有系内行星质量大得多的太阳主导。

轨道距离太阳相对比较近的行星有四颗：水星、金星、地球和火星。再远处是四个大得多的行星：木星、土星、天王星和海王星。太阳系还包括一些其他天体，比如彗星、小行星、卫星和人造宇宙飞船。当我们去观测它们的运动，或者在某些情况下和它们相对运动，我们就可以了解引力的很多性质。

对太阳系内引力正式的实验和观测始于20世纪后半叶。在古代天文学家们几个世纪以来持续追踪行星的运动了后，随着20世纪新技术的发展，人们进行了一系列史无前例的观测和实验。为了合理地展示这些结果，我把它们分成如下几类：对基本假设的探索、验证牛顿引力定律的实验和研究爱因斯坦引力定律的实验。

对基本假设的探索

现代引力理论有很多基本假设，比如，物体的位置以及它们与其他物体的相对运动状态，和它们的静质量无关；光速在任何方向上都相等；所有下落物体(不受除引力之外的其他力时)的加速度都一致。这些假设都已在20世纪被验证过了。我将在这里列出其中最好的一些实验，之后再分别详述牛顿和爱因斯坦关于理论的实验。

让我们先回忆一下质量的定义：质量是这样一个量，它告诉我们使物体以固定的加速度运动时需要施加多少力。我们认为它是物体的基本特征。它与重量不同，重量是你把物体拿在手中时，它施加在你手上的一个向下的力。同一个物体的重量在不同星球上是不一样的。质量出现在牛顿引力定律中，在爱因斯坦的著名方程中，质量和能量等价。因为这两个理论是引力理论的核心，所以我们需要了解，质量是不是真的和物体的位置及其在引力场中的运动无关。我们必须通过实验来证明这一点。

奇妙的是，验证质量的最佳实验，是观察光在穿过引力场时如何改变颜色。其基本思路为：光子(组成光的粒子)从有质量物体(如恒星或行星)周围的引力场中逃离时会损失能量，这样它才能从引力场中“爬”出来。就像你在爬楼梯的时候需要消耗能量一样，为了从地球或太阳表面飞走，光子也需要消耗一些能量。光子能量的改变导致颜色(波长)改变，所以一束光在穿过引力场后颜色会发生变化，能量改变的大小则取决于它和引力场源的距离。这就是为什么在远离恒星的地方探测到的光会比其刚发射出来时稍微红(波长略大)一些。这个效应被称为光的引力红移(gravitational redshifting)。

为什么引力红移会告诉我们质量是否与位置有关呢？首先，想想我们怎样在引力场中测得物体的质量：用一个绞车把物体升起来，然后测量绞车做了多少功。由于能量和质量直接相关，所以把一个物体从一个高度升到另一个高度所需的能量可以直接告诉我们物体在这两个高度之间的质量。不幸的是，我们很难准确地测出绞车使用了多少能量，因为它实在是太低效了(绞车上升浪费的能量大部分用于噪声、摩擦以及拉伸绳子)。这时候，引力红移就派上了用处：光的频率可以很精确地测量出来，而且光子在爬出引力场时损失的能量和举起一个相同质量的物体(能量通过计算出来)所需的能量相等。我们只要测量光的红移，就可以得到与绞车实验完全相同的信息。

20世纪60年代，科学家罗伯特·庞德(Robert Pound)和格伦·雷布卡(Glen Rebka)最先测量了光的引力红移。他们测量了光从下往上穿过哈佛大学杰斐逊物理实验室的高塔时的红移。观测发现，光的颜色确实在向上传播的时候发生了改变，其能量改变大小完全支持质量与位置无关这一结论。唯一可能的偏差必须小于实验本身的精确度——大约在1%。另外一个与此相似的实验测量了太阳光的红移，并且同样以1%的误差水平证实了上述结论。

最近人们开始使用原子钟来研究红移效应。这些实验背后的逻辑在于光束自身在某些意义上就像时钟。光的颜色取决于光子的波长，波长则和它们振动的频率相关。如果我们把每一次振动当成一个时间单位，我们就可以把光子看成时钟。这样，就可以将光的红移与时钟的走时率(即时钟每次“嘀嗒”声之间的时间间隔)相类比，时钟不同位置的走时率不一样，光在不同位置的红移效应也不同。实际上，我们甚至不需要在实验中去测量光的频率，因为其中以某一光子频率作基准的钟如果走慢了，那么其他以这一光子频率为基准的所有的钟都会走慢。我们需要做的仅仅是把两个钟放在不同的高度，并使它们每一次“嘀嗒”的瞬间都能通过无线电信号告诉我们。于是，两个钟的无线电信号的频率差就等价于光在两个高度之间的引力红移。

因此，我们可以利用两个无比精确的原子钟，把其中一个放在火箭上，另一个放在我们身边。我们可以对比火箭上的钟传来的无线电信号和我们身边的钟显示的时间。一般情况下它们是不同的，这个效应被称为引力时间延迟(gravitational time dilation)。1976年罗伯特·韦索特(Robert Vessot)及马丁·莱温(Martin Levine)首次通过实验直接观测到这一时间延迟，并以误差小于1/10 000的精确度(比哈佛实验精确了100倍)证实了质量与位置无关。这一实验是该结论最强有力的证据之一。

除了位置外，实验还能证明无论是光速还是质量，都和运动方向无关。这些实验有很重要的历史地位。在爱因斯坦发表他的引力理论之前，人们相信空间中充斥着一种叫做以太(ether)的物质。以太被认为是光传递的媒介。20世纪以前，这个概念在物理学家之间很流行。如果以太存在，那么相对以太以不同方式运动的观察者测量到的光速就会不同。根据爱因斯坦的理论，所有观察者测得的光速都应该是相等的，这和以太说矛盾，因此，以太存在与否成了检验爱因斯坦理论是否正确的关键。与此相关的实验中，最著名的当属1887年的迈克尔逊-莫雷实验。这个实验测试了光的速度是否和传播方向有关。

迈克尔逊-莫雷实验使用了一种叫做干涉仪(interferometer)的装置。它由两条相互垂直的臂组成(见图6)。一束激光沿着两条臂射入，然后在各自的另一端被一片镜子反射回来。当反射光到达两条臂的交叉点时发生干涉。因为光具有波的性质，我们可以让这两束光产生干涉条纹(就像池塘里的两列波浪在水面干涉那样)。干涉条纹的形状取决于干涉仪两臂的长度和光穿过臂的时间。如果不同方向光速不一致，那么迈克尔逊和莫雷就会在装置上观察到这个效应。

图6　干涉仪的示意图。分光镜把激光分成两束，每一束都被一片平面镜反射回来，并在交叉点干涉，干涉结果最后被导入探测器

迈克尔逊-莫雷实验得到的数据为零，也就是说，他们没有观测到光速在两个不同方向上有任何差别。对当时的很多科学家来说，这个结果出乎意料，因为他们都认为地球与以太存在相对运动。如果光是以太中的波，那么仅在相对以太静止的实验室中，光速才与光的方向无关。而地球并非如此，它绕着太阳以大约每秒30 000米的速度公转。就这样，迈克尔逊和莫雷的实验被当成否定以太存在以及确定光速运动与方向无关的重要证据。它对爱因斯坦的理论至关重要。

20世纪60年代，弗农·休斯(Vernon Hughes)与罗纳德·德雷弗(Ronald Drever)各自独立进行实验，证明了质量和物体运动方向无关。他们的实验利用了锂原子中围绕原子核以大约百万米每秒速度运动的电子。因为这些电子质量很小，所以它们之间的引力相互作用极其微弱。不过，他们还是想出了能精密测量质量和运动方向相关程度的方法。具体做法是利用电子改变能级的时候释放的光子。这些光子频率非常特殊，而具有这些频率的光也被称为跃迁谱线(transition lines)。如果电子质量和它们的运动方向有关，那么跃迁谱线的位置也将和运动方向有关。休斯和德雷弗通过仔细研究，十分精确地证实了电子质量和电子的运动方向无关。

现在让我们回到自由落体的普遍性。回忆一下，伽利略提出，所有下落物体的加速度都一致。伽利略的实验尽管史无前例，但可能并不十分精确(以现代人的眼光来看)。因此，考虑到自由落体的普遍性在牛顿和爱因斯坦的理论中都十分重要，一直以来人们都十分努力地在尽量高的精确度下验证它。现在，它已经在不同的环境下得到了证实，

包括大量的室内实验和空间观测。

其中最著名的实验发生在19世纪末，由厄特沃什·罗兰(Loránd
)主导完成。厄特沃什使用了一种叫扭秤(torsion balance)的仪器，它由一根中点挂在细丝上的40厘米的细棒组成，如图7所示，两个材料完全不同的物体挂在细棒两端。这个实验的设想是，如果两个物体朝向地球的加速度不同，那么扭秤将会旋转。通过测量细棒的运动方式，我们可以限制两个物体所受引力的不同，从而限制它们自由落体的加速度。

图7　厄特沃什的扭秤实验图解。两个物体由不同的材料组成，如果它们下落加速度不同，那么细棍将绕着细丝转动

厄特沃什以十亿分之一的精确度发现两个物体下落的加速度完全一致。这是伽利略实验的一个极其精确的加强版。19世纪后，这一类型的实验精确度变得更高。普林斯顿大学、华盛顿大学和莫斯科大学的研究组把实验精确度提高到了万亿分之一。这一精确度上的巨大进步得益于现代实验可以在真空中操作，以及科学家们考虑了太阳和地球对实验器材的引力的综合效应。目前限制精确度的因素还剩下地层变动造成的微小震动和其他邻近物体的引力(甚至包括实验仪器本身的引力!)。人们已经开始考虑在太空中进行实验，以便进一步提高实验精确度。

另一种方法是把地球和月亮当成两个自由下落的物体，然后探测它们的加速度。这个想法于1969年实现，当时阿波罗11号在月球上放了一台反射器。用这台反射器反射来自地球的激光，从而测量地月距离，其大小可以精确到厘米。从这些数据中，人们同样以误差小于十亿分之一的精确度证实了自由下落的普遍性。虽然这一实验的精确度并没有高于室内实验，但它的风格略有不同，因为我们看到的是地球和月亮之间引力场的效应，因为这个引力场相当强，因此它们提供了验证这一理论的“更强”实验版本。

总的来说，现在我们有了足够的实验得出的足够好的证据，可以证明物体质量和它们的位置及运动方向无关。我们还可以很自信地说：光速在任何方向上都是一样的，并且所有物体都以相同的加速度下落。这些是关于牛顿和爱因斯坦理论的基本假设。从现在开始，让我们来讨论关于二者本身的实验。

验证牛顿引力定律的实验

现在，爱因斯坦的理论已作为牛顿理论的补充而被广泛接受，我们将在这一章的后半部分讨论它。我们知道，在地面现象和天文现象中，牛顿的平方反比定律都适用，因此在了解它到底是如何描述内文前，有必要先研究牛顿理论本身。现在，我们来讲一讲迄今为止在这方面最重要的一些实验。

第一个在实验室验证平方反比定律的人是活跃于18世纪末的亨利·卡文迪许(Henry Cavendish)。他和厄特沃什一样利用了扭秤(见图7)。不同的是，他在细棍两端放置了额外的物块来使扭秤旋转。扭秤旁边的物块和扭秤两端的物体之间的引力导致扭秤扭转，引力大小可以由扭转程度推测出。卡文迪许实验还可以在尺度仅有23厘米的情况下研究引力。他发现即使在这一尺度下，引力的性质也和牛顿平方反比定律描述的完全一致。现在，人们已经能够在更小的尺度下进行相同的实验。

理论上，关于牛顿引力定律的室内实验，主要挑战在于引力和其他相互作用比起来太弱了。这意味着只要某个实验器材上有一点残余净电荷，其产生的电磁力就能完全盖过引力，使得它无法被测量。所有的实验器材都必须经过谨慎处理，那些无法避免的潜在电荷需要通过金属护罩来屏蔽，削弱其影响。这些挑战让引力的室内实验很难成功，也说明了为什么直到现在我们对引力的研究也不能在小于1毫米的尺度下进行(与之相对，我们已经能在百亿亿分之一毫米的尺度下研究电磁力)。

近年来有三个实验组引领着全世界室内引力实验的研究，它们分别位于华盛顿大学、科罗拉多大学和斯坦福大学。华盛顿大学的实验组将一个带有10个孔的摆悬挂在一个同样有10个孔的盘子上方，这个摆因为孔内质量被挖走而损失引力，从而发生扭转。通过测量这一扭转，人们可以在二十分之一毫米的尺度下测量引力。科罗拉多大学和斯坦福大学的实验组则利用一个振动的物体把引力测量尺度推进到四十分之一毫米。即使实验尺度很小，到目前为止，这些室内实验的结果仍然都和牛顿的平方反比定律完全一致。

在更大的距离尺度下，我们可以考虑很多其他类型的实验。为了让讨论更加容易理解，我们先考虑几十米到几千米尺度下的实验。这些尺度看似很直观，因为它们和我们日常感知的距离尺度很接近，但实际却问题重重。

到目前为止，在日常距离尺度下进行的引力实验中，得出最好结果的实验是：测量物体位于一座高塔上的不同高度受到的引力。20世纪80年代末，一批科学工作者在600米高的WTVD塔(位于美国北卡罗来纳州的加纳)上完成了这一实验。根据牛顿平方反比定律，引力在塔上不同高度的大小可以很容易计算出来，该实验则能够很精确地测量它们。大约同一时间，另一批研究者测量了不同海的水库中水的重力。这一实验是通过称量水的质量以测试平方反比定律。几年后，人们进一步测量了海洋不同深度下的引力。这些精确度几乎达到了0.1%的实验，都得出了和平方反比定律相同的结果。

天文观测数据使更大尺度下的实验成为可能，它们比测量水库和海水中的重力得出的结果要精确得多。百万和上亿米尺度下可以研究绕地球旋转的人造卫星、月球以及绕太阳公转的其他行星。1976年和1992年发射的LAGEOS卫星在这类实验中发挥了重要作用。它们的轨道是闭合的椭圆，这正好符合平方反比定律给出的条件。通过观测所有这些天体，人们以百万分之一到十亿分之一的精确度证实了牛顿引力定律。

这样，我们就有了很好的证据表明牛顿平方反比定律从亚毫米尺度到上亿米尺度，都是适用的。不同尺度下实验精确度也不一样：从千分之一(几十米尺度)到大约十亿分之一(行星轨道的尺度)。这是一个巨大的成功，但我们的故事还没有结束。现在，让我们跨越牛顿引力定律，进入爱因斯坦的理论带来的全新世界中。

研究爱因斯坦引力定律的实验

上述实验中用到的概念，大多数人都在学校的物理课中接触过：质量一致性、自由落体的普遍性、牛顿平方反比定律等。我在这一节将介绍的实验验证的是大家不大熟悉的爱因斯坦的引力理论。这一理论的特殊效应一般都在很小的尺度上发生，实验很难把握。但它们其实十分重要，因为它们让我们对引力理解更加深刻。

爱因斯坦的理论带来了大量的新效应。这里我只谈其中的四个。它们是：水星公转轨道逆行；太阳周围的星光偏折；掠过太阳的无线电信号的延时；以及环地球轨道上陀螺仪的行为。这四个至关重要的效应都可以在太阳系内观测到。在极端天体物理环境下更多的效应我们留到第3章继续讨论。

我们从水星轨道逆行开始谈起。在本书第1章我们说过，牛顿引力定律解释了开普勒的观测结果，即行星绕太阳公转的轨道是椭圆。对于单个行星来说这是对的，但是如果我们同时考虑好几个行星的轨道，事情就变得复杂起来。这是因为行星之间也存在引力，它们虽然微弱但仍旧是可观的，并能够把行星从标准的椭圆轨道拉开。

很长时间以来，物理学家们对行星之间的引力都有了解。这些引力在牛顿理论的范围内很容易计算，几个世纪以来的天文学家们也测量了它们产生的效果。实际上海王星就是在19世纪中期靠研究天王星(比海王星稍离太阳近一些的行星)轨道之后才发现的。天王星的运行轨道距离天文学家们的预期稍微有所偏移，如果在太阳系更远的位置有一个大一些的行星的话，这一偏移就合理了。奥本·勒维耶(Urbain Le Verrier)和约翰·亚当斯(John Adams)分别在1845年预测了这一行星的存在，1846年它就被发现了。显然，这是一个了不起的成就。

这样一来，1859年勒维耶宣布水星(距离太阳最近的行星)轨道也有一些偏移时，人们并没有感到特别惊讶。有了海王星的前车之鉴，勒维耶预言水星轨道内还有一颗更靠近太阳的行星。他甚至给它起了个名字——火神星(Vulcan)，然而这次它并没有出现。人们作了很多很多的努力，但没能在水星和太阳之间发现任何新的天体。水星轨道仍旧反常，看来像是被一个不知其源的天体产生的引力所扰动。

水星轨道逆行的问题在1915年得到了解决。并不是因为发现了新的天体，而是因为爱因斯坦提出了他那革命性的理论。根据爱因斯坦的新理论，牛顿引力只是引力本质的一个粗略的概括。除了平方反比定律之外，爱因斯坦预言引力存在着新的、更小的贡献。对于一个像太阳系那样由大质量天体主导的系统，爱因斯坦的计算结果表明引力的新贡献中最强的一项和距离的立方成反比。因此，相对于平方反比定律，越靠近太阳，引力这一新贡献的作用就越明显。

水星一直以来都是距离太阳最近的行星，所以爱因斯坦给出的引力的新贡献对水星比对其他行星有更强的影响。爱因斯坦的计算表明：水星轨道每个世纪被拽着绕太阳进动43角秒(1角秒等于1/3600度
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)。这个量非常微小，但足以被天文学家们捕捉到，它和勒维耶测量的水星轨道逆行结果一致。这样，爱因斯坦的引力理论在1915年解释了水星轨道问题，这是它在观测上获得的第一个大成功。

现在对水星轨道的观测比起19世纪来要容易多了。我们对所有行星的轨道现在都有了非常精确的了解，这对于计算水星轨道偏移是十分重要的。举个例子，金星对水星的扰动是爱因斯坦引力修正值的六倍大。因此人们必须很精准地知道金星的位置。然而这还不是现代观测最大的误差来源，太阳形状的不确定性才是。太阳形状和球形的一点点偏差都会和爱因斯坦引力效应混在一起。太阳形状很不容易精确测量，所以我们只能说水星轨道异常与爱因斯坦理论是一致的，其精确度为1/1000。

对水星轨道的解释令人印象深刻，但它不能称为一个预言，因为在爱因斯坦出生之前它就被人熟知了。爱因斯坦理论一个天才般的预言是光线经过太阳时会发生偏折。在爱因斯坦之前人们并不知道光会不会被引力影响，因为牛顿引力定律只适用于有质量物体(而光是无质量的)。而在爱因斯坦的理论中，光和其他物体一样都走弯曲时空中最短的路线，因此爱因斯坦预言光会被大质量天体附近的引力场折弯。

爱因斯坦的计算表明：光线在刚好掠过大质量天体表面时弯折得最厉害。太阳系内最大质量的天体就是太阳，但是我们得等到日全食发生时才能看到太阳附近的星光，否则太阳光会吞没一切。验证星光偏折的第一个好机会出现在1919年，那时第一次世界大战刚结束。亚瑟·爱丁顿爵士(Sir Arthur Eddington)领导了一支探险队去测量太阳附近星星的位置，从而验证爱因斯坦的引力理论。

爱丁顿的远征队去了非洲的普林西比岛，因为那里可以观测到日全食。他利用当时最先进的感光板很仔细地做了测量。当时的条件并不理想，但爱丁顿还是成功测量了全食发生时星星的位置。他发现它们确实都因为星光偏折在视觉上偏移了本来的位置，正如爱因斯坦预言的那样。爱丁顿的结果足以证明爱因斯坦的理论是正确的，虽然精确度只有大约30%。

现如今对轨道的测量比19世纪要准确得多，其中一个原因是人们利用了一种非常明亮的天体——类星体(quasars)。它们在天空中的位置恰好可以用来验证爱因斯坦的预言。当它们从太阳后方穿过时，我们可以测量它们发出的光线的偏折。人们利用甚长基线干涉仪(interferometer，它是一类利用大量探测器组合而产生高分辨率的天文望远镜)观测了数百万类星体。这一工作的结果完美地符合爱因斯坦的理论，精确度达到了万分之一左右。

爱因斯坦理论一个比较新一些的预言是：射电信号在经过大质量天体的时候会发生时间延迟。由于某些原因，科学家们直到1964年才观测到这一爱因斯坦引力理论的结论，而现在人们已经能够在不同的情况下测量它。其中包括行星反射太阳的射电信号，以及人造卫星自主发射射电信号。利用行星的优势在于人们能非常精确地了解它们的位置，而且很容易就能预测它们的运动轨迹。这一稳定性使它们成为非常好的观测来源。但是行星形状的不规则又会给证明过程带来一些麻烦。人造卫星发射的信号则很容易把握，虽然它们的轨迹略微难以确定。

人们已经利用了水星和金星来探测射电时间延迟效应。相关实验用到了水手6号、7号旅行者2号、海盗号火星登陆着陆器及轨道飞行器、卡西尼号探测器。其中卡西尼号作出了最新和最精确的观测。这个飞船本来的任务是观测土星，但2003年它却转向了引力相关的研究，并以1/100000的精确度确认了时间具有延迟效应。这是爱因斯坦理论另一次漂亮的验证，它比之前的实验精确度都要高。部分原因是人们采用了多波段射电观测，有效去除了日冕的影响。

现在我们来看看本节的最后一个实验：环地球轨道上的陀螺仪(gyroscopes)。陀螺仪本质上就是一个转轴可以指向任意方向的陀螺。根据爱因斯坦的引力理论，当我们把陀螺仪放在环地球轨道上运动的时候会产生两个新的效应。第一个是陀螺转轴的方向会发生改变，这一效应被称为测地线进动(geodetic precession)，它的产生原因是地球周围的时空弯曲。另一个效应被称为参考系拖曳(framedragging)，产生原因是地球自转时拖着周围的空间一起转动。这是两个全新的引力相互作用，所以人们急切地希望通过实验证实它们。

虽然参考系拖曳这一预言在爱因斯坦发表新的引力理论之后几年内就被提出，但直到20世纪60年代人们才计算出这一效应对绕地陀螺仪的影响，接下来更是到21世纪才被实验证实。激光地球动力学卫星网络(LAGEOS satellite network)测量了卫星轨道的变化以观测拖曳效应。2011年，引力探测器B(Gravity Probe B)实现了人们期待已久的陀螺仪实验。它测量到的测地线进动和参考系拖曳效应的误差分别在0.3%和20%。激光地球动力学卫星的准确度则达到了90%~95%。所有的结果再一次符合爱因斯坦理论。

我们手中的证据都支持爱因斯坦的引力理论，无疑令人鼓舞。这一理论最基础的部分，如质量一致性和自由落体的普遍性都高度精确地被验证了。它的一阶近似——牛顿平方反比定律——从亚毫米尺度到天体物理尺度范围也都得到了验证。我们还有许多探测爱因斯坦理论中精细和微妙的效应的实验。这些数据让我们从现实层面理解了物质和时空弯曲的关系，到目前为止它们全都符合爱因斯坦的预言。爱因斯坦的理论几乎完全诞生于纯粹的思考，而这些实验确认了这一理论。这确实令人惊讶。爱因斯坦希望得到一个和光速不变原理相容的引力理论，他做到了，而且我们现在还看到他给宇宙描绘的革命性的新图景。不过这仍然不是故事的结局：爱因斯坦的引力理论还有许多更加惊人的推论，我们将在后面的章节讨论它们。

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此处原文“1角秒等于1/360度”有误。

03 太阳系外的引力测验

我们已经能够在太阳系内探索多种多样的引力效应，其中不乏精确度相当高的实验，这是因为我们能很好地把握邻近的行星和人造卫星的运动。但是太阳系内天体运动速度偏慢，密度偏低，所以它们产生的引力场都非常弱。如果我们把目光放得更远，我们就能看到比身边的太阳系更加极端的天体。

我先讲讲一颗恒星的一生。第一代恒星被认为是从氢分子云中诞生的。这些氢分子云产生于宇宙大爆炸，它们在自身的引力作用下逐渐坍缩变得又热又致密，直到最后发生了核反应。核反应产生的向外的压力和向内的引力平衡时，一颗由气体坍缩成的剧烈核反应大火球——恒星——就这样诞生了。以上是对坍缩气体和核反应的一个粗略描述，我们的太阳内部也正发生着这样的过程。

但故事还没有结束。像太阳这样的恒星寿命有限。到最后，核聚变的燃料——氢——将会耗尽，然后恒星就会开始燃烧其他燃料。这使它们膨胀成红巨星。这些替代氢的燃料会依次耗尽，恒星的引力坍缩会再度发生。阻止这一坍缩的方式决定于恒星的大小。一颗小质量恒星会变成一颗白矮星(white dwarf)。在白矮星中电子的量子力学性质
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会阻止它继续缩小。到这一步，恒星内的空间已经容不下更多的电子。

如果恒星质量更大些，它最后就会变成一颗中子星(neutron star)。对于这一类恒星，核聚变到终点时会产生核心坍缩，然后导致剧烈的爆炸，这一爆炸被称为超新星(supernova)。在这一过程中引力强到足以把电子和质子压到一起形成中子。此时电子压消失，恒星一直坍缩，直到不可能有更多的中子能被塞进它所在的空间。到最后，形成的中子星密度变得和原子核的差不多，在这个意义下我们可以把中子星看作一颗巨大的原子核(不过没有质子和电子环绕)。中子星又小又致密，它们的密度比太阳系内任何物体都大，而且一般以极快的速度自转。

中子星还不是恒星坍缩可以形成的最极端天体。这一头衔应该颁给一类叫黑洞(black hole)的天体。如果一颗恒星质量大到最后连中子都不能支持引力，它将会坍缩成一个黑洞。黑洞是自然界中存在的最极端的物质之一。在坍缩之后只剩下引力场本身。黑洞由一个被事件视界(event horizon)包裹的时空区域组成。黑洞里的引力场强到没有任何物质可以从事件视界内逃出来，连光都不行，这也就是黑洞名字的来由。

在这一节我们将考虑上述恒星系统。天文学家们现在已经发现了大量这样的系统，在对它们的观测中我们能够以新的方法探索引力，这些方法在太阳系内是不可能实施的。这些天体的极端性质使爱因斯坦理论的效应变得非常明显，它们为我们提供了探索引力的令人激动的全新窗口。

赫尔斯-泰勒脉冲双星

赫尔斯-泰勒脉冲双星(Hulse-Taylor binary pulsar)，或者叫PSR B1913+16，是一个由相互绕转的中子星组成的双星系统。这个系统有个值得注意的地方：其中一颗中子星是脉冲星(pulsar， pulsating star的简称)。从地球上看，脉冲星会非常规律地发射出脉冲辐射。这一辐射产生于它们周围的强磁场引起的超强光束。由于中子星的迅速自转，这些光束在远处的天文学家们看起来就像快速亮灭的闪光，就像灯塔旁边的船员看到灯塔的信号闪光那样。脉冲星最早于1967年被乔瑟琳·贝尔·伯奈尔(Jocelyn Bell Burnell)和安东尼·休伊什(Antony Hewish)发现。他们观测到了很规则的闪光，这一闪光现在被视为脉冲星存在的标志。实际上，它最早被看成外星文明的信号。那些天文学家甚至给这些信号的来源命名为小绿人一号(Little Green Men-

1，缩写为LGM-1)。后来人们在天空的其他位置发现了相似的信号，这使他们意识到这些信号来自快速自转的中子星。现在我们已经确认了1000多颗脉冲星，这个数字将来还会越来越大。

赫尔斯和泰勒在1974年发现的PSR B1913+16，其意义不在于找到一颗脉冲星，而是它正绕着另一颗中子星转。这一结论基于他们发现该脉冲星的脉冲频率稍有变化，也就是说脉冲有时候早三秒钟，有时候晚三秒钟。这一变化的周期大约是七小时四十五分钟。因为这个脉冲星每秒脉冲17次，我们可以画出一个带有明显振动模式的脉冲图像，对于这一现象唯一能得的解释是，它正在围绕着另一个天体公转，轨道半径大约3光秒(也就是光在3秒内走过的距离，大约为100万千米)。

因此，赫尔斯-泰勒脉冲星被认为属于一个双星系统，但人们并没有找到双星系统中的另一颗星。这意味着它并不是一个普通的恒星，虽然它有恒星那样的质量。这一双星系统另一个天体最有可能的是不发射脉冲的中子星(或者至少不朝我们发射任何脉冲)。这样的系统对于研究引力来说非常有用，因为两个天体都非常致密，而且以极高的速度绕转。这使得爱因斯坦理论预言的微小效应变得更加明显。而这两颗中子星的其中之一还发射出和原子钟一样精确的脉冲信号，这更是锦上添花，我们可以从这一信号中提炼出更多关于引力相互作用的信息。

从1974年被发现起，人们一直在收集关于赫尔斯-泰勒双星的数据。这一任务主要由位于波多黎各的阿雷西博望远镜(Arecibo telescope)完成。阿雷西博望远镜是一个直径达305米大的射电天线(看过电影《黄金眼》的人应该十分熟悉)，它收集了大量关于这一非常特别的双星系统的数据。我将在后文讨论一些其他的脉冲双星系统，但对它们的观测时间都没有比赫尔斯-泰勒脉冲星长。人们可以利用脉冲双星系统的巨大数据库对引力做非常精确的实验。

现在，让我们来考虑关于引力的信息是如何隐藏在这些脉冲星信号的特征里的。其中一种方式是脉冲星信号穿过中子星伴星时发生的引力红移和时间延迟。回忆一下，我们已经在太阳系内测量了这两种效应。现在它们在遥远的双中子星系统中也得到了验证，而这两颗中子星之间的距离差不多就太阳那么大。另一个效应更为人熟知，即轨道进动，人们可以在赫尔斯-泰勒脉冲双星系统中观测到它。就像水星一样，赫尔斯-泰勒脉冲双星系统的双中子星围绕着彼此进动。它们能在一天内完成水星要一个世纪才能完成的进动。

关于双脉冲星的最后一个观测效应是引力波辐射导致的轨道周期变化，这一效应在太阳系内是不可能被测到的。我们还没有讨论引力波，它是爱因斯坦理论的一个重要预言：它们是存在于时空中的涟漪，能带走某个系统的能量。引力波在牛顿理论中是不存在的，所以它对于爱因斯坦理论的验证非常重要。我将在第4章详细解释引力波。而现在，我们只需要知道引力波是爱因斯坦预言的，而且脉冲双星系统辐射的引力波会带走它们的能量。

我们可以在赫尔斯-泰勒系统的信号中测量三种相对论效应。它们是中子星伴星引力场导致的时间延迟、双星轨道的进动以及引力波辐射带走能量导致轨道周期变短。这三种效应中的任意两种都可以用来计算两颗中子星的质量(在这样的双脉冲星系统被发现之前，还没有什么办法可以测量中子星质量)，第三种则可以用来验证爱因斯坦的理论是否正确。

利用上述方法测量，赫尔斯-泰勒双星系统中两颗中子星各有1.4个太阳质量。这一结论来自测量时间延迟效应(0.02%精确度)以及轨道进动(0.000 1%精确度)。利用两颗中子星的质量，我们就可以计算爱因斯坦理论预言中引力波带走的能量，以及它导致的轨道周期如何变化。结论是，爱因斯坦理论预言赫尔斯-泰勒系统的轨道半径大约每年减少3.5米。天文观测以0.2%的精确度证实了这一结果。这是验证爱因斯坦理论的另一个卓越的实验，赫尔斯和泰勒因此获得了1993年的诺贝尔物理学奖。

人们预测赫尔斯-泰勒脉冲双星系统中会发生的最后一种效应叫测地进动(geodetic precession，即陀螺自转轴的指向的变化)。由于脉冲星自己就像一个绕着伴星公转的陀螺，这一效应可以由脉冲星信号的形状测出。虽然它是可能被观测到的，但是现有的数据精确度不足以用来验证爱因斯坦的理论。这主要是因为我们不大清楚脉冲辐射来自中子星表面的哪个位置。

