亚 里士多德认为物质是连续的，也就是说，人们可以将物质无限制地分割成越来越小的小块，即人们永远不可能得到一个不可再分割下去的最小颗粒。然而有几个希腊 人，例如德漠克里特，则坚持物质的固有的颗粒性，而且认为每一件东西都是由不同种类的大量的原子所组成（在希腊文中原子的意义是“不可分的“）。争论一直 持续了几个世纪，任何一方都没有任何实际的证据。直至1803年英国的化学家兼物理学家约翰·道尔顿指出，化合物总是以一定的比例结合而成的。这一事实可 以用来解释所谓分子的单元是由原子组成的。然而，直到本世纪初这两种学派的争论才以原子论的胜利而告终。爱因斯坦提供了一个重要的物理学证据。1905 年，在他关于狭义相对论的著名论文发表前的几周，他在所发表的另一篇文章里指出，所谓的布朗运动——悬浮在液体中的尘埃小颗粒的无则规的、随机的运动—— 可以解释为液体原子和灰尘粒子碰撞的效应。
当 时已经有人怀疑这些原子终究不是不可分割的。几年前，一位剑桥大学三一学院的研究员汤姆逊演示了一种称为电子的物质粒子存在的证据。电子所具有的质量比最 轻原子小1千倍。 他使用了一种和现代电视显像管相当类似的装置：由一根红热的金属细丝发射出电子，由于它们带负电荷，可用一电场去将其加速飞到一个涂磷光物质的屏幕上。电 子一打到屏幕上就会产生一束束的闪光。人们很快即意识到，这些电子必须从原子里出来。英国物理学家恩斯特·卢瑟福在1911年最后证明了物质的原子确实有 内部结构：它们是由一个极其微小的带正电荷的核以及围绕着它转动的一些电子组成。他是根据从放射性原子释放出的带正电荷的。粒子和原子碰撞会引起的偏折这 一现象，以及分析了此偏折的方式后而推出这一结论的。
最 初，人们认为原子核是由电子和不同数量的带正电的叫做质子的粒子所组成。质子是由希腊文中的“第一“演化而来的，因为质子被认为是组成物质的基本单位。然 而，卢瑟福在剑桥的一位同事詹姆斯·查德威克在1932年发现，原子核还包含另外称为中子的粒子，中子几乎具有和质子一样大的质量但没有带电荷；查德威克 因此而获得诺贝尔奖，并选为剑桥龚维尔和凯尔斯学院（我即为该学院的研究员）院长。后来，他因为和其他人不和而辞去院长的职务。一群战后回来的年轻的研究 员将许多已占据位置多年的老研究员选掉后，曾有过一场激烈的辩论。这是在我去以前发生的；在这场争论尾声的1965年我才加入该学院，当时另一位获诺贝尔 奖的院长奈维尔·莫特爵士也因类似的争论而辞职。
直到20年以前，人们还总以为质子和中子是“基本“粒子。但是，将质子和另外的质子或电子在高速度下碰撞的实验表明，它们事实上是由更小的粒子构成的。加州理工学院的牟雷·盖尔曼将这些粒子命名为夸克。由于对夸克的研究，他获得1969年的诺贝尔奖。 此名字起源于詹姆斯·约依斯神秘的引语： “Three quarksfor Muster Mark！ “夸克这个字应发夸脱的音，但是最后的字母是k而不是t，通常和拉克（云雀）相押韵。
存 在有几种不同类型的夸克——至少有六种以上的“味“，这些味我们分别称之为上、下、奇、魅、底和顶。每种味都带有三种“色“，即红、绿和蓝。（必须强调， 这些术语仅仅是记号：夸克比可见光的波长小得多，所以在通常意义下没有任何颜色。这只不过是现代物理学家更富有想像力地去命名新粒子和新现象而已——他们 不再将自己限制于只用希腊文！）一个质子或中子是由三个夸克组成，每个一种颜色。一个质子包含两个上夸克和一个下夸克；一个中子包含两个下夸克和一个上夸 克。我们可用其他种类的夸克（奇、魅、底和顶）构成粒子，但所有这些都具有大得多的质量，并非常快地衰变成质子和中子。
