一位著名的科学家（据说是贝特郎·罗素）曾经作过 一次关于天文学方面的讲演。他描述了地球如何绕着太阳运动，以及太阳又是如何绕着我们称之为星系的巨大的恒星群的中心转动。演讲结束之时，一位坐在房间后 排的矮个老妇人站起来说道：“你说的这些都是废话。这个世界实际上是驮在一只大乌龟的背上的一块平板。“这位科学家很有教养地微笑着答道：“那么这只乌龟 是站在什么上面的呢？““你很聪明，年轻人，的确很聪明，“老妇人说，“不过，这是一只驮着一只一直驮下去的乌龟群啊！“
大 部分人会觉得，把我们的宇宙喻为一个无限的乌龟塔相当荒谬，可是为什么我们自以为知道得更多一些呢？我们对宇宙了解了多少？而我们又是怎样才知道的呢？宇 宙从何而来，又将向何处去？宇宙有开端吗？如果有的话，在这开端之前发生了什么？时间的本质是什么？它会有一个终结吗？在物理学上的一些最新突破，使一部 分奇妙的新技术得以实现，从而对于回答这些长期以来悬而未决问题中的某些问题有所启发。也许有一天这些答案会像我们认为地球绕着太阳运动那样显而易见—— 当然也可能像乌龟塔那般荒唐可笑。不管怎样，唯有让时间来判断了。
早 在公元前340年， 希腊哲学家亚里士多德在他的《论天》一书中，就已经能够对于地球是一个圆球而不是一块平板这一论点提出两个很好的论据。第一，他认为月食是由于地球运行到 太阳与月亮之间而造成的。地球在月亮上的影子总是圆的，这只有在地球本身为球形的前提下才成立。如果地球是一块平坦的圆盘，除非月食总是发生在太阳正好位 于这个圆盘中心之下的时候，否则地球的影子就会被拉长而成为椭圆。第二，希腊人从旅行中知道，在越往南的地区看星空，北极星则显得越靠近地平线。（因为北 极星位于北极的正上方，所以它出现在处于北极的观察者的头顶上，而对于赤道上的观察者，北极星显得刚好在地平线上。）根据北极星在埃及和在希腊呈现出来的 位置的差别， 亚里士多德甚至估计地球大圆长度为4000000斯特迪亚。 现在不能准确地知道，一个斯特迪亚的长度究竟是多少，但也许是200码左右，这样就使得亚里士多德的估计为现在所接受数值的两倍。希腊人甚至为地球是球形 提供了第三个论据，否则何以从地平线外驶来的船总是先露出船帆，然后才是船身？
亚 里士多德认为地球是不动的，太阳、月亮、行星和恒星都以圆周为轨道围绕着它转动。他相信这些，是由于神秘的原因，他感到地球是宇宙的中心，而且圆周运动最 为完美。在公元后两世纪，这个思想被托勒密精制成一个完整的宇宙学模型。地球处于正中心，包围着它的是八个天球，这八个天球分别负载着月亮、太阳、恒星和 五个当时已知的行星： 水星、金星、火星、木星和土星（图1.1）。这些行星被认为是沿着附在相应天球上的更小的圆周运动，以说明它们在天空中被观察到的相当复杂的轨迹。最外层 的天球被镶上固定的恒星，它们总是停在不变的相对位置，但是总体绕着天空旋转。最后一层天球之外为何物一直不清楚，但有一点是肯定的，它不是人类所能观测 到的宇宙的部分。
图1.1 从最里面往最外面顺序为月亮球、 水星球、金星球、太阳球、火星球、木星球、土星球和固定恒星球。最中心为地球。
托 勒密模型为预言天体在天空的位置提供了相当精密的系统。但为了正确地预言这些位置，托勒密必须假定月亮轨道有时离地球比其他时候要近一倍，这意味着月亮有 时看起来要比其他时候大一倍。托勒密承认这个瑕疵，尽管如此，他的模型虽然不是普遍地、却是广泛地被接受。它被基督教接纳为与《圣经》相一致的宇宙图象。 这是因为它具有巨大的优点，即在固定恒星天球之外为天堂和地狱留下了很多地方。
然 而，1514年一位名叫尼古拉·哥白尼的教士提出了一个更简单的模型。（起初，可能由于害怕教会对异端的迫害，哥白尼只能将他的模型匿名地流传。）他的观 念是，太阳是静止地位于中心，而地球和其他行星绕着太阳作圆周运动。将近一个世纪以后，他的观念才被认真地接受。后来，两位天文学家——德国的约翰斯·开 普勒和意大利的伽利雷·伽利略开始公开支持哥白尼的理论，尽管它所预言的轨道还不能完全与观测相符合。直到1609年，亚里士多德——托勒密的理论才宣告 死亡。那一年，伽利略用刚发明的望远镜来观测夜空。当他观测木星时，发现有几个小卫星或月亮绕着它转动。这表明不象亚里士多德和托勒密所设想的，并不是所 有的东西都必须直接围绕着地球转。（当然，仍然可能相信地球是静止地处于宇宙的中心，而木星的卫星沿着一种极其复杂的轨道绕地球运动，表观上看来它们是绕 着木星转动。然而哥白尼理论是简单得多了。）同时，开普勒修正了哥白尼理论，认为行星不是沿圆周而是沿椭圆（椭圆是被拉长的圆）运动，从而使预言最终和观 察相互一致了。
就 开普勒而言，椭圆轨道仅仅是想当然的，并且是相当讨厌的假设，因为椭圆明显地不如圆那么完美。虽然他几乎是偶然地发现椭圆轨道能很好地和观测相符合，但却 不能把它和他的行星绕太阳运动是由于磁力引起的另一思想相互调和起来。对这一切提供解释是晚得多的事，那是由于1687年伊萨克·牛顿爵士出版了他的《数 学的自然哲学原理》，这部也许是有史以来物理科学上最重要的单独的著作。在这本书中，牛顿不但提出物体如何在空间和时间中运动的理论，并且发展了为分析这 些运动所需的复杂的数学。此外，牛顿提出了万有引力定律，根据这定律，宇宙中的任一物体都被另外物体所吸引，物体质量越大，相互距离越近，则相互之间的吸 引力越大。这也就是使物体落到地面上的力。（由于一个苹果落到牛顿的头上而使他得到灵感的故事，几乎肯定是不足凭信的。所有牛顿自己说过的只是，当他陷入 沉思之时，一颗苹果的落下使他得到了万有引力的思想。）牛顿继而指出，根据他的定律，引力使月亮沿着椭圆轨道绕着地球运行，而地球和其他行星沿着椭圆轨道 绕着太阳公转。