赫尔斯-泰勒脉冲双星系统为验证引力理论提供了一些卓越的方法。虽然它非常独特，但那只是过去，现在，它已经不再是我们知道的唯一的脉冲双星系统。现在让我们来看看一些新发现的系统，它们中有一些在对于引力理论的验证上得到了足以比肩赫尔斯-泰勒脉冲双星系统的结果，将来甚至会超越它。

其他脉冲双星系统

鉴于赫尔斯-泰勒脉冲双星系统的重要历史地位，在冠以学名(PSR B1913+16)的同时，它还以它的发现者命名。而其他脉冲双星系统一般我们只叫学名。习惯上，我们把这一系统叫作PSR，也就是“脉动源的辐射(Pulsating Source of Radiation)”，然后加上它们的赤经和赤纬(用来描述天空中位置的坐标)。字母“B”或“J”也被用来表示该系统是发现于1993年之前或之后(在1993年之后发现的脉冲双星系统一般具有较高的位置精确度)。

直到2006年以前，我们只发现了其他8个轨道周期短于1天的脉冲双星系统。它们中有一些存在特殊性质，人们对此兴致勃勃，并利用它们研究引力。虽然观测时间没有赫尔斯-泰勒脉冲双星那么长，它们还是让人们对引力有了更深入的理解。在这一节的后半部分，我将粗略地介绍一下其中最有代表性的几个系统，最后再来展望一下太阳系外引力测验的未来。

让我们从PSR B1534+12开始。它的学名告诉我们这一脉冲双星系统发现于1993年之前。这一系统引人注目的是，在我们看来它差不多完全是侧向的。也就是说，我们的视线几乎完全和这一系统的轨道平面重合。这一方向的时间延迟效应最强，因为在某些时候天文学家们观测到的脉冲星射电信号在传播途中会非常接近伴星。脉冲星的脉冲非常强，而且很窄，这使它们成为非常好的时钟。不幸的是，我们并不能非常准确地测量地球到这一系统的距离，这限制了用它来测验引力的精确度。直到今天，和赫尔斯-泰勒系统比起来，我们也没有从它身上了解更多关于引力的信息。

另一个非常有趣的脉冲双星系统是PSR J1738+0333。人们发现这一系统的脉冲星绕着一颗白矮星旋转(白矮星是中子星的老大哥，详见本节前文的介绍)。这类系统的特殊之处在于：两个天体迥然相异。因此我们可以利用它来做关于引力的新实验。爱因斯坦理论指出，引力波对两个天体是否相似这一点并不敏感，而其他的引力理论则预测引力波对两个天体是敏感的。我们可以测量PSR J1738+0333这类系统中引力波带走的能量，从而验证爱因斯坦的理论。如果爱因斯坦是错的，那么我们将看到PSR J1738+0333以非常高的损失率损失能量。到目前为止，我们并没有看到这一异常，所以爱因斯坦的理论再一次得到了证实。

然而，2006年以前最令人兴奋的系统当属PSR J0737-3039A/B。这一系统发现于2003年，它拥有一系列令人难以置信的性质。这一系统的两颗中子星都是脉冲星，人们把它叫双脉冲星(the double pulsar)，这使它在所有系统中独树一帜。这一系统不再仅仅是拥有一个产生引力场的大质量天体，而是两个天体都会辐射脉冲，这使我们能前所未有地利用两个天体的轨道来研究引力。除此之外，这两颗脉冲星还在以极高的速度自转(即使是以双中子星的标准而言)，并且这一系统也是侧向的。这些性质综合到一起，使得这一系统的相对论引力效应非常之强，强到2008年其中一颗脉冲星的进动过远，以至于我们都观测不到它的脉冲了。

现在，我们不再需要花上几十年才能观测到爱因斯坦引力理论产生的效应了，有了脉冲双星系统，这一过程需要几年时间。PSR J0737-3039A/B提供了比赫尔斯-泰勒系统更好的证据证实引力波的存在。由于两颗脉冲星都是可见的，这一系统能提供六种方法来测量引力场，而赫尔斯-泰勒系统只有三种。在这一系统中，确定了两颗中子星的质量后，我们还有四种互相独立的实验来测试引力。爱因斯坦的引力理论将再一次大获全胜。

未来

虽然太阳系系外引力系统的观测已经给我们带来了惊人的发现，但未来仍旧值得期待。我们之所以如此乐观，是因为人们正在修建新一代的望远镜，其中最大的叫做平方千米阵(Square Kilometre Array，缩写为SKA)。平方千米阵能接收非常遥远的信号源发射的射电辐射，它将成为地球上最大规模的望远镜。

平方千米阵由几千个射电天线组成，覆盖包括非洲南部、澳大利亚和一些其他撒哈拉以南国家，面积有几千平方千米。这一望远镜的接收面积(所有射电天线面积加起来)高达100万平方米，它的灵敏度将比已有的射电望远镜高50倍，其配套的计算机网络系统带宽比现有所有因特网加起来还大。平方千米阵的预算估计为20亿欧元，由澳大利亚、新西兰、加拿大、中国、印度、南非、意大利、瑞典、荷兰、英国和德国资助。平方千米阵在任何层面上来讲都是一个里程碑。

计划和修建像平方千米阵这样的巨型项目需要很长时间。但在2020年它开始接收数据以后，人们将可以利用它进行一些前所未有的实验。为了研究引力，最重要的实验之一就是观测大量脉冲星。首先，平方千米阵很可能会发现大量新的脉冲双星系统，我们可以按照前一节的方式利用它们研究引力。其次，平方千米阵可能会发现成百上千的微秒级脉冲星(microsecond pulsars，它们1秒能完成百万次自转)。通过仔细测量它们发射的信号，平方千米阵甚至能够直接测出经过我们这里的长波引力波。也就是说，平方千米阵可以看作一个巨型引力波探测器。

天文学家们期望利用平方千米阵做的引力效应观测将比太阳系内观测精确100倍。这会是巨大的进步。现在，脉冲双星观测的精确度刚刚开始超越太阳系内观测，平方千米阵开始成为最佳的引力测验工具。除了在这方面具有优越性之外，平方千米阵还具有更多令人期待的潜力。其中之一就是利用它去探测引力在极大尺度宇宙范围内的效应。我将在第5章回到这一课题。另一方面是它可能发现围绕黑洞公转的脉冲星系统。黑洞具有宇宙中最强的引力场，它由恒星不可逆转的剧烈坍缩形成。脉冲星和黑洞组成的双星系统应该非常稀少，但如果它们真的存在，平方千米阵就有机会发现它们。这一类系统将提供在最极端环境下验证引力的可能，它是一个非常激动人心的构想。

在不远的将来，人们有理由对太阳系外引力试验充满希望。原因在于最近发现的一种新脉冲星系统。2014年，一组天文学家宣布他们发现一个一颗脉冲星绕着两颗白矮星公转的系统。他们把这个三体系统称为PSR J0337+1715。三体系统的公转轨道比两体系统存在丰富得多的可能性，而且看上去这些轨道的结构还可以划分等级，也就是说，脉冲星绕着其中一颗白矮星做闭合轨道公转，而另一颗白矮星以很远的距离绕着这两颗星公转。人们发现外面这颗白矮星的存在加速了里面这对天体的公转速度。三体系统是研究强引力物理的新“实验室”。

我们可以期待，包括平方千米阵在内的新的望远镜会帮助我们研究脉冲双星和脉冲三星系统。天文学家们甚至可能利用它们看到参考系拖曳现象(详见第2章的描述)，也就是旋转星体拖着空间本身转动的效应。这些观测不仅可以用来研究引力物理，还能让天文学家们了解中子星内部物质的特性。如果这些构想成真的话，我们将能够研究密度高达万亿千克每立方厘米的物质。

[1]
即下文提到的电子压。

04 引力波

我们在第3章曾经提到过引力波(gravitational waves)。现在我们来详细地讨论它。第1章讲过，在爱因斯坦的理论中，引力产生于时空弯曲。恒星或行星这样的大质量天体使它们周围的时空发生弯曲，导致其他的一些物体从它们旁边经过时轨道发生偏折。如果错误地认为这些东西在平直时空中运动，我们就会以为存在一种叫做引力的东西。实际上这一切都是时空弯曲导致的。

引力波和时空弯曲有关。如果一组大质量天体之间有相对运动(比如太阳系、脉冲双星系统等)，那么它们周围时空的弯曲就不是一成不变的。有质量物体导致了时空弯曲，所以如果这些物体在运动，那么时空的形态也会不停变化。描述这一情况更科学的说法是：在爱因斯坦的理论中，时空是动态的。

我们用前面讨论过的超新星作例子来解释这一点。在它们的核心坍缩导致灾难性的爆炸之前，它们就像我们的太阳一样，是比较稳定的天体。因此，在这一阶段，它们周围的时空弯曲方式应该和太阳周围是一样的，也就是说，和太阳周围的引力场相似。它们爆发之后最终会形成中子星或黑洞，再一次回到相对稳定的状态，此时引力场便不随时间变化。爆炸的时候，它们会往外喷射巨大的质量和能量。它们的引力场，也就是周围的时空弯曲在这段时间发生着剧烈的变化。

和很多系统从平衡状态转变为快速变化状态时的情况类似，超新星爆发产生了一种波形式的扰动。用更加接地气的例子作类比，就像你往平静的水池里扔一块石头，落水位置的池水会从稳定状态开始迅速变化。池水希望可以回到它最先平静的状态，这导致了一种向外传播的扰动，这种扰动以波纹的形式从石头落入的位置向外扩散。相似地，原本安静的房间里突然出现的响亮的噪声会引起房里各点的大气压力的改变。由于空气试图回到稳定状态，气压的扰动也会以压力波的形式向外传播，这种压力波叫声音。

引力也一样。如果时空曲率受到质量或能量的扰动，那么这种扰动就会以波的形式传播开去。当恒星坍缩时，它们的外层会被爆炸的压力推出去，此时就会发生引力扰动。和上文池水的例子相似，这一剧烈过程就像往水里扔石头一样激发了时空曲率的波动。

波传播的速度一般取决于它们通过的介质。比如说，我们知道声波在热空气中比在冷空气中传播速度要快一些。引力波的介质是时空本身，根据爱因斯坦的理论，引力波的传播速度和光的传播速度相同。和光一样，这一速度的大小和观察者以及波源的运动状态都无关。引力波传递信息的速度是最大可能速度，因为它与光速相同，没有任何东西能跑得比光还快。

引力波产生的效应

为了理解引力波到底是什么，我们可以考虑当它经过一群物体时会发生什么。比如说，如果你尝试给一个不熟悉水的外星人去描述池子里的水波是什么，你可以先描述水波如何让浮在水面的花瓣上下运动。现在，我们来看看与之类似的引力波的情况。

先来考虑空间中有一团均匀的气体云。我们不考虑地球自身的引力场对它的作用(因为地球引力通常比引力波强太多)，同时我们也不考虑其他任何东西对这片云的作用。如果引力波穿过了这一片云(见图8)，最主要的效应是改变垂直引力波传播方向上气体的分布。也就是说，如果引力波从左往右传播，那么气体粒子将会在上下或者纸面内外方向运动。

图8　引力波穿过一片气体云的示意图。引力波从左往右传播，使气体云粒子在上下，或者纸面内外方向运动

乍一听，引力波对气体云的作用好像是在说引力波是气体云本身运动形成的，就像水的运动形成水波一样。但实际上两者完全不同。引力波是时空本身的波动，所以引力波对气体云的作用可以更好地类比于水波对水面上花瓣的作用，而不是把气体直接类比于池水。换句话说，引力波并不是气体中的波，而是气体所在的时空中向前传播的扰动。

在这个例子中，引力波实际的作用是改变了垂直于传播方向的空间的“多少”。这意味着引力波穿过时气体原子彼此靠近(或者远离)并不是因为原子动了，而是它们之间的空间由于波动变少了(或者变多了)。引力波通过改变物体间空间的大小来改变物体之间的距离，而不是让它们在固定的空间中运动。这种解释只有在爱因斯坦的理论中是可能的，因为此时空间是动态的。

我们可以更加详细地考虑引力波的效应。我们假设排成环状的一圈粒子，有一列引力波穿过它们。图9显示了当引力波由纸面内往外传播时会发生什么。引力波只对垂直传播方向起作用，从而页面上粒子环的变化很形象地展示了引力波作用的结果。

图9　当引力波从纸面上往外传播时纸面内的粒子组成的环发生了形变。最左的图显示的是原先粒子的排列形状，从左往右依次是四个时刻粒子环的形状

如果粒子一开始就排列成完美的圆形，彼此之间相互分离，并且不附着在其他任何物体上，那么引力波的效应就是在一个方向上压缩并在另一个方向上抻长这个圆。于是圆就变成了椭圆。当波穿过的时候，它会连续地改变圆的形状直到它的形变达到上限，之后这个过程会反过来，沿着之前抻长的方向压缩这个圆。图9展示了引力波穿过时这一拉伸和挤压的过程。

我们已经在脉冲双星系统中讨论过引力波辐射的结果。引力波从双星系统中带走了能量，于是两颗中子星会一边绕转一边缓缓地靠近。人们测量到的靠近速率就是引力波存在的很好的证据，但科学家们依然非常期待直接看到引力波本身。2015年9月，LIGO首次成功地观测到了引力波。引力波的发现十分激动人心，因为它给我们提供了观测宇宙的全新窗口。这是史上第一次，我们不再局限于观测遥远物体发过来的光，我们已经可以直接观测它们的引力场本身。从今以后，我们还可以研究黑洞相撞的时候发生了什么。

直接观测引力波同样可以让我们以新的方式验证爱因斯坦的引力理论。人们可以假想引力波经过产生的种种现象。比如图9展示的粒子环可能的形变，或者在引力波传播方向垂直的空间也会有所变化，等等。爱因斯坦提出的关于时空弯曲的方程明确地否决了这些可能性，但是如果他错了，那么上述两种设想实际上是可能的。利用LIGO这样的实验，我们可以看看引力波是不是表现出爱因斯坦理论预测的那些行为。就这样，引力波提供了另一种验证爱因斯坦理论的方法。除此之外，我们还能以新的方式了解黑洞相撞时发生了什么，从而产生不少令人激动的可能性去进一步研究引力物理。

引力波探测器

爱因斯坦在1916年就预测了引力波的存在，差不多一个世纪后，人类终于在2015年第一次探测到了它。为什么用了这么长时间？因为引力波信号的强度极其微弱。图9只是为了更好地展示引力波而将其效应夸张了。在现实中，粒子的形变只占其10 20的大小的量级。也就是说如果我们做一个1000千米直径的粒子环，引力波只会导致10 -12 厘米的形状变化，这显然是非常难以探测到的。

尽管探测任务艰巨，或者说正因为如此，反而激励了很多人为直接探测引力波而努力。非常重要的早期工作之一由一类叫韦伯棒(Weber bars)的仪器完成。这类仪器的名字来源于马里兰大学的约瑟夫·韦伯(Joseph Weber)，它们由巨大的金属圆柱组成，大约1米宽，几米长。人们设想当引力波穿过地球时，它会导致圆柱振动，就像用木槌敲击铃铛一样。只有某种频率的引力波存在时才能引起圆柱振动。

当年用来探测引力波的韦伯棒精确度能达到10 -15 。虽然听上去十分灵敏，但还不足以探测到今天人们熟知的引力波。韦伯棒在历史上曾经收到过好几次假警报。1968年，韦伯声称他得到了引力波存在的证据，这一发现足以让他成为诺贝尔奖的有力竞争者。不幸的是没有人能复制他所声称的发现，因此现在人们普遍相信这是一次假警报。

一些最新版本的韦伯棒今天仍在运作。其中一个例子是莱顿大学的MiniGRAIL实验。它由一个1150千克的金属球组成，比韦伯自己建造的韦伯棒灵敏1000倍左右。不过今天的人们更多地使用另一种技术来探测引力波，这就是干涉法(interferometry)。基于干涉法的引力波探测器原理和第2章介绍的迈克尔逊-莫雷干涉仪类似。而现在的引力波干涉仪比第2章介绍的干涉仪要大得多得多。截至本书完稿的时候，世界上最大的引力波干涉仪当属美国的LIGO。

LIGO即激光干涉引力波天文台(Laser Interferometer Gravitational-Wave Observatory)，它有两个台址。其中一个在路易斯安那州的利文斯顿，另一个在华盛顿州的里奇兰。每一个台址都有一台巨大的干涉仪，它由两根相互垂直的“臂”组成(如前文图6所示)。每一根臂都有几千米那么长，里面是一根约1米粗接近真空的管子。激光从这些管子的一端射入，从悬挂着镜子的另一端反射回来。我们主要是研究激光反射回到双臂交会处产生的干涉条纹。当引力波穿过干涉仪时，臂的长度会发生变化，于是两束激光产生的干涉条纹也会发生变化。

LIGO的探测器被设计得十分精确，它的灵敏度比韦伯棒强百万倍。要实现这么高的精确度在技术上有着惊人的难度。实验物理学家们需要克服各种各样的假信号污染，包括地震的噪声，也就是地球内部的运动导致的反射镜振动，以及管道外的强风。实际上，LIGO的探测器现在已经敏感到人们必须考虑极端微小的限制因素，其中包括激光，它由一个个光子组成，因此在镜子处反射时不可能是连续的。

尽管有这些大问题，还要面对庞大的经费、政治和工程上的困难，LIGO的探测器最后还是收获了巨大的成功。2015年9月14日，人类利用LIGO史上第一次直接探测到双黑洞并合形成的引力波。这一事件的意义怎么标榜都不为过，它将来可能成为我们这个时代最伟大的科学成就之一。因此，让我们来具体地讨论一下LIGO实验。

LI GO的引力波观测

格林尼治时间2015年9月14日9点50分45秒，位于路易斯安那州利文斯顿的LIGO引力波探测器的干涉仪中出现了震荡信号。这一信号只持续了0.2秒的时间，它导致干涉仪那条4千米长的悬臂伸缩了1/1000个质子大小的尺度。大约0.007秒后，位于华盛顿州汉福德的探测器收到了相似的信号。这一信号激发了警报，操作这一实验的科学家们立刻毫无疑问地确信，他们探测到了穿过地球的引力波。

在讨论引力波的源头之前，我们先考虑信号本身。如果你去读两个LIGO台址任意一个收到的数据，它们看起来不过是源于探测器本身持续不断的噪声背景中的一个小突起。这一信号的峰值只有随机噪声污染振幅的两倍，因此很不容易被注意到，也很难被确认是不是真的信号。科学家们如此确信它是真实信号的原因有两点：第一，两个在不同地点的探测器的振动非常相似。地球本身的振动可能导致其中一个台址的探测器晃动，但同时在两个位置上产生相同的震颤是几乎不可能的。第二，也是非常重要的一点，LIGO的科学家们知道真正的信号会是什么样子。这让他们可以利用一种叫做匹配滤波器(match filtering)的技术去扫描他们的数据，从中筛选符合期望的信号。考虑以上两个因素，LIGO的科学家们有99.999％的把握确信他们探测到的振动信号的来源是经过地球的引力波，而不是噪声造成的假信号。

显然，这个结果对LIGO小组来说是巨大的成功，毕竟他们操作的是全世界有史以来最精密的科学仪器。同时，它也是理论物理学家们重要的成就。上文说的匹配滤波器的原理是理论物理学家们给一类最极端引力场——并合双黑洞——建立的理论模型，这对于引力波探测至关重要。只有了解了黑洞相撞时到底会发生什么，科学家们才有可能建立正确的滤波器来找出引力波信号，这可比想象中困难多了。黑洞相撞有很多种方式，利用爱因斯坦理论去预测这样的系统会产生什么样的引力波，需要极其复杂烦琐的数学计算。

在这里，我不会讨论卷帙浩繁的数学细节，但我们可以考虑激发这些引力波的实际天体物理过程。结合探测器收到的信号和我们前文讨论过的并合黑洞的模型，人们得出结论：这一信号的来源是两个相互绕转的黑洞，它们越靠越近，最后合并成了单个巨大的黑洞。这两个相互靠近的黑洞质量分别是大约29和36个太阳质量，它们合并之后形成的大黑洞大概是62倍太阳质量。听起来挺平凡的，但它却是宇宙中可能发生的最剧烈的过程之一。

一些机智的读者可能已经发现29加36并不等于62。这是因为黑洞在并合时产生的引力波恰好带走了3个太阳质量对应的能量(回想一下爱因斯坦的质能公式：)。这一系统损失了如此巨量的能量，在某种意义上也可以体现为什么我们称它为“剧烈过程”。为了更直观地理解这个数字，我们可以想象一下两个黑洞并合产生的引力波，它的能量甚至比全宇宙所有恒星发出的光能加起来还要大。它们在13亿光年外都能被观测到，这已经是整个可观测宇宙
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中非常大的一部分了。在引力物理学家眼中，这是既极端又非常令人激动的事件。

未来的展望

虽然我们已经探测到了引力波，但不能止步于此。LIGO的探测结果既是长时间探索的终点，又是一种新天文学的起点。我们对此充满希望，因为不出意外的话，将来LIGO还会探测到更多的引力波。而且，人们已经开始计划和修建新一代的引力波探测器，包括在美国之外的地区建立LIGO的新台址，比如印度就是比较好的选项。更多的台址可以让LIGO更好地在天空中定位引力波源，只有这样，引力波才能成为更好的非电磁波天文学工具。

除了LIGO之外，另一个引力波探测项目叫做eLIS(thAe Evolved Laser Interferometer Space Antenna，演化激光干涉空间天线)。eLISA项目是欧洲空间局规划的空间引力波探测器。它有不少地面望远镜没有的优势，其中最重要的是它不会被地震噪声影响。这意味着它在一定的频率范围可以达到地面上极难达到的灵敏度。它还可以建造得比地面探测器大很多，因为激光会在卫星之间的真空里传播，不需要建造任何管道。eLISA计划利用三颗卫星相互发射激光，从而组成一个三角形。三颗卫星两两之间的距离大约百万千米。要探测引力波，探测器需要越大越好——因此eLISA在将来很可能做出更加高质量的发现。

虽然eLISA的臂可以设计得非常长，且不会受到地震波影响，但它还需要面对其他的挑战。太空中的环境接近真空，但并不是完全的真空。太阳发射的带电粒子，以及持续不断朝地球方向轰炸的宇宙射线，都可能对这类空间探测器产生影响。地面上有地球大气和地球磁场的保护，但空间望远镜没有。另一方面，在太空中正确地排列和保持探测器的稳定是非常困难的。尽管存在上述挑战，eLISA还是非常有可能成功启动，并在太空中探测到引力波。

将来另一种探测引力波的方法是利用宇宙学观测。宇宙学是研究宇宙整体的现状和演化的学科，人们期待用新的宇宙学项目看到引力波在宇宙中留下的足迹。我们将在第5章讨论这些课题。

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以观测者作为中心的球体空间，其中物体发出的光在宇宙年龄的时间内足以到达观测者，也就是说只有可观测宇宙内的物体是看得到的，目前可观测宇宙可达920亿光年。

05 宇宙学

20世纪初，随着阿尔伯特·爱因斯坦和爱德温·哈勃的工作的进展，宇宙学开始成为科学的一个分支。爱因斯坦构建的理论使人们能够理性地思索整个宇宙；哈勃则发现了一些宇宙正在膨胀的最早观测证据。在20世纪之前这些都是不可想象的，宇宙学一直以来都属于宗教和哲学的范畴。20世纪之后宇宙学才作为科学开始繁荣发展起来，并且现在正朝着精确科学的方向迈进。

引力主导了大尺度下的相互作用，这使得引力成为宇宙学研究的基础。不幸的是，单靠牛顿的引力理论无法建立一个统一的宇宙模型。虽然牛顿的平方反比引力适用于宇宙中的万事万物，但它的传播是瞬时的。这一情况其实不算糟糕，因为这意味着我们在地球上能够体验到宇宙中所有物体带来的引力。真正的麻烦在于当人们试着把无穷多物体在宇宙中某一点的引力场叠加起来时，牛顿理论告诉我们总引力场大小与我们对单个物体的引力场求和的顺序有关。这显然不能令人满意。

当然，我们现在已经知道牛顿引力近似爱因斯坦引力理论，只是后者更完整。好在上面所述的问题并没有发生在爱因斯坦的理论中。相反，我们得到了许多自洽的模型可以用来描述我们所在的宇宙。爱因斯坦把人们的注意力集中到时间和空间，这使我们通过他的理论对宇宙有更深刻的理解，这是牛顿理论无法做到的。利用爱因斯坦的理论，我们不仅能给宇宙中万事万物的相对运动建立模型，还能够描述构成宇宙的时间与空间的行为。我们现在来好好看看这是如何做到的。

现代宇宙学史

我们所知的现代宇宙学是在20世纪20年代诞生于苏联物理学家亚历山大·弗里德曼(Alexander Friedman)的工作中。利用当时刚发表的广义相对论，弗里德曼展示了宇宙在空间上任意一点朝任何方向看起来都相同，而且它要么膨胀，要么收缩。可以肯定，这一非凡的预言在当时引起了轰动，因为那时的天文学家们无法从观测中得到这些结论。然而弗里德曼却得出了一组方程来描述宇宙，并意识到在这些宇宙模型中，空间要么是平直的，要么有正或者负的曲率。也就是说，他认识到爱因斯坦的方程中存在一些解，它们对应的空间是弯曲的，就像一个巨大的三维球面或者马鞍面(见图10)。

图10　弯曲空间的例子：恒定正曲率(k〉0)，没有曲率(k=0)，恒定负曲率(k〈0)

弗里德曼是宇宙学的先驱，但他的工作起先并没有被广泛认可。爱因斯坦从一开始就批评他是错的，然后提出了另一个宇宙模型，在这个模型中引入了一个他所谓的“宇宙学常数”到他的方程中，从而迫使宇宙处于静态。比利时的神父乔治·勒梅特(Georges LemaÎtre)在20世纪20年代末产生了和弗里德曼类似的想法，并指出爱因斯坦的模型是不稳定的。实际上，早在1927年，他(那时候已经成为亚瑟·爱丁顿爵士的同事)就发表了一篇论文指出观测证实宇宙确实在膨胀，这个结论便是后来广为人知的哈勃定律。这个意义深远的发现最早发表在一篇法语写成的文章里，并被投到一本不知名的比利时刊物上。比较神秘的是，1931年它被翻译成英语的时候，包含哈勃定律的那一章消失了。尽管如此，勒梅特在今天仍然被人们认为是现代宇宙学发展史上最重要的人物之一。

弗里德曼和勒梅特都是数学家，尽管后者了解很多天文学知识，但直到1929年爱德温·哈勃发表他的重要结果时，宇宙学才真正开始成为观测的科学。哈勃通过计算一些天体(现在我们知道是星系)的距离，并利用它们运动的信息向世界展示了宇宙正在膨胀。哈勃发现一个星系的退行速度和它到我们的距离成正比(也就是说，如果星系A到我们的距离是星系B的两倍，那么它远离我们的速度也是B的两倍)。这正是勒梅特根据爱因斯坦的理论给出的预言，现在这个观测结果毫无疑问地证明了宇宙确实是在膨胀。于是，爱因斯坦放弃了他的静态宇宙观点，并把宇宙学常数描述成他一生中“最大的错误”。

宇宙膨胀可能听起来和我们一般了解的引力效应大相径庭，但其实是一样的：宇宙大尺度的膨胀和引力有着密切联系。实际上人们可以把弗里德曼、勒梅特和哈勃发现的宇宙膨胀理解为相邻的星系在它们之间的引力制约下相互远离。我们可以考虑一个相同但是更加容易理解的例子：把一个网球扔上天。一般来说这个网球会上升到一个最大高度，然后落下来。在网球上升的过程中，它同样受到引力作用。利用引力方程我们可以计算它如何运动，比如在未来的某任意时刻它的速度，等等。两个邻近星系的情况和这非常相似。星系也许在相互远离，但它们移动的速度，以及它们是否会重新落到一起，都取决于它们之间的引力。我们无非是在利用爱因斯坦的理论描绘一个所有物体都在相互远离的宇宙图景。

网球类比中有一个很明显的问题：如果星系像网球从地面扔上去一样相互远离，那么这些星系会不会最终停止远离，并开始朝着彼此回落呢？换句话说，宇宙会不会最终停止膨胀并开始坍缩？这是一个绝妙的问题，它的答案同样可以从网球的情况中得出。如果我们不是把网球扔上去，而是放进一个超高能大炮里，高速发射出去，那么有可能它就永远不会落下来了。科学家们把产生这种情况的速度叫做逃逸速度(escape velocity)，人们很容易就能计算出它的值。当网球的发射速度大于逃逸速度时，它就永远不会落回地球上；反之，它最终还是会落下来。星系的情况和这个非常相似。如果它们相互远离的速度足够快，它们就将永远渐行渐远，宇宙就会永远地膨胀；如果相互远离的速度太慢，它们会渐渐停止远离，开始越来越靠近，并最终撞在一起。星系之间相互退行的速度被称为哈勃速度
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(Hubble rate)，星系永远远离彼此需要的最小速度被称为临界(critical)速度。理论并没有告诉我们宇宙膨胀的速度比临界速度快还是慢。为了解决这个问题，我们需要用望远镜观测太空。

在观测宇宙膨胀效应的时候，我们也拥有了另一种考察引力作用结果的方式。实际上，我们现在可以提出和回答一些引力相关的问题，这些问题很难在太阳系内的实验中找到答案。比如说，引力作用的强度一直以来都是一致的吗？光自身会不会也有引力场，就像爱因斯坦的理论预言的那样？物体密度非常大的时候引力是什么情况？通过研究宇宙我们就能回答这些问题，因为这样的研究涉及非常大的尺度、因为宇宙正在膨胀、因为光的传播速度是有限的。现在让我们来讨论这些问题。

日常生活中，大部分情况下我们认为自己会在某件事发生的同时看到它。然而这并不是真的，因为光速有一个上限(大约30万千米每秒)，所以光从某个东西上面发射或反射到我们的眼睛需要一定的时间。光速非常快，所以我们日常生活中并不会在意这一延迟。但如果一个天体距离非常遥远，延迟就会变得非常明显。比如太阳突然爆炸了，我们需要经过8分多钟才能知道，因为这是光从太阳发射并传播到我们眼里需要的时间(而且没有任何东西比光跑得更快)。还可以这样设想，我们现在看到的太阳实际上是8分多钟以前的太阳。宇宙学里这种情况经常出现，而且由于可观测宇宙比太阳和地球之间的距离大得多，这种效应就会变得更为明显。比如说，光从最近的恒星传到我们眼里需要四年多，从最近的星系传播过来则需要几万年。如果我们去观测极其遥远的天体，那我们实际上看到的是几十亿年前的它们。某种意义上说，我们看向远方时，实际上是在回溯过去，如果我们可以看得足够远，我们就能看到宇宙年轻的时候长什么样子。

在热力学中，有一个广为人知的实验，就是当你压缩一个物体(比如充满空气的气球)，它就会变热；如果你让一个物体膨胀，它就会变冷。宇宙也不例外。如果我们把宇宙膨胀看成是一台放映机放出来的电影，那么我们把电影胶卷反向播放，就会看到宇宙变得越来越小、越来越热，直到很久很久以前，宇宙就像一团火在燃烧。上一段说我们实际上可以看到宇宙演化的早期，那么你可以期待如果我们看得足够远(也就是沿着时间回溯得足够早)我们就会看到一个火球。拉尔夫·阿尔法(Ralph Alpher)和罗伯特·赫尔曼(Robert Herman)在20世纪40年代晚期提出了这个预言，但直到1965年它才偶然被射电天文学家阿诺·彭齐亚斯(Arno Penzias)和罗伯特·威尔逊(Robert Wilson)发现。他们探测到的信号现在被叫做宇宙微波背景辐射(Cosmic Microwave Background)，简称CMB。

CMB的发现向世界宣告：人们可以通过天文学来观测宇宙演化中和现在迥然相异的早期阶段。同时它给验证引力理论开启了新的大门，这个大门通向新的宇宙环境，在这样的环境中，光的引力场甚至比普通物质的更强，而且在这里我们的计算可以跨越整个可观测宇宙的时间和距离。

早期宇宙

从20世纪60年代到现在，早期宇宙学一直蓬勃发展，渐渐成为观测和理论物理中十分成熟的领域。人们测量了成千上万星系的位置，看到了十几亿年前发生的天体物理事件，以及精确地测量了彭齐亚斯和威尔逊发现的CMB。我们利用这些天文观测来明确回答以下问题：宇宙年龄有多大？宇宙会不会永远膨胀下去？宇宙中的物质都是以什么样的形式存在的？有些问题令人疑惑，但对于理解引力意义重大。我们将在这一节中讨论它们。