现 在我们知道，不管是原子还是其中的质子和中子都不是不可分的。问题在于什么是真正的基本粒子——构成世界万物的最基本的构件？由于光波波长比原子的尺度大 得多，我们不能期望以通常的方法去“看“一个原子的部分，而必须用某些波长短得多的东西。正如我们在上一章所看到的，量子力学告诉我们，实际上所有粒子都 是波动， 粒子的能量越高，J则其对应的波动的波长越短。所以，我们能对这个问题给出的最好的回答，取决于我们的设想中所能得到多高的粒子能量，因为这决定了我们所 能看到的多小的尺度。这些粒子的能量通常是以称为电子伏特的单位来测量。（在汤姆逊的电子实验中，我们看到他用一个电场去加速电子，一个电子从一个伏特的 电场所得到的能量即是一个电子伏特。）19世纪，当人们知道如何去使用的粒子能量只是由化学反应——诸如燃烧——产生的几个电子伏特的低能量时，大家以为 原子即是最小的单位。在卢瑟福的实验中，α粒子具有几百万电子伏特的能量。更近代，我们知道使用电磁场给粒子提供首先是几百万然后是几十亿电子伏特的能 量。这样我们知道，20年之前以为是“基本“的粒子，原来是由更小的粒子所组成。如果我们用更高的能量时，是否会发现这些粒子是由更小的粒子所组成的呢？ 这一定是可能的。但我们确实有一些理论的根据，相信我们已经拥有或者说接近拥有自然界的终极构件的知识。
用 上一章讨论的波粒二象性，包括光和引力的宇宙中的一切都能以粒子来描述。这些粒子有一种称为自旋的性质。自旋可以设想成绕着一个轴自转的小陀螺。但这可能 会引起误会，因为量子力学告诉我们，粒子并没有任何很好定义的轴。粒子的自旋真正告诉我们的是， 从不同的方向看粒子是什么样子的。一个自旋为0的粒子像一个圆点： 从任何方向看都一样（图5.1－i）。而自旋为1的粒子像一个箭头：从不同方向看是不同的（图5.1-ii） 。只有把当它转过完全的一圈（360°）时，这粒子才显得是一样。 自旋为2的粒子像个双头的箭头（图5.1－iii）：只要转过半圈（180°） ，看起来便是一样的了。类似地，更高自旋的粒子在旋转了整圈的更小的部分后，看起来便是一样的。所有这一切都是这样的直截了当，但惊人的事实是，有些粒子 转过一圈后，仍然显得不同，你必须使其转两整圈！这样的粒子具有1／2的自旋。
宇 宙间所有已知的粒子可以分成两组：组成宇宙中的物质的自旋为1／2的粒子；在物质粒子之间引起力的自旋为0、 1和2的粒子。物质粒子服从所谓的泡利不相容原理。这是奥地利物理学家沃尔夫冈·泡利在1925年发现的，他并因此获得1945年的诺贝尔奖。他是个模范 的理论物理学家，有人这样说，他的存在甚至会使同一城市里的实验出毛病！泡利不相容原理是说，两个类似的粒子不能存在于同一个态中，即是说，在不确定性原 理给出的限制内，它们不能同时具有相同的位置和速度。不相容原理是非常关键的， 因为它解释了为何物质粒子在自旋为0、1和2的粒子产生的力的影响下不会坍缩成密度非常之高的状态的原因：如果物质粒子几乎在相同位置，则它们必须有不同 的速度，这意味着它们不会长时间存在于同一处。如果世界创生时不相容原理不起作用，夸克将不会形成不相连的、很好定义的质子和中子，进而这些也不可能和电 子形成不相连的、很好定义的原子。所有它们都会坍缩形成大致均匀的稠密的“汤“。