按 照他的引力理论，牛顿意识到恒星应该相互吸引，看来它们不能保持基本上不动。那么它们会一起落到某处去吗？在1691年写给当时另一位最重要的思想家里查 德·本特里的一封信中，他论证道，如果只有有限颗恒星分布在一个有限的空间区域里，这确实是会发生的。但是另一方面，他推断如果存在无限多颗恒星，多少均 匀地分布于无限的空间，这种情形就不会发生，因为这时不存在任何一个它们落去的中心点。
当 人们议论到无穷时，这种论证是你会遭遇到的一种陷阱。在一个无限的宇宙，每一点都可以认为是中心，因为在它的每一边都有无限颗恒星。正确的方法是很久以后 才被意识到的，即是先考虑有限的情形，这时所有恒星都相互落到一起，然后在这个区域以外，大体均匀地加上更多的恒星，看情况会如何改变。按照牛顿定律，这 额外的恒星平均地讲对原先的那些根本没有什么影响，所以这些恒星还是同样快地落到一起。我们愿意加上多少恒星就可以加上多少，但是它们仍然总是坍缩在一 起。现在我们知道，由于引力总是吸引的，不可能存在一个无限的静态的宇宙模型。
在 20世纪之前从未有人暗示过，宇宙是在膨胀或是在收缩，这有趣地反映了当时的思维风气。一般认为，宇宙或是以一种不变的状态已存在了无限长的时间，或以多 多少少正如我们今天所看的样子被创生于有限久的过去。其部分的原因可能是，人们倾向于相信永恒的真理，也由于虽然人会生老病死，但宇宙必须是不朽的、不变 的这种观念才能给人以安慰。
甚 至那些意识到牛顿的引力理论导致宇宙不可能静止的人，也没有想到提出宇宙可能是在膨胀。相反的，他们试图修正理论，使引力在非常大距离时成为斥力。这不会 对行星运动的预言有重大的影响，然而却允许无限颗恒星的分布保持平衡——邻近恒星之间的吸引力被远隔恒星之间的斥力所平衡。然而，现在我们知道，这样的平 衡是不稳定的：如果某一区域内的恒星稍微互相靠近一些，引力就增强，并超过斥力的作用，这样这些恒星就会继续落到一起。反之，如果某一区域内的恒星稍微互 相远离一些，斥力就起主导作用，并驱使它们离得更开。
另 一个反对无限静止宇宙的异见通常是归功于德国哲学家亨利希·奥勃斯，1823年他发表了这个理论。事实上，牛顿的同时代的一些人已经提出过这个问题。甚至 奥勃斯的文章也不是貌似有理地反驳这模型的第一篇。不管怎么说，这是第一篇被广泛注意的文章。这无限静止模型的困难，在于几乎每一道视线必须终结于某一恒 星的表面。这样，人们可以预料，整个天空甚至在夜晚都会像太阳那么明亮。奥勃斯反驳说，远处恒星的光线由于被它所穿过的物质吸收所减弱。然而如果真是如 此，这相干的物质将会最终被加热到发出和恒星一样强的光为止。唯一的能避免整个天空像太阳那么亮的结论的方法是，假定恒星并不是永远那么亮，而是在有限久 的过去才开始发光。这种情况下，吸光物质还没加热，或者远处恒星的光线尚未到达我们这儿。这使我们面临着是什么首次使恒星发光的问题。
当 然，宇宙开端的问题在这之前很久就被讨论过。根据一些早先的宇宙论和犹太人／基督教／穆斯林传统，宇宙开端于有限的、并且不是非常远的过去的某一时刻。对 这样一个开端，有一种议论是感到必须有“第一原因“来解释宇宙的存在。（在宇宙中，你总可以将一个事件解释为由于另一个更早的事件所引起的，但是宇宙本身 的存在只有当存在某个开端时才能被解释。）另一种论证是圣·奥古斯丁在他的《上帝之城》的著作中提出的。他指出，文明在进步，我们将记住创造这些业绩和发 展技术的人们。这样人，也许宇宙，不可能已经存在了太长的时间。圣·奥古斯丁根据《创世纪》一书，接受公元前5000年作为宇宙的被创生的时间。（有趣的 是， 这和上一次的冰河时间的结束，大约公元前10000年相距不远。考古学家告诉我们，文明实际上是从那时开始的。）
另 一方面，亚里士多德和大多数其他希腊哲学家不喜欢创生的思想，因为它带有太多的神学干涉的味道。所以他们相信，人类及其周围的世界已经并且将继续永远存 在。古代的人们已经考虑到上述的文明进步的论点，用周期性洪水或其他灾难的重复出现，使人类回到文明的开初，来回答上面的话难。
1781 年，哲学家伊曼努尔·康德发表了里程碑般的（也是非常模糊的）著作——《纯粹理性批判》，在这本书中，他深入地考察了关于宇宙在时间上是否有开端、空间上 是否有极限的问题。他称这些问题为纯粹理性的二律背反（也就是矛盾）。因为他感到存在同样令人信服的论据，来证明宇宙有开端的正命题，以及宇宙已经存在无 限久的反命题。他对正命题的论证是：如果宇宙没有一个开端，则任何事件之前必有无限的时间。他认为这是荒谬的。他对反命题的论证是：如果宇宙有一开端，在 它之前必有无限的时间，为何宇宙必须在某一特定的时刻开始呢？事实上，他对正命题和反命题用了同样的论证。它们都是基于他的隐含的假设，即不管宇宙是否存 在了无限久，时间均可无限地倒溯回去。我们将会看到，在宇宙开端之前时间概念是没有意义的。这一点是圣·奥古斯丁首先指出的。当他被问及：上帝在创造宇宙 之前做什么？奥古斯丁没有这样地回答：他正为问这类问题的人准备地狱。而是说：时间是上帝所创造的宇宙的一个性质，在宇宙开端之前不存在。
当 大部分人相信一个本质上静止不变的宇宙时，关于它有无开端的问题，实在是一个形而上学或神学的问题。按照宇宙存在无限久的理论，或者按照宇宙在某一个有限 时刻，以给人的印象似乎是已经存在了无限久的样子启动的理论，我们可以同样很好地解释所观察到的事实。但在1929年，埃德温·哈勃作出了一个具有里程碑 意义的观测，即是不管你往那个方向看，远处的星系正急速地远离我们而去。换言之，宇宙正在膨胀。这意味着，在早先星体相互之间更加靠近。事实上，似乎在大 约100亿至200亿年之前的某一时刻，它们刚好在同一地方，所以那时候宇宙的密度无限大。这个发现最终将宇宙开端的问题带进了科学的王国。