让我们从时间的起点开始说起。如果宇宙越早的时候越小越热，那么宇宙中物质的密度也会越早越致密。我们现在知道，当我们回溯时间时，不是所有物质的密度都是以相同的速率增大的。光[也就是物理学家们经常说的辐射(radiation)]的密度比其他大部分形态的物质密度增长得快。这意味着早期宇宙的光子的密度甚至比组成常见物质的电子、中子和质子更高。这种情况下辐射的引力场主导了宇宙的膨胀。

辐射主导宇宙演化的时间相对比较短，它只持续到大爆炸之后最初的几万年。这个时期非常有趣，尤其对于研究引力来说。辐射主导时期发生的其中一类物理过程就是轻元素(氢、氦、锂等)的合成。影响这一过程的因素非常多，其中最重要的是宇宙膨胀率。理论学家们对此做了严密的计算，观测家们测量了我们周围宇宙的氢和氦元素的含量，精确地推断出宇宙早期辐射产生的引力场到底有多强。这类研究和爱因斯坦理论的预测一致，误差仅仅在百分之几的水平。这比太阳系内或者脉冲双星观测的精确度要低，但考虑到它测试的是几十亿年前的情况，这听起来就不那么糟糕了。

除了轻元素合成之外，宇宙早期历史中还发生了其他有趣的物理过程。其中一个过程后来让宇宙形成了历史上最早的结构。自彭齐亚斯和威尔逊发现CMB时起，人们普遍认为早期宇宙看起来近乎光滑。近乎，意思就是并不完全光滑。天文学家们发现CMB存在非常微小的起伏，他们认为这些起伏就是我们今天看到的复杂的星系和星系团网络的种子。引力致使这些起伏坍缩成星系，不过在这之前，引力就已经扮演了非常重要的角色。

在宇宙的早期，引力和辐射之间有一场“战争”。引力使物体聚集在一起，辐射则与物质发生作用并让它们倾向于弥散开来。因此，在引力和辐射不停相互作用的物质“汤”中，任何非常小的扰动都会引起震荡，它们被引力拉在一起，又被辐射推开。这一震荡的周期取决于空间尺度的大小，且十分容易计算。物质密度的这一震荡持续了很长时间，直到宇宙冷却到一定程度，变得透明(在很早的时候宇宙是不透明的，前文说过，就像火球一样)。这时候，辐射就可以穿过物质传播，一路几乎畅通无阻，并最终在几十亿年后到达远处的观测者——也就是我们。彭齐亚斯和威尔逊发现的CMB就是由130亿年前的这个大火球最后发出的辐射组成的。引力和辐射的对抗在CMB上留下了印记，也就是那些很小的起伏。这些起伏包含了关于宇宙膨胀速率、宇宙的辐射总量、辐射和其他物质相互作用的方式的大量信息。它同时也告诉我们CMB辐射穿过空间到达地球之前的情况。简单来说，CMB就是科学家们手里的百宝箱。

对CMB更加细致的观测始于1989年，NASA发射了宇宙背景探测者卫星(Cosmic Background Explorer，缩写为COBE)。这一卫星实验观测了整个天空的背景辐射，并发现背景辐射的性质和理论预测的原初大火球发射的辐射相同。COBE实验同时也成为最早尝试观测上述“波纹”的实验。虽然最后证明COBE的分辨率并不足以从波纹中提取信息，但它使人们看到了希望。从那时开始，人们又做了一系列热气球实验。其中包括20世纪90年代晚期升空的BOOMERanG和MAXIMA实验。这些实验的探测器有足够的分辨率测到那些尺度最大的波纹，这些波纹提供的信息足以证明宇宙膨胀的速率差不多恰好处于永恒膨胀和重新坍缩的临界点上。然而如果把它和我们观测到的现有的宇宙膨胀率做比较，你会发现一些奇怪的事情：从原初大火球到现在，宇宙似乎经历过相当程度的加速膨胀。

21世纪初期，宇宙微波背景辐射的实验有了新的飞跃。2001年，NASA向太空发射了威尔金森微波各向异性探测器(Wilkinson Microwave Anisotropy Probe，缩写为WMAP)。WMAP实验不仅仅可以测到最大尺度，同时也能分辨更细微的波纹。这一点相当重要，因为人们可以借此观测并研究这些小波纹的演化。在之后的2009年，欧洲空间局发射了普朗克卫星(Planck Surveyor)。普朗克卫星比WMAP又更进一步地观测到了更多微小的波纹。WMAP和普朗克卫星的结果证实了那些描述早期宇宙波纹演化的物理理论。它们发现，由引力导致的坍缩方式和爱因斯坦理论预言的一致，早期宇宙中辐射的总量和原初核合成计算中要求的总量相同。但它们同时也发现，宇宙中存在大量并不和辐射发生除了引力之外的任何相互作用的物质，

这和普通物质大相径庭。

宇宙微波背景辐射包含的信息量远超我刚刚描述的几种。其中一些我之后会讲，因为那些信息更像是对将来研究的展望而不是描述已有的发现。但我们仍然有必要提及，当背景辐射从原初大火球出发穿过宇宙传播到我们这里来，途中它携带上很多物体的引力场信息。其中之一就是第2章讨论过的引力导致光线弯曲。当背景辐射经过大质量天体时也会受到这个效应的影响，它的轨迹会被这些天体的引力场折弯。这使得背景辐射上的波纹产生扭曲，这些扭曲是可以计算的。普朗克卫星观测到了引力场导致的背景辐射上波纹形状的改变。另一种关于背景辐射的可观测效应源自宇宙膨胀导致空间中引力场的演化。引力场的演化使得光子进出引力场时的场强不一样，这改变了光子的能量，使得光从引力场出来时得到更多(或者更少)的能量
[2]

。通过对比这一现象的观测数据和理论，我们再次得出结论：宇宙的膨胀正在加速。

宇宙膨胀的历史

宇宙冷却到变得透明后的一段时间，被天文学家们称为黑暗时代(Dark ages)。黑暗时代指的是原初大火球之后，最古老的恒星和星系形成之前的一段时间。关于宇宙的这段历史，天文学家们所知甚少，因为那时候的物质大部分都是以气体云的形式存在。几亿年后，初代恒星和星系才开始形成。从黑暗时代开始，随着宇宙的演化，大尺度结构不断增长，且规模越来越大。当然是引力导致了这一切，所以我们可以通过研究周围的天文结构来获得关于引力的信息。现在，我们先来看看人们是如何利用宇宙中的天体来研究宇宙膨胀的历史。

哈勃于1929年发表的那篇论文使他成为这一领域的开者。和其他伟大的科学发现一样，一代又一代的后来者在他工作的基础上加以扩充。所有这些工作的目的就是为了解决两个问题：天体离我们多远？它们远离我们的速度有多快？这些信息可以用来确定宇宙膨胀的速率。实际上，第二个问题更直接一些。恒星，以及其他大多数天体只发出特定频率的光，此频率和它们的化学组成相关。现在，如果一个物体发生运动，就像大多数天体那样，那么我们接收到它们发出的光的频率就会由于多普勒效应发生频移。这种现象和救护车靠近或远离你时你听到的警报声变化是一样的：当救护车朝你驶来时警报的频率比远离你时要高一些。在靠近或远离这两种情况下，频率的变化和物体的运动速度直接相关。这意味着如果我们知道一个天体的化学组成(大部分情况下我们是知道的)，那么计算物体远离我们的速度就相对来说比较容易。

然而，精确地测量天体的距离是更加有挑战性的任务。比较常用的方法是去观测一些离我们比较近的天体。如果可以确定这些邻近天体的距离(一般来说也比较容易)，那么我们就能利用它们去校准更远处的同类天体。这一方法的其中一个例子就是哈勃在他的论文中使用的造父变星(Cepheids)。造父变星是一类亮度呈周期性变化的天体。人们很早就知道造父变星的光变周期和它们的光度(也就是它的实际亮度。这和视亮度不同，视亮度还取决于它到我们的距离)相关。这个结论是基于对已知距离的邻近恒星的研究得出的。哈勃利用这一信息去测量更远的造父变星的距离。其中的逻辑非常直接：你可以持续观测造父变星并测量它的周期，然后利用周期信息去计算它辐射的光度，最后把光度和你的相机胶卷上实际拍到的造父变星的亮度作对比。有一个简单的定律告诉你一个已知光度的天体在给定距离下有多亮，你就可以利用这个定律，用测得的亮度和算出的造父变星的光度来计算它的距离。

不幸的是，这个方法里面有很多步骤都可能出错。用来确定天体距离的一些定律(比如造父变星光变周期和光度的关系)可能仅仅是近似正确。你还需要假设这些定律同时适用于遥远的天体和近处的天体。这不一定总是正确，因为当一个天体很远的时候人们很难弄清楚它到底是什么天体，另一种可能性是那些定律在随着时间变化(注意，你看远处时，看到的是远处物体很久以前的样子)。人们需要仔细考虑这些问题，因为它们有时候会导致错误的推断。比如说，哈勃在1929年的论文中推测的宇宙膨胀速度是现在测量结果的10倍左右。这一错误是由于哈勃利用造父变星估算出的星系距离有误。

测量天体距离领域现在有了很大的进步，人们利用超新星观测来测距，这个方法本质上和哈勃的方法还是一致的。我们在第3章讨论过，超新星是爆炸的恒星，单个超新星的亮度可以和整个星系的亮度相同。所以人们可以相对容易地看到它。现在人们知道超新星爆发有好几种方式，天文学家们已经给它们都起好了名字。对于研究宇宙膨胀最有用的一类超新星叫做I a型(Type Ia)超新星。这类超新星爆发的源头是吸积伴星物质的白矮星。当白矮星上聚集了足够的质量，它就不可能继续抵抗自身引力的压力，于是产生坍缩和爆炸。Ia型超新星的好处在于，无论它发生在哪里，发生在什么时候，其发生的方式都是非常相似的。这意味着如果人们能够确定一个天体是Ia型超新星，就能利用它们的亮度来很好地估计其距离。

第一批利用Ia型超新星研究宇宙膨胀历史的结果在20世纪90年代末才开始出现。超新星宇宙学项目(Supernova Cosmology Project)和高红移超新星搜寻小组(High-Z Supernova Search Team)两个研究组都参与了这项工作，他们大约在同一时间发表了各自的结果。利用对超远距离的超新星(也就是几十亿年前爆发的超新星)的观测，他们有了一些令人惊讶的发现。他们确认了宇宙膨胀的速度并没有减慢，而是在加速。这一结果完全出乎意料，因为理论上在引力作用下相互远离的物体只会减速远离，整个物理学界都被震惊了。当然对于理解引力来说，这其实是非常迷人的结果。我们将在第6章仔细研究这些结果，现在让我们回到宇宙大尺度结构。

晚期宇宙

和恒星会聚集在一起形成星系一样，星系也会聚集在一起形成一种叫星系团(clusters)或超星系团(super-clusters)的结构。这就是宇宙学家们所说的大尺度结构(large-scale structure)。大尺度结构研究也始于哈勃。正是哈勃第一次意识到天文学家们用望远镜看到的螺旋状的天体实际上是遥远的星系。在那之前，人们一直在问银河系是不是宇宙中唯一的星系，就像大海中的孤岛那样。利用上文提到的造父变星，哈勃发现那些螺旋状天体比我们看到的周围的恒星更加遥远。对此唯一的解释是，它们是由很多很多恒星组成的更大的天体。从那时起，人们开始描绘一张天图，它能表现我们周围的大尺度结构在空间上是如何分布的。

和观测宇宙学的很多分支一样，这一新领域一开始发展得非常缓慢，直到20世纪末期才开始加快步伐。其中一个标志性的观测项目是1977年到1995年的哈佛-史密松CfA巡天计划(HavardSmithsonian CfA survey)。CfA巡天计划测量了大约20 000个星系的退行速度并记录了它们在天空中的位置。利用哈勃定律，人们把退行速度转化成了距离，于是描绘了宇宙中大尺度结构的“天图”。他们发现星系们成团地聚集在一起形成了跨越相当大范围的结构，其中最引人注目的是所谓的Cf A2长(CfA2 Great Wall)。这一结构是大量星系聚集的产物，它大到光从其中一端传播到另一端需要五亿年以上的时间。

最近的星系巡天发现了更大量的星系。2dF巡天利用南威尔士的盎格鲁-澳大利亚望远镜从1997年到2002年的观测了超过200 000个星系。2000年开始，计划到2020年结束的斯隆数字巡天(Sloane Digital Sky Survey，缩写为SDSS)到目前为止已经测量了几百万的星系。实际上现在人们已经有了浩如烟海的星系(以及其他类型的天体)图像，天文学家们不可能一个个去研究它们。计算机程序可以快速检阅星系，但和人眼(和大脑)比起来，它们对辨别星系的重要特征没那么拿手。一个聪明的办法是把这些图像都放到网上，并让公众参与进来辨认它们的身份——这一项目被称作“星系动物园(Galaxy Zoo)”。

2dF和SDSS发现了更多大尺度结构，甚至比CfA巡天发现的更大。其中最大尺度的结构被称为斯隆长城(Sloane Great Wall)，它大约是CfA2长城的两倍大。实际上斯隆长城的尺度大到如果把类似尺度的东西首尾相接排起来，整个可观测宇宙只能装下几十个这样的结构。它们实在是巨大无比，但你最好记住这仅仅是利用超新星和CMB研究的距离尺度的一小部分。还有更多的星系没有被发现，人们还在观测是否存在更大的结构(人们期望它们并不存在，不过期望的事情未必是真的)。

这些发现都非常令人印象深刻，现在让我们来看看它们对研究引力来说意味着什么。这些观测所发现的结构都是由引力造成的。CMB观测表明宇宙很早的时候看起来十分光滑。为了把光滑的宇宙变成像现在看到的那样充满各种网状结构，宇宙中的物质必须聚集在一起。物质聚集的形式在大尺度研究得很清楚，但小尺度上就会变得复杂起来。对于那些对引力感兴趣的人来说，这两个尺度上都包含了丰富的信息，所以我们要把它们分开考虑。

在大尺度下结构的生长比较容易预测。这主要是因为宇宙中大尺度成团的物体的运动速度和宇宙膨胀相比很慢。同时大尺度结构的生长对宇宙膨胀的准确速率非常敏感。宇宙膨胀开始由普通物质主导时，结构就会开始生长。这一生长先发生于小尺度，然后再到大尺度。现在，因为能从CMB里了解到生成宇宙结构的种子是什么样的，我们也能计算在大尺度下的宇宙结构是什么样子，然后和天文学家们实际上看到的做对比。其结果非常有意思。

首先，大尺度下结构的观测有力地表明了宇宙中有某种物质并不和光发生作用。其中的原因是，如果不存在这样的物质，那么在某些尺度下宇宙应该只有更少的结构。也就是说，如果所有的物质都和光发生作用，那么早期宇宙的大量辐射就会抑制宇宙大尺度结构的种子的生长，我们能够计算这一抑制。然而我们看到的辐射并没有抑制大尺度结构的种子的生长。符合逻辑的结论就是：宇宙中存在一些物质不和辐射发生作用，这些物质的引力激发了它们周围大尺度结构的生长。另外，存在于不同距离尺度下的结构可以提供珍贵的信息，我们可以利用它们研究极大距离下引力是如何作用的。

其次，宇宙的大尺度结构也可以被当成尺子，用来测量宇宙的大小以及它膨胀了多少。这是因为原初的波纹有一个特征长度。通过比较这些宇宙微波背景辐射中波纹的尺度和我们周围大尺度结构的尺度，我们就可以比较直接地弄清楚宇宙膨胀了多少(因为前者是后者的源头)。这导致了另一个惊人的结果。假设宇宙膨胀是由物质的引力场主导的话，宇宙好像膨胀得太多了。换句话说，晚期宇宙的尺子好像太长了。

现在让我们来考虑比上述的星系长城尺度小得多的情况。小尺度下的天体(如恒星和星系)的运动速度不见得比宇宙膨胀的速度慢。这些天体的运动和相互作用非常复杂，分析起来也困难得多。现在，研究这种情况的最好办法是利用电脑做超大型多体模拟。这些天体存在的空间，如爱因斯坦描述的那样在膨胀，但它们之间的相互作用还是可以很好地用牛顿引力来描述。这是牛顿理论的一个重要延伸，而且一般被认为是比较可靠的方法。让我们来看看这个尺度下人们如何研究引力。

首先我们可以记录星系的运动，以及它们形成的大尺度结构的形状。这是一项比较棘手的工作，因为人们很难把有关天体在宇宙中发生的所有物理过程的效应都包括进来。比如说，一颗超新星可能阻断结构的生长，而气体云却能增强它。然而人们还是可以给这些现象建立模型。21世纪以来，这项工作取得了大量成果。和以前的结果一样，人们越来越确定宇宙中存在一些无法直接观测的物质，它们的引力场造成了观测结果中星系和星系团的运动。

第二种方法是观察星系和星系团导致的光线偏折。你应该还记得太阳能够偏折靠近它的星光，爱丁顿当年正是利用它让世界相信爱因斯坦的理论是对的。这也适用于星系。我们可以看到来自遥远的星系的光是如何被近处的星系折弯的，这一过程被称为引力透镜(gravitational lensing)。这一效应一般来说比较微弱，想看到它们是一项巨大的挑战。然而，如果我们恰好看到了那些被引力场折弯的星系，或者收集了足够的数据，那我们就可以利用它们来确定存在于空间中的引力场的分布。人们再一次发现空间中的引力场比我们期望的要多——如果空间中只存在我们可以直接看到的天体的话。宇宙中似乎存在很多的质量，它们的引力场折弯了光线，但并不和光发生其他相互作用。折弯的具体程度可能同时也暗示了星系及星系团尺度下引力作用的性质。

对于更小尺度，我们可以观察单个星系的情况。早在20世纪70年代，人们就发现星系旋转的速度太快了。我的意思是，如果星系内引力的来源仅仅是可见物质(大部分是恒星和气体)，那么我们就可以观察到周围星系旋转的速度快到把自己给撕裂。类比来说，就像你用两只手搓着一根蒲公英的茎让它转动，如果你搓得足够快，蒲公英的种子就会飞散开来，因为花托的拉力无法再和旋转产生的离心力抗衡。星系中的恒星和它情况相同。恒星并没有由于高速旋转而飞散开来，这表明星系中的引力场比我们一开始设想的要强。再一次，合乎逻辑的结论是星系中存在一些我们无法看到的物质，它们贡献了部分引力场。

协和模型

通过观测周围的宇宙中各种各样的物理过程，我们得到了令人惊讶的结论。我们从观测结果中计算出的引力场比望远镜里看到的物质的引力场要强。除此之外，如果宇宙中最大尺度的结构要演化成它们今天这个样子，以及它们的种子来源于CMB，那么那些新的物质就不允许和光发生相互作用(或者说，至多只能有非常弱的相互作用)。这意味着我们不仅不能直接看到它们，而且也不能通过其他物体的光观测它们，因为光能直接穿过它们。

这真是一件非常奇怪的事情。这种能产生引力场但不可见的物质，被称为暗物质(dark matter)。为了解释观测结果，要预估的暗物质的量并不少——几乎是正常物质的五倍多。当大部分人第一次听到这个消息的时候，都会感觉什么地方肯定出现了非常严重的错误。大自然不可能这么奇怪。但是，关于暗物质的证据源自相当多不同的实验，人们实在是很难否认它的存在。如果仅有一个实验证据，那么你大可以努力去证明收集数据的人，或者做观测的人可能犯了错误。但要去证明上述那么多种不同类型的实验都有错则不太可能。很难想象人们犯了那么多错误，而这些错误都指向了同样的结果。所以我们只能得出结论：宇宙中大部分物质并不是我们熟悉的物质，而是一些新的、我们以前不知道的物质。

而且，还存在另外的惊人的事实。我们不仅需要额外的物质来提供足够的引力场，以解释大尺度结构的形成以及光线偏折的观测结果，还需要解释为什么宇宙膨胀的速度比我们想象中的快。回忆一下我们可以把宇宙膨胀理解为宇宙中的物体(例如星系)在引力的作用下远离对方。如果这是真的，如果引力总是相互的，那么我们会期望宇宙大尺度结构的膨胀应该总是在减速。也就是说，宇宙膨胀应该变得越来越慢。但是，上述很多天文观测都表明宇宙正在加速膨胀。我们的结论是，宇宙中应该存在一种排斥(repulsive)的力场——换句话说，我们看到的宇宙中似乎存在一种反引力(antigravity)在影响宇宙膨胀。人们需要这种反引力来迫使物体相互远离，而不是把它们拉到一起，这样的话宇宙膨胀才可能加速。这简直骇人听闻。这种排斥力的源头被科学家们称为暗能量(dark energy，不要和暗物质混淆了)。为了解释我们测到的宇宙膨胀的加速度，宇宙中需要存在三倍于暗物质的暗能量。

因此，我们现在对于宇宙整体的图像如下：宇宙中大约只有5%的能量以普通物质的形式存在；剩下大约25%被认为是由暗物质组成，它们之间由引力相互吸引；另外70%则是产生排斥力的暗能量。这些成分的百分比可能稍微有些波动，但它们足以解释迄今为止的所有天文观测。所有三种能量形式加起来差不多恰好使宇宙平坦(而不是有正或者负的曲率，就像球面或者马鞍面，见图10)所需要的量。平坦宇宙模型中大部分物质和能量由暗能量和暗物质组成，它也经常被称为宇宙的协和模型(Concordance Model)。天文学家们已经达成共识：协和模型是和他们的数据符合得最好的宇宙模型。

推导出协和模型的观测数据以及协和模型本身无疑是21世纪物理学的重大突破。但是，无论是宇宙的历史、内容还是其中引力场，我们对它们的了解肯定不够全面。直截了当地说，统一模型有不少弊端。第一，它暗示着宇宙的形状一开始是非常特殊的。宇宙的空间十分平直，背景辐射和星系分布非常均匀，这说明宇宙早期的密度需要极度完美地趋于均匀。第二，我们看到的CMB上的一些波纹的尺度大于光从大爆炸到大火球那段时间内能走过的距离。在爱因斯坦的理论中，没有任何东西能比光还要快，所以这真的非常奇怪。第三，我们完全不清楚暗物质到底是什么。我们只知道它能产生引力，以及它不会和光相互作用。它不可能在粒子物理标准模型(它已经包括了所有其他已知种类的粒子)中存在，也没有在任何粒子物理实验中被发现。第四，暗能量的存在，以及它产生的排斥力场，似乎需要大量的微调以使其符合我们今天看到的现象。稍微多一点，星系就不可能形成；稍微少一点，它就不会引起我们的注意。

上述四个问题是物理学家们主要关注的对象。前两个的解决方案是：宇宙早期有一段非常剧烈的膨胀时期，也就是宇宙暴涨(cosmic inflation)。我将在第6章描述宇宙暴涨。第三个问题的解决方案有望通过往标准模型中添加新的粒子来解决，现在已经有了不少可能的解决方案。在笔者写作本书的时候，物理学家们提出暗物质粒子的性质可以利用大型强子对撞机(Large Hadron Collider，缩写LHC)作直接的研究。人们还不知道大自然是不是足够仁慈，让这些粒子的能量恰好落在LHC可以探测的范围内。这些问题中最后一个是最神秘的。一些物理学家在解释暗能量这件事上作出了非凡的努力。我将在第6章更加详细地解释它们。

当然，现在还有一些物理学家在质疑暗物质和暗能量到底是不是真的存在。他们认为在确定它们是什么之前，应该先搞清楚引力在宇宙的尺度下是怎么作用的。毕竟我们只能通过它们之间引力的相互作用来了解它们。如果我们误解了引力，就可能错误地理解暗物质和暗能量。未来的天文观测将会用来探索这些可能性，以及进一步研究暗物质和暗能量的性质。

宇宙学的未来

预测科学的未来通常是荒唐的，但我们还是可以比较有把握地认为21世纪的宇宙学将会有极大的进展。我们已经知道了很多关于宇宙如何膨胀，以及宇宙中的结构如何形成的知识，但和将来几十年的观测比起来还是相形见绌。这些工作重要的动力是暗物质和暗能量。搜寻这些黑暗的东西将会让人们进一步理解引力。

让我们从CMB说起。到现在为止，CMB的大部分观测都集中于测量天空中不同方向的CMB温度，然后尝试还原早期宇宙的波纹形式。这一领域最尖端的研究项目是普朗克卫星。这个任务已经获得了巨大成功，而将来的空间项目几乎不可能比它做得更好。不过，人们还可以在地面上建立更大的望远镜。人们正在智利的阿塔卡马沙漠和南极进行这些工作。这两个地区是我们星球上湿度最低的两个区域，稀薄而干燥的空气使它们成为观测太空的理想地点。这些望远镜将非常精确地测量CMB在天空中的分布，以及告诉我们更多关于宇宙的结构故事。

除了温度以外，人们还可以观察CMB中的其他东西。比如，天文学家们能够测量CMB的偏振(polarization，也就是电磁波的振动方向，见图11)。背景辐射的偏振昭示了更多早期宇宙发生的事情。通过寻找偏振中的一些特殊的模式，天文学家们就可以推测早期宇宙的引力场是什么样子。

这些信息中的一部分与CMB温度告诉我们的东西相同，而其他部分是全新的。特别是，如果可以观察到CMB偏振中一类特殊的螺旋状的模式，人们就能够推测早期宇宙中是不是有引力波在传播。回忆一下第4章的内容，为了探测穿过地球的引力波，人们已经付出了巨大的努力。CMB偏振相当于是在完全不同的条件下做的类似的实验。

图11　(a)偏振光和(b)非偏振光示意图。非偏振光的振动方向是随机的，而偏振光的振动方向是一致的。箭头表示的是光的传播方向

2014年3月，在南极的BICEP2实验的科学家们宣布他们利用这种方法探测到了早期宇宙的引力波。但到本书写作的时候人们又发现，似乎全世界为这个宣告而激动，有点太早了。科学家们确实看到了CMB中的那种螺旋状的模式，但看起来它像是来自近处的东西，而不是引力波。当然，这并不意味着早期宇宙不存在引力波。将来的实验会在更多的频段，更加准确地测量背景辐射中的偏振。如果早期宇宙真的存在一定强度的引力波，那么我们在未来10年左右就可能看到它们。BICEP2的继承者已经在修建了，第一批数据马上就要问世。

另一个尖端的项目是下一代星系巡天。我们早先讨论过2dF和SDSS巡天，它们很有野心地试图记录我们周围的宇宙中所有星系的位置。将来的巡天项目将会更加庞大。其中最大的三个是正在智利修建的大型综合巡天望远镜(Large Synoptic Survey Telescope，缩写为LSST)、2018年开工的平方千米阵(Square Kilometre Array，缩写为SKA)以及由欧洲空间局主持计划于2020年发射升空的欧几里得卫星望远镜。它们将会测量几十亿个天体，并为宇宙绘制迄今无法企及的巨大尺度的画卷。

LSST、SKA和欧几里得卫星将把宇宙学变成更精确的科学。当它们开始运作时，我们就会知道关于暗物质和暗能量的更多信息。具体方法包括探测它们对宇宙大尺度结构的影响，光从这些结构中传播过来的方式，还有它们演化的历史。实际上，它们提供的信息有望使人们比研究太阳系内和脉冲双星系统还要精确地研究引力，这在历史上还是第一次。这将开启一个新的窗口，让我们能够以新的方法在新的距离尺度下探索引力的本质。

[1]
一般被称为“哈勃常数”。

[2]
这一效应被称为积分萨克斯-沃尔夫效应(Integrted Sac-Whoslfe effect)。

06 引力物理前沿

这本书大部分内容都在讨论从毫米到整个可观测宇宙尺度下的前沿引力物理研究。在这一章中，我们将聊聊引力理论当中表述上的一些问题。

自1915年以来，我们对引力相互作用的理解一直参考着爱因斯坦的理论。这一理论把时间和空间统一成一个客体，并且让时空中的物质影响时空的性质。我的读者们应该已经相信这个事实，爱因斯坦的理论取得了非凡的成功!只用一个理论就能解释如此大量的物理现象，是多么伟大!然而，爱因斯坦的理论还不是我们理解引力的终点。1915年之后，引力物理学领域里发生了很多事情，其中有不少暗示着我们需要一个更加基础的理论。

量子力学和引力

在爱因斯坦发表他的引力理论之后不久，20世纪初的理论物理世界就被玻尔(Bohr)、海森堡(Heisenberg)、薛定谔(SchrÖdinger)等科学家再一次永远地改变了。从牛顿一直到那个改变之前，我们都认为物理理论属于决定论。也就是说，如果你知道某一时刻宇宙中所有物体的位置和速度，那么你就可以准确无误地预测将来。这样的物理学现在被称为经典理论(classical theories)。爱因斯坦的理论就是经典理论的一个例子。玻尔、海森堡和薛定谔他们领导的革命却创造了另一种理论——量子力学(quantum mechanics)。新的量子理论以概率为基础，其结论是：人们只能计算未来发生某种事件的概率，但无法准确地知道未来究竟会发生什么。

量子力学的成就是惊人的。它极其精确地描述了光的本质，以及所有已知物质的基本构成单元。再后来，剑桥大学的保罗·狄拉克(Paul Dirac)教授利用这些新想法建立了量子化的电磁学理论。他的理论又能导出粒子物理的标准模型(Standard Model)，也就是对所有已知粒子和粒子间相互作用的量子理论表述。现如今已经很少有人怀疑是否能用量子力学描述大自然。2012年被称为皇冠上的明珠的希格斯玻色子(Higgs boson，被理论预言的一种粒子，能赋予其他粒子质量，是标准模型中的重要内容)被发现了，这标志着标准模型的预言已经全部得到了验证。量子力学是现代化学和材料学的基础，它让我们造出计算机中的半导体、DVD放映机和电视机中的激光和发光二极管。量子力学是毋庸置疑的，它描述了大自然如何运作，尤其是当我们试图描述微观世界的时候。

虽然量子力学在各个物理学领域中无所不在，但如何利用它来研究引力还是个谜。电磁力可以相对直接地量子化，宇宙中的物质也都可以用量子力学来描述，可引力的量子理论仍旧难以捉摸。这可能是近50年来物理学上最大的未解之谜。把其他物理领域中百战百胜的逻辑应用到引力上却屡战屡败，所以当今引力的最优表述依然使用了爱因斯坦的经典理论。

这就有些尴尬了。比如有些问题人们需要同时用量子力学和引力来处理。举个例子——黑洞的中心。我们已经讨论过黑洞是巨型恒星经过毁灭性坍缩形成的——恒星里的物质被引力压缩到密度极大。根据爱因斯坦的理论，坍缩会一直持续到所有物质都被压缩成一个点。现在有了量子理论，在很小的尺度和很高的能量下，量子力学效应会非常显著。因此上述黑洞同时需要引力和量子力学来描述其中的物理状态。但普适的引力理论还不存在，所以到现在人们还是无法了解恒星坍缩之后的核心是什么样的。人们当然不满足于此。如果我们希望能够描述自然存在的一切，那么我们就需要一个适用于引力的量子理论。

量子理论和引力不相容的原因有很多，而且比较复杂。第一，爱因斯坦的引力理论和量子力学，在处理力的方法上有概念性差别。在爱因斯坦的理论中，引力是时空弯曲的结果，并不存在什么外力把物体拉到一起，有质量物体相互靠近仅仅是时空弯曲导致的。例如地球并不是被太阳拉着，它实际上是沿弯曲时空中的最短路径在自由下落。但其他的力并非如此。比如电场力就是带电粒子的电场产生的，电场存在于时间和空间中，但却不是时间和空间本身。时间和空间仅仅是电场力“表演”的“舞台”。量子力学中，处理大部分问题时都把时间和空间仅当成独立于其他物体的存在——一个被动的角色。这样处理引力就违反了爱因斯坦所规定的一切。