直 到保尔·狄拉克在1928年提出一个理论，人们才对电子和其他自旋1／2的粒子有了相当的理解。狄拉克后来被选为剑桥的卢卡逊数学教授（牛顿曾经担任这一 教授位置，目前我担任此一位置）。狄拉克理论是第一种既和量子力学又和狭义相对论相一致的理论。它在数学上解释了为何电子具有1／2的自旋，也即为什么将 其转一整圈不能、而转两整圈才能使它显得和原先一样。它并且预言了电子必须有它的配偶——反电子或正电子。1932年正电子的发现证实了狄拉克的理论，他 因此获得了1933年的诺贝尔物理奖。现在我们知道，任何粒子都有会和它相湮灭的反粒子。（对于携带力的粒子，反粒子即为其自身。）也可能存在由反粒子构 成的整个反世界和反人。然而，如果你遇到了反你，注意不要握手！否则，你们两人都会在一个巨大的闪光中消失殆尽。为何我们周围的粒子比反粒子多得多？这是 一个极端重要的问题，我将会在本章的后部分回到这问题上来。
携 带力的粒子不服从泡利不相容原理，这是它的一个重要的性质。这表明它们能被交换的数目不受限制，这样就可以产生根强的力。然而，如果携带力的粒子具有很大 的质量，则在大距离上产生和交换它们就会很困难。这样，它们所携带的力只能是短程的。另一方面，如果携带力的粒子质量为零，力就是长程的了。在物质粒子之 间交换的携带力的粒子称为虚粒子，因为它们不像“实“粒子那样可以用粒子探测器检测到。但我们知道它们的存在，因为它们具有可测量的效应，即它们引起了物 质粒子之间的力， 并且自旋为0、1或2的粒子在某些情况下作为实粒子而存在，这时它们可以被直接探测到。对我们而言，此刻它们就呈现出为经典物理学家所说的波动形式，例如 光波和引力波；当物质粒子以交换携带力的虚粒子的形式而相互作用时，它们有时就可以被发射出来。（例如，两个电子之间的电排斥力是由于交换虚光子所致，这 些虚光子永远不可能被检测出来；但是如果一个电子穿过另一个电子，则可以放出实光子，它以光波的形式为我们所探测到。）
携 带力的粒子按照其携带力的强度以及与其相互作用的粒子可以分成四种。必须强调指出，将力划分成四种是种人为的方法；它仅仅是为了便于建立部分理论，而并不 别具深意。大部分物理学家希望最终找到一个统一理论，该理论将四种力解释为一个单独的力的不同方面。确实，许多人认为这是当代物理学的首要目标。最近，将 四种力中的三种统一起来已经有了成功的端倪——我将在这章描述这些内容。而关于统一余下的另一种力即引力的问题将留到以后再讨论。
第 一种力是引力，这种力是万有的，也就是说，每一粒子都因它的质量或能量而感受到引力。引力比其他三种力都弱得多。它是如此之弱，以致于若不是它具有两个特 别的性质，我们根本就不可能注意到它。这就是，它会作用到非常大的距离去，并且总是吸引的。这表明，在像地球和太阳这样两个巨大的物体中，所有的粒子之间 的非常弱的引力能迭加起来而产生相当大的力量。另外三种力或者由于是短程的，或者时而吸引时而排斥，所以它们倾向于互相抵消。以量子力学的方法来研究引力 场， 人们把两个物质粒子之间的引力描述成由称作引力子的自旋为2的粒子所携带。它自身没有质量，所以所携带的力是长程的。太阳和地球之间的引力可以归结为构成 这两个物体的粒子之间的引力子交换。虽然所交换的粒子是虚的，它们确实产生了可测量的效应——它们使地球绕着太阳公转！实引力构成了经典物理学家称之为引 力波的东西，它是如此之弱——并且要探测到它是如此之困难，以致于还从来未被观测到过。