哈 勃的发现暗示存在一个叫做大爆炸的时刻，当时宇宙的尺度无穷小，而且无限紧密。在这种条件下，所有科学定律并因此所有预见将来的能力都失效了。如果在此时 刻之前有过些事件，它们将不可能影响现在所发生的一切。所以我们可以不理它们，因为它们并没有可观测的后果。由于更早的时间根本没有定义，所以在这个意义 上人们可以说，时间在大爆炸时有一开端。必须强调的是，这个时间的开端是和早先考虑的非常不同。在一个不变的宇宙中，时间的端点必须由宇宙之外的存在物所 赋予；宇宙的开端并没有物理的必要性。人们可以想像上帝在过去的任何时刻创造宇宙。另一方面，如果宇宙在膨胀，何以宇宙有一个开端似乎就有了物理的原因。 人们仍然可以想像，上帝是在大爆炸的瞬间创造宇宙，或者甚至在更晚的时刻，以便它看起来就像发生过大爆炸似的方式创造，但是设想在大爆炸之前创造宇宙是没 有意义的。大爆炸模型并没有排斥造物主，只不过对他何时从事这工作加上时间限制而已！
为 了谈论宇宙的性质和讨论诸如它是否存在开端或终结的问题，你必须清楚什么是科学理论。我将采用头脑简单的观点，即理论只不过是宇宙或它的受限制的一部分的 模型，一些联结这模型和我们所观察的量的规则。它只存在于我们的头脑中，（不管在任何意义上）不再具有任何其他的实在性。如果它满足以下两个要求，就算是 好的理论：它必须在只包含一些任意元素的一个模型的基础上，准确地描述大批的观测，并对未来观测的结果作出确定的预言。例如，亚里士多德关于任何东西是由 四元素，土、空气、火和水组成的理论是足够简单的了，但它没有做出任何确定的预言。另一方面，牛顿的引力理论是基于甚至更为简单的模型，在此模型中两物体 之间的相互吸引力和它们称之为质量的量成正比，并和它们之间的距离的平方成反比。然而，它以很高的精确性预言了太阳、月亮和行星的运动。
在 它只是假设的意义上来讲，任何物理理论总是临时性的：你永远不可能将它证明。不管多少回实验的结果和某一理论相一致，你永远不可能断定下一次结果不会和它 矛盾。另一方面，哪怕你只要找到一个和理论预言不一致的观测事实，即可证伪之。正如科学哲学家卡尔·波帕所强调的，一个好的理论的特征是，它能给出许多原 则上可以被观测所否定或证伪的预言。每回观察到与这预言相符的新的实验，则这理论就幸存，并且增加了我们对它的可信度；然而若有一个新的观测与之不符，则 我们只得抛弃或修正这理论。至少被认为这迟早总会发生的，问题在于人们有无才干去实现这样的观测。
实 际上经常发生的是，所设计的新理论确实是原先理论的推广。例如，对水星的非常精确的观测揭露了它的运动和牛顿理论预言之间的很小差异。爱因斯坦的广义相对 论所预言的运动和牛顿理论略有不同。爱因斯坦的预言和观测相符，而牛顿的预言与观测不相符，这一事实是这个新理论的一个关键证据。然而我们在大部分实际情 况下仍用牛顿理论，因为在我们通常处理的情形下，两者差别非常小。（牛顿理论的另一个巨大的优点在于，它比爱因斯坦理论容易处理得多！）
科 学的终极目的在于提供一个简单的理论去描述整个宇宙。然而，大部分科学家遵循的方法是将这问题分成两部分。首先，是一些告诉我们宇宙如何随时间变化的定 律；（如果我们知道在任一时刻宇宙是什么样子的，则这些定律即能告诉我们以后的任一时刻宇宙是什么样子的。）第二，关于宇宙初始状态的问题。有些人认为科 学只应过问第一部分，他们认为初始状态的问题应是形而上学或宗教的范畴。他们会说，全能的上帝可以随心所欲地启动这个宇宙。也许是这样。但是，倘若那样， 他也可以使宇宙以完全任意的方式演化。可是，看起来他选择宇宙以一种非常规则的、按照一定规律的方式演化。所以，看来可以同样合理地假定，也存在着制约初 始状态的定律。
毕 全功于一役地设计一种能描述整个宇宙的理论，看来是非常困难的。反之，我们是将这问题分成许多小块，并发明许多部分理论。每一部分理论描述和预言一定有限 范围的观测，同时忽略其他量的效应或用简单的一组数来代表之。可能这方法是全错的。如果宇宙中的每一件东西都以非常基本的方式依赖于其他的任何一件东西， 很可能不能用隔离法研究问题的部分去逼近其完备的答案。尽管如此，这肯定是我们在过去取得进展所用的方法。牛顿引力理论又是一个经典的例子，它告诉我们两 个物体之间的引力只决定于与每个物体相关的一个数——它的质量；而与物体由何物组成无关。这样，人们不需要太阳和行星结构和成份的理论就可以计算它们的轨 道。
今 天科学家按照两个基本的部分理论——广义相对论和量子力学来描述宇宙。它们是本世纪上半叶的伟大的智慧成就。广义相对论是描述引力和宇宙的大尺度结构， 也就是从只有几英哩直到大至1亿亿亿（1后面跟24个0）英哩，即可观测到的宇宙范围的尺度的结构。另一方面，量子力学处理极小尺度的现象，例如万亿分之 一英寸。然而，可惜的是，这两个理论不是互相协调的——它们不可能都对。当代物理学的一个主要的努力，以及这本书的主题，即是寻求一个能将其合并在一起的 理论——量子引力论。我们还没有这样的理论，要获得这个理论，我们可能还有相当长的路要走，然而我们已经知道了这个理论所应具备的许多性质。在以下几章， 人们将会看到，我们已经知道了相当多的量子引力论所应有的预言。
现 在，如果你相信宇宙不是任意的，而是由确定的定律所制约的，你最终必须将这些部分理论合并成一套能描述宇宙中任何东西的完整统一理论。然而，在寻求这样的 完整统一理论中有一个基本的自相矛盾。在前面概括的关于科学理论的思想中，假定我们是有理性的生物，既可以随意自由地观测宇宙，又可以从观察中得出逻辑推 论。在这样的方案里可以合理地假设，我们可以越来越接近找到制约我们宇宙的定律。然而，如果真有一套完整的统一理论，则它也将决定我们的行动。这样，理论 本身将决定了我们对之探索的结果！那么为什么它必须确定我们从证据得到正确的结论？它不也同样可以确定我们引出错误的结论吗？或者根本没有结论？
对 于这个问题，我所能给出的回答是基于达尔文的自然选择原理。这思想是说，在任何自繁殖的群体中，存在有不同个体在遗传物质和发育上的变异。这些差异表明， 某些个体比其他个体对周围的世界更能引出正确的结论，并去适应它。这些个体更可能存活、繁殖，因此它们的行为和思维的模式将越来越起主导作用。这一点在过 去肯定是真的，即我们称之为智慧和科学发现的东西给我们带来了存活的好处。这种情况是否仍会如此不是很清楚：我们的科学发现也可以将我们的一切都毁灭。即 使不是这样，一个完整的统一理论对于我们存活的机会不会有很大影响。然而，假定宇宙已经以规则的方式演化至今，我们可以预期，自然选择赋予我们的推理能力 在探索完整统一理论时仍然有效，并因此不会导致我们得到错误的结论。