引力和量子力学不兼容也有数学上的一些原因，其中最严重的是引力的不可重整性(nonrenormalizability)。当用量子力学描述力的时候，我们的计算结果通常会包括一些无穷项。举例来说，当利用量子力学来计算两个带电粒子之间的作用力时，我们需要把两个粒子在所有可能位置的力的分量都加起来。有些情况下粒子间距非常非常小，于是它们之间的力就相当相当大。把所有可能的位置的力都叠加起来会产生一个无穷大的结果。电场力的这种不合理结果可以用一种数学手段解决，那就叫做重整化(renormalization)。这一手段消去了方程中导致无穷大的部分。也就是在一开始无穷项就从方程中被扣除了。于是人们就得到了一个合理的，可以由实验验证的结果。但爱因斯坦的引力理论中，重整化却不起作用。因为原始方程中找不到一个能被扣除的无穷项，没东西可以消除。于是量子引力的计算结果还是无穷大的。显然方程中有些东西是错的。

为了解决这些问题，人们付出了很多努力。他们尝试过修改爱因斯坦的方程(让它们看起来更加可重整化)；改变量子力学(让它们不再以粒子为基础)；改变我们对时空本性的理解(让它们变得不那么连续)。在这本书里大致介绍了这些方法，或详细地说明其中任何一种都是不可能的。它们都是非常复杂的理论，而且都还在不断完善中。但我觉得我有必要提及一些理论——弦论(String Theory)和圈量子引力论(Loop Quantum Gravity)。它们都是无比大胆且雄心勃勃的尝试，都想建立引力的量子理论。如果它们是正确的，那么我们希望物理学家们可以利用这些理论来描述黑洞的核心正发生着什么。但是两个理论之间差异巨大。它们关注引力量子理论问题的不同方面，两者表述技术和概念难点上也使用了完全不同的方法。

弦论是从粒子物理中孕育的。它的基本思想是，物质的基本单元并不是一个个点状粒子，而是一根根很小的一维弦。这是一个十分激进的想法，人们从中得到了很多有趣的数学工具和物理结论。实际上，很多物理学家都把它当成找到量子引力理论的希望。假设中弦的尺度非常小，所以大部分情况下，我们眼中弦们和点状粒子没什么两样。但当我们试图量子化它们的时候，弦的本质导致了不一样的结果。弦遵守的方程在某些方面和爱因斯坦理论中引力遵守的方程是非常相似的，因此引力似乎可以包含于弦论中。但弦论也有一些弊端。为了满足它方程之间的一致性，我们在描述宇宙时要给空间增加6个到22个额外的维度。

弦论物理学家们认为这些额外的维度通常紧紧地卷曲在一起，所以我们不可能在日常生活中看见它们。但为了让理论自洽(自圆其说)它们必须存在。有趣的是，这些微小的额外维度的存在使引力可能在小尺度下表现得完全不同于大尺度下。

圈量子引力论常被认为是弦论的主要竞争对手。它源自这样的想法：时空在非常小的尺度下是颗粒状结构的。也就是说，时间和空间并不是我们以为那种光滑连续变量。相反地，时空是粗粒化的。那量子理论就可以应用在组成这种新结构的圈上。这同样是非常激进的想法，它被很多广义相对论的狂热粉丝所青睐，因为它强调时空是我们应该关注的对象——而不是一个舞台背景。但圈量子引力论还尚待完善。目前人们还不知道这种理论或者弦论，或者其他没有提到的理论中哪一个是对自然的正确描述。在我们为这辩论的结果下赌注之前，还有相当多的研究要做。

引力场中的粒子

研究引力量子的路上荆棘密布。不如来看看另一个问题：量子力学在引力场中是怎样运用的？在这里我们将用和爱因斯坦相同的经典引力方法来处理时空。但把经典时空中的物质带到量子理论的规定下，我们要考虑的是会发生些什么。像上述利用量子力学处理物质，但用经典物理处理时空是一种混合的手法。这种方法一般被称为半经典(semiclassical)物理。这种方法不如完整的量子引力论那样野心勃勃，但还是让我们对量子体系在有引力情况下的表现有了更多有趣的理解。

这一领域的先驱者之一是史蒂芬·霍金(Stephen Hawking)，他在1974年证明量子力学会导致黑洞辐射这一结论。这一发现震惊了科学界，因为根据爱因斯坦的理论，没有任何东西能够逃离黑洞。霍金的计算就是半经典的，他利用经典的手法描述黑洞周围的时空，并利用量子力学去描述其中存在的粒子。他通过较为简单的量子力学计算证明：如果黑洞周围在遥远的过去不存在辐射，那么在未来它一定会有辐射。对此唯一的解释是辐射是由黑洞发出的。当然，辐射携带着能量，在这种情况下唯一的能量来源就是黑洞内部的质量(还记得吗，爱因斯坦的理论中，质量就是能量的一种形式)。所以霍金证明黑洞实际上在不断地辐射掉它的质量，不断缩小，最终消失。

霍金的发现是新奇的，它引发了引力物理中好几个新的研究领域的出现。在霍金之后没多久，比尔·昂鲁(Bill Unruh)证明当我们在相对论的框架下考虑粒子的时候，它们的存在可以被质疑。粒子物理学基本上包含在量子力学的领域中，昂鲁证明如果观察者有相对运动——相对加速移动，那么完全可能其中一人探测到粒子，而另一人什么都看不到。那就是说，粒子的存在与否决定于观察者们的运动状态。

为了更清楚地理解这一结果的怪异之处，让我们来看一个例子。假设你是一个宇航员，在外太空的某处自由漂浮。你看到周围什么都没有。但如果你抓住一架路过的宇宙飞船并开始加速，那么你以为空无一物的空间瞬间就变成了粒子的海洋。我这里当然有些夸张，需要非常大的加速度你才能看到大量粒子。但是其中的原理是可靠的。你加速的时候会看到原本看不到的粒子。然后我们引入引力，现在事情就变得更加复杂了。引力是由加速度产生的，所以当我坐在书桌前，处于地球的引力场中，我实际上就能看到周围有一些粒子，而当我自由下落的时候就看不到它们了。这些粒子的数量小到无法测量，但当我把我的书桌挪到黑洞边上时(那里的引力场要强得多)，情况就更不一样了。我将会被一连串的高能粒子和辐射持续轰炸。

上述效应对黑洞产生了很有趣的影响，现在我们可以基于黑洞周围的粒子以及黑洞的辐射，联系上述效应得到黑洞的温度。它还影响着其他引力物理领域，比如宇宙学。某些方面宇宙学当中宇宙模型的引力场和黑洞的引力场相似，确实如此，加里·吉本斯(Gary Gibbons)和史蒂芬·霍金证明宇宙膨胀同样可以产生黑洞那样的辐射。宇宙膨胀得越快，这一辐射的温度就越高。它并不是从存在于宇宙中的哪个物体发射的，而是宇宙膨胀本身的产物。当人们考虑引力场中粒子的时候，会自然得出这样的结果。

宇宙暴涨

到目前为止，在引力物理学中应用量子理论最成功的例子应该是极早期的宇宙历史。物理学家们把宇宙在这一阶段的行为称作宇宙暴涨(cosmic inflation)。在第5章我们已经考虑过宇宙大爆炸的模型，它很成功。虽然大爆炸模型解释了很多观测数据，它还是留下了很多问题。其中最大的问题是我们在CMB中看到的一些波纹尺度太大了，大到在宇宙诞生以来这段的时间内，光都来不及从波纹的一端跑到另一端。这个问题非常严重，因为不可能有任何东西跑得比光还要快。那么这些波纹是由什么产生的呢？

没有确凿不移的答案。其中一个可能的解释是宇宙在很早的时候经历过一次非常快速的膨胀。如果这是真的，那么很小的波纹就会被迫扩张为非常大尺度的波纹，这个问题就解决了。宇宙迅速膨胀的时期被称为宇宙暴涨。现在，科学家们检验这类假说的方法，就是尝试去预言这一假说导致的其他后果，并拿出我们的望远镜去验证这些预言。对于宇宙暴涨来说这非常困难，因为我们还不知道是什么导致了暴涨。而且它发生的时间也太早了。但是，还是有一些可以预言的大方向，我们可以通过观察夜空来验证它们。其中一个预言就是空间的几何结构应该非常接近平直。我们已经知道它和观测是符合的。这个可能是最令人印象深刻的预言，涉及了刚才讨论的半经典方法。

回顾一下，吉本斯和霍金证明了膨胀的空间会产生辐射的海洋。实际上辐射的海洋在空间中每一点并不都是均匀的。量子力学的本性是统计，这意味着人们需要引入一些随机的涨落，也就是说在某些空间点辐射多一些，另一些空间点又少一些。预测这些量子力学涨落具体会在哪里发生是不可能的，但理论可以让我们了解空间中随机的一个点高于或低于平均辐射密度的概率。它也能告诉我们高于或低于平均辐射密度的区域的空间分布。这些都是半经典物理做出的预言，我们可以通过观测它带来的后果以验证这一理论。而且我们可以通过观测量子涨落产生的结果来估测宇宙暴涨。

现在来回顾一下第5章我们讨论过的CMB中的波纹。这些波纹对宇宙学家们来说是非常重要的百宝箱。但到现在为止我还没有介绍过它的来源是什么。也就是说，我们还没有讨论过是什么产生了这些大尺度结构的种子。这些种子需要有非常特殊的特征才能解释科学家们在CMB中测量统计出的性质，而且在宇宙暴涨理论出现之前，没有人能够解释这些种子是怎么产生的。如果早期宇宙真的发生过暴涨，那么一种可能的给大尺度结构“播种”的方式，就是吉本斯和霍金预言的量子力学涨落。COBE， WMAP和普朗克卫星的观测表明，这些波纹确实是在这种情况下产生的。

这是一项意义重大的发现。它不仅验证了关于暴涨时期最普遍的预言，而且验证了在引力场中考虑量子力学独特的计算方法是合理的。霍金在1974年预言的那种辐射还没有被直接观测到，但它的结果在CMB中明明白白地展示出来了。证据就藏在天文学家们测绘的CMB天图中。但是，我们的探索依然没有结束，我们还要发掘更多的证据。产生CMB波纹的量子力学过程同时也会产生引力波。该引力波就是BICEP2团队在2014年3月错误地以为他们探测到了的那种(见第5章)。在本书写作之时，宇宙暴涨产生的引力波还没有得到观测证实，然而一旦未来的观测发现了它们，那就会为研究早期宇宙开启一扇全新的窗口。

宇宙学常数

我们前面讨论过宇宙加速膨胀似乎是由暗能量导致的，但我们并没有详细讨论暗能量的本质。这一问题的真相是我们实际上还不知道暗能量到底是什么。但我们有一个最受欢迎的候选者：宇宙学常数(cosmological constant)。这一节我将详细地讲讲宇宙学常数。

宇宙学常数最初是由阿尔伯特·爱因斯坦在1917年引入的。在那时人们还不知道宇宙正在膨胀，爱因斯坦引入了他的宇宙学常数是为了得到一个静态(也就是既不膨胀也不收缩)的宇宙学模型。当然我们现有很多证据都表明宇宙正在膨胀。当爱因斯坦知道这一点时立马就撤销了他的宇宙学常数，把它当做自己的失误扔进了垃圾堆。但是实际上，宇宙学常数是他的理论中一个自洽的修正，只是当时还用不上罢了。这样的认知一直持续到人们发现了宇宙加速膨胀。

宇宙学常数描述的是一个无处不在的力，它可以同时以相同的强度吸引(或者排斥)宇宙中所有的粒子。这正是人们解释宇宙加速膨胀需要的东西。我们需要做的就是确定宇宙学常数的数值，使宇宙以正确的加速度膨胀。以上就是到目前为止对宇宙加速膨胀最简单的解释。

人们已经把宇宙学常数定为符合所有当前观测结果的数值。当然，我们可以期待我们拥有的数据的质量在将来的几十年内得到显著提升。在那时我们将再次确定宇宙学常数还能不能与之相符。如果符合，就将证明宇宙学常数确实存在。如果不符合，那么我们就需要再次开动想象力了。至于现在，我们可以猜猜宇宙学常数的存在意味着什么。这个问题很有意思，因为宇宙学常数虽然简单，但却带来了一些问题。

关于宇宙学常数第一个，也是最重要的问题是：如果它导致了现在宇宙的加速膨胀，那么它的值在早期宇宙必须经过非常仔细的微调。而“微调”一直是物理学中棘手的东西。难点在这里，如果你提出一个理论去解释一个物理现象，但你的论证要求一些东西必须取极度特殊的值，这会导致你的理论变得不那么让人信服。宇宙学常数的微调来源于宇宙学常数不随时间改变这一事实(它是一个常数)。这意味着如果我们要求今天宇宙膨胀的加速度是一个恰当的值，那么在非常早期的宇宙，宇宙学常数和当时的能量尺度相比必须非常非常非常小，但并不是零。相反宇宙学常数太大，那么宇宙加速膨胀就会在早得多的时间发生。这样的话，恒星和星系将永远不可能形成，生命也不可能出现了。而如果它再小一些，就不会产生足够的加速度，我们就可能永远都不会注意到宇宙加速膨胀。为了使我们的宇宙膨胀恰好处于符合观测的甜区，宇宙学常数必须有一个十分特殊且高度精确的值。这一精确度一般被定为10的120次方(1后面跟着120个0)分之一。

在加入量子力学后，刚刚描述的宇宙学常数问题更严重了。量子力学的效应也会对宇宙学常数的数值有所贡献，而根据我们现有的对量子力学的理解，我们期望的量子力学的贡献比我们实际观测得到的那个值小太多了。你可以说：我们还没有完全理解导致宇宙膨胀的量子力学过程，而且我们还不了解它是怎么处理引力的。你可以怀疑实际上存在一个还不为人所知的量子力学过程可以抵消掉那个巨大无比的宇宙学常数。这些都是有可能的，但却引发了进一步的问题。我们期待的那个导出合理的宇宙学常数的量子力学过程并不是恒常的，它们会随着宇宙演化而变化。考虑一系列量子力学过程之间彼此消除的可能性是一回事，假设它们无时无刻不在相互抵消又是另一回事。当我们考虑量子力学效应时，我们反而会更加惊讶于宇宙学常数是经过微调的这一事实。这也就是为什么一些人把宇宙学常数问题称为物理学里最糟糕的微调问题。

多重宇宙

宇宙学常数问题如此重要和紧迫，以至于很多物理学家甚至开始考虑一些骇人听闻的假说去解释它。其中最具有想象力，且被最多人接受的假说就是有可能存在不止一个宇宙。如果是这样，以及如果其他宇宙中的宇宙学常数由于某种原因取值和我们宇宙中的值不一样，那么我们也就可能测量到任意宇宙学常数的值。即使观测到的值看起来经过微调，那也可能仅仅意味着我们身处一个相对稀有的宇宙之中，还存在其他很多宇宙，那里的宇宙学常数取一些更加自然的值。

有多个宇宙这一想法叫做多重宇宙(multiverse)。这个假说并没有实质上消除宇宙学常数必须精确取为观测值这一问题。在这一假说中，我们并不是要求宇宙学常数有微调，而是假设我们居住的宇宙必须经过了精挑细选而且十分少见。但是，当我们把多重宇宙假设结合人择原理(anthropic)来考虑时，事情就变得不一样了。人择原理大概是说，我们(也就是一切生命形式)只能观测到可以支持生命出现的宇宙。这听起来是显而易见的，但实际上它提供了一种机制去选择我们可以生存的宇宙。如果某一个宇宙的宇宙学常数大到恒星和行星都无法形成，那么我们也不可能生存在那样的宇宙中。这就自动排除了大部分的多重宇宙，并且让我们的宇宙变得更加可能被选中。

这种想法又引发了很多问题。那些其他的宇宙存在于哪里？它们是如何和我们的宇宙发生联系的？它们的宇宙学常数有什么不同？我们处于其中任意一个的概率又是多少？这些都是非常基本的问题。有一些关于宇宙暴涨的理论提供了产生多重宇宙的机制，使科学可以把多重宇宙纳入现实的物理学以供我们研究。对于一些人来说，多重宇宙的想法是辉煌的，它受到观测引力在天文尺度下的作用启发，又充实了大爆炸理论。但对于另一些人来说，多重宇宙甚至比它试图解决的问题还要糟糕。后一类人中不少人认为它是错的，因为它利用不可观测的时间和空间区域去解决我们自己的宇宙问题。它可能听起来是自洽的，甚至是有根据的，但其他宇宙的存在毕竟不能被直接验证。因此一些科学家提出，这样的方法本质上并不是科学，而是属于形而上学的范畴。

科学的界限是不是应该展到多重宇宙，正是现在非常激烈的辩题，不同的人都在热情洋溢地提出自己的观点。未来的天文将会观测那些导致宇宙加速膨胀的元凶，研究它们的性质，从而得到更多的论据。理论物理学在发展，也许未来的理论物理学能更清晰地阐明我们测量到的宇宙学常数的本质。但现在，我们必须等待。

后记

在最近的一个世纪，我们对引力的理解处于相当快速的发展中。这一发展开始于爱因斯坦革命性的新理论，一直以来我们都在发展可以用来证明它的数学和观测手段。我已经概括了新的引力效应在太阳系内外，以及在整个宇宙中是如何被理论预言以及由观测验证的。虽然我尝试让读者理解相关概念，以及它们带来的物理结果的优美之处，但这本书毫无疑问是不完整的。这只是一本对这一主题的非常简短的介绍。为了理解爱因斯坦所有深刻的成就，以及它们带来的漂亮的理论，我们只能去钻研艰深的数学和物理。这些经历应该是值得的，因为爱因斯坦的引力理论让我们理解了时间和空间究竟是什么。它让我们去想象一些从未存在的宇宙，以及去理解我们所在的宇宙。它让我们有可能去计算一些极其陌生和怪异的环境，这使我们对现实的日常理解被彻底颠覆。但有一点可以肯定，它仍旧是不完备的理论。关于引力的最终判决将留给将来的人书写。

全书完

索引

A

anthropic principle 人择原理

Aristotle's theory of gravity 亚里士多德的理论

B

bending of starlight 星光偏折

binary pulsar systems 脉冲双星系统

black hole radiation 黑洞辐射

black holes 黑洞

C

Cavendish's experiment 卡文迪许实验

CMB polarization CMB 偏振

concordance model of cosmology 宇宙的协和模型

constancy of mass 质量一致性

cosmic inflation 宇宙暴涨

Cosmic Microwave Background 宇宙微波背景辐射（CMB）

cosmological constant 宇宙学常数

cosmology 宇宙学

critical rate of cosmic expansion （宇宙膨胀的）临界速度

D

dark energy 暗能量

dark matter 暗物质

double pulsar 双脉冲星

E

early universe 早期宇宙

Eddington's expedition 爱丁顿的远征队

effect of gravitational waves 引力波的效应

Einstein's theory of gravity 爱因斯坦的引力理论

Eötvös experiment 厄特沃什（的扭秤）实验

ether 以太

Euclid satellite 欧几里得卫星

event horizons 事件视界

expanding universe 宇宙膨胀

expansion history of the universe 宇宙膨胀历史

experimental probes of Einstein'stheory
爱因斯坦理论的实验验证

experimental probes of Newton'slaw
牛顿定律的实验验证

F

fine-tuning of the cosmologicalconstant
宇宙常数的微调

flat and curved spaces 平直和弯曲空间

frame dragging 参考系拖曳

G

galaxy rotation 星系旋转

General Theory of Relativity 广义相对论

geodetic precession 测地线进动

gravitational lensing 引力透镜

gravitational redshifting 引力红移

gravitational time dilation 引力时间延迟

gravitational wave detectors 引力波探测器

gravitational waves 引力波

Gravity Probe B 引力探测器B

H

history of cosmology 宇宙学史

Hubble's law 哈勃定律

Hughes-Drever experiment 休斯- 德雷弗实验

Hulse-Taylor binary pulsar system 赫尔斯- 泰勒脉冲双星

I

interferometry 干涉法

K

Kepler's laws 开普勒定律

L

laboratory tests of gravity 引力的实验

large-scale structure in the Universe 宇宙大尺度结构

Large Synoptic Survey Telescope 大型综合巡天望远镜

late universe 晚期宇宙

life of a star 恒星的一生

LIGO experiment 激光干涉引力波天文台

Loop Quantum Gravity 圈量子引力

M

Maxwell's theory of light 麦克斯韦的光理论

Mercury's anomalous orbit 水星的轨道偏移

Michelson-Morley experiment 迈克尔逊- 莫雷实验

microsecond pulsars 微秒级脉冲星

multiverses 多重宇宙

N

neutron stars 中子星

Newton's force law 牛顿力学定律

Newton's theory of gravity 牛顿的引力理论

non-renormalizability of gravity 引力的不可重整性

O

observation of gravitational waves 引力波观测

observations of the CMB CMB 观测

P

particles in gravitational fields 引力场中的粒子

Planck Surveyor 普朗克卫星

pulsars 脉冲星

Q

quantum gravity 量子引力

quantum mechanics 量子力学

R

radio time-delay effect 射电时间延迟效应

S

seeds of structure in cosmology 宇宙结构的种子

Solar System 太阳系

space with positive and negativecurvature
正负曲率空间

space-time 时空

Special Theory of Relativity 狭义相对论

speed of light 光速

Square Kilometre Array 平方千米阵

String Theory 弦论

supernovae 超新星

synthesis of the light elements 轻元素合成

T

triple pulsar 脉冲三星

U

Universality of Free Fall 自由落体的普遍性

W

Weber bars 韦伯棒

WMAP experiment 威尔金森微波各向异性探测器实验

Preface

This is a book about gravity. Gravity is what causes massive objects to fall towards each other. It's gravity that causes apples to fall from trees, and it was gravity that caused the Earth to form. Gravity is the most familiar of all the fundamental forces of nature, yet the true way in which gravity works is far from obvious. In reality, the phenomenon we refer to as ‘gravity’ is deeply tied up with the nature of space and time. This means that a modern understanding of gravity doesn’t just tell us how objects in the Universe move, it also allows us to understand the behaviour of the very space and time that make up the fabric of the Universe itself.

The purpose of this book is to give the reader a very brief introduction to various diferent aspects of gravity. We start by looking at the way in which the theory of gravity developed historically, before moving on to an outline of how it is understood by scientists today. We will then consider the consequences of gravitational physics on the Earth, in the Solar System, and in the Universe as a whole. The final chapter describes some of the frontiers of current research in theoretical gravitational physics.

By the end, I intend to have conveyed to the reader not only what gravity is, but how the study of gravity has led scientists to reach extraordinary conclusions about the nature of space, time, and the Universe in which we live.

Chapter 1 From Newton to Einstein

Gravity is by far the weakest of the four fundamental forces that exist in nature—the others being the electromagnetic force, and the strong and weak nuclear forces. Yet over large distances it is gravity that dominates. This is because gravity is only ever attractive and because it can never be screened. So while most large objects are electrically neutral, they can never be gravitationally neutral. The gravitational force between objects with mass always acts to pull those objects together, and always increases as they become more massive.

It is thanks to geniuses like Newton and Einstein that we understand gravity at all, yet it is gravity, more than any other force, that continues to present scientists with the most enigmatic of puzzles. To understand why, let's start at the beginning, and consider the historical development of gravity.

The pre-history of gravity

It seems safe to assume that mankind has always known that when we drop an object it will fall downwards. In this sense, we've always been aware of the existence of gravity. It was the cause of this motion that appears to have been the focus of many early thinkers.

Aristotle, who's Physics played a dominant role in European science until as late as the 17th century, based his explanation of gravity on the idea that objects should move towards their natural place in the Universe. Where this place was, he reasoned, should be determined by the composition of the object in question. More specifically, it should depend on how much it contained of each of the four elements: Earth, Water, Air, and Fire.

Aristotle argued that objects composed predominantly from Earth and Water should move towards the centre of the Universe. To him, the centre of the Universe was the place beneath his feet. Objects made from Earth, and that are thrown into the air, must therefore move down towards the ground. Water, he reasoned, is lighter than Earth, as can be verified by dumping some soil into a half-full glass of it. All Water must therefore come to rest on top of the Earth. Similarly, Air is lighter than Water, as bubbles rise in water. The natural place for Air is therefore above Water, and the natural place for Fire is above the Air.

This framework provides a logical sort of order to the world that was observed, in terms of what were thought to be the basic constituents of matter at the time. It even allows one to make some statements about the speed at which objects should fall. Aristotle argued that the velocity of a falling object should be in proportion to its weight, and in inverse proportion to the density of the medium through which it travels. That is, Aristotle thought that an object that weighs 2kg should fall twice as fast as one that weighs 1kg.

Sadly, Aristotle's theory cannot be correct. We now know that there is no centre to the Universe for objects to move towards. We can also demonstrate, by direct experimentation, that the rate at which an object accelerates due to gravity is not in proportion to its mass. In fact, it can be shown that all objects fall at the same rate. This discovery was one of the milestones in the modern understanding of gravity, and so it bears some further explanation.

The fact that all objects accelerate under gravity at the same rate is not an obvious one. In fact, if I were to drop a feather from my left hand, and a lump of iron from my right, I should not expect them to hit the floor at the same time. The lump of iron will get there first. So what is meant by the statement ‘all objects accelerate under gravity at the same rate’？ To understand this phrase, we have to think about all of the forces that act upon these objects.

When I let go of the feather it is acted on by the force of gravity, but it is also acted on by other forces. As it starts to drop, there is resistance to its motion from the air around it. This slows the feather more than it does the heavier lump of iron. Any slight gust of air will also have a large efect on the feather while perturbing the motion of the lump of metal by only a tiny amount. So, the meaning of the phrase ‘all objects accelerate under gravity at the same rate’ is not a statement about the motion of objects in our immediate environment. Rather, it is a statement about what should happen to an object if it were to fall under the influence of gravity alone. That is, if all other interactions are suppressed, then all objects should fall at the same rate.

Galileo is widely credited with having shown the truth of this proposition. In 1638, he supposedly dropped cannonballs with diferent masses of the top of the leaning tower of Pisa. The cannonballs were found to fall at the same rate, independent of their composition. More recently, and perhaps even more dramatically, the same result was demonstrated by the Apollo astronaut David Scott. Scott dropped a feather and a hammer while standing on the surface of the Moon. There is no air on the Moon to slow the motion of the feather, and so both objects landed at his feet at the same time (see Figure 1). Today we refer to this phenomenon as the Universality of Free Fall. It is a key ingredient in both Newton's and Einstein's theories of gravity, as we will see later.

1. (a) Galileo dropping cannonballs of the leaning tower of Pisa; and (b) a painting of David Scott dropping a hammer and a feather on the surface of the moon.

Newton’s theory of gravity

Sir Isaac Newton’s theory of gravity and motion was first published in his Principia Mathematica in 1687, and it changed the world forever. This was the first genuinely scientific theory of how gravity worked. Unlike Aristotle, Newton didn’t try and seek an explanation for gravity. Instead he quantified its efects, and in the process deduced physical laws that accurately described the motion of not only objects on Earth, but also the motion of the Earth itself, as well as all other bodies in the Solar System.

Newton’s achievement was truly a work of genius. He created new branches of mathematics, and for the first time demonstrated that the laws of physics that apply to us, on Earth, are the same as those that apply to the heavenly bodies. All the complexity of motion, which Aristotle had tried to explain, was boiled down to a handful of simple laws. Newton’s theory was glorious,and went unchallenged for over 200 years. In one book, Newton revolutionized the worlds of science, industry, and warfare, and provided the framework within which many of us still think today.

The basic ingredients of Newton’s theory are the existence of absolute space and time as the stage on which all motion occurs, and the existence of a universal gravitational force that acts instantaneously between every pair of massive bodies in the Universe. And that is all.

Space to Newton was, as it appears to most of us in our day-today experience, simply the eternal and unchanging arena within which all matter exists. I can position object X at one point in space, and work out the distance to any other object, Y, by simply using a measuring tape held out in a straight line. In Newton’s mechanics there is no ambiguity in this process. Objects X and Y may move in space, but the space itself is fixed and forever unchanged.

Likewise, Newton’s conception of time followed the everyday intuition that most of us grow up with. Instants of time unfold in Newton’s theory, one after the other. Objects can change their position during an interval of time, but time itself is universal and the same for everyone. In Newton’s theory all true clocks measure time in the same way, just as all true measuring tapes measure the same distance between any two given objects.

Now, according to Newton, all bodies move at a constant rate, unless acted on by an external force (this was a departure from Aristotle’s physics). If a force should act upon an object, then the efect of that force is to cause the object to accelerate. More force means more acceleration, and, if an object has more mass, then it needs more force to reach the same acceleration. Within this framework, gravity is simply an external force acting on all massive bodies, pulling them together.Newton deduced that his gravitational force must be proportional to the mass of each of the objects it acts between, and inversely proportional to the square of the distance between them. That is, the force of gravity between two massive bodies must be given by an equation of the form:

where M and m are the masses of the two objects in question, and r is the distance between them. This simple equation, together with Newton's laws of motion, is suicient to get a good approximation to the motion of the vast majority of astrophysical bodies as well as all bodies that exist on Earth.

That all bodies fall under Newton's gravity at the same rate, and hence obey Galileo's observation, can be seen from the fact that in Newton's mechanics a given force causes a heavy body to accelerate more slowly than a light one. Consider this together with the fact that, according to Newton, the gravitational force must increase with mass. In Newton's theory these two things happens at exactly the required rate to cancel each other out. A body being acted on by Newton's gravity, and obeying Newton's laws of motion, must therefore accelerate at a fixed rate, independent of its mass. That this happens is no accident: the Universality of Free Fall is built into Newton's theory from the start.

The first great success of Newton's theory was that it could be used to derive the laws of motion for the planets. These laws had been deduced empirically by Johannes Kepler earlier in the 17th century, using cutting-edge astronomical data. Kepler's laws stated that:

·The orbit of a planet traces out an ellipse, and the Sun is at one of the foci of this ellipse.

·If a line is drawn between a planet and the Sun, then, as the planet orbits the Sun, that line will sweep out an equal area of space in any two intervals of equal time.

2. An illustration of a planetary orbit. The shaded regions, marked A and B, are of equal area, if they are swept out by the orbiting planet in equal time.

·The square of the time taken for a planet to complete one orbit is proportional to the cube of the distance between the two furthest points on that orbit (the major axis of the ellipse).

The quantities described in these three laws are all illustrated in Figure 2 (with the exception of the orbital period). The good thing about Kepler's laws was that they seemed to apply to all known planets, even though at the time they had no known basis in any physical theory. They were simply seen to be a good fit to the data.Newton knew about Kepler's laws, and included in his Principia Mathematica an explanation of how they could be derived from his laws of motion and from his universal theory of gravitation. This derivation was one of the great success stories of physics. Empirical laws, derived from cutting-edge observations of the planets, were explained for the first time in terms of simple mathematical equations. Newton had shown that the same laws that describe the motion of a cannonball fired on the surface of the Earth could also be used to describe the motions of the planets themselves. This was the beginning of much of physics as we know it today.

Einstein’s theory of gravity

More than 200 years after its publication, Newton's theory of gravity was supplanted by Albert Einstein's. If Newton's theory was simple and useful, then Einstein's was beautiful and truly universal. Einstein didn’t just change the equations involved in Newton's theory, he pulled up the very foundations upon which it rested. Einstein changed everything.

As with much of the progress that happens in physics, Einstein's theory was motivated primarily by the inconsistency of existing ideas. Newton had given us a theory of how gravity and motion operate. But Newton's ideas were not compatible with the theory of light that James Clerk Maxwell had developed in the middle of the 19th century. Maxwell's new theory stated that everyone in the Universe should measure the speed of light to have the same value: just under 300 million metres per second. This might not sound terribly profound, until you take a few moments to consider what it means.

The point is that, according to Newton's mechanics, if I fire a bullet forwards at 1,000 miles per hour while seated on a train moving at 100 miles per hour, then an observer on the side of the track will see that bullet moving at 1,100 miles per hour. In mathematical terms we say that the velocity of the bullet and the velocity of the train add linearly. Now consider that I turn on a torch, while still seated facing forwards on the same train. From my seated position I will see the light from the torch propagate forwards through the train carriage at the speed of light (i.e. at about 300 million metres per second). Consider again the observer watching me from the side of the train track. If you listened to Newton, you might expect this person to see the light travel at the 300 million metres per second, plus 100 miles per hour (the speed of the train). But according to Maxwell this is not what happens. Maxwell says that the person at the side of the track sees the light propagate at the same speed as the person on the train. That is, Maxwell’s equations imply that velocities do not add linearly.