另一种力是电磁力。它作用于带电荷的粒子（例如电子和夸克）之间，但不和不带电荷的粒子（例如引力子）相互作用。 它 比引力强得多：两个电子之间的电磁力比引力大约大100亿亿亿亿亿（在1后面有42个0） 倍。然而，共有两种电荷——正电荷和负电荷。同种电荷之间的力是互相排斥的，而异种电荷则互相吸引。一个大的物体，譬如地球或太阳，包含了几乎等量的正电 荷和负电荷。由于单独粒子之间的吸引力和排斥力几乎全抵消了，因此两个物体之间纯粹的电磁力非常小。然而，电磁力在原子和分子的小尺度下起主要作用。在带 负电的电子和带正电的核中的质子之间的电磁力使得电子绕着原子的核作公转，正如同引力使得地球绕着太阳旋转一样。 人们将电磁吸引力描绘成是由于称作光子的无质量的自旋为1的粒子的交换所引起的。而且，这儿所交换的光子是虚粒子。但是，电子从一个允许轨道改变到另一个 离核更近的允许轨道时，以发射出实光子的形式释放能量——如果其波长刚好，则为肉眼可以观察到的可见光，或可用诸如照相底版的光子探测器来观察。同样，如 果一个光子和原子相碰撞，可将电子从离核较近的允许轨道移动到较远的轨道。这样光子的能量被消耗殆尽，也就是被吸收了。
第 三种力称为弱核力。它制约着放射性现象，并只作用于自旋为1／2的物质粒子， 而对诸如光子、引力子等自旋为0、1或2的粒子不起作用。直到1967年伦敦帝国学院的阿伯达斯·萨拉姆和哈佛的史蒂芬·温伯格提出了弱作用和电磁作用的 统一理论后， 弱作用才被很好地理解。此举在物理学界所引起的震动，可与100年前马克斯韦统一了电学和磁学并驾齐驱。温伯格——萨拉姆理论认为，除了光子，还存在其他 3个自旋为1的被统称作重矢量玻色子的粒子， 它们携带弱力。它们叫W＋（W正）、W－（W负）和Z0（Z零），每一个具有大约100吉电子伏的质量（1吉电子伏为10亿电子伏）。上述理论展现了称作 自发对称破缺的性质。它表明在低能量下一些看起来完全不同的粒子，事实上只是同一类型粒子的不同状态。在高能量下所有这些粒子都有相似的行为。这个效应和 轮赌盘上的轮赌球的行为相类似。在高能量下（当这轮子转得很快时），这球的行为基本上只有一个方式——即不断地滚动着；但是当轮子慢下来时，球的能量就减 少了，最终球就陷到轮子上的37个槽中的一个里面去。换言之，在低能下球可以存在于37个不同的状态。如果由于某种原因，我们只能在低能下观察球，我们就 会认为存在37种不同类型的球！
在 温伯格——萨拉姆理论中， 当能量远远超过100吉电子伏时，这三种新粒子和光子的行为方式很相似。但是，大部份正常情况下能量要比这低，粒子之间的对称就被破坏了。W＋、W－和 Z0得到了大的质量，使之携带的力变成非常短程。萨拉姆和温伯格提出此理论时，很少人相信他们，因为还无法将粒子加速到足以达到产生实的W＋、W－和Z0 粒子所需的一百吉电子伏的能量。但在此后的十几年里，在低能量下这个理论的其他预言和实验符合得这样好，以至于他们和也在哈佛的谢尔登·格拉肖一起被授予 1979年的物理诺贝尔奖。格拉肖提出过一个类似的统一电磁和弱作用的理论。由于1983年在CERN（欧洲核子研究中心）发现了具有被正确预言的质量和 其他性质的光子的三个带质量的伴侣，使得诺贝尔委员会避免了犯错误的难堪。领导几百名物理学家作出此发现的卡拉·鲁比亚和发展了被使用的反物质储藏系统的 cERN工程师西蒙·范德·米尔分享了1984年的诺贝尔奖。（除非你已经是巅峰人物，当今要在实验物理学上留下痕迹极其困难！）
第 四种力是强作用力。它将质子和中子中的夸克束缚在一起，并将原子中的质子和中子束缚在一起。一般认为，称为胶子的另一种自旋为1的粒子携带强作用力。它只 能与自身以及与夸克相互作用。强核力具有一种称为禁闭的古怪性质：它总是把粒子束缚成不带颜色的结合体。由于夸克有颜色（红、绿或蓝），人们不能得到单独 的夸克。反之，一个红夸克必须用一串胶子和一个绿夸克以及一个蓝夸克联结在一起（红＋绿＋蓝＝白）。这样的三胞胎构成了质子或中子。其他的可能性是由一个 夸克和一个反夸克组成的对（红＋反红，或绿＋反绿，或蓝＋反蓝＝白）。这样的结合构成称为介子的粒子。介子是不稳定的，因为夸克和反夸克会互相湮灭而产生 电子和其他粒子。类似地，由于胶子也有颜色，色禁闭使得人们不可能得到单独的胶子。相反地，人们所能得到的胶子的团，其迭加起来的颜色必须是白的。这样的 团形成了称为胶球的不稳定粒子。