因为除了最极端 的情况外，我们已有了对所有一切都足够给出精确的预言的部分理论，看来很难以现实的理由为探索宇宙的终极理论辩护。（值得指出，虽然可用类似的论点来攻击 相对论和量子力学，但这些理论已给我们带来了核能和微电子学的革命！）所以，一套完整的统一理论的发现可能对我们种族的存活无助，甚至也不会影响我们的生 活方式。然而自从文明开始，人们即不甘心于将事件看作互不相关而不可理解的。他们渴求理解世界的根本秩序。今天我们仍然渴望知道，我们为何在此？我们从何 而来？人类求知的最深切的意愿足以为我们所从事的不断的探索提供正当的理由。而我们的目标恰恰正是对于我们生存其中的宇宙作完整的描述。
A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.“ The scientist gave a superior smile before replying, “What is the tortoise standing on.“ “You’re very clever, young man, very clever,“ said the old lady. “But it’s turtles all the way down!“ Most people would find the picture of our universe as an infinite tower of tortoises rather ridiculous, but why do we think we know better? What do we know about the universe, and how do we know it? Where did the universe come from, and where is it going? Did the universe have a beginning, and if so, what happened before then? What is the nature of time? Will it ever come to an end? Can we go back in time? Recent breakthroughs in physics, made possible in part by fantastic new technologies, suggest answers to some of these longstanding questions. Someday these answers may seem as obvious to us as the earth orbiting the sun – or perhaps as ridiculous as a tower of tortoises. Only time (whatever that may be) will tell.
As long ago as 340 BC the Greek philosopher Aristotle, in his book On the Heavens, was able to put forward two good arguments for believing that the earth was a round sphere rather than a Hat plate. First, he realized that eclipses of the moon were caused by the earth coming between the sun and the moon. The earth’s shadow on the moon was always round, which would be true only if the earth was spherical. If the earth had been a flat disk, the shadow would have been elongated and elliptical, unless the eclipse always occurred at a time when the sun was directly under the center of the disk. Second, the Greeks knew from their travels that the North Star appeared lower in the sky when viewed in the south than it did in more northerly regions. (Since the North Star lies over the North Pole, it appears to be directly above an observer at the North Pole, but to someone looking from the equator, it appears to lie just at the horizon. From the difference in the apparent position of the North Star in Egypt and Greece, Aristotle even quoted an estimate