The contradiction just described is a profound one. If we are unable to agree on how to add velocities, then we are unable to use physics to calculate the motion of objects at all. It was impossible for both Newton and Maxwell to be correct. At least one of them must be wrong. A lesser scientist might have tried to re-write either Newton’s or Maxwell’s theories, but this was not what

Einstein did. Einstein treated both Newton’s and Maxwell’s work with the utmost respect. He recognized their great strengths, and worked to solve the contradiction in a truly ingenious way.Einstein hypothesized that if the speed of light was the same for everyone, then time and space cannot be universal concepts. Instead, he reasoned, each observer must have their own personal concept of time, and their own personal concept of space. According to Einstein’s new theory, a clock carried by a person on the train is seen, by a person standing beside the track, to tick slower than a clock they carry themselves. Likewise, the person on the train sees the clock of the person standing beside the track to tick slower than his or her own.

This result initially sounds odd, but that’s only because we’ve been programmed from a young age to think of time as universal. What Einstein showed us is that our childhood understanding of time is mistaken. Time is not a universal concept, unfolding at the same rate for everyone. Time is a personal thing, and depends on our relative motion, with respect to others. Likewise, space is not the fixed backdrop that we think it is. What we think of as distances, and the lengths of objects, are actually dependent on how we are moving.

These are startling ideas. At first they can seem unsettling, as if the crutches we've used to understand the world have suddenly been kicked away. But we need not despair. There is a concept involving space and time that survives in Einstein’s theory, and that maintains an observer-independent reality. This is what is known as space-time. Instead of Newton’s concepts of universal time and universal space, what we are left with is a larger structure that encompasses them both. A person or object, like you or me, follows a line through this structure, known as our world-line. Our personal time is measured along our world-line, and while my world-line might be diferent to yours, they both exist in the same space-time (see Figure 3).

So, it is the promotion of space and time to space-time that allows us to make Newton’s mechanics consistent with Maxwell’s. This realization was one of Einstein’s early contributions to science, and it is the backbone of what is now known as the Special Theory of Relativity. It has a wide variety of profound consequences, many of which have been confirmed experimentally. The most famous of these is probably the equation:

3. An example of two world-lines, for two observers, moving in the same space-time. The observers meet where the lines cross.

which tells us that mass and energy are intricately connected (a fact that became devastatingly apparent with the advent of nuclear weapons). Other consequences are the longer lifetime that unstable particles appear to have when they move quickly, and the fact that nothing can ever move faster than light.

It is this last result, together with the new concept of space-time, which led Einstein to his theory of gravity. Again, the impetus for this development was an apparent contradiction. And again, it was Newton’s theory that was causing problems. This time, however, it seemed that there was a contradiction with Einstein’s own work. This was because Newton’s gravity acted between objects instantaneously. That is, if the Sun were to suddenly explode, according to Newton we should feel the gravitational efects of this at the very same moment it happens. But Einstein now knew that this was impossible. First, he had found out that nothing could move faster than light. Second, he had shown that there was no such thing as universal time, so the idea of two things happening simultaneously in two diferent places made no sense at all (if they happened simultaneously for one observer, they would not be simultaneous for any other who was in a diferent state of motion). So, once again, something was wrong and needed fixing.

Einstein’s solution to this problem was even more amazing. He hypothesized that gravity, instead of being a force that simply pulled things through space, was the result of the curvature of space-time. The fact that massive objects were drawn towards each other was then, according to Einstein, just a result of those objects following the shortest paths they could in the curved space-time in which they existed. The idea was that mass and energy caused space-time to curve, and that this curvature caused the paths of the objects that move through space to appear to bend towards each other. The beauty of this idea is that we now no longer need to include gravity as an extra force that exists in the Universe. In this new picture, the only thing responsible for the attraction of massive bodies is space-time itself (which has to be there anyway). This is the fundamental idea behind the General Theory of Relativity.

Even more impressive is that Einstein’s idea explained Galileo’s result that all objects fall at the same rate. Recall that in Newton’s theory this result wasn’t really explained at all. It was simply taken as a fact, and a law of gravity was devised that was compatible with it. Einstein went one better. Now, in Einstein’s theory, there is no external force called gravity; the motion of every object is just a result of the curvature of space-time. But all objects are moving in the same space-time, so all objects must follow the same paths. In other words, all objects must fall at the same rate, just as Galileo had observed.

These ideas can sometimes be confusing, so let’s think about an example. Imagine the paths of two objects that have no forces acting on them. In a flat space the paths of these objects are straight lines, as shown in Figure 4.

If the space is curved, however, then this is no longer true. Consider the simplest curved space: the surface of a sphere. The shortest path between any two points on the surface of a sphere is called a great circle (the equator is an example of a great circle-on the globe). If two objects follow two diferent great circles, on the same sphere, then they will initially move away from each other, before finally coming together again, as shown in Figure 5.This is how Einstein envisaged gravity working. He imagined that it was curvature that was responsible for the paths of objects meeting, and not anything external that pulls them left or right as they move. The curvature of space-time is usually more irregular than the surface of a sphere, but the basic idea is the same. As far as the consequences for gravity go, the largest efects of Einstein's new theory were found to look very similar to the law that Newton had prescribed 200 years earlier. The diference is that this law now comes with a new understanding of space and time. It also comes with the prediction of a variety of smaller, more subtle, efects (to be discussed in the following chapters).

4. Two straight lines, indicating the paths that two particles might follow if they travelled through a flat space, without any external forces acting upon them.

5. Two great circles, indicating the paths that particles might travel in a spherically curved space, if no external forces act upon them. The lines are no longer parallel forever, but meet at a point.

Think now about what all of this means in a practical situation. Consider a skydiver jumping out of an airplane. The skydiver falls freely, up to the efects of air resistance. According to Einstein, the skydiver’s path is the straightest line possible through the curved space-time around the Earth. From the skydiver’s perspective this seems quite natural. Except for the air rushing past her, the skydiver feels no perturbing forces at all. In fact, if it weren’t for the air resistance, she would experience weightlessness in the same way that an astronaut does in orbit. The only reason we think the skydiver is accelerating is because we are used to using the surface of the Earth as our frame of reference. If we free ourselves from this convention, then we have no reason to think the skydiver is accelerating at all.

Now consider yourself on the ground, looking up at the falling daredevil. Normally, your intuitive description of your own motion would be that you are stationary. But again this is only because of our slavish regard to the Earth as the arbiter of what is at rest and what is moving. Free yourself from this prison, and you realize that you are, in fact, accelerating. You feel a force on the soles of your feet that pushes you upwards, in the same way that you would if you were in a lift that accelerated upwards very quickly. In Einstein’s picture there is no diference between your experience standing on Earth and your experience in the lift. In both situations you are accelerating upwards. In the latter situation it is the lift that is responsible for your acceleration. In the former, it is the fact that the Earth is solid that pushes you upwards through space-time, knocking you of your free-fall trajectory. That the surface of the Earth can accelerate upwards at every point on its surface, and remain a solid object, is because it exists in a curved space-time and not in a flat space.

With this change in perspective the true nature of gravity becomes apparent. The freely falling skydiver is brought to Earth because the space-time through which she falls is curved. It is not an external force that tugs her downwards, but her own natural motion through a curved space. On the other hand, as a person standing on the ground, the pressure you feel on the soles of your feet is due to the rigidity of the Earth pushing you upwards. Again, there is no external force pulling you to Earth. It is only the electrostatic forces in the rocks below your feet that keep the ground rigid, and that prevents you from taking what would otherwise be your natural motion (which would also be free fall).

So, if we free ourselves from defining our motion with respect to the surface of the Earth we realize that the skydiver is not accelerating, while the person who stands on the surface of the Earth is accelerating. Just the opposite of what we usually think. Going back to Galileo’s experiment on the leaning tower of Pisa, we can now see why he observed all of his cannonballs to fall at the same rate. It wasn’t really the cannonballs that were accelerating away from Galileo at all, it was Galileo that was accelerating away from the cannonballs! If I leave a number of objects at rest at some position in space and accelerate away from them, I shouldn’t be at all surprised that the distance between me and each of these objects increases at the same rate. So it is with Galileo and his cannonballs.

For some, the beauty in this description is obvious. For others it is the fact that it is possible to probe Einstein’s theory experimentally that is most compelling. These experiments range from looking for small perturbations to the orbits of the planets, to the bending of light around the Sun, and many, many more besides. We will explore these exciting phenomena in the chapters that follow. But bear in mind throughout: it is the curvature of space-time that is responsible for it all.

Chapter 2 Gravity in the Solar System

The Solar System, including the Earth, is our most immediate laboratory for observing the consequences of gravity. The gravitational field in the Solar System is dominated by the Sun, which is far more massive than any of the planets.

In orbits that are relatively close to the Sun are the four smallest planets: Mercury, Venus, Earth, and Mars. Further out, there are four much larger planets: Jupiter, Saturn, Uranus, and Neptune. The Solar System contains a number of other objects, such as comets, asteroids, moons, and man-made spacecraft. By observing the motion of these objects, and in some cases by interacting with them, we can learn a great deal about the behaviour of gravity.

The study of experimental and observational gravity in the Solar System took of in earnest during the latter half of the 20th century. While astronomers had been tracking the motion of the planets for centuries, the development of new technologies and methods in the 20th century allowed observations and experiments to be carried out in ways that had never previously been possible. In order to try and present the results of this work in some kind of sensible order, I will classify them into experiments that probe the foundational assumptions of gravity theories; experiments that probe Newton’s law; and experiments that probe the subtle efects that result from Einstein’s theory.

Testing foundational assumptions

There are a number of foundational assumptions that go into the modern theory of gravity. These include the fact that the rest mass of an object should be independent of its position, and independent of its motion with respect to other bodies. Other assumptions are the idea that the speed of light should be the same in every direction, and that all objects should fall at the same rate (in the absence of non-gravitational forces). Over the course of the past century all these ideas have been tested to extremely high accuracy. I’ll outline some of the best of these tests here, before we move on to thinking about experiments that test the particulars of Newton’s and Einstein’s theories of gravity.

Let’s start of by thinking about mass. Recall that mass is the quantity that tells us how much force we need to apply to an object in order to make it accelerate by a fixed amount. It’s thought to be a property of the object itself. This is diferent to weight, which is the name of the downwards force that an object exerts on your hand when you hold it, and which would be diferent if you held the same object while standing on a diferent planet. It is mass that appears in Newton’s law of gravity, and it is mass that was shown to be equivalent to energy in Einstein’s famous formula (E = mc^2
). Because these two equations are so central to gravity, we need to have some idea of whether or not the mass of an object really is independent of its position and motion in a gravitational field. This can only be done experimentally.

Oddly enough, the best test of whether mass depends on position is to look at how light changes colour as it travels through a gravitational field. The basic idea behind this test is that photons (particles of light) should lose energy as they escape from the gravitational fields of massive objects such as stars or planets. This is because it takes energy to pull something upwards through a gravitational field. So, just as you would have to use energy to run up a flight of stairs, it takes a photon some amount of energy to travel upwards from the surface of the Earth, or away from the surface of the Sun. A change in energy of a photon results in a change in its colour (its wavelength), and so a beam of light travelling through a gravitational field should be expected to have a diferent colour depending on how far it is above the source of that field. This is the reason why light detected far from the surface of a star is found to be slightly redder, or longer in wavelength, than it was when it was emitted. The efect is known as the gravitational redshifting of light.

So, how can the gravitational redshifting of light be expected to tell us anything about whether the mass of an object depends on its position in a gravitational field？ To answer this, let’s consider the most direct way of measuring the mass of an object in a gravitational field: lifting it upwards with a winch and recording the amount of energy it took to do so. This energy should be directly related to the mass of the object, so recording the energy required to lift the object between two diferent heights should tell us something very direct about its mass at, and between, those two positions. Unfortunately, it’s dicult to accurately measure the amount of energy used by a winch, as they tend to be quite ineicient (they give out energy in noise and heat, and by stretching the rope and their own components). This is where the gravitational redshifting of light comes in. The frequency of light can be measured to very high precision, and the energy the photons lose by climbing out of the gravitational field is expected to be exactly the same as that which would be used to lift an object with a mass that corresponds to the same energy (as calculated using E = mc^2
). If we can measure the redshifting of light, we therefore have a highly accurate proxy experiment, which is expected to convey exactly the same information as the winch experiment.

An experiment designed to measure the gravitational redshifting of light was performed for the first time by the scientists Robert Pound and Glen Rebka in the early 1960s. They used a tower at the Jeferson Physical Laboratory at Harvard University, and looked at the redshifting of photons as they travelled up its height. They found that the light did indeed change colour as it travelled upwards, and by an amount that was entirely consistent with mass being independent of position. The only deviations possible would have to be smaller than the accuracy of the experiment itself, which was at the level of about 1 per cent. A similar experiment has since been carried out using the light emitted from the Sun, which also had results that were consistent with mass being independent of position, again at an accuracy of about 1 per cent.

More recently, atomic clocks have been used to probe the same efect. The idea behind these experiments is that beams of light are themselves, in some sense, like clocks. The colour of light is determined by the wavelength of the photons that make up the light, which is itself related to the frequency at which they oscillate. If we were to take these oscillations to be the basis of a clock, by saying that each oscillation is one unit of time, then we can see that the redshifting of light is equivalent to the appearance of clocks at diferent positions running at diferent rates. In fact, we don’t even need to measure the frequency of light to perform this experiment, because if a clock based on the oscillations of a photon appears to run slow, then so must every other clock. All we have to do is put two clocks at two diferent heights and arrange for them to transmit the time they display via radio signals. The diference in the rate at which they appear to tick, according to the radio signals that are observed, is then entirely equivalent to the rate at which a light signal between them should be redshifted.

We can therefore take two highly accurate atomic clocks and put one on a rocket while leaving the other at our feet. If the clock in the rocket transmits its time via radio signals, then we can compare this signal to the time displayed by the clock we kept beside us. They should, in general, be diferent: an efect known as gravitational time dilation. This experiment was carried out for the first time by Robert Vessot and Martin Levine in 1976. They observed the time dilation efect directly, and found it to be consistent with mass being independent of position to an accuracy of about 1 part in 10,000 (about a hundred times more accurate than the Harvard experiment). This experiment therefore provides very strong evidence that mass is indeed independent of position in a gravitational field, to very high accuracy.

Moving on from position dependence, it is possible to construct experiments that test whether the speed of light, or the mass of an object, are dependent on direction. These experiments are historically very important, because before Einstein produced his theory of gravity it was widely believed that there was a substance called the ether that permeated the whole of space. The ether was invoked as the medium through which waves of light travelled, and was popular among physicists until as late as the 20th century. If the ether existed, then the speed of light that an observer measured should depend on their motion as they travelled through it. Einstein’s theory is incompatible with the existence of an ether, as he had constructed it so that all observers measure the same speed of light, independent of their state of motion. Performing tests for the existence of the ether was therefore an important part of verifying his theory. The most famous of these tests was the Michelson—Morley experiment, carried out in 1887. It is a test to see if the speed of light depends on its direction of propagation.

The Michelson—Morley experiment used a device known as an interferometer, consisting of two arms, built at right-angles to each other. This is illustrated in Figure 6. Light from a laser is shone down each of the arms, and re’ected back on itself by mirrors positioned at each of their ends. When the reflected light reached the intersection of the two arms it was allowed to interact. As light is known to have the properties of a wave, it would be possible to let the two beams of light interact to form a pattern(like two sets of waves interacting on the surface of a pond). The form of the pattern that is produced in the interferometer depends on the length of each of the arms, and the time it takes the laser light to travel along them. If the speed of light was diferent in diferent directions, then Michelson and Morley should have seen the consequences of this by using their apparatus.

6. A schematic diagram of an interferometer. The beam splitter separates the laser light into two beams, each of which is re’ected of a mirror. The light then re-traces its path, and interacts, before being directed into the detector.

Michelson and Morley’s experiment had a null result. No diference was observed in the speed of light, as it travelled in the two diferent directions. This was unexpected by many scientists at the time, as the Earth was supposed to be in motion with respect to the ether. If light was a wave in the ether, then the speed of light should have been direction independent only in a laboratory that was stationary with respect to the ether. This wasn’t thought to be the case for the Earth, which orbits the Sun at around 30,000 metres per second. The experiment performed by Michelson and Morley is therefore taken to be strong evidence against the existence of an ether, and in favour of a speed of light that is truly the same in every direction. This was very important for Einstein’s theory.

Evidence for the direction independence of mass was given by the experiments that were independently performed by Vernon Hughes and Ronald Drever in the early 1960s. These investigators considered the electrons that exist within lithium atoms, and that orbit the nucleus at velocities of around a million metres per second. Now, the gravitational interaction between these electrons, and anything else in their immediate environment, is extremely small. This is because electrons have such tiny masses. Nevertheless, it is still possible to put extremely tight bounds on any possible direction dependence of their mass. This is because electrons give out photons when they change energy levels within atoms, and because these photons have a very specific set of frequencies known as transition lines. If the mass of the electrons depended on their direction of motion, then this would change the precise position of the transition lines that resulted from changes in energy levels. Careful studies, by both Hughes and Drever, found no evidence for the direction dependence of the mass of the electron, to extremely high accuracy.

Let’s now return to the idea of the Universality of Free Fall. Remember that this is the name given to the idea that all objects fall at the same rate, as demonstrated by Galileo. But Galileo’s experiment, while ground-breaking, was probably not very accurate (by modern standards). So, given the enormous significance of the Universality of Free Fall for both Newton and Einstein’s theories, there has subsequently been a lot of efort to verify it to the highest possible level of accuracy. This has now been done in a number of diferent environments, including numerous laboratory experiments as well as space-based observations.

The most famous of the laboratory tests for the Universality of Free Fall was performed by Lorá’nd
at the end of the 19th century. E’tv’s used a device called a torsion balance, which consisted of a 40cm bar suspended by a fibre at its mid-point. This is illustrated in Figure 7. Two diferent objects were then hung from the two ends of the bar. These objects were chosen to be made of two very diferent materials. The idea was that if the two objects accelerated towards the Earth at diferent rates then the torsion balance would be forced to rotate. By measuring the motion of the beam it would then be possible to place limits on the diference between the gravitational force that acted on each of the objects and hence to put limits on the diferent rates at which they would fall if they were released.

7. A schematic illustration of the torsion balance experiment, used by E
. The two masses are made from diferent materials. If the masses were to fall at diferent rates, then the bar would rotate around the fibre.

E
found that there was no difference in the rates at which any two objects would fall, to an accuracy of around one part in a billion. This, then, was a very precise version of Galileo’s experiment. Since the 19th century the accuracy of this type of experiment has been improved still further, with groups at Princeton, the University of Washington, and Moscow University increasing its precision to better than one part in a trillion. This progress was made possible by the availability of technologies that have allowed the experiment to be performed in near vacuum conditions, as well as because the experimenters now make use of the gravitational field of the Sun in addition to that of the Earth. The current limiting factors in these experiments are the tiny rumblings from the Earth’s shifting tectonic plates, together with the tiny gravitational fields from other nearby objects (including from the experimenters themselves!). Space-based experiments are being considered that would remove some of these diiculties and increase the accuracy of the experiments still further.

An alternative approach to the E
experiments is to use the Earth and Moon themselves as the two objects in free fall, and see if a diference in their acceleration can be detected. This idea was made possible after 1969, when the astronauts from Apollo 11 left a re’ector on the moon. By bouncing a laser beam of this re’ector it is now possible to determine the distance between the Earth and the Moon to an accuracy of about 1cm. Careful analysis of the resultant data has allowed the Universality of Free Fall to be probed to the level of about one part in a billion. Although this accuracy does not exceed the lab-based results, it is a slightly diferent type of experiment, as the Earth and Moon have their own sizeable gravitational fields. This allows a ’strong’ version of the same principle to be tested.

So, to summarize, there now exists good evidence, from a variety of diferent experiments, that the mass of an object is independent of both its position and the direction of its motion. There is also strong evidence that the speed of light is the same in every direction, and that all objects fall under gravity at the same rate. These are the foundational assumptions under which Newton’s and Einstein’s theories were constructed. Let’s now move on to experiments that aim to investigate these theories themselves.

Experiments that probe Newton’s law

Later on in this chapter we will consider the predictions of Einstein’s theory, which is now universally accepted to supplant that of Newton. However, we know that Newton’s inverse square law of gravity is a good enough approximation to Einstein’s theory to describe a wide variety of both terrestrial and astronomical phenomena. It’s therefore very much worthwhile testing Newton’s law to see exactly how well it describes gravity. Here we will consider some of the most important tests that have been performed so far.

The first laboratory test of the inverse square law was performed by Henry Cavendish, at the end of the 18th century. Cavendish’s experiment made use of a torsion balance, like the one used by E’tv’s (illustrated in Figure 7). Unlike E’tv’s, however, Cavendish positioned extra masses in order to make the torsion balance rotate. He put these masses close to the ones that were attached to the torsion bar. The gravitational force between the test objects hanging from the torsion balance, and the extra masses that Cavendish introduced, could then be inferred by the rate of rotation of the apparatus. The new masses pulled at the masses attached to the torsion bar through the gravitational force between them, and caused the bar to rotate. The results of Cavendish’s experiment thus allowed for the gravitational force to be probed over a distance scale of only 23cm. He found that gravity operated on these scales in a way that was entirely consistent with Newton’s inverse square law. Today, experimenters have tested these same ideas on much smaller distance scales.

The challenges involved in testing Newton’s law of gravity in the laboratory arise principally due to the weakness of the gravitational force compared to the other forces of nature. This weakness means that even the smallest residual electric charges on a piece of experimental equipment can totally overwhelm the gravitational force, making it impossible to measure. All experimental equipment therefore needs to be prepared with the greatest of care, and the inevitable electric charges that sneak through have to be screened by introducing metal shields that reduce their in’uence. This makes the construction of laboratory experiments to test gravity extremely dicult, and explains why we have so far only probed gravity down to scales a little below 1mm (this can be compared to around a billionth of a billionth of a millimetre for the electric force).

There are three groups of experimenters that have led the way in laboratory tests of gravity in recent times: one at the University of Washington, another at the University of Colorado, and a third at Stanford University. The Washington group took a pendulum with ten holes cut into it and held it over a disk that contained another set of holes. The pendulum was found to twist due to the missing gravitational force from the missing mass in the holes, and this allowed gravity to be measured down to scales as small as a twentieth of a millimetre. The groups at Colorado and Stanford, on the other hand, measured the gravitational field of a vibrating mass, and used this information to probe gravity all the way down to 1/40 of a millimetre. The results of these laboratory experiments have so far all been entirely consistent with Newton’s inverse square law of gravity, even on the very smallest of scales.

On larger distance scales, however, there are a variety of other tests that we must consider. To order the discussion of these tests sensibly, let’s first of all consider distances from tens of metres, up to about to about a few kilometres. These scales may seem like they should be the easiest to probe as they are closest to the type of distances we consider in our everyday lives. They are, however, quite problematic.

One of the best constraints that has so far been achieved on gravity over these everyday distance scales is due to measurements of the gravitational force that an object experiences at various heights up a tall tower. Towards the end of the 1980s, a team of scientists performed this test using the 600-metre-high WTVD tower in Garner, North Carolina. The change in gravity expected from Newton’s inverse square law at diferent points up the tower is easy to calculate, and the experimenters were able to measure it to good accuracy. At around the same time, other researchers were measuring the gravitational force due to the water in a reservoir filled to diferent levels. In essence, this allowed the water to be weighed and Newton’s inverse square law of gravity to be tested. Further tests, a couple of years later, were performed by measuring the gravitational attraction of sea water at diferent depths in the ocean. These experiments all produced results that were consistent with Newton’s inverse square law, and all at a level of accuracy of around 0.1 per cent.

On larger scales it starts to become possible to use astronomical data, which is much more accurate than trying to measure the gravitational field of the water in reservoirs and oceans. Distance scales of between a million and a few hundreds of millions of metres can be probed by studying the orbits of man-made satellites around the Earth, the orbit of the Moon, and the orbits of the planets around the Sun. The LAGEOS satellites, launched in 1976 and 1992, are particularly useful for experiments of this type’as are the orbits of the planets, which form closed ellipses (to first approximation) when the gravitational attraction is of the form given by Newton’s inverse square law. Observations of all of these bodies, and objects, have shown consistency with Newton’s law at accuracies of between one part in a million and one part in a billion.

We therefore have very good evidence that Newton’s inverse square law is a good approximation to gravity over a wide range of distance scales. These scales range from a fraction of a millimetre, to hundreds of millions of metres. The accuracy of the experiments that probe gravity over these distances varies wildly, between about 1 part in 1,000 (for scales of tens of metres) to about one part in a billion (for distances that correspond to the orbits of the planets). This is a great success, but it’s not the end of the story. Let’s now go beyond Newton’s law and start considering the new efects that arise from Einstein’s theory.

Experiments that probe Einstein’s theory

The experiments discussed earlier have all involved concepts that are familiar to most people who have studied physics at school: the constancy of mass; the Universality of Free Fall; and Newton’s inverse square law of gravity. In this section, I will introduce experiments that probe the more unfamiliar ground of Einstein’s theory of gravity. The specific efects that result from this theory are often small and dicult to detect experimentally. Nevertheless, they are very important, as they provide us with a window that can be used to view and understand gravity at a deeper level.

There are a large number of efects that result from Einstein’s theory. Here I am going to limit myself to describing four of them. These are the anomalous orbit of the planet Mercury; the bending of starlight around the Sun; the time delay of radio signals as they pass by the Sun; and the behaviour of gyroscopes in orbit around the Earth. These are four of the most prominent relativistic gravitational efects that can be observed in the Solar System. Further efects, which become apparent in more extreme astrophysical environments, will be discussed in Chapter 3.

Let’s start with the anomalous orbit of Mercury. Earlier on in this book, I stated that Newton’s theory explained Kepler’s observation that the planets follow elliptical orbits around the Sun. This is true for a single planet, but things start to get a bit more complicated when we consider the orbits of multiple planets simultaneously. This is because there exist gravitational forces between the planets themselves and not just between each planet and the Sun individually. These interplanetary gravitational forces are smaller but measurable, and have the efect of pulling the orbits of the planets of what might otherwise be perfect ellipses.

Physicists have known about the efects of interplanetary gravitational forces for a long time. These forces can be easily calculated within Newton’s theory, and astronomers have measured their consequences on the orbits of the planets for centuries. In fact, the existence of the planet Neptune was deduced in the mid-19th century by carefully studying the orbit of Uranus (the next nearest planet to the Sun). The orbit of Uranus was perturbed a little from where astronomers expected it to be, and the perturbation could be explained if there was a slightly larger planet a little bit further out in the Solar System. Urbain Le Verrier and John Couch Adams both predicted the existence of this planet in 1845’and by 1846 it had been observed. This was clearly a momentous achievement.

It therefore wasn’t too much of a shock when, in 1859, Le Verrier announced that the orbit of Mercury (the planet closest to the Sun) also seemed to deviate a little from the path that it was expected to take. No doubt buoyed by his prediction of the existence of Neptune, Le Verrier predicted that there must be another planet still closer to the Sun than Mercury. He even named it’Vulcan. This time, however, the discovery of the predicted planet never occurred. Despite much efort, no new object could be seen between Mercury and the Sun. Nevertheless, the anomalous orbit of Mercury persisted. It seemed as if its orbit was being dragged around the Sun by a gravitational force that had no obvious origin.

The mystery of the anomalous orbit of Mercury was solved in 1915, not by the discovery of any new massive bodies in the Solar System, but by Einstein’s revolutionary new theory. You see, according to Einstein’s new theory, the Newtonian gravitational force is only a rough approximation to the true nature of gravity. As well as the inverse square law, Einstein predicted that there should be new, smaller contributions to the gravitational force law. For an astrophysical system dominated by a large mass at the centre, like the Sun at the centre of the Solar System, Einstein calculated that the largest of these new forces should vary as the inverse of the distance cubed. Therefore, the closer one is to the Sun, the larger the contribution from this new force should be, relative to Newton’s inverse square law.

Mercury was, and still is, the closest known planet to the Sun, and so Einstein’s new gravitational force should be more in’uential on Mercury’s orbit than on the orbits of any of the other planets.

Einstein calculated that Mercury’s orbit should be dragged around the Sun by an extra 43 arcseconds per century (1 arcsecond is 1/360 of a degree). This is a tiny amount, but it is enough to be observed by astronomers. It is also consistent with the anomalous observations made by Le Verrier. So Einstein’s theory of gravity had its first observational success as early as 1915, by explaining the anomalous orbit of the planet Mercury.

Modern measurements of the orbit of Mercury are much better than those that existed in the 19th century. We now know the orbits of all the planets to very high accuracy, which is essential for calculating the deviation of Mercury’s orbit from an ellipse. The extra drag caused by Venus alone, for example, is more than six times that of the correction due to Einstein’s gravity. Its position therefore needs to be known to very high accuracy. This isn’t the largest source of uncertainty in modern observations though. That distinction goes to the uncertainty associated with the shape of the Sun itself. Any deviations from a perfectly spherical shape cause efects in the orbit of Mercury that could be confused with Einstein’s new gravitational force. The shape of the Sun is hard to know exactly, so the best we can currently do is to say that the anomalous orbit of Mercury is consistent with Einstein’s theory to an accuracy of about 1 part in 1,000.

The explanation of Mercury’s orbit is impressive but probably doesn’t count as a prediction, because the anomaly itself was known about long before Einstein was even born. What does count as a genuine prediction of Einstein’s theory is the bending of starlight around the Sun by its gravitational field. It was previously uncertain whether or not light should be afected by gravity, because in Newton’s theory the gravitational force is only between objects that have mass (which light does not). This ambiguity was removed in Einstein’s theory, as light simply follows the shortest paths available in the curved space-time, just like everything else. Einstein therefore predicted that light should be bent by the gravitational fields of massive objects.

Einstein’s calculations showed that the deflection of light would be greatest for beams that just skim the surface of massive objects. The most massive object in the Solar System is the Sun. But to see starlight that passes very close to the Sun we have to wait for a solar eclipse, otherwise the Sun’s own light overwhelms that of the much fainter stars. The first good opportunity to test the idea of bending starlight came after the end of World War I, in 1919. The expedition to measure the positions of the stars nearby the Sun, and therefore to test Einstein’s theory of gravity, was led by Sir Arthur Eddington.

Eddington’s expedition went to the island of PrÍncipe, in Africa, where the solar eclipse that was going to happen that year would be total. He made careful measurements, using the best photographic plates that were available at the time. The conditions were less than ideal, but Eddington succeeded in measuring the positions of the stars during the eclipse. He found that they had indeed shifted, just as Einstein had predicted, because the trajectory of the light had been bent by the gravitational in’uence of the Sun. Eddington’s results were suicient to confirm Einstein’s theory, but only within an accuracy of around 30 per cent.

Once again, modern observations have improved this result dramatically. This has been helped partly by the fact that there are, coincidentally, a number of very bright objects, known as quasars, which lie in just the right part of the sky to test Einstein’s prediction. As these objects pass behind the Sun, the de’ection of the light that they emit can be measured. Several million observations of these quasars have now been made using very large baseline interferometers (this is a type of telescope that mixes the signals from a number of diferent detectors to create a high-resolution image). The result of this work shows perfect consistency with Einstein’s theory, at a level of accuracy of about 1 part in 10,000.

A more recent prediction from Einstein’s theory is the time delay of radio signals that pass by massive objects. For some reason, it took until 1964 for scientists to notice that this efect is a necessary outcome of Einstein’s gravity, but it has now been measured in a number of diferent situations. These have included the observation of radio signals that bounce of planets as they are about to pass behind the Sun, as well as by looking at the signals that are emitted from man-made probes as they do the same. The first of these methods has the benefit of the position of the planets being very well known, and their trajectories being easy to predict. This stability makes them a good target, but the imperfections in their shape can cause some problems in interpreting the re’ected signals. Man-made probes, on the other hand, emit very easily predictable signals, but their trajectories can be somewhat less certain.

Radio targets that have been used to measure the time delay efect include the planets Mercury and Venus, and the space probes Mariners 6 and 7, Voyager 2, the Viking Mars Lander and Orbiters, and the Cassini probe. The most recent, and most accurate, of these observations was made using Cassini. The primary mission of this spacecraft was to observe Saturn, but its relevance for the study of gravity was perhaps best served in 2003, when it was announced it had confirmed the existence of the time delay efect with an accuracy of 1 part in 100,000. This was yet another spectacular confirmation of Einstein’s theory, and one which was achieved at higher accuracy than any previous experiment. This was, in part, due to the observations of the radio signals being made at multiple frequencies, which allowed interference from the Sun’s corona to be extracted.