that the distance around the earth was 400,000 stadia. It is not known exactly what length a stadium was, but it may have been about 200 yards, which would make Aristotle’s estimate about twice the currently accepted figure. The Greeks even had a third argument that the earth must be round, for why else does one first see the sails of a ship coming over the horizon, and only later see the hull? Aristotle thought the earth was stationary and that the sun, the moon, the planets, and the stars moved in circular orbits about the earth. He believed this because he felt, for mystical reasons, that the earth was the center of the universe, and that circular motion was the most perfect. This idea was elaborated by Ptolemy in the second century AD into a complete cosmological model. The earth stood at the center, surrounded by eight spheres that carried the moon, the sun, the stars, and the five planets known at the time, Mercury, Venus, Mars, Jupiter, and Saturn.
Figure 1:1 The planets themselves moved on smaller circles attached to their respective spheres in order to account for their rather complicated observed paths in the sky. The outermost sphere carried the so-called fixed stars, which always stay in the same positions relative to each other but which rotate together across the sky. What lay beyond the last sphere was never made very clear, but it certainly was not part of mankind’s observable universe.
Ptolemy’s model provided a reasonably accurate system for predicting the positions of heavenly bodies in the sky. But in order to predict these positions correctly, Ptolemy had to make an assumption that the moon followed a path that sometimes brought it twice as close to the earth as at other times. And that meant that the moon ought sometimes to appear twice as big as at other times! Ptolemy recognized this flaw, but nevertheless his model was generally, although not universally, accepted. It was adopted by the Christian church as the picture of the universe that was in accordance with Scripture, for it had the great advantage that it left lots of room outside the sphere of fixed stars for heaven and hell.
A simpler model, however, was proposed in 1514 by a Polish priest, Nicholas Copernicus. (At first, perhaps for fear of being branded a heretic by his church, Copernicus circulated his model anonymously.) His idea was that the sun was stationary at the center and that the earth and the planets moved in circular orbits around the sun.
Nearly a century passed before this idea was taken seriously. Then two astronomers – the German, Johannes
Kepler, and the Italian, Galileo Galilei – started publicly to support the Copernican theory, despite the fact that the orbits it predicted did not quite match the ones observed. The death blow to the Aristotelian/Ptolemaic theory came in 1609. In that year, Galileo started observing the night sky with a telescope, which had just been invented. When he looked at the planet Jupiter, Galileo found that it was accompanied by several small satellites or moons that orbited around it. This implied that everything did not have to orbit directly around the earth, as Aristotle and Ptolemy had thought. (It was, of course, still possible to believe that the earth was stationary at the center of the universe and that the moons of Jupiter moved on extremely complicated paths around the earth, giving the appearance that they orbited Jupiter. However, Copernicus’s theory was much simpler.) At the same time, Johannes Kepler had modified Copernicus’s theory, suggesting that the planets moved not in circles but in ellipses (an ellipse is an elongated circle). The predictions now finally matched the observations.
As far as Kepler was concerned, elliptical orbits were merely an ad hoc hypothesis, and a rather repugnant one at that, because ellipses were clearly less perfect than circles. Having discovered almost by accident that elliptical orbits fit the observations well, he could not reconcile them with his idea that the planets were made to orbit the sun by magnetic forces. An explanation was provided only much later, in 1687, when Sir Isaac Newton published his Philosophiae Naturalis Principia Mathematica, probably the most important single work ever published in the physical sciences. In it Newton not only put forward a theory of how bodies move in space and time, but he also developed the complicated mathematics needed to analyze those motions. In addition, Newton postulated a law of universal gravitation according to which each body in the universe was attracted toward every other body by a force that was stronger the more massive the bodies and the closer they were to each other. It was this same force that caused objects to fall to the ground. (The story that Newton was inspired by an apple hitting his head is almost certainly apocryphal. All Newton himself ever said was that the idea of gravity came to him as he sat “in a contemplative mood“ and “was occasioned by the fall of an apple.“) Newton went on to show that, according to his law, gravity causes the moon to move in an elliptical orbit around the earth and causes the earth and the planets to follow elliptical paths around the sun.
The Copernican model got rid of Ptolemy’s celestial spheres, and with them, the idea that the universe had a natural boundary. Since “fixed stars“ did not appear to change their positions apart from a rotation across the sky caused by the earth spinning on its axis, it became natural to suppose that the fixed stars were objects like our sun but very much farther away.
Newton realized that, according to his theory of gravity, the stars should attract each other, so it seemed they could not remain essentially motionless. Would they not all fall together at some point? In a letter in 1691 to Richard Bentley, another leading thinker of his day, Newton argued that this would indeed happen if there were only a finite number of stars distributed over a finite region of space. But he reasoned that if, on the other hand, there were an infinite number of stars, distributed more or less uniformly over infinite space, this would not happen, because there would not be any central point for them to fall to.
This argument is an instance of the pitfalls that you can encounter in talking about infinity. In an infinite universe, every point can be regarded as the center, because every point has an infinite number of stars on each side of it. The correct approach, it was realized only much later, is to consider the finite situation, in which the stars all fall in on each other, and then to ask how things change if one adds more stars roughly uniformly distributed outside this region. According to Newton’s law, the extra stars would make no difference at all to the original ones on average, so the stars would fall in just as fast. We can add as many stars as we like, but they will still always collapse in on themselves. We now know it is impossible to have an infinite static model of the universe in which gravity is always attractive.
It is an interesting reflection on the general climate of thought before the twentieth century that no one had suggested that the universe was expanding or contracting. It was generally accepted that either the universe had existed forever in an unchanging state, or that it had been created at a finite time in the past more or less as we observe it today. In part this may have been due to people’s tendency to believe in eternal truths, as well as the comfort they found in the thought that even though they may grow old and die, the universe is eternal and unchanging.
Even those who realized that Newton’s theory of gravity showed that the universe could not be static did not think to suggest that it might be expanding. Instead, they attempted to modify the theory by making the
gravitational force repulsive at very large distances. This did not significantly affect their predictions of the motions of the planets, but it allowed an infinite distribution of stars to remain in equilibrium – with the attractive forces between nearby stars balanced by the repulsive forces from those that were farther away. However, we now believe such an equilibrium would be unstable: if the stars in some region got only slightly nearer each other, the attractive forces between them would become stronger and dominate over the repulsive forces so that the stars would continue to fall toward each other. On the other hand, if the stars got a bit farther away from each other, the repulsive forces would dominate and drive them farther apart.
Another objection to an infinite static universe is normally ascribed to the German philosopher Heinrich Olbers, who wrote about this theory in 1823. In fact, various contemporaries of Newton had raised the problem, and the Olbers article was not even the first to contain plausible arguments against it. It was, however, the first to be widely noted. The difficulty is that in an infinite static universe nearly every line of sight would end on the surface of a star. Thus one would expect that the whole sky would be as bright as the sun, even at night.