Now let’s move on to the final experiment I want to discuss in this section: the behaviour of gyroscopes in orbit around the Earth. A gyroscope is essentially a spinning top, whose central axis is allowed to point in any direction. According to Einstein’s theory of gravity, there should be two new efects that can be observed when a gyroscope is put in orbit around the Earth. The first of these is a change in direction of the gyroscope’s axis of rotation, as it orbits the Earth. This efect, known as geodetic precession, is due to the curvature of space-time around the Earth. The second efect is known as frame-dragging, and is due to the rotation of the Earth efectively pulling space around with it as it rotates. This is an entirely new type of gravitational interaction, and so it is of great interest to see if it can be confirmed experimentally.

Although the prediction of the frame-dragging efect was made only a few years after Einstein published his new theory of gravity, it took until the 1960s before the efect on gyroscopes in orbit was calculated, and the experimental observation of the efects themselves did not take place until the 21st century. The LAGEOS satellite network provided an observation of the frame-dragging efect by measuring the change in the orbit of its satellites as they went around the rotating Earth. The long-awaited gyroscope experiment was performed by a mission called Gravity Probe B, in 2011. The geodetic precession and frame-dragging efects were measured by this experiment with accuracies of about 0.3 per cent and 20 per cent, respectively. The accuracy of the corresponding results from the LAGEOS satellites are estimated at between 5 and 10 per cent. All results were once again found to be consistent with Einstein’s theory.

So the overall picture we are left with is very encouraging for Einstein’s theory of gravity. The foundational assumptions of this theory, such as the constancy of mass and the Universality of Free Fall, have been tested to extremely high accuracy. The inverse square law that formed the basis of Newton’s theory, and which is a good first approximation to Einstein’s theory, has been tested from the sub-millimetre scale all the way up to astrophysical scales. We are also now in possession of a number of accurate experimental results that probe the tiny, subtle efects that result from Einstein’s theory specifically. This data allows us direct experimental insight into the relationship between matter and the curvature of space-time, and all of it is so far in good agreement with Einstein’s predictions. This is a truly spectacular confirmation of a theory that was borne out of almost pure thought. Einstein wanted to make a theory of gravity that was compatible with a speed of light that was measured to be the same by every observer. He did so, and we have now seen the numerous consequences of his revolutionary new picture of the Universe.

This isn’t the end of the story though: Einstein’s gravity has many more spectacular consequences, which we will discuss in the following chapters.

Chapter 3 Extrasolar tests of gravity

The Solar System allows us to investigate a number of diferent gravitational efects. Many of them can be measured to high accuracy, because we have easy access to the nearby planets and satellites. They are, however, quite weak gravitational fields. This is because all of the objects in the Solar System are, relatively speaking, rather slow moving and not very dense. If we set our sights a little further though, we can find objects that are much more extreme than anything we have available nearby.

Let’s start by considering the life of a star. First-generation stars are thought to form when the clouds of hydrogen gas that emerged from the Big Bang collapse under their own gravitational field, and become hotter and denser. Eventually nuclear reactions start occurring, and the outward pressure from these reactions becomes strong enough to balance the inward attraction of gravity.

This results in a star: a hot ball of collapsed gas undergoing violent nuclear reactions. This process of collapsing gas and nuclear reactions is, of course, also a rough description of what happens in our own Sun.

But this isn’t the end of the story. A star such as the Sun can only ever have a finite lifetime. Eventually the hydrogen required for nuclear fusion will run out, and the star will have to start burning other materials. This makes it swell into a red giant. In turn, even these alternative fuels must eventually run out, and the gravitational collapse of the star will resume. What stops the collapse at this point depends on the size of the star. A small star will settle down to become a white dwarf. This is a state in which the quantum mechanical properties of the electron prevent it from becoming any smaller. At this point it’s just not possible to fit any more electrons in the space that the star takes up.

If a star is a bit bigger, then instead of becoming a white dwarf it will end up as a neutron star. In a star of this type, the end of nuclear fusion leads to a collapse of its core. The star then collapses, which in turn causes a colossal explosion, known as a supernova. During this process the gravitational force is strong enough to force the electrons and protons to combine into neutrons. The electron pressure is then absent, and the star collapses until the neutrons are so dense that no more can fit into the same space. The end result is a star that has a density that’s comparable to the nucleus of an atom. In a sense, a neutron star can be thought of as a giant atomic nucleus (but without any protons and without electrons orbiting it). Neutron stars are very small and very dense. They are denser than anything that exists in the Solar System, and tend to move at extremely high velocities.A neutron star isn’t the most extreme object that can result from a collapsing star though. That title goes to a type of object called a black hole. If a star is so large that even the pressure from neutrons can’t support it, then it will collapse to a black hole.

A black hole is one of the most extreme objects that can exist in nature. All that is really left after a collapse of this type is the gravitational field itself. A black hole consists of a region of space-time enclosed by a surface called an event horizon. The gravitational field of a black hole is so strong that anything that finds its way inside the event horizon can never escape. Even light. Hence the name.In this section we are going to consider star systems that contain some of the objects just described. Astronomers have now discovered a large number of these systems, and observations of them have allowed us to explore gravity in ways that are simply impossible in our own Solar System. The extreme nature of these objects amplifies the efects of Einstein’s theory, so that, even though they are very far away, they ofer us a new and exciting window through which to see the efects of gravity.

The Hulse–Taylor binary pulsar

The Hulse—Taylor binary pulsar, or PSR B1913+16, is a star system that contains two neutron stars in orbit around each other. The remarkable thing about this system is that one of the neutron stars is what is known as a pulsar (an abbreviation of ‘pulsating star’). These are stars that appear to emit regular pulses of radiation, when viewed from Earth. This radiation is the result of the strong magnetic fields that surround the star and that cause powerful beams to be projected outwards from its surface. Together with the rapid rotation of neutron stars, these beams appear as rapid ’ashes of radiation to distant astronomers, much like the signal from a lighthouse appears as ’ashes of light to nearby sailors.

Pulsars were discovered for the first time in 1967, by Jocelyn Bell Burnell and Antony Hewish. These astronomers saw the characteristic ’ashes of radiation that are now known to signal the existence of a pulsar, but at the time were quite unexpected. Indeed, it was originally thought that these ’ashes could be signals from another civilization. The astronomers even went as far as to call the source of the signal LGM-1 (Little Green Men-1). Later, similar signals were discovered from other parts of the sky, and it was realized that the pulses were from a rapidly rotating neutron star. At present we know of the existence of thousands of pulsars. In the future we are likely to find many more.

The significance of the discovery of PSR B1913+16 by Joseph Taylor and Russell Hulse in 1974 was not that it was a pulsar, but that it was a pulsar in orbit around another neutron star. This information was obtained by noticing that the arrival times of the pulses varied slightly. That is, the arrival times of the pulses were sometimes three seconds earlier and sometimes three seconds later. The period over which this change happened was about seven hours and forty-five minutes. As the pulsar emitted seventeen pulses a second, it was possible to make a smooth chart that showed a clear pattern. The only explanation was that the pulsar was in orbit around another object, and that the radius of the orbit was about three light seconds (that is, the distance light travels in a period of three seconds, equal to about a million kilometres).

So the Hulse—Taylor pulsar was known to be part of a binary system, but it was still not possible to see the other object in the system. This meant it couldn’t be a regular star, but it had to be something with a similar mass to a star. It was decided that the most plausible explanation was that the pulsar was part of a binary system, with the other body in the system being a neutron star that wasn’t pulsating (or, at least, wasn’t sending any pulses of radiation in our direction). Such a system is of particular interest for the study of gravity because the objects involved are so dense and are orbiting each other at such extremely high velocities. This makes the small efects that are predicted from Einstein’s theory much more prominent. The fact that one of the neutron stars was emitting a signal that was as accurate as an atomic clock was the icing on the cake. Information could be extracted from this signal about the details of the gravitational interaction.

Data has been collected from the Hulse—Taylor binary pulsar since its discovery in 1974. This has been done primarily with the Arecibo telescope in Puerto Rico, which is a 305-metre-wide radio antenna (and which will be familiar to anyone who has seen the film GoldenEye). It is this large collection of data that makes this particular binary pulsar system special. Later, I will discuss some other binary pulsar systems that are now known to exist, but none of these have been observed for as long as the Hulse—Taylor pulsar. The large database that has been constructed for this system allows for some very precise tests of gravity to be performed.

Let’s now consider the specifics of how information about gravity is encoded in the pulsar’s signal. One way that this happens is through time delays and redshift efects that the signal experiences, as it travels through the gravitational field of the companion neutron star. You will recall that both of these efects have been measured in the Solar System. Now they can be measured in two distant neutron stars, which orbit each other at a distance that is similar to the radius of our own Sun. Another efect that will be familiar, and that is visible in the Hulse—Taylor binary system, is the precession of the orbit. Just as the orbit of Mercury precesses around the Sun so too the neutron stars in the Hulse—Taylor binary system precess around each other. To compare with similar efects in our Solar System, the orbit of the Hulse—Taylor pulsar precesses as much in a day as Mercury does in a century.

A final efect which it is possible to measure with the binary pulsar, and which is impossible to measure in the Solar System, is the change in period of an orbit due to the emission of gravitational waves. The existence of gravitational waves has not yet been discussed, but it is a definite prediction of Einstein’s theory: there should exist ripples in space-time that can carry energy out of a system. This is a phenomenon that has no counterpart in Newton’s theory, and is therefore of particular interest for testing Einstein’s gravity. I will explain gravitational waves in more detail in Chapter 4, including attempts to measure them directly. For now, I just want you to keep in mind that they were predicted by Einstein, and that they should act to remove energy from the binary pulsar system, as they are emitted from the orbiting bodies.

So there are three relativistic efects that can be measured in the arrival times of the pulses from the Hulse—Taylor system. These are the time delay efect from the gravitational field of the companion neutron star; the precession of the orbit of each star; and the decrease in orbital period due to the loss of energy through gravitational waves. Any two of these pieces of information can be used to infer the masses of the two neutron stars, which up until this point have not been measured in any way. The third piece of data can then be used to see if Einstein’s theory is correct.

Using this method the masses of the two neutron stars in the Hulse—Taylor binary system can each be determined to be about 1.4 times that of the Sun. This is inferred using the size of the time delay efect, which can be measured to about 0.02 per cent accuracy, and the amount of precession of the orbit, which can be measured to an accuracy of about 0.0001 per cent. From the masses of the two stars, we can then calculate what Einstein’s theory predicts for the amount of energy lost through gravitational waves, and what this means for the orbital period. It turns out that Einstein’s theory predicts the orbits should decrease by about 3.5 metres per year. This is exactly what is measured, up to the accuracy of the observations, which is currently around 0.2 per cent. This is another spectacular confirmation of Einstein’s theory of gravity, and one for which Hulse and Taylor were awarded the Nobel Prize in Physics in 1993.

One last efect that is expected to occur in the Hulse—Taylor pulsar, is geodetic precession (the change in direction of the axis of a spinning top). This efect will be encoded in the shape of the signals that arrive from the binary pulsar, because the pulsar itself acts as a spinning top in its orbit around its companion. Although it has probably been observed, the interpretation of this data is currently not good enough to give another precision test of Einstein’s theory. This is mainly due to the unknown details of the region that emits the pulses of radiation on the surface of the neutron star.

The Hulse—Taylor binary pulsar ofers some excellent tests of gravity, but while it is unique historically, it is now no longer the only binary pulsar that we know about. Let us now consider newly discovered systems that in some cases can already rival the tests of gravity we can perform with the Hulse—Taylor system, and which promise to outstrip it in the future.

Other binary pulsar systems

Due to its historical significance, the Hulse—Taylor binary pulsar has the privilege of being named after its discoverers, as well as having a scientific name (PSR B1913+16). Other binary pulsar systems are usually just referred to by their scientific names. The convention that’s been adopted for this is to call the system PSR, for ’Pulsating Source of Radiation’, and then to write its position on the sky in terms of right ascension and declination (these are coordinates that indicate positions on the sky). The letter ‘B’ or ‘J’ is also used to denote whether the pulsar was discovered before or after 1993 (the ones discovered after this date usually have their position recorded to higher accuracy).

Up until 2006, we only knew about the existence of eight other binary pulsar systems that had orbital periods of less than a day. Some of these systems have special properties that make them particularly interesting for studying gravity, and although they haven’t been observed for as long as the Hulse—Taylor pulsar, they still ofer new insights into how gravity works. In the rest of this section, I will give a very brief summary of some of the most interesting of these systems, before finishing of with a look forward at what the future holds for extrasolar tests of gravity.

Let’s start with PSR B1534+12. As the name shows, this binary pulsar system was discovered before 1993. The remarkable thing about this system is that we see it almost exactly edge on. That is, our line of sight to the system lies almost exactly in the orbital plane of the two neutron stars. This amplifies the time delay of the radio signals, as at some points in the orbit the radio waves from the pulsar have to pass very close by to its companion before they can make their way to Earth to be observed by our astronomers. The pulsar also has particularly strong and narrow radio pulses, which makes it a very good clock. Unfortunately the distance to this system is not known with much accuracy, which limits the precision with which it can be used as a test-bed for gravity. To date, this system has therefore not provided as much information about gravity as the Hulse—Taylor pulsar.

Another binary pulsar system of special interest is PSR J1738+0333. This system is thought to contain a pulsar in orbit around a white dwarf (the bigger brother of the neutron star, described earlier in this section). The special thing about this system is that the two objects involved are very diferent from each other. This allows for a new test of gravity. It just so happens that in Einstein’s theory the emission of gravitational waves from a binary system isn’t particularly sensitive to whether or not the two objects are similar or diferent. Most of the possible alternatives to Einstein’s theory do, however, predict sensitivity to this type of diference. By looking at how much energy is lost to gravitational waves in a system such as PSR J1738+0333, it is therefore possible to provide an additional test of Einstein’s theory. If Einstein were wrong, then we should expect PSR J1738+0333 to lose energy at an anomalously high rate. So far, no such anomaly has been detected, which provides still further verification of Einstein’s theory.

However, probably the most exciting system that was known about before 2006 is PSR J0737-3039A/B. This system was discovered in 2003, and has a number of almost unbelievable properties. Chief amongst these is the fact that both the neutron stars in the system were observed to be emitting pulses of radiation leading to it being called the double pulsar. No longer was it the case that the second object in the system was simply a passive companion, providing only a gravitational field through which the radio signals of the pulsar travelled. In this system both objects were emitting pulses of radiation, which allowed both of their orbits to be tracked in ways that were not previously possible. As if this amazing discovery wasn’t enough, however, it also turned out that the two pulsars were moving at extremely high velocities (even by the standards of binary neutron stars), and that the system was almost exactly edge-on. This combination of properties greatly enhanced the efects of relativistic gravity in the system, to such an extent that by 2008 one of the pulsars had precessed so far that its radio pulses went completely out of view.

No longer do we have to observe for many decades to see the subtle efects of Einstein’s gravity; with the double pulsar system we could see them in just a few short years. It is now the case that PSR J0737-3039A/B provides even better evidence for the existence of gravitational waves than does the Hulse—Taylor pulsar. While both pulsars were visible, this system provided six ways to measure the gravitational fields of the neutron stars compared with the three that are available for the Hulse—Taylor system. After determining the two unknown masses of the neutron stars, this leaves four independent tests of gravity in a single system. Yet again, Einstein’s theory passed these tests with ’ying colours.

The future

While astonishing discoveries have already been made by observing gravitational systems outside of the Solar System, it is highly likely that we have even more to look forward to in the future. The reason for this optimism is partly due to the construction of a new generation of telescopes, the largest of which is known as the SKA (Square Kilometre Array). The SKA will be a telescope designed to receive radio waves from distant sources, and it will be built on a scale never before seen on Earth.

The SKA will consist of thousands of radio antennas and dishes, spread over distances of several thousand kilometres in South Africa and Australia as well as several other sub-Saharan states.

The total collecting area of the telescope (the sum of all dishes and antennas combined) will be one million square metres. It will be fifty times more sensitive than any other radio telescope ever built, and will require a computer network with a capacity larger than all current internet traic combined. The estimated cost of the SKA, at the time of writing, is around €2 billion, which is being supplied by an international collaboration between Australia, New Zealand, Canada, China, India, South Africa, Italy, Sweden, the Netherlands, the UK, and Germany. By any standard, the SKA is a monumental undertaking.

A project the size of the SKA takes a long time to plan and build, but when it starts taking data in 2020 it will allow experiments to be performed that were never previously possible. For the purposes of studying gravity, one of the most important of these will be the measurement of large numbers of pulsars. First of all, the SKA is very likely to discover a large number of new binary pulsar systems, each of which can be used to study gravity in the way just described. Second, and perhaps even more exciting, the SKA will likely detect hundreds of rapidly rotating microsecond pulsars (i.e. pulsars that rotate millions of times a second). The idea is that by carefully measuring the arrival times of the signals from each of these pulsars, the SKA will be able to directly measure the efect of long wavelength gravitational waves as they pass through our part of the Universe. In this way, the SKA promises to be a giant gravity wave detector (something I will explain in more detail in Chapter 4).

It is expected that the observations of gravitational phenomena made by the SKA will be about a hundred times more accurate than those made by observing bodies within the Solar System. This will be a huge leap forward. At present, binary pulsar observations are just starting to overtake observations made in the Solar System as the best testing ground for gravity. The SKA will do considerably better. Beyond even this though, the SKA ofers a few more tantalizing possibilities for testing gravity. One of these involves using the SKA to test how gravity works over very large distance scales in the Universe. I will return to this in Chapter 5. Another is the possibility of discovering a pulsar in close orbit around a black hole. A black hole is expected to be the most extreme gravitational field that exists anywhere in the Universe. It is the result of a large star collapsing in on itself at such a rate that nothing can stop it. The existence of binary systems comprised of a pulsar and a black hole are expected to be rare, but if they do exist, then there’s a good chance the SKA will find them. Such a system would provide the opportunity to test gravity in the most extreme of all environments. It is a very exciting prospect.

Another, more immediate, reason for being hopeful about the future of extrasolar gravitational physics is the recent discovery of another new type of pulsar system. In 2014, a team of astronomers announced that they had discovered a pulsar in orbit with not one, but two, white dwarfs. They named this triple system PSR J0337+1715. The orbits that are possible in a triple star system are much more varied than the possibilities in a binary system, and it looks as though the system is structured in a hierarchical way, such that the pulsar is in a close orbit with one of the white dwarfs, while the second white dwarf orbits them both at a larger distance. The outer white dwarf appears to be accelerating the orbits of the inner pair, providing a new type of laboratory within which strong gravitational physics can be studied.

It’s expected that new telescopes such as the SKA will aid the study of both double and triple pulsar systems. It may even be the case that it allows astronomers to observe the frame-dragging efect (described in Chapter 2), in which space itself is dragged around with the rotating stars. Such a measurement would not only be of interest for the study of gravitational physics, but also for astrophysicists who want to know how matter inside neutron stars behaves. If such observations could be made, they would allow us to study a material with a density of around a trillion kilograms per cubic centimetre.

Chapter 4 Gravitational waves

Gravitational waves have already been mentioned, in Chapter 3. Now let’s consider them in a little more detail. You will recall from Chapter 1 that, in Einstein’s theory, gravity is due to the curvature of space-time. Massive objects like stars and planets deform the shape of the space-time in which they exist, so that other bodies that move through it appear to have their trajectories bent. It is the mistaken interpretation of the motion of these bodies as occurring in a flat space that leads us to infer that there is a force called gravity. In fact, it is just the curvature of space-time that is at work.

The relevance of this for gravitational waves is that if a group of massive bodies are in relative motion (such as in the Solar System, or in a binary pulsar), then the curvature of the space-time in which they exist is not usually fixed in time. The curvature of the space-time is set by the massive bodies, so if the bodies are in motion, the curvature of space-time should be expected to be constantly changing. The scientific way to describe this situation is to say that, in Einstein’s theory, space-time is a dynamical entity.

As an example of this, consider the supernovae that we discussed previously. Before their cores collapse, leading to catastrophic explosion, they are relatively stable objects, much like our own Sun. In this stage of their life they should therefore be expected to curve the space-time around them in the same way that the Sun does, and should therefore have a similar gravitational field. After they explode they settle down to a neutron star or a black hole, and once again return to a relatively stable state, with a gravitational field that doesn’t change much with time. During the explosion, however, they eject huge amounts of mass and energy. Their gravitational field changes rapidly throughout this process, and therefore so does the curvature of the space-time around them.

Like any system that is pushed out of equilibrium and made to change rapidly, this causes disturbances in the form of waves. A more down-to-earth example of a wave is what happens when you throw a stone into a previously still pond. The water in the pond was initially in a steady state, but the stone causes a rapid change in the amount of water at one point. The water in the pond tries to return to its tranquil initial state, which results in the propagation of the disturbance, in the form of ripples that move away from the point where the stone landed. Likewise, a loud noise in a previously quiet room originates from a change in air pressure at a point (e.g. a stereo speaker). The disturbance in the air pressure propagates outwards as a pressure wave as the air tries to return to a stable state, and we perceive these pressure waves as sound.

So it is with gravity. If the curvature of space-time is pushed out of equilibrium, by the motion of mass or energy, then this disturbance travels outwards as waves. This is exactly what occurs when a star collapses and its outer envelope is ejected by the subsequent explosion. The violent process that occurs in the star causes a disturbance in the curvature of space-time, much like the stone falling into the pond causes a disturbance in the water. And again, just as in the examples just given, the disturbance propagates outwards as waves.

The speed with which waves propagate usually depends on the medium through which they travel. For example, we know that sound waves travel slightly faster in warm air than they do in cold air. The medium for gravitational waves is space-time itself, and according to Einstein’s theory, they propagate at exactly the same speed as light. Just as with light, they are also expected to have a speed that is independent of the motion of the person who observes them, and that is independent of the motion of their source. They therefore propagate information at the maximum possible speed, as nothing can travel faster than light.

The efect of a gravitational wave

To try and make sense of what a gravitational wave is, it might be useful to consider what its efects should be on a group of objects as it passes through them. For example, if you were trying to describe the waves on a pond to an alien who wasn’t familiar with water, you might start by suggesting that the efect of the wave is to make the lilies on the surface of the pond move up and down in a smooth, repetitive way. Let us consider the corresponding situation with gravitational waves.

Let’s start by considering a uniform cloud of gas ’oating in space. This removes the efect of the Earth’s own gravitational field, which is many times stronger than any gravitational wave that we are ever likely to see, as well as removing any disturbance the gas might feel from interacting with anything else. If the gravitational wave travels through the cloud of gas, as in Figure 8, then the principal efect of the wave is to displace the gas in the directions transverse to its direction of propagation. That is, if the wave travels from left to right, then the particles in the gas are displaced up and down, and in and out of the plane of the page.

The efect of the gravitational wave on the cloud of gas may initially make it look a little bit like the wave is being supported by the gas itself, much like the wave in the pond is supported by the water. It is, however, quite diferent. With the gravitational wave it is space-time that carries the wave. The efect of the gravitational wave on the gas is therefore more analogous to the efect that the water wave has on a lily that sits on the surface of the pond, rather than the water in the pond itself. That is, the gravitational wave is not a wave in the gas, but rather a propagating disturbance in the space-time in which the gas exists.

8. An illustration of a wave passing through a cloud of gas. The wave travels from left to right, and displaces the particles of gas up-and-down, and in-and-out of the plane of the page.

In fact, what the gravitational wave is really doing in this example is changing the amount of space that exists in the directions that are transverse to its direction of propagation. This means that although the atoms in the gas might be closer together (or further apart) than they were before the wave passed through them, it is not because the atoms have moved, but because the amount of space between them has been decreased (or increased) by the wave. The gravitational wave changes the distance between objects by altering how much space there is in between them, not by moving them within a fixed space. This is only possible because of the fact that space is not fixed in Einstein’s theory but is itself dynamical.

To consider the efects of gravitational waves in more detail, let us now consider a ring of particles, and think what would happen to this ring if a gravitational wave passed through it. This is illustrated in Figure 9, where in this case the gravitational wave is being imagined to be coming upwards, out of the plane of the page. The efect of the wave is only really in the directions transverse to its direction of propagation. A ring of particles in the plane of the page should therefore give us a pretty good idea of its consequences.

9. The deformation that a ring of particles would experience if a gravitational wave passed through it, in an upwards direction (i.e. coming directly out of the page). The leftmost image shows the initial configuration, and the other images (from left to right) show the ring at four subsequent instances of time.

If the particles are initially arranged in a perfect circle, and are not attached to anything or each other, then the efect of the wave will be to compress the circle in one direction and to stretch it in another. The result is that the particles start to form an ellipse. As the wave passes through, it stretches the circle smoothly until it reaches a maximum deformation, at which point it stops and then reverses the process until the direction in which it initially stretched is at a minimum. This stretching and squashing in diferent directions is illustrated in Figure 9, and continues until the wave has passed.

The consequences of the emission of gravitational waves has already been discussed for the binary pulsar. The waves carry energy away from the system, so that the two neutron stars slowly circle in towards each other. The measured rate of in-spiral in the binary pulsar has given good evidence for the existence of gravitational waves, but it is of great scientific interest to try and see the efects of these waves directly as well. This was done for the first time in September 2015 by the LIGO experiment. The direct detection of gravitational waves is particularly exciting because it provide us with an entirely new way to view the Universe. For the first time, we don’t need to rely on light to see distant objects as we can now look at them through their gravitational fields directly. This allows us to see what happens, for example, when black holes collide.

The direct detection of gravitational waves also allows for new and exciting tests of Einstein’s theory of gravity. In general, one could conceive of a number of diferent possible efects from a passing gravitational wave. For example, the area of the circle of particles in Figure 9 could have been changed, or there could be deformations of space along the direction of propagation of a gravitational wave (as well as in transverse directions). It is the equations that Einstein proposed for the curvature of space and time that forbids these possibilities within his theory, but if he was wrong then they could be there in nature. By using experiments like LIGO, we can look to see if gravitational waves have the specific efects that Einstein predicted. This provides yet another test of his theory. Beyond this, being able to gain a new window into what happens when black holes collide provides a number of exciting possibilities for the further study of gravitational physics.

Gravitational wave detectore

The existence of gravitational waves was first predicted by Einstein in 1916, and, after nearly a century of efort, they were detected for the first time in 2015. The reason it took so long to do this is largely a consequence of the extremely low amplitude of the signal. In the diagram shown in Figure 9, the efect of the gravitational waves was enormously exaggerated in order to try and make it easier to visualize their efect. In reality, the ’uctuations in the shape of the ring should only be expected to be at the level of about one part in a hundred million trillion. That is, if we made a ring of particles that was a 1,000km across, we shouldn’t expect its shape to change by more than a trillionth of a centimetre. This is obviously very dicult to detect.

Despite the diculty, or perhaps because of it, a huge amount of efort has been expended in trying to detect gravitational waves directly. Much of the early history of this work involved what are now called Weber bars. These instruments, named after Joseph Weber of the University of Maryland, consisted of large cylinders of metal. They were about a metre wide, and a couple of metres long. The idea was that if a gravitational wave passed through the Earth, and hence also through the detector, then it might cause the bar to start ringing, like a bell hit by a hammer. For this to happen, the gravitational wave needs to be of just the right frequency. If such a wave were to exist, it should be expected to cause small vibrations in the bar.

The detectors that were used to see if the bar was vibrating were sensitive enough to detect changes in length of 1 part in 1,000 trillion. Remarkably sensitive as this is, it’s not enough to measure the gravitational waves that we now know to exist. This didn’t stop a few false alarms being sounded though. In 1968, Weber claimed he had evidence for the existence of gravitational waves, which would have made him a prime contender for a Nobel Prize. Unfortunately, the claimed detection couldn’t be reproduced, and it is now widely believed that it was erroneous.

Some modern versions of the Weber bar are still being used today. An example is the MiniGRAIL experiment in Leiden. It consists of a 1,150kg metal sphere, and is about 1,000 times more sensitive than the ones used by Weber himself. However, most modern attempts at detecting gravitational waves use a diferent technology, known as interferometry. Detectors based on this technology are similar, in principle, to the Michelson—Morley device described in Chapter 2. The modern devices are, however, much, much larger. The largest of all, at the time of writing, is the LIGO detector, in the USA.

LIGO, or the Laser Interferometer Gravitational-Wave Observatory, has two bases of operation; one is in Livingston, Louisiana, and the other is in Richland, Washington. Each site contains a giant interferometer. The interferometers consist of two ‘arms’, which are built to be at right angles to each other, as illustrated in Figure 6. Each arm is several kilometres long, and contains a tube of near vacuum about a metre wide. Lasers are fired down each of these tubes, and are re’ected from hanging masses at the end of each. When the laser light makes its way back to the point where the arms meet it can be studied, and the length of each of the arms inferred from the pattern it makes when the two laser beams interact. When a gravitational wave passes through them, the arm lengths change, and the patterns made by the interacting laser light also change.

The LIGO detector is exquisitely accurate, and has a sensitivity that is about a million times greater than a Weber bar. The technical challenges required to reach this accuracy are phenomenal. The experimentalists have had to overcome all kinds of rogue signals that pollute the data. These range from seismic noise, in which the tiny internal motions of the Earth cause the re’ecting objects to vibrate, to the vibrations caused by a strong wind outside. In fact, the detectors are now becoming so precise that one of the limiting factors is currently the fact that laser light is made up from photons, so that a continuous signal from the reflecting objects is not possible.

Despite these great problems, and despite the enormous financial, political, and engineering diculties it has taken to overcome them, the LIGO detector has ultimately been a great success. On 14 September 2015 it detected, for the first time in human history, direct evidence for the existence of gravitational waves from colliding black holes. It’s almost impossible to overstate the significance of this event, which will probably go down in history as one the greatest scientific achievements of the modern age. So let’s consider it in more detail.

The observation of gravitational waves by LIGO

At precisely 45 seconds past 9:50 a.m. (Greenwich Mean Time), on 14 September 2015, the LIGO gravitational wave detector at Livingston, Louisiana, detected a fluctuation in their interferometer. This signal lasted for only 0.2 seconds, and appeared to make the 4km-long arms of their interferometer change length by about 1/1,000 the width of proton. About 0.007 seconds later, a similar signal was detected by the detector in Hanford, Washington. This set alarm bells ringing, and the scientists who ran the experiment were soon in little doubt: they had detected a gravitational wave passing through the Earth.

Before we think about the event that caused the wave, let’s consider the signal itself. If you were to look at the data from either LIGO site, it would appear as little more than a blip on the back of the constant noise that exists within the detectors. The signal, at its peak, was only ever about twice the amplitude of the random noise that pollutes the detectors’ output. This makes it dicult to see, and dicult to confirm it as a true detection. The reasons why the scientists were so convinced it really was a gravitational wave are twofold. First, the wobble in the two detectors, at the two diferent locations, were very similar. It might be possible to have a random tremor at one location on the Earth that caused something that looked like a gravitational wave, but to have exactly the same tremor at almost the same time at two diferent geographic locations is highly unlikely. Second, and just as importantly, the LIGO scientists knew what shape the wave should take. This allowed them to scan the data, in a process known as match filtering, to look for their signal. Taking these two facts into account means that the LIGO scientists are more than 99.999 per cent confident that the wobbles they observed really were due to a passing gravitational wave and not to any spurious source of noise.

This result is clearly an enormous achievement for the experimental team at LIGO, who produced and operated two of the most sensitive pieces of scientific equipment that have ever existed. It is, however, also a huge achievement for a very large number of theoretical physicists. This is because the match filtering process I mentioned before, and which is crucial for the detection, requires the detailed modelling of some of the most extreme gravitational fields in nature: merging black holes. It is only by understanding the details of what happens when black holes collide that scientists were able to produce filters for the expected gravitational wave signals that LIGO might detect, and this is a lot more dicult than it sounds. There are a number of diferent ways that two black holes can merge, and an awful lot of mathematical and computational work has been needed to understand exactly what Einstein’s theory predicts for the gravitational waves that should be emitted from such systems.