Olbers’ counter-argument was that the light from distant stars would be dimmed by absorption by intervening matter. However, if that happened the intervening matter would eventually heat up until it glowed as brightly as the stars. The only way of avoiding the conclusion that the whole of the night sky should be as bright as the surface of the sun would be to assume that the stars had not been shining forever but had turned on at some finite time in the past. In that case the absorbing matter might not have heated up yet or the light from distant stars might not yet have reached us. And that brings us to the question of what could have caused the stars to have turned on in the first place.
The beginning of the universe had, of course, been discussed long before this. According to a number of early cosmologies and the Jewish/Christian/Muslim tradition, the universe started at a finite, and not very distant, time in the past. One argument for such a beginning was the feeling that it was necessary to have “First Cause“ to explain the existence of the universe. (Within the universe, you always explained one event as being caused by some earlier event, but the existence of the universe itself could be explained in this way only if it had some beginning.) Another argument was put forward by St. Augustine in his book The City of God. He pointed out that civilization is progressing and we remember who performed this deed or developed that technique. Thus man, and so also perhaps the universe, could not have been around all that long. St. Augustine accepted a date of about 5000 BC for the Creation of the universe according to the book of Genesis. (It is interesting that this is not so far from the end of the last Ice Age, about 10,000 BC, which is when archaeologists tell us that civilization really began.) Aristotle, and most of the other Greek philosophers, on the other hand, did not like the idea of a creation because it smacked too much of divine intervention. They believed, therefore, that the human race and the world around it had existed, and would exist, forever. The ancients had already considered the argument about progress described above, and answered it by saying that there had been periodic floods or other disasters that repeatedly set the human race right back to the beginning of civilization.
The questions of whether the universe had a beginning in time and whether it is limited in space were later extensively examined by the philosopher Immanuel Kant in his monumental (and very obscure) work Critique of Pure Reason, published in 1781. He called these questions antinomies (that is, contradictions) of pure reason because he felt that there were equally compelling arguments for believing the thesis, that the universe had a beginning, and the antithesis, that it had existed forever. His argument for the thesis was that if the universe did not have a beginning, there would be an infinite period of time before any event, which he considered absurd.
The argument for the antithesis was that if the universe had a beginning, there would be an infinite period of time before it, so why should the universe begin at any one particular time? In fact, his cases for both the thesis and the antithesis are really the same argument. They are both based on his unspoken assumption that time continues back forever, whether or not the universe had existed forever. As we shall see, the concept of time has no meaning before the beginning of the universe. This was first pointed out by St. Augustine. When asked: “What did God do before he created the universe?“ Augustine didn’t reply: “He was preparing Hell for people who asked such questions.“ Instead, he said that time was a property of the universe that God created, and that time did not exist before the beginning of the universe.
When most people believed in an essentially static and unchanging universe, the question of whether or not it had a beginning was really one of metaphysics or theology. One could account for what was observed equally well on the theory that the universe had existed forever or on the theory that it was set in motion at some finite
time in such a manner as to look as though it had existed forever. But in 1929, Edwin Hubble made the landmark observation that wherever you look, distant galaxies are moving rapidly away from us. In other words, the universe is expanding. This means that at earlier times objects would have been closer together. In fact, it seemed that there was a time, about ten or twenty thousand million years ago, when they were all at exactly the same place and when, therefore, the density of the universe was infinite. This discovery finally brought the question of the beginning of the universe into the realm of science.
Hubble’s observations suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense. Under such conditions all the laws of science, and therefore all ability to predict the future, would break down. If there were events earlier than this time, then they could not affect what happens at the present time. Their existence can be ignored because it would have no observational consequences. One may say that time had a beginning at the big bang, in the sense that earlier times simply would not be defined. It should be emphasized that this beginning in time is very different from those that had been considered previously. In an unchanging universe a beginning in time is something that has to be imposed by some being outside the universe; there is no physical necessity for a beginning. One can imagine that God created the universe at literally any time in the past. On the other hand, if the universe is expanding, there may be physical reasons why there had to be a beginning. One could still imagine that God created the universe at the instant of the big bang, or even afterwards in just such a way as to make it look as though there had been a big bang, but it would be meaningless to suppose that it was created before the big bang. An expanding universe does not preclude a creator, but it does place limits on when he might have carried out his job! In order to talk about the nature of the universe and to discuss questions such as whether it has a beginning or an end, you have to be clear about what a scientific theory is. I shall take the simpleminded view that a theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make. It exists only in our minds and does not have any other reality (whatever that might mean). A theory is a good theory if it satisfies two requirements. It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations. For example, Aristotle believed Empedocles’s theory that everything was made out of four elements, earth, air, fire, and water. This was simple enough, but did not make any definite predictions. On the other hand, Newton’s theory of gravity was based on an even simpler model, in which bodies attracted each other with a force that was proportional to a quantity called their mass and inversely proportional to the square of the distance between them. Yet it predicts the motions of the sun, the moon, and the planets to a high degree of accuracy.
Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory. As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation. Each time new experiments are observed to agree with the predictions the theory survives, and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory.
At least that is what is supposed to happen, but you can always question the competence of the person who carried out the observation.
In practice, what often happens is that a new theory is devised that is really an extension of the previous theory.
For example, very accurate observations of the planet Mercury revealed a small difference between its motion and the predictions of Newton’s theory of gravity. Einstein’s general theory of relativity predicted a slightly different motion from Newton’s theory. The fact that Einstein’s predictions matched what was seen, while Newton’s did not, was one of the crucial confirmations of the new theory. However, we still use Newton’s theory for all practical purposes because the difference between its predictions and those of general relativity is very small in the situations that we normally deal with. (Newton’s theory also has the great advantage that it is much simpler to work with than Einstein’s!) The eventual goal of science is to provide a single theory that describes the whole universe. However, the
approach most scientists actually follow is to separate the problem into two parts. First, there are the laws that tell us how the universe changes with time. (If we know what the universe is like at any one time, these physical laws tell us how it will look at any later time.) Second, there is the question of the initial state of the universe.
Some people feel that science should be concerned with only the first part; they regard the question of the initial situation as a matter for metaphysics or religion. They would say that God, being omnipotent, could have started the universe off any way he wanted. That may be so, but in that case he also could have made it develop in a completely arbitrary way. Yet it appears that he chose to make it evolve in a very regular way according to certain laws. It therefore seems equally reasonable to suppose that there are also laws governing the initial state.
It turns out to be very difficult to devise a theory to describe the universe all in one go. Instead, we break the problem up into bits and invent a number of partial theories. Each of these partial theories describes and predicts a certain limited class of observations, neglecting the effects of other quantities, or representing them by simple sets of numbers. It may be that this approach is completely wrong. If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution by investigating parts of the problem in isolation. Nevertheless, it is certainly the way that we have made progress in the past. The classic example again is the Newtonian theory of gravity, which tells us that the gravitational force between two bodies depends only on one number associated with each body, its mass, but is otherwise independent of what the bodies are made of. Thus one does not need to have a theory of the structure and constitution of the sun and the planets in order to calculate their orbits.
Today scientists describe the universe in terms of two basic partial theories – the general theory of relativity and quantum mechanics. They are the great intellectual achievements of the first half of this century. The general theory of relativity describes the force of gravity and the large-scale structure of the universe, that is, the structure on scales from only a few miles to as large as a million million million million (1 with twenty-four zeros after it) miles, the size of the observable universe. Quantum mechanics, on the other hand, deals with phenomena on extremely small scales, such as a millionth of a millionth of an inch. Unfortunately, however, these two theories are known to be inconsistent with each other – they cannot both be correct. One of the major endeavors in physics today, and the major theme of this book, is the search for a new theory that will incorporate them both – a quantum theory of gravity. We do not yet have such a theory, and we may still be a long way from having one, but we do already know many of the properties that it must have. And we shall see, in later chapters, that we already know a fair amount about the predications a quantum theory of gravity must make.
Now, if you believe that the universe is not arbitrary, but is governed by definite laws, you ultimately have to combine the partial theories into a complete unified theory that will describe everything in the universe. But there is a fundamental paradox in the search for such a complete unified theory. The ideas about scientific theories outlined above assume we are rational beings who are free to observe the universe as we want and to draw logical deductions from what we see.
In such a scheme it is reasonable to suppose that we might progress ever closer toward the laws that govern our universe. Yet if there really is a complete unified theory, it would also presumably determine our actions.
And so the theory itself would determine the outcome of our search for it! And why should it determine that we come to the right conclusions from the evidence? Might it not equally well determine that we draw the wrong conclusion.? Or no conclusion at all? The only answer that I can give to this problem is based on Darwin’s principle of natural selection. The idea is that in any population of self-reproducing organisms, there will be variations in the genetic material and upbringing that different individuals have. These differences will mean that some individuals are better able than others to draw the right conclusions about the world around them and to act accordingly. These individuals will be more likely to survive and reproduce and so their pattern of behavior and thought will come to dominate.
It has certainly been true in the past that what we call intelligence and scientific discovery have conveyed a survival advantage. It is not so clear that this is still the case: our scientific discoveries may well destroy us all, and even if they don’t, a complete unified theory may not make much difference to our chances of survival.
However, provided the universe has evolved in a regular way, we might expect that the reasoning abilities that natural selection has given us would be valid also in our search for a complete unified theory, and so would not lead us to the wrong conclusions.
Because the partial theories that we already have are sufficient to make accurate predictions in all but the most extreme situations, the search for the ultimate theory of the universe seems difficult to justify on practical grounds. (It is worth noting, though, that similar arguments could have been used against both relativity and quantum mechanics, and these theories have given us both nuclear energy and the microelectronics revolution!) The discovery of a complete unified theory, therefore, may not aid the survival of our species. It may not even affect our lifestyle. But ever since the dawn of civilization, people have not been content to see events as unconnected and inexplicable. They have craved an understanding of the underlying order in the world. Today we still yearn to know why we are here and where we came from. Humanity’s deepest desire for knowledge is justification enough for our continuing quest. And our goal is nothing less than a complete description of the universe we live in.