I won’t go into the lengthy details of any of the mathematics, but we should consider the actual astrophysical event that led to the emission of the waves. From the shape of the signal in the detectors, and the detailed modelling of merging black holes described earlier, it is thought that the waves were created by two black holes that spiralled towards each other before eventually merging, and settling down to form one large black hole. The two black holes that came together in this scenario were around twenty-nine and thirty-six times the mass of the Sun, and they settled down to a final end state in which the resulting black hole was about sixty-two times the mass of the Sun. This might sound rather peaceful, but it’s actually one of the most violent processes that can occur in nature.

The astute reader will notice that twenty-nine plus thirty-six does not equal sixty-two. This is because the gravitational waves emitted during the merger carried away 3 solar masses of energy (remember that E = mc^2
, in Einstein’s theory). This is an extraordinary amount of energy for a system to lose, and goes some way to illustrating why it should be thought of as a violent event. To give some context to this number, consider the following: while these two black holes were emitting gravitational waves, they were giving out more energy than all the stars in the observable universe put together. They were also observable from 1.3 billion light years away, which is a sizable fraction of the entire observable universe. This, then, was a very extreme event, and a highly exciting one, from the point of view of gravitational physicists.

Future prospects

Although gravitational waves have now been detected, there’s no reason for us to rest on our laurels. The detection by LIGO, as well as being the end of a long quest, is also the start of a new type of astronomy. One part of the reason for this hopeful statement is that LIGO will, with any luck, continue to detect more and more of these events. Another, however, is due to the new generation of gravitational wave detectors that is being planned and built. This includes the possibility of building a LIGO site outside of the USA, with India being the current favoured location. An extra site of this type would increase the ability of LIGO to determine the direction on the sky from which a gravitational wave originated, and hence improve the prospect of using gravitational waves as a new tool for doing astronomy without light.

Beyond LIGO, another possibility for the future detection of gravitational waves is a project called eLISA (the Evolved Laser Interferometer Space Antenna). The eLISA mission is a European Space Agency proposal to create a detector in space. This brings certain benefits over Earth-based gravitational wave detectors, the foremost of which is that it would be immune to seismic noise. This means it would be sensitive to a range of frequencies that is extremely hard to detect from the ground. It could also be much larger than Earth-based detectors, as the lasers can simply be fired between satellites, without any protective housing. The proposal for eLISA is to create a triangle of laser beams between three diferent satellites, each of which is separated from the others by a few million kilometres. When it comes to gravitational wave detectors, bigger is better’so eLISA is a great prospect for future detections.

But while the arm lengths of eLISA can be huge, and the seismic noise is completely absent, it does face its own challenges. The environment in space is close to vacuum, but isn’t entirely empty.

The charged material that the Sun throws of should be expected to interfere with any space-based detector of this kind, as should the cosmic rays that continuously bombard the Earth. On the ground we are shielded from this interference by the Earth’s atmosphere and magnetic field, but a gravitational wave detector in space would not be. And, of course, it is much more diicult to arrange and maintain an experiment when it’s in space. Nevertheless, there are high hopes that eLISA will be built, and that it will detect gravitational waves in space.

One further way in which gravitational waves might be detected in the future is using cosmological observables. Cosmology is the study of the state and evolution of the Universe as a whole, and there are considerable prospects for finding the fingerprints of gravitational waves in a number of upcoming cosmology missions. We will discuss these in more detail in Chapter 5.

Chapter 5 Cosmology

Cosmology began as a scientific discipline at the beginning of the 20th century, with the work of Albert Einstein and Edwin Hubble. It was Einstein that provided the theory within which it was possible to sensibly consider the entire Universe, and it was Hubble that provided some of the first observations that showed the Universe was expanding. Before the 20th century neither of these things had been possible, and cosmology had remained almost exclusively within the province of religion and philosophy. Since then it has flourished as a science, and it is currently in the process of becoming a precision science.

The gravitational interaction is fundamental to the study of cosmology, as gravity dominates over all other forces on large distance scales. Unfortunately, it is not possible to create consistent models of the Universe with Newton’s theory of gravity alone. This is because Newton assumed that his inverse square law of gravity is applicable to everything in the Universe, and that it is transmitted instantaneously. This means that, according to Newton, the gravitational field we experience on Earth should be a sum of the gravitational fields of every object that exists in the entire Universe. This isn’t necessarily a problem by itself, but it does become problematic if you try to add up the gravitational fields of infinitely many objects. In this case it turns out that Newton’s theory tells us that the total gravitational field at any given point in the Universe depends on the order in which we add up the gravitational fields of all of these objects. This is obviously not a very satisfactory situation.

Of course, we now know that Newton’s theory is only an approximation of the more complete theory developed by Einstein. Thankfully, the problem described above does not occur in Einstein’s theory. Instead, we get a rich set of models that are self-consistent, and that can be used to model the Universe we see around us. In fact, because of Einstein’s focus on space and time, we get a much deeper understanding of the Universe through his theory than we ever would have got from Newton’s. This is because, using Einstein’s theory, we are not only able to model how objects in the Universe move, with respect to each other, we are also able to create a model of how the space and time that make up the Universe behave. Let us now consider this in more detail.

The modern history of cosmology

Modern cosmology, as we now understand it, began in Russia in the early 1920s with the work of Alexander Friedmann. Using the recently published General Theory of Relativity, Friedmann showed that a universe that was the same at all points in space, and that looked the same in all directions, should be expected to either expand or contract. This remarkable prediction must have come as quite a surprise, because at this time no astronomer had been able to reach such a conclusion using observations. Nevertheless, Friedmann was able to produce a set of equations that such a universe would have to obey, and had even been aware that the geometry of space in these models could either be flat or have positive or negative curvature. That is, he was aware that there existed solutions to Einstein’s equations in which the geometry of space could be curved, like the surface of a giant three-dimensional sphere, or the surface of saddle (see images in Figure 10).

10. Examples of spaces with constant positive curvature (k 〉 0), vanishing curvature (k = 0), and negative curvature (k 〈 0), respectively.

Friedmann was a pioneer, but his work was not widely recognized at first. He was initially criticized by Einstein, who thought he was in error. Einstein later introduced an alternative model of the Universe, which he forced to be static by introducing a new term into his equations that he called the cosmological constant. This model was shown to be unstable by the Belgian priest Abb’ Georges Lema’tre, who was developing similar ideas to Friedmann towards the end of the 1920s. In fact, Lema’tre, who had been a colleague of Sir Arthur Eddington, had written in a scientific paper in 1927 that observations suggested that the Universe was indeed expanding, in what later became known as Hubble’s law. The article containing this monumental discovery was initially published in French, in an obscure Belgian journal. Strangely, when it was translated into English, in 1931, the section on Hubble’s law was missing. Nevertheless, Lema’tre is remembered today as one of the most important figures in the development of modern cosmology.

Friedmann and Lema’tre were both mathematicians, and although the latter had a good knowledge of astronomy, it was not until the astronomer Edwin Hubble published his famous results in 1929 that cosmology really got started as an observational science. Hubble showed the world that the Universe was expanding. He did this by calculating the distances to what we now refer to as galaxies, and by using known information about their motions. Hubble showed that the recessional velocity of a galaxy is proportional to its distance from us (so that, e.g., if galaxy A is twice as far away as galaxy B then it should recede at twice the velocity). This is just what LemaÎtre had predicted from Einstein’s theory, and it proved beyond reasonable doubt that the Universe was indeed expanding. Einstein gave up on the idea of a static universe, and described the cosmological constant as the ‘biggest blunder’ of his life.

The expansion of the Universe might perhaps seem like quite a diferent phenomenon to those we usually think of as being due to gravity, but it isn’t really. The large-scale expansion of the Universe is intimately connected with gravity. In a very real sense, one can think of the expansion that Friedmann, Lema’tre, and Hubble discovered as being due to nearby galaxies falling away from each other under their mutual gravitational interaction. As a more domestic example of the same phenomenon, consider throwing a tennis ball directly upwards into the sky. Normally the tennis ball will reach a maximum distance from the surface of the Earth, before it starts falling back down. In the period before this, however, when the ball is travelling upwards, it is still being acted on by gravity, and it is by using the equations that govern the gravitational force that we can calculate the properties of its motion, such as how fast it will be moving at any given time in the future. Two nearby galaxies are very similar to this. The galaxies may be moving apart, but the rate at which they move, and whether or not they will fall back towards each other, is dictated by the gravitational force between them. Einstein’s theory simply allows us to construct a consistent picture of an entire Universe filled with objects that are ’ying away from each other.

The tennis ball analogy raises an obvious question. If galaxies are ’ying away from each other, like the tennis ball ’ies upwards from the surface of the Earth when we throw it, then does this mean the galaxies will eventually stop ’ying apart, and start falling back towards each other？ Or in other words, could the Universe eventually stop expanding and start to re-collapse？ This is a perfectly good question, and the answer can again be given by considering the tennis ball. If instead of throwing the tennis ball upwards we launch it at high speed, from some super-powered cannon, then it’s possible it might never come back down to Earth. Scientists call the speed required to make this happen the escape velocity, and it’s very easy to calculate. If the tennis ball is launched at a speed greater than the escape velocity then it will never return to Earth. If it’s launched with a speed less than the escape velocity, it will eventually fall back down. The situation with galaxies is very similar. If they are receding away from each other with suicient velocity then they should be expected to ’y away from each other forever, and the Universe should then be expected to expand forever. If the rate of recession is too low, then the galaxies will eventually fall back towards each other, and the Universe will start to collapse. The rate of recession between galaxies is known as the Hubble rate, and the velocity required to make them ’y away from each other forever is known as the critical rate. Theory doesn’t tell us if our Universe is expanding above or below the critical rate. To discover this, we have to point our telescopes out into space, and observe.

By observing the expansion of the Universe, we therefore have another way to observe the consequences of the gravitational interaction. Indeed, in this way we can ask and answer questions about gravity that cannot be easily probed by experiments in the Solar System. These include questions such as: Has gravity always had the same strength？ Does light have its own gravitational field, in the way that Einstein’s theory predicts？ And what happens to gravity when the density of matter becomes very large？ The reason why we can answer these questions in cosmology is because of the very large length scales involved; because of the fact that the Universe is expanding; and because of the finite speed of light. Let’s think about how this works.

In most situations in life we’re used to the idea that we can see what’s happening, as it happens. However, this isn’t quite true. It just appears that way. Because light has a fixed velocity (about 300 million metres per second), it takes some time for the light emitted or re’ected of an object to actually reach our eyes. The speed of light is very high, so we don’t usually concern ourselves with this delay. When an object is very far away, however, the delay can become significant. If the Sun suddenly exploded, for example, it would take more than eight minutes for us to know anything about it, because that’s how long it takes the light emitted from the Sun to reach us (and nothing can move faster than light). Another way of thinking about this is that when we look at the Sun we see it as it was a little over eight minutes ago. The same thing happens in cosmology, but the observable Universe is very much larger than the distance from the Earth to the Sun, so the efect becomes huge. For example, it takes more than four years for light from the nearest stars to reach us, and some tens of thousands of years for light from the nearest galaxies. If we look even further away we see objects as they were billions of years ago. In a sense, we can see back in time by looking far away, and if we look far enough away we can see what the Universe looked like when it was very young.

Now, it’s a well-known result in thermodynamics that when you compress an object (like a balloon full of air), it gets hotter. Likewise, if you make the same object expand then it gets cooler. The Universe is no exception to this rule. If we think of the expanding Universe as playing on a movie reel, then if we run the reel backwards we should expect to see the Universe getting smaller and hotter, until at very early times it bursts into ’ames. Now recall that we can in fact see the early stages of the Universe’s evolution, and you might expect that we should see a fireball if we look far enough away (and hence, look far enough back in time). This possibility was first predicted by Ralph Alpher and Robert Herman in the late 1940s, but it wasn’t until 1965 that it was accidentally observed by the radio astronomers Arno Penzias and Robert Wilson. The signal they detected is now known as the CMB, or the Cosmic Microwave Background.

The discovery of the CMB confirmed to the world that astronomy could be used to see the very early stages of the Universe’s evolution, when it was in an entirely diferent state of being. At the same time it opened the door to testing gravity in wildly new environments, where the gravitational field of light could be stronger than that of normal matter, and where we can consider time and distance scales that range over the entire observable Universe.

The early Universe

Since the early days of the 1960s, cosmology has blossomed into a well-studied field of both observational and theoretical physics. The positions of hundreds of thousands of galaxies have been mapped, we’ve seen astrophysical events that occurred many billions of years ago, and the CMB that Penzias and Wilson discovered has been measured to incredible accuracy. These observations, and others, have been used to give precise answers to questions such as ’How old is the Universe？’, ’Will the Universe expand forever？’, and ’What types of matter exist in the Universe？’. The answers to these questions are somewhat puzzling, but have profound consequences for our understanding of gravity. We will consider them in this section.

Let’s start at the beginning of time. If the Universe was smaller and hotter in the past, then if we consider earlier and earlier times, then the density of matter should be expected to become larger and larger. Now, it turns out that not all types of matter increase in density at the same rate, as we go back in time in this way. The density of light (or radiation, as it’s often referred to by physicists) increases at a faster rate than the density of most other types of matter. This means that at very early times the density of radiation can be even higher than the density of the electrons, neutrons, and protons that make up normal matter. In this case the gravitational field of radiation becomes the dominant in’uence on the expansion of the Universe.

The radiation-dominated stage of the Universe’s evolution is relatively brief. It only lasts for the first few tens of thousands of years after the Big Bang. Nevertheless, it is an extremely interesting period of time, particularly for the study of gravity. One of the physical processes that takes place during the radiation-dominated period is the synthesis of the light elements (hydrogen, helium, lithium, etc.). Among the many factors that in’uence this process, one of the most important is the expansion rate of the Universe. Detailed calculations, and observations of the amounts of hydrogen and helium we see in the Universe around us, allow us to place tight constraints on the gravitational field produced by radiation in the very early Universe. The results of such studies are consistent with the predictions of Einstein’s theory, with uncertainties at the level of only a few per cent. This is less precise than observations of gravity in the Solar System or in binary pulsar systems, but it’s not bad considering it involves testing what happened billions of years ago.

As well as the synthesis of light elements, however, there are other interesting physical processes that take place during the early stages of the Universe’s history. One of these is the process that eventually leads to the formation of the first astrophysical structures in the Universe. It’s been known since the findings of Penzias and Wilson that the early Universe looks very close to being perfectly smooth. Very close, that is, but not exactly so. There are small ripples in the CMB radiation that these astronomers found, and these ripples are thought to be the seeds of what eventually turned into the complex network of galaxies and clusters of galaxies that we see around us today. It is gravity that was responsible for the collapse of these small ripples into galaxies, but before this occurred gravity still played a crucial role.

In the early Universe there was a battle between gravity, on the one hand, which tends to make matter clump together, and radiation, on the other, which interacts with the matter, and can cause it to spread out. Any small ’uctuations that exist in the interacting soup of matter and radiation therefore start to oscillate, as they’re pulled together by gravity, and pushed apart by the radiation. The period of these oscillations depend on their size in space, but are easy to calculate. This ’uctuation in the density of matter continues until the Universe cools to a suicient degree that it becomes transparent (at very early times it’s opaque, like a fireball, as discussed before). At this stage the radiation can stream past the matter, and reach the telescopes of distant observers billions of years later, with very little interruption. The CMB that Penzias and Wilson discovered is made up of exactly this type of radiation, measured more than thirteen billion years after the fireball ended. The efects of the war between gravity and radiation are imprinted as tiny ripples in the CMB. These ripples contain a lot of information about the rate of the Universe’s expansion; the amount of radiation in the Universe; and the ways in which radiation and other types of matter interact. They also contain information about the space through which the radiation has travelled, before we observe it on Earth. In short, the CMB is a scientific treasure chest.

Detailed observations of the CMB first began with the launch of NASA’s Cosmic Background Explorer (COBE) in 1989. This satellite experiment observed the background radiation over the entire sky, and showed that the radiation was of exactly the form one would expect if it was emitted from the primordial fireball. The COBE experiment also made the first attempt at observing the small ripples we just discussed. In the end, COBE didn’t have the resolution required to extract much information from these ripples, but it made a promising start. Since then, a series of balloon-based experiments have been performed. Among these were the BOOMERanG and MAXIMA experiments, which were launched in the late 1990s. The detectors in these experiments had suicient resolution to see the largest of the ripples, and this was enough information to determine that the Universe was extremely close to the ’critical’ value of expansion, right at the borderline between re-collapse and eternal expansion. For this to be compatible with the rate of expansion we see around us in the Universe today, however, it looked like something strange had to have happened. Something had to have sped up the Universe’s expansion between the time of the fireball and now’and by some considerable degree.

Background radiation experiments took another leap forward at the beginning of the 21st century. In 2001, NASA launched the Wilkinson Microwave Anisotropy Probe (WMAP) into space. The WMAP experiment was able to see not only the largest of the ripples, but some of the smaller ones too. This was tremendously important, as it allowed the processes involving the growth of these ripples in the early Universe to be made the subject of observational scrutiny. This was followed, in 2009, by the launch of the Planck Surveyor, by the European Space Agency. Planck was a step beyond WMAP, and allowed many more of the ripples to be measured. The results of WMAP and Planck were a glorious confirmation of the theoretical physics that had been developed to understand the growth of the ripples in the early Universe. They showed that the collapse due to gravity expected from Einstein’s theory took place just as expected, and that the amount of radiation in the early Universe was compatible with that required by the primordial nucleosynthesis calculations. They also found, however, that there appeared to be a large amount of matter in the Universe that didn’t interact with radiation in any way, other than through its gravitational field. This isn’t how normal matter behaves.

The background radiation contains further information beyond what I’ve just described. Some of this I’ll describe later on, as it is more a prospect for the future rather than something that has already been detected. It’s worth mentioning here, however, that as the radiation travels through the Universe, from the primordial fireball to our telescopes, it picks up a lot of information about the gravitational fields of objects in between. One way this happens is through the bending of light, as discussed in Chapter 2. The background radiation is no exception to this phenomenon, and as it passes by massive objects, its trajectory is bent by their gravitational fields. This distorts the pattern of ripples in a calculable way. It changes what the ripples look like, and is an efect that was observed by Planck. Another efect that can be seen in the background radiation is due to the evolution of gravitational fields as the Universe expands. If this happens, then a photon that enters a gravitational field with a given amplitude could find itself leaving a field with a diferent amplitude. The diference in these amplitudes gives (or takes away) energy from the photon. Comparing observations of this efect to the theoretical predictions gives further evidence that the expansion of the Universe is speeding up.

The expansion history

After the Universe became cool enough to see through, there was a period that astronomers refer to as the dark ages. This was the period after the initial fireball, but before the first stars and galaxies formed. There is very little for astronomers to look at during this part of the Universe’s history, as most of the matter was in clouds of gas. After about a few hundred million years, however, the first stars and galaxies had begun to form. Since then, structures have grown continuously, and on ever larger scales, as the Universe has evolved. Of course it’s gravity that has caused this to happen, and much information can be obtained about gravity by looking at the astronomical structures around us. For the moment though, let’s think about how astrophysical bodies can be used to probe the expansion history of the Universe.

Hubble started this field, with his famous paper in 1929. As with most great scientific results, his work was built upon and extended by the generations that followed. The aim of all this work has been to determine how fast a distant object is moving away from us, as well as exactly how far away from us that object is. This information can then be used to determine how fast the Universe is expanding. The former of these two problems is actually relatively straightforward. Light from stars, and most other bodies, is emitted in specific frequencies that correspond to the chemical elements that it’s made from. Now, when a body is in motion, as most astrophysical objects tend to be, then the frequency of the light that reaches us is shifted by the Doppler Efect. This phenomenon is the same as the shift in frequency you hear when an ambulance drives past you; the sound it emits seems higher pitched when it’s travelling towards you than when it’s moving away. In both cases, the change in frequency can be straightforwardly related to the velocity of the body in motion. This means that if we know the chemical elements in an astrophysical body (which we often do), then it’s relatively easy to work out how fast that body is moving away from us.

Accurately determining the distance to astrophysical bodies is, however, a more challenging task. The general methodology that’s used for this job is to look at objects that are reasonably nearby. If we can determine the distance to these nearby objects, which is usually a bit easier, then we can use them to calibrate the distance to similar objects that are further away. As an example of this method, let’s consider the Cepheids that Hubble used in his famous paper. A Cepheid is a star whose brightness varies in a periodic way. It was already known that there is a relationship between the period of a Cepheid and its luminosity (its actual brightness, as opposed to its apparent brightness, which depends on distance from us). This was determined from nearby stars whose distances were known. Hubble used this information to work out the distance to faraway Cepheids. The logic is quite straightforward: you look at the Cepheid and measure its period; you use this information to work out how much light it’s emitting; and you compare this to how bright the object appears on your photographic plate. There’s a simple law that tells you how bright an object at a certain distance should be when it’s emitting a certain amount of light, so you have all the information you need to determine its distance.

Unfortunately there are a number of things that can go wrong with this method. The rules used to determine the distance to an object (such as the relationship between period and brightness in Cepheids) might only be approximately true. You also have to assume that the distant objects observed are the same as the nearby objects that were used to determine the rule. This isn’t always true, as it can be hard to identify objects when they are very distant, and because it might be that some rules change over time (recall that when you look far away, you are looking at objects as they were long ago). These problems, and more, need to be carefully considered, as they can sometimes lead to incorrect inferences. In his 1929 paper, for example, Hubble inferred an expansion rate for the Universe that’s approximately ten times larger than all modern measurements. This error was due to incorrectly inferring the distances to galaxies using the Cepheids.

The current state of the art in this field is achieved using observations of supernovae (exploding stars), but the underlying methodology is still quite similar to the one used by Hubble. An individual supernova can be as bright as an entire galaxy, so they are reasonably easy to spot, if you know what to look for. They can also be seen from very far away. Now, there are diferent ways that a supernova can happen, and, of course, astronomers have given names to them all. The type of supernovae that are most useful for probing the expansion of the Universe are known as Type Ia. These explosions are caused by the accretion of matter on to a white dwarf from a nearby star. When enough matter has accumulated, the white dwarf can no longer hold itself up against the pressure of gravity, and it collapses and explodes. The good thing about Type Ia supernovae is that they tend to happen in a very similar way, wherever or whenever they occur. This means that, if they can be properly identified, then their brightness can be used to get quite a good estimate of their distance.

It wasn’t until the late 1990s that the first results on the expansion history of the Universe from Type Ia supernovae began to emerge.Both the Supernova Cosmology Project and the High-Z Supernova Search Team were working on this idea, and they published their first results at around the same time. Using observations of supernovae that were at vast distances, and hence that had exploded several billions of years ago, they found something very surprising. They determined that the expansion of the Universe was not slowing down, as one would expect for objects that fall away from each other under their mutual gravitational attraction, but was instead speeding up. This was entirely unexpected, and it shocked the physics community. In terms of our understanding of gravity, however, it’s especially fascinating. We’ll go into its consequences further in Chapter 6, but for now let’s return to the large-scale structure of the Universe.

The late universe

Just as stars group together to form galaxies, galaxies group together into structures called clusters and super-clusters. These are what cosmologists are referring to when they talk about large-scale structure. The study of the large-scale structure of the Universe, once again, was started by Hubble. It was Hubble who realized that the spiral-shaped objects that astronomers observed through their telescopes were, in fact, distant galaxies. Up until this point it had been a real question as to whether or not our own galaxy was the only one that existed in the Universe, like an island in the infinite cosmos. Using the Cepheids that we discussed earlier, Hubble showed that the spirals were much more distant than the stars we see around us. The only explanation was that they were larger bodies, themselves made up from very many stars. This started the quest to map the structures that exist around us.

As with most branches of observational cosmology, progress in this new field was initially rather slow, and only began to pick up pace towards the end of the 20th century. One of the landmark missions in this field was the Harvard-Smithsonian CfA survey, which began in 1977 and ran until 1995. The CfA survey measured the recessional velocity of almost 20,000 galaxies, and recorded the position of each of them on the sky. Using Hubble’s law, they then converted these velocities into distances, and started to map out the structure that existed in the Universe on very large scales. They discovered that galaxies clump together to form structures that span enormous distance scales. One of the most impressive of these is what is known as the CfA2 Great Wall. This structure is a huge concentration of galaxies, which is so large it would take light more than half a billion years to get from one end to the other.

More recent galaxy surveys have discovered even larger numbers of galaxies. The 2dF survey, which used the Anglo-Australia Telescope in New South Wales, ran from 1997 to 2002, and observed more than 200,000 galaxies. The Sloane Digital Sky Survey (SDSS), which started in the year 2000 and is planned to continue until 2020, has so far measured millions. In fact, there are now so many images of galaxies (and other astrophysical bodies) that it is impossible for astronomers to go through all of them individually. Computer programs can be used for this, but they tend to be worse at recognizing important features than the human eye (and brain). A clever way around this problem was therefore to put the images online and let the public take part in identifying them’a project known as ’Galaxy Zoo’.

Many more structures were found by 2dF and SDSS, and on even larger scales than the CfA survey. The biggest of these was the Sloane Great Wall, which is around twice as big as the CfA2 Great Wall. In fact, the Sloane Great Wall is so big that if you took similar sized structures and put them end to end, you could only fit a few dozen in the entire observable Universe. It’s truly enormous, but one should bear in mind that this is still only a fraction of the distance probed by supernovae and the CMB. There are many more galaxies out there waiting to be discovered, and it remains to be seen if there are any structures that are even larger (the expectation is that there are not, but expectations are not always realized).

This is all very impressive, but let’s return to what it means for the study of gravity. The structures that are observed in these surveys are the result of gravitational attraction. At very early times the Universe looked smooth, as verified by observations of the CMB. In order to get from that state to the present day situation, where there exists vast networks of structure, the matter in the Universe must have clumped together. The way in which this should happen is thought to be well understood on large scales, but starts to get a bit more complicated on small scales. Both of these regimes contain a wealth of information for those who are interested in gravity, so let’s consider them separately.

On large scales the growth of structure happens in a predictable way. This is essentially because the large-scale bulk motion of the matter in the Universe is small on these scales when compared to the cosmological expansion. The growth of structure on large scales is, however, very sensitive to the precise rate of cosmological expansion. If the expansion is dominated by normal matter, then structures grow. This happens on smaller scales first, and on larger scales later on. Now, because we know what the seeds of structure look like, from the CMB, we can calculate what we expect the structure on large scales to look like, and we can compare this to what astronomers actually see. The results are very interesting.

First, the results of observing structures on large scales indicates quite strongly that there is matter in the Universe that does not interact with light. The reason we know this is because there is more structure on certain length scales than there would be if this were not true. That is, if all matter interacted with light, then the high levels of radiation in the early Universe should have suppressed the seeds of structure in a predictable way. What we see, however, is the level of structure that one should expect if radiation hadn’t done this. The logical conclusion is that there exists matter in the Universe that does not interact with radiation, and that it was the gravitational field of this matter that served as the seeds of the structures that we see around us today. What is more, by looking at how much structure exists on diferent length scales, we can gain valuable information about how gravity works over very large distances.

Second, the large-scale structure in the Universe can be used as a kind of ruler, to measure the size of the Universe and how much it has expanded. This is because the initial ripples have a characteristic length. By comparing the scale of these ripples in the background radiation, to the scales that occur in the large-scale structure around us, we can therefore see in quite a direct way how much the Universe has expanded (as the former is the source of the latter). This leads to yet another surprising result. The Universe seems to have expanded more than it should have done if its expansion were dominated by the gravitational field of the matter within it. In other words, the rulers in the late Universe seem to be too big.

Let’s now consider what happens on smaller distance scales, much smaller than the great walls discussed earlier. On these scales the velocities of astrophysical bodies, like stars and galaxies, are not necessarily small compared to the cosmological expansion. The analysis is therefore much more complicated, as the bodies move and interact in much more complicated ways. The current best method for studying this situation is to create huge computer simulations of very many bodies. The space that the bodies exist within is expanding, as Einstein argued that it should, but the gravitational fields of the bodies within the space are usually treated in the way that Newton specified. This is a vast extrapolation of Newton’s ideas, but it is widely thought that it’s a valid way to proceed. Let’s now consider how gravity can be explored in this regime.

The first and most obvious thing to do here is to track the motion of the galaxies, and the form of the larger structures that they create. This is very tricky, as it’s diicult to take into account all the complicated efects that can occur from the many astrophysical processes that take place in the Universe. A supernova, for example, could disrupt the growth of structure, or clouds of gas could enhance it. Nevertheless, one can try to model all such phenomena’and there has been a lot of progress in doing this since the turn of the century. What seems clear, as before, is that there appears to be a large amount of matter that we can’t see directly, but whose gravitational field is required to make galaxies move and cluster in the way they do.

A second approach is to look at how galaxies, and clusters of galaxies, bend the path of light. You will recall that the Sun bends the path of starlight that passes close by it, and that this was how Eddington convinced the world that Einstein’s theory was correct. The same can be done with galaxies. We can look at how the shapes of distant galaxies are distorted by the gravitational fields of those that are much closer to us’in a process known as gravitational lensing. This efect is often very small, and it’s usually an enormous challenge to see it at all. If we look at the right galaxies, or collect enough data, however, then we can use it to determine the gravitational fields that exist in space. Once more, we find that there is more gravity than we expected there to be, from the astrophysical bodies that we can see directly. There appears to be a lot of mass, which bends light via its gravitational field, but that does not interact with the light in any other way. The exact amount of bending that occurs also potentially encodes a lot of information about the way that gravity behaves on the scales of galaxies, and clusters of galaxies.

Moving to even smaller scales, we can look at how individual galaxies behave. It has been known since the 1970s that the rate at which galaxies rotate is too high. What I mean is that if the only source of gravity in a galaxy was the visible matter within it(mostly stars and gas), then any galaxy that rotated as fast as those we see around us would tear itself apart. It would be like taking a head of dandelion seeds and rotating its stem quickly between your hands. If you rotate it fast enough then you would expect the seeds to fly of, as the bonds that hold them together are not strong enough to resist the forces that result from the rotation. The same is true with the stars in galaxies. That they do not ’y apart, despite their rapid rotation, strongly suggests that the gravitational fields within them are larger than we initially suspected. Again, the logical conclusion is that there appears to be matter in galaxies that we cannot see but which contributes to the gravitational field.

The concordance model

Many of the diferent physical processes that occur in the Universe lead to the same surprising conclusion: the gravitational fields we infer, by looking at the Universe around us, require there to be more matter than we can see with our telescopes. Beyond this, in order for the largest structures in the Universe to have evolved into their current state, and in order for the seeds of these structures to look the way they do in the CMB, this new matter cannot be allowed to interact with light at all (or, at most, interact only very weakly). This means that not only do we not see this matter, but that it cannot be seen at all using light, because light is required to pass straight through it.

This is obviously a very strange state of afairs. The substance that gravitates in this way but cannot be seen is referred to as dark matter. The amount of dark matter required to explain the observations is not small. There needs to be approximately five times as much dark matter as there is ordinary matter. Most people, when they first hear this news, think something must have gone terribly wrong. That nature cannot be this strange. Yet, the evidence for the existence of dark matter comes from so many diferent sources that it is hard to argue with it. If the evidence only came from one place, you could try and make a case that whoever collected the data, or made the observations, might have made a mistake. It’s very diicult, though, to make this argument for all of the diferent types of observations listed here. To make so many mistakes, and for all those mistakes to conspire to suggest the same result, seems highly unlikely. So we are led to the conclusion that most of the matter in the Universe is not of the type with which we are most familiar, but is instead some new type of matter that was previously unknown.

But this is not the end of the surprises. Not only do we require extra matter to give extra gravitational fields in order to make structures form and light bend in the way that it’s observed to do, but we also have to explain why the Universe is expanding faster than we thought it should. Recall that we can think of the expansion of the Universe as objects made of matter (such as galaxies) ’ying away from each other under their mutual gravitational interaction. If this is true, and if gravity is always attractive, then we should expect the large-scale expansion of the Universe to be always decelerating. That is, the expansion should be getting slower over time. The results of the various astronomical observations we have discussed, however, have shown that the expansion is speeding up. The conclusion is that there must be a type of gravitational field that is repulsive’in other words, there seems to be a type of anti-gravity at work when we look at how the Universe expands. This anti-gravity is required in order to force matter apart, rather than pull it together, so that the expansion of the Universe can accelerate. This is truly astonishing. The source of this repulsive gravity is referred to by scientists as dark energy (not to be confused with dark matter). There needs to be around three times as much dark energy as there is dark matter, in order to make the Universe accelerate in its expansion at the current rate.

So our current overall picture of the Universe is as follows: only around 5 per cent of the energy in the Universe is in the form of normal matter; about 25 per cent is thought to be in the form of the gravitationally attractive dark matter; and the remaining 70 per cent is thought to be in the form of the gravitationally repulsive dark energy. These proportions, give or take a few percentage points here and there, seem suicient to explain all astronomical observations that have been made to date. The total of all three of these types of energy, added together, also seems to be just the right amount to make space flat (rather than positively or negatively curved, like a sphere or a saddle, as illustrated in Figure 10). The flat Universe, filled with mostly dark energy and dark matter, is usually referred to as the Concordance Model of the Universe. Among astronomers, it is now the consensus view that this is the model of the Universe that best fits their data.

The Concordance Model, and all of the observations that have led to it, is undoubtedly a great achievement of 21st-century physics. However, it is certainly not the end of the story. Not with regard to our understanding of the history of the Universe, nor with regards to the way we understand its contents, or the gravitational fields within it. To be blunt, the Concordance Model has a number of shortcomings. First, it appears to have started of in a particularly special configuration. For space to be so close to flat, and to have the background radiation and the distribution of galaxies look so evenly spread, the early Universe needs to have been extremely close to perfectly uniform in density. Second, some of the ripples we see in the CMB appear to be larger than the distance light could have travelled since the Big Bang. Nothing should travel faster than light, in Einstein’s theory, so this is genuinely puzzling. Third, we have no idea what dark matter really is. We only know that it should gravitate, and that it should not interact with light. It doesn’t show up in the Standard Model of particle physics, which has a place for every other known type of particle, and it hasn’t yet been seen in any particle physics experiment. Fourth, the existence of dark energy, and its repulsive gravitational field, seems to require enormous fine-tuning in order to have the efect that we see today. A bit more of it and galaxies would never have formed. A bit less and we wouldn’t have ever noticed it at all.

These four problems are the focus of much attention for physicists. The first two are thought to be solved by a period of very rapid expansion in the early Universe, called cosmic in’ation. I’ll describe cosmic in’ation in Chapter 6. It is hoped that the third will be solved by extending the Standard Model of particle physics, and there are a number of proposals on how this could be done. At the time of writing, it is thought that the properties of dark matter particles can be investigated directly by using the Large Hadron Collider (LHC) in Geneva. Whether or not nature will have been kind enough to allow them to fall into the range of energy levels that the LHC can probe remains to be seen. But the last of these problems is probably the most mystifying of all. The lengths that some physicists have gone to try to explain dark energy are truly extraordinary. Again, I’ll describe this further in Chapter 6.

Of course, there remain a few physicists that are sceptical that dark energy and dark matter exist at all. They maintain that we need to understand in more detail how gravity works on the scale of the Universe before we can be sure that they are really there. After all, it’s only through their gravitational interaction that we know about these substances at all. If we’ve misunderstood gravity, we may therefore have misidentified them. Future astronomical observations will be used to investigate this possibility and to further explore the properties of dark matter and dark energy.

The future of cosmology

It often turns out to be folly to try to predict the future in science, but it seems reasonably clear that the 21st century will see significant advances in cosmology. We now know a lot about the way the Universe is expanding and the way that structures in the Universe have formed, but our current knowledge will be dwarfed by observations that will happen over the next couple of decades. Much of the motivation for this work comes from dark matter and dark energy. The search for these dark materials will shed further light on gravity.

Let’s start with the CMB. To date, most observations of this radiation have focused on measuring its temperature in diferent directions on the sky, and trying to infer what the ripples in the early Universe must have looked like. The cutting edge in this work has so far been the Planck satellite. This mission was so successful, however, that it is almost impossible to do any better with future space-based missions. What can be done, however, is build bigger telescopes on the surface of the Earth. This is currently being done in the Atacama Desert in Chile, and at the South Pole. These are two of the lowest-humidity locations on the planet, and the thin dry air makes them ideal places for looking into space. These telescopes will map the CMB to very high resolution, and will supply a wealth of information about the structures that exist in the Universe.

As well as temperature, there are other things that can be observed in the CMB data. Astronomers can also measure its polarization (the orientation of a set of electromagnetic waves, as illustrated in Figure 11). The polarization of the background radiation carries additional information about what happened in the early Universe, and by looking for particular patterns astronomers can infer what the gravitational field looked like very early on in the Universe’s history.

Some of this information duplicates what can be deduced from the temperature, but some of it is entirely new. In particular, by looking for a characteristic curl pattern in the polarization, it is possible to deduce whether there were gravitational waves travelling around the early Universe. You will recall, from Chapter 4, that considerable efort has been expended to directly detect the gravitational waves that travel through the Earth. The polarization of the CMB provides the scope for similar experiments in an entirely diferent environment.

11. An illustration of (a) polarized light; and (b) unpolarized light. The orientation of the waves in the unpolarized light is random, while the waves in the polarized case are aligned. Arrows denote the direction in which the light is travelling.

In March 2014, scientists working on the BICEP2 experiment at the South Pole announced that they had used this method to discover gravitational waves in the early Universe. At the time of writing, it appears that the excitement generated by this announcement was premature. While the scientists had seen the curl pattern in the polarization of the CMB, it now seems that this was generated by sources closer to us and not from gravitational waves at all. This doesn’t mean that gravitational waves aren’t out there, in the early Universe. Future experiments will measure the polarization of the background radiation to even higher accuracy, and in more frequency bands. If gravitational waves were present in the early Universe, to any considerable level, then it’s likely we’ll know about them in the next decade or so. The successor to BICEP2 has already been built, and will give its first scientific results soon.

Also of great promise are the next generation of galaxy survey missions. We discussed the 2dF and SDSS surveys earlier, which were very ambitious attempts to record the positions of the galaxies in the Universe we see around us. Future surveys will be much, much bigger. Three of the grandest of these will be the Large Synoptic Survey Telescope (LSST), which is already under construction in Chile; the Square Kilometre Array (SKA), which will begin construction in 2018; and the European Space Agency’s Euclid satellite, which is expected to launch around 2020. These missions will measure billions of astronomical sources, which will be used to construct maps of the Universe on unprecedented scales.

The LSST, the SKA, and the Euclid satellite will turn cosmology into a precision science. When they are in operation, we will know much more about the nature of the dark matter and dark energy: through the efects they have on the structure in the Universe; from the way in which light travels to us from those structures; and from the way that they evolve in time. In fact, it is expected that this information will be so precise that, for the first time, we will be able to start performing tests of gravity that will rival those we can already perform in the Solar System and in binary pulsar systems. This will open up a whole new window on gravity, and will allow us to test it in new ways and on new distance scales.

Chapter 6 Frontiers of gravitational physics

Throughout most of this book we have been considering the cutting edge of experimental gravitational physics research, ranging from tests on the scale of millimetres to those on the size of the entire observable Universe. In this chapter we will consider some of the issues involved in the theoretical description of gravity.

Since 1915, it has been Einstein’s theory that has shaped our understanding of the gravitational interaction. This theory treats space and time as a single object, and lets the properties of that object be determined by the matter that exists within it. I hope that the reader has, by now, been convinced of the phenomenal success of Einstein’s theory. It is truly extraordinary that a single theory should be able to explain such a wide array of physical efects. Einstein’s theory, however, is unlikely to be the final word in our understanding of gravity. A lot has happened in the world of theoretical physics since 1915, and much of it suggests that we should expect there to be an even more fundamental theory.

Quantum mechanics and gravity

Not long after Einstein published his theory of gravity, at the beginning of the 20th century, the world of theoretical physics was forever changed (once again) by scientists such as Bohr,Heisenberg, Schr’dinger, and others. Since Newton, and up until this point, physics had been thought to be deterministic. That is, if you know enough information about the position and motions of all objects in the Universe, then you should be able to predict the future with arbitrarily high precision. Physical theories that work in this way are now referred to as classical theories. Einstein’s relativity theory is an example of a classical theory. The revolution led by Bohr, Heisenberg, and Schr’dinger created another type of theory, quantum mechanics. The new quantum theory was based on probability, and resulted in a description of nature in which it was only ever possible to calculate the odds that certain events will happen in the future, and within which it is never certain what the future holds.

Quantum mechanics was an astonishing success. It described the nature of light, and the building blocks of all known matter, to extraordinary precision. Later, Paul Dirac, a professor at the University of Cambridge, showed the world how these new ideas could be used to create quantum theories of electricity and magnetism. This led to what is now called the Standard Model of particle physics: a quantum mechanical description of all of the known particles in nature, and the forces between them. Winding forward to the present day there can be no serious doubt that nature is quantum mechanical. The predictions of the Standard Model have all been verified, with the crowning jewel being the experimental verification in 2012 of the existence of the Higgs boson (a theorized particle that is an important component of the modern Standard Model, and which gives the other particles their mass). It is quantum mechanics that underpins much of modern chemistry and material science, giving us the semi-conductors that our computers are made from; and the lasers and LEDs that are used to construct our DVD players and televisions. Quantum mechanics is a fact of life. It is how nature works, and it becomes increasingly important when we seek to describe the microscopic world.

Yet despite its ubiquity in all other areas of physics, the application of this approach to gravity is still not understood. While the electromagnetic force can be quantized in a relatively straightforward way, and while the matter in the Universe has long been described using quantum mechanics, the quantum theory of gravity remains elusive. This is probably the single biggest unsolved problem in physics, and has been for the past fifty years. It is extraordinarily diicult to apply the logic that has been so successful in other areas of physics to gravity, and so our current best description of gravity is still Einstein’s classical theory.

Part of the problem with this state of afairs is that there are situations in which one would expect both quantum mechanics and gravity to be required. One example of this is the centre of a black hole. As we’ve discussed already, black holes form when large stars undergo catastrophic collapse. The matter that was originally part of the star gets compressed by gravity to ever higher densities. In fact, according to Einstein’s theory, the collapse should continue until all the matter is squashed to a single point. Now, according to quantum theory we should expect new quantum efects to become apparent when we consider very small distance scales and very high energies. What I’ve described is therefore a regime where both quantum mechanics and gravity are expected to be required in order to get a description of the physics at play. But there is no agreed-upon theory of quantum gravity, so it is (at present) impossible to know what should happen at the centre of a star after it has collapsed. This is obviously an unsatisfactory state of afairs. If we want to be able to describe everything that exists in nature, then we need a quantum theory of gravity.

The reasons for the apparent incompatibility of quantum theory and gravity are many, and can be somewhat complicated. First there is a conceptual diference between Einstein’s approach to gravity, and how forces are treated in quantum mechanics. In Einstein’s theory, gravity is a result of the curvature of space-time. There is no external force that pulls things together. The apparent way in which massive bodies move towards each other is simply a result of the curvature of space-time. The Earth, for example, is not pulled towards the Sun, it is simply in free fall, following the shortest path available to it in a curved space-time. This is not the case for other forces. The electric force, for example, is a result of the electric field that gets generated by charged particles. The electric field exists within space and time, but is not the same as space or time, in any sense. Space and time are simply the arena within which the electric force plays out. This idea of space and time having their own independent existence, and being passive parts of the problem, is built into most approaches to quantum mechanics. To try to use these approaches to describe gravity therefore goes against what we were taught by Einstein.

There are also very good mathematical reasons why gravity and quantum mechanics are incompatible. The foremost of these is a property of gravity called non-renormalizability. When quantum mechanics is used to describe a force, the result of the calculations that we perform can often result in answers that contain infinities. An example of this occurs when we consider two charged particles. To work out the force between them, quantum mechanically, we have to add the contributions from all of the possible positions of the two particles. Some of these configurations are when the particles become very, very close,in which case the force becomes very, very large. Summing over all possible positions then gives a result that is infinite. This unreasonable answer can be corrected for, in the case of the electric force, by using a process called renormalization. This process removes the parts of the equations that contributed the infinities. That is, the infinities are essentially subtracted from the original equation. The result is then a sensible answer, which can be tested with experiments. Renormalization, however, doesn’t work with Einstein’s gravity. The infinities cannot be subtracted, as there is nothing in the original equations that looks anything like the terms that become infinite. Quantum gravity calculations therefore seem to give infinite answers. Something is obviously wrong.

There have been many attempts to fix these problems. They range from changing Einstein’s equations (so that they appear to be more renormalizable); to changing quantum mechanics (so that it is no longer based on particles); through to changing the nature of what we think of as space and time (so that they are not continuous). It is not possible to give a fair representation of all of these approaches here, or to go into any one of them in any detail. They are very complicated ideas and they are all works-in-progress. There are a couple of theories that I feel I should mention though’these are String Theory and Loop Quantum Gravity. These are both extremely bold and ambitious attempts to construct quantum theories of gravity. If correct, the hope is that physicists could use these theories to describe what happens at the centre of black holes. They are, however, quite diferent from each other. They prioritize diferent aspects of the problem, and approach the technical and conceptual diculties just described in quite diferent ways.

String Theory was born out of particle physics. It is based on the idea that the basic constituents of matter are not point-like particles, but are instead tiny one-dimensional strings. This is a radical idea, and it has led to a lot of interesting maths and physics. Indeed, many physicists consider it to be our best hope of finding a theory of quantum gravity. The hypothesized strings are very small, so that for the most part they appear to us efectively as point-like particles. When we try and quantize them, however, their stringy-nature leads to diferent results. The equations that govern the strings also contain aspects that look a lot like the equations that govern Einstein’s theory of gravity. It therefore appears that gravity is, to some extent, built into String Theory. There are drawbacks, however, as the consistency of the equations that govern the strings require us to add between six and twenty-two extra dimensions of space to our description of the Universe.

These extra dimensions are thought to be wound up and compact, so that we don’t see them in our everyday lives. Nevertheless, they have to be there for the theory to be self-consistent. Interestingly, the existence of these small extra dimensions leads to the possibility that gravity could work diferently on very small scales.

Loop Quantum Gravity is often seen as the main competitor to String Theory. The starting point for this theory is the idea that on very small scales space-time has a granular structure. That is, space and time are not the smooth continuous variables that we usually consider them to be. Instead, space-time is atomized. Quantum theory is then applied to the loops that make up this new structure. This is also a radical idea, and it tends to be favoured by aficionados of General Relativity because of its emphasis on space-time as the fundamental object of interest’instead of as a background. Loop Quantum Gravity is, however, very much a work in progress. It remains to be seen whether the approach it employs is the correct one or whether String Theory, or some other as yet undiscovered theory, is a preferable description of nature. Further work is needed before most of us would be prepared to make any bets on the outcome of this debate.

Particles in gravitational fields

Quantizing gravity is fraught with diculties. So let’s turn to another question: how does quantum mechanics work in a gravitational field？ Here we will treat space-time in the same way that Einstein did in his classical theory of gravity. Once we have a classical space-time at our disposal, however, we will consider what happens when we try to treat the matter content as being governed by quantum theory. This mixed approach, with matter being treated quantum mechanically, and gravity being treated classically, is usually referred to as semi-classical physics. It is a less ambitious project than full quantum gravity but nevertheless gives us interesting insights into how quantum systems work in the presence of gravity.

One of the pioneers of this subject was Stephen Hawking, who in 1974 showed that quantum mechanics should lead to black holes emitting radiation. This discovery shocked the scientific community, as according to Einstein’s theory nothing can ever escape from a black hole. Hawking’s calculation was a semi-classical one. He took the classical description for the space-time around a black hole and allowed quantum mechanical particles to exist within it. He showed, using a fairly simple quantum mechanical calculation, that if there was no radiation in the distant past, then there must exist radiation in the future. The only possible explanation for this was that the radiation was produced by the black hole. Of course, radiation carries energy, and in this situation the only source of energy is the mass within the black hole (remember that mass is a type of energy in Einstein’s theory). So Hawking had shown that black holes naturally shrink, by radiating away their mass, and that they must eventually cease to be.

Hawking’s result was novel, and sparked several new fields of research in gravitational physics. Almost immediately after Hawking’s discovery it was shown, by Bill Unruh, that the very existence of particles can be questioned when we consider them within relativity theory. Particle physics is very much the domain of quantum mechanics, and Unruh showed that if observers are in relative motion, with one accelerating with respect to the other, then it is entirely possible for one of them to detect the existence of quantum particles while the other detects nothing at all. That is, whether or not particles exist depends on the motion of the person who is trying to measure them.

To get across the strangeness of this result, let me illustrate it with an example. Consider that you’re an astronaut, ’oating around freely in outer space somewhere. You see nothing anywhere near you. If you then start accelerating, by holding on to a passing spaceship, say, then suddenly what you thought was empty space bursts into a sea of particles. I’m exaggerating a little here, of course. You would need to accelerate very quickly indeed to see a large number of particles. Nevertheless, the principle is sound. When you accelerate you detect particles where previously there were none. Now introduce gravity and the situation becomes even more complicated. Gravity is caused by acceleration, so by sitting at my desk, in the gravitational field of the Earth, I am being exposed to a small number of particles that wouldn’t be there if I were falling freely. The number is too small to measure, but if I moved my desk so that it was near a black hole (where gravity is much stronger) then it would be an entirely diferent story. I would be bombarded with high-energy particles and radiation.

All of this has interesting consequences for black holes, which can now have a temperature associated with them based on the temperature of the particles and radiation that they emit. But it also has consequences for other areas of gravitational physics, including cosmology. In some ways the gravitational field of a cosmological model of the Universe is similar to the gravitational field of a black hole, and indeed Gary Gibbons and Stephen Hawking showed that the radiation that black holes produce should also be produced by the expansion of the Universe. The faster the expansion, the more radiation there should be, and the higher its temperature. This radiation isn’t emitted from anything within the Universe, but is a by-product of the expansion itself. It is a direct consequence of considering quantum particles existing in a gravitational field.

Cosmic inflation

To date, the most successful application of quantum theory to gravity has probably been in the very early stages of the Universe’s history. The name that physicists use to describe what happened during this period is cosmic in’ation. In Chapter 5, we considered the Big Bang model of the Universe, and its various successes. As well as explaining a lot of astronomical data, however, the Big Bang model presents us with a few problems. One of the gravest of these is that some of the ripples we see in the CMB appear to be so large that light could not have made it from one of their edges to the other within the lifetime of the Universe. This is a very serious problem, because nothing can travel faster than light. So what could possibly have caused these ripples？

The answer is not obvious, but one possible explanation for their existence is that the Universe might have expanded very quickly in its very early history. If this happened, then very small ripples would have been forced to grow into large ones, and the problem would be solved. The hypothesized period of rapid expansion is what is called cosmic in’ation. Now, as scientists, the way to test a hypothesis of this type is to try and predict other consequences that it might have, and to get out our telescopes to see if we can verify those predictions. This is dicult when considering in’ation, as we do not know exactly what caused it. It also happened a very long time ago. Nevertheless, there are a number of generic predictions one can make, and that can be verified by observing the night sky. One of these is that the geometry of space should be close to ’at. This matches observations, as we have seen. Probably the most impressive prediction, however, involves the application of the semi-classical physics just described.

You will recall that Gibbons and Hawking demonstrated that an expanding space creates a sea of radiation. It turns out that the radiation produced is not perfectly uniform at every point in space. The statistical nature of quantum mechanics means that random ’uctuations are introduced, so that at some points there is a little more radiation, and at other points there is a little less. It’s impossible to predict where any one of these quantum mechanical ’uctuations will occur, but the theory does let us predict how often we should expect a randomly selected point to be over-dense or under-dense. It also tells us how we should expect the over-dense and under-dense regions to be distributed, on average. These are all predictions of semi-classical physics, and we can test the theory by looking for their consequences. In particular, we can test the idea of cosmic in’ation by looking for the consequences of the quantum ’uctuations that it would produce.

Now recall that in Chapter 5 we discussed the ripples that exist in the CMB. These ripples are a very important source of information for cosmologists, but so far we haven’t spelt out where they came from. That is, we haven’t said what caused the small seeds from which they grew. These seeds need to have a very special form in order to explain the statistical properties of the ripples that astronomers measure in the CMB, and, before in’ation was introduced, there was no clear idea about where they should have come from. If in’ation really did happen in the very early Universe, then one way of sowing these seeds could have been through the small quantum mechanical ’uctuations that Gibbons and Hawking predicted. It turns out the ripples that were measured by COBE, WMAP, and the Planck Surveyor are just what we should expect from such a scenario.

This was a remarkable discovery. Not only has the most generic prediction of the in’ationary epoch been verified, but it also appears that we have verified the peculiar calculations that result from considering quantum mechanical processes in a gravitational field. The type of radiation that Hawking had predicted in 1974 still hasn’t been seen directly, but its consequences appear quite plainly in the CMB. The evidence is all there, in the maps of the CMB that have been recorded by astronomers. But, again, this is not the end of the story; there is very likely more evidence out there, waiting to be collected. The same quantum mechanical processes that generate ripples in the CMB should also be expected to generate gravitational waves. These are exactly the gravitational waves that the observers running the BICEP2 experiment mistakenly thought that they had detected in March 2014 (see Chapter 5). At the time of writing, the gravitational waves from cosmic in’ation have still not yet been confirmed observationally, but if they can be found by future experiments then they will open up a whole new window on the early Universe.

The cosmological constant

We noted earlier that the acceleration of cosmic expansion is said to be caused by dark energy, but we didn’t go into any detail about what dark energy might be. The truth is that we don’t yet know what dark energy is, but we do have a favourite candidate: the cosmological constant. In this section we will consider the cosmological constant in more detail.

The cosmological constant was first introduced by Albert Einstein in 1917. At that time, it was not known that the Universe was expanding, and Einstein introduced his cosmological constant in order to produce a cosmological model that was static (neither expanding nor contracting). Of course, we now know that there is very good evidence to support the idea that the Universe is expanding. When Einstein became aware of this he withdrew his cosmological constant, which was promptly brushed under the carpet as something of a scientific embarrassment. However, the cosmological constant remained a perfectly consistent modification that one could make to the field equations of his theory of gravity. It’s just that there was no need for it. Not, that is, until it was noticed that the expansion of the Universe was accelerating.

A cosmological constant can be thought of as a universal gravitational force, pulling or pushing all particles in the Universe together at the same rate. This is exactly the sort of thing that’s required to make the Universe accelerate. All we have to do is make sure the cosmological constant is set up to push things apart, give it the right magnitude, and it will make the expansion of the Universe accelerate. In fact, it’s by far the simplest way to make the Universe accelerate.

The cosmological constant, tuned to have the correct magnitude, fits all of the current observations. Of course, we expect the quality of this data to improve considerably over the coming decades. When this happens we will be able to see whether the cosmological constant remains a good fit’or not. If it is, then this will be good evidence for its existence. If it’s not, then we will have to be more imaginative. For now, we can speculate on what it would mean if there really was a cosmological constant in our Universe. This is interesting because the cosmological constant, although simple, brings with it a number of problems.

The first and foremost problem associated with the cosmological constant is that, if it is to cause the expansion of the Universe to accelerate at the present time, then it must have been very finely tuned in the early Universe. Fine-tuning is one of the bugbears of theoretical physics. It’s one thing to come up with an explanation for a physical efect, but if your explanation requires things to be arranged in an extremely special way then it starts to look less and less compelling. The fine-tuning associated with the cosmological constant comes from the fact that its value doesn’t change in time (it’s a constant). This means that if we want it to have the correct magnitude today, then in the very early Universe we have to pick a value that is very, very, very small compared to the energy scale of matter at the time, but not quite zero. If the cosmological constant were too large, it would have caused the expansion of the Universe to accelerate at much earlier times. If this happened, then stars and galaxies would never have formed, and there would have been no life anywhere. If it were any smaller, it would not cause the required amount of acceleration, and we would never have noticed it. To fit into this sweet spot we need to pick the magnitude of the cosmological constant to have a very particular value, with very high precision. This precision is widely thought to be at the level of about one part in 10120 (that’s one followed by one hundred and twenty zeroes).

The cosmological constant problem, just described, is exacerbated by the fact that quantum mechanical efects also contribute to its magnitude. Given our current understanding of quantum mechanics, we would expect these contributions to throw the value way of from the very special value that is needed observationally. One might counter this argument by saying that we do not yet fully understand the quantum processes that would cause these efects, and how they work in the presence of gravity. One could speculate that there might be some reason why the various quantum contributions should cancel each other out, and that we just don’t know about it yet. This might be possible, but there’s a further problem. The particular quantum contributions that we expect the cosmological constant to receive are not always the same’they change during the diferent epochs of the Universe’s expansion history. To consider the possibility that a set of quantum corrections might all cancel each other out is one thing. To assume this should happen over and over again is quite another. The fact that the cosmological constant is so very finely tuned therefore looks even more surprising when we take quantum mechanical efects into account. This is why the cosmological constant problem has been called, by some, the worst fine-tuning problem that has ever occurred in physics.

The multiverse

The problem of the cosmological constant is considered so great, and so pressing, that many physicists have started to entertain some quite drastic proposals in order to try and explain it. One of the most fantastical, and most widely considered, ideas is the possibility that there is more than one universe. If this were the case, and if the cosmological constant were somehow to take a diferent value in each universe, then it might be possible for us to find ourselves in a universe with any given value for the cosmological constant. Even if the value we observe looks fine-tuned, this might just mean that we are in a relatively rare universe, and that there are many other universes in which the cosmological constant takes a more natural-looking value.

This idea of many universes, or a multiverse, doesn’t by itself alleviate the problems associated with the improbability of measuring the cosmological constant to have the value that we observe. Instead of fine-tuning the value of this constant, we are instead forced to carefully select an unlikely universe for ourselves to live in. However, if we couple the idea of a multiverse with what is known as the anthropic principle, then things become very diferent. The anthropic principle, roughly stated, says that we(as life forms) can only ever observe a universe that is capable of supporting life. This sounds obvious, but it provides a mechanism to select which of the possible universes we might be able to find ourselves within. If a particular universe contains a cosmological constant that is so large that stars and planets can never form, then it is unlikely that we would find ourselves living there. This automatically de-selects a large part of the multiverse, and makes our universe look a lot more likely.

This idea raises a lot of questions. Where are these other universes？ How are they connected to ours？ How does the value of the cosmological constant change between them？ And how likely are we to find ourselves in any one of them？ These are very fundamental questions, and although there are mechanisms for generating many universes from some theories of cosmic in’ation, it is pushing the boundaries of science to say that we can investigate them as if they were physical realities. For some, the idea of a multiverse is a glorious one, motivated by observations of how gravity works on astronomical scales, and ’eshed out by our theories of what happened near the Big Bang. For others it is worse than the problem it was intended to solve. Many in this latter group consider it wrong to invoke unobservable regions of space and time in order to solve a problem in our own observable Universe. While it might be self-consistent, and even well motivated, to do so, the existence of these other universes cannot be tested directly. Some people within this group therefore argue that such an approach is essentially unscientific, and belongs to the realm of metaphysics.

Whether or not the limits of science can be stretched to include a multiverse is a topic of lively debate, with diferent groups passionately arguing their various cases. Future astronomical missions will advance this argument by measuring the properties of whatever it is that’s causing the Universe to accelerate in its expansion. The future development of theoretical physics may also shed light on the naturalness of the cosmological constant we appear to measure. For now, however, we must wait.

Epilogue

Our understanding of gravity has developed rapidly over the past century. This began with Einstein’s revolutionary new theory and continued with sustained developments in our understanding of both the mathematics and the observations that can be used to probe it. I’ve outlined how new gravitational efects have been predicted and observed in the Solar System; in exotic astrophysical systems; and in the Universe as a whole. While I’ve attempted to give some idea of the elegance of the concepts involved, and the details of the wondrous physics that results, this book must inevitably be left incomplete. It is only a very short introduction to the subject. To understand the full profundity of what Einstein achieved, and the beauty of the theory that resulted, there is no alternative but to delve deeper into the maths and physics. This should be a rewarding experience, as Einstein’s theory of gravity lets us understand space and time as they really are. It lets us imagine universes that never were, as well comprehend the one in which we live. It lets us calculate what happens in environments so alien and exotic that our everyday understanding of reality is turned entirely on its head. Yet it is almost certainly incomplete. The final words on gravity have yet to be written.

Further reading

Chapter 1: From Newton to Einstein

Russell Stannard, Relativity: A Very Short Introduction (Oxford University Press, 2008).

*Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler,Gravitation (W. H. Freeman and Company, 1973).

Chapter 2: Gravity in the Solar System

Clifford M. Will, Was Einstein Right？ Putting General Relativity to the Test (Basic Books, 1993).

*Clifford M. Will, Theory and Experiment in Gravitational Physics(Cambridge University Press, 1993).

Chapter 3: Extrasolar tests of gravity

Katherine Blundell, Black Holes: A Very Short Introduction (Oxford University Press, 2015).

*Ingrid H. Stairs, Testing General Relativity with Pulsar Timing, Living Reviews in Relativity 6/5 (2003) at: 〈http://www.livingreviews.org/lrr-2003-5〉.

Chapter 4: Gravitational waves

Harry Collins, Gravity’s Shadow: The Search for Gravitational Waves(University of Chicago Press, 2004).

*B. S. Sathyaprakash and Bernard F. Schutz, Physics, Astrophysics and Cosmology with Gravitational Waves, Living Reviews in Relativity12/2 (2009) at: 〈http://www.livingreviews.org/lrr-2009-2〉.

Chapter 5: Cosmology

Peter Coles, Cosmology: A Very Short Introduction (Oxford University Press, 2001).

*Scott Dodelson, Modern Cosmology (Academic Press, 2003).

Chapter 6: Frontiers of gravitational physics

Brian Greene, The Elegant Universe (Vintage, 1999).

Leonard Susskind, The Cosmic Landscape (Back Bay Books, 2005).

*References labelled with an asterisk are advanced-level texts,intended for readers who want to learn about the subject in all its glory. They require degree-level knowledge of mathematics and physics. Readers wishing to take part in the Galaxy Zoo project should visit 〈www.galaxyzoo.org〉.

Index

A

anthropic principle 96

Aristotle’s theory of gravity 2

B

bending of starlight 30

binary pulsar systems 41

black hole radiation 89

black holes 36

C

Cavendish’s experiment 25

CMB polarization 80

concordance model of

cosmology 76

constancy of mass 17

cosmic in’ation 90

Cosmic Microwave Background

(CMB) 63

cosmological constant 60, 93

cosmology 58

critical rate of cosmic expansion 62

D

dark energy 77

dark matter 76

double pulsar 42

E

E = m c^2
11

early Universe 64

Eddington’s expedition 31

efect of gravitational waves 48

Einstein’s theory of gravity 8

E
experiment 22

ether 20

Euclid satellite 82

event horizons 36

expanding Universe 58

expansion history of the

Universe 68

experimental probes of Einstein’s

theory 27

experimental probes of Newton’s

law 24

F

fine-tuning of the cosmological

constant 94

flat and curved spaces 13

frame dragging 33

G

galaxy rotation 75

General Theory of

Relativity 12

geodetic precession 33

gravitational lensing 75

gravitational redshifting 18

gravitational time dilation 20

gravitational wave detectors 51

gravitational waves 46

gravity as acceleration 14

gravity from curvature 11

Gravity Probe B 33

H

history of cosmology 59

Hubble’s law 60

Hughes-Drever experiment 22

Hulse-Taylor binary pulsar

system 37

I

interferometry 21

K

kepler’s laws 6

L

laboratory tests of gravity 26

large-scale structure in the

Universe 71

Large Synoptic Survey

Telescope 82

late Universe 71

life of a star 35

LIGO experiment 50, 52

Loop Quantum Gravity 88

lunar laser ranging 24

M

Maxwell’s theory of light 8

Mercury’s anomalous orbit 28

Michelson-Morley

experiment 20

microsecond pulsars 44

multiverses 95

N

neutron stars 36

Newton’s force law 6

Newton’s theory of gravity 4

non-renormalizability of

gravity 86

O

observation of gravitational

waves 53

observations of the CMB 66

P

particles in gravitational

fields 88

Planck Surveyor 67

pulsars 37

Q

quantum gravity 85

quantum mechanics 83

R

radio time-delay efect 31

S

seeds of structure in

cosmology 92

Solar System 16

space-time 10

space with positive and negative

curvature 60

Special Theory of Relativity 10

speed of light 8

Square Kilometre Array 43

String Theory 87

supernovae 36, 70

synthesis of the light

elements 65

T

testing foundational

assumptions 17

triple pulsar 45

U

Universality of Free Fall 3

Unruh radiation 89

W

Weber bars 51

WMAP experiment 67