色 禁闭使得人们观察不到一个孤立的夸克或胶子，这事实使得将夸克和胶子当作粒子的整个见解看起来有点玄学的味道。然而，强核力还有一个叫做渐近自由的性质， 它使得夸克和胶子成为定义得很好的概念。在正常能量下，强核力确实很强，它将夸克很紧地捆在一起。但是，大型粒子加速器的实验指出，在高能下强作用力变得 弱得多， 夸克和胶子的行为就像自由粒子那样。图5.2是张一个高能质子和一个反质子碰撞的照片。碰撞产生了几个几乎自由的夸克，并引起了在图中可以看到的“喷射“ 轨迹。
对电磁和弱力统一的成功，使许多人试图将这两种力和强核力合并在所谓的大统一理论（或GUT） 之中。这名字相当夸张，所得到的理论并不那么辉煌，也没能将全部力都统一进去，因为它并不包含引力。它们也不是真正完整的理论，因为它们包含了许多不能从这理论中预言而必须人为选择去适合实验的参数。尽管如此，它们可能是朝着完全的统一理论推进的一步。 GUT的基本思想是这样：正如前面提到的，在高能量时强核力变弱了；另一方面，不具有渐近自由性质的电磁力和弱力在高能量下变强了。在非常高的叫做大统一能量的能量下，这三种力都有同样的强度， 所以可看成一个单独的力的不同方面。在这能量下，GUT还预言了自旋为1／2的不同物质粒子（如夸克和电子）也会基本上变成一样，这样导致了另一种统一。
大统一能量的数值还知道得不太清楚， 可能至少有1千万亿吉电子伏特。而目前粒子加速器只能使大致能量为100吉电子伏的粒子相碰撞， 计划建造的机器的能量为几千吉电子伏。要建造足以将粒子加速到大统一能量的机器，其体积必须和太阳系一样大——这在现代经济环境下不太可能做到。因此，不可能在实验室里直接证实大统一理论。然而，如同在弱电统一理论中那样，我们可以检测它在低能量下的推论。
其 中最有趣的是预言是，构成通常物质的大部分质量的质子能自发衰变成诸如反电子之类更轻的粒子。其原因在于，在大统一能量下，夸克和反电子之间没有本质的不 同。正常情况下一个质子中的三个夸克没有足够能量转变成反电子，由于测不准原理意味着质子中夸克的能量不可能严格不变，所以，其中一个夸克能非常偶然地获 得足够能量进行这种转变，这样质子就要衰变。夸克要得到足够能量的概率是如此之低， 以至于至少要等100万亿亿亿年（1后面跟30个0）才能有一次。这比宇宙从大爆炸以来的年龄（大约100亿年——1后面跟10个0） 要长得多了。因此，人们会认为不可能在实验上检测到质子自发衰变的可能性。但是，我们可以观察包含极大数量质子的大量物质，以增加检测衰变的机会。（譬 如，如果观察的对象含有1后面跟31个0个质子， 按照最简单的GUT，可以预料在一年内应能看到多于一次的质子衰变。）
人 们进行了一系列的实验，可惜没有一个得到质子或中子衰变的确实证据。有一个实验是用了8千吨水在俄亥俄的莫尔顿盐矿里进行的 （为了避免其他因宇宙射线引起的会和质子衰变相混淆的事件发生）。由于在实验中没有观测到自发的质子衰变，因此可以估算出，可能的质子寿命至少应为1千万 亿亿亿年（1后面跟31个0）。这比简单的大统一理论所预言的寿命更长。然而，一些更精致更复杂的大统一理论预言的寿命比这更长，因此需要用更灵敏的手段 对甚至更大量的物质进行检验。
尽 管观测质子的自发衰变非常困难，但很可能正由于这相反的过程，即质子或更简单地说夸克的产生导致了我们的存在。它们是从宇宙开初的可以想像的最自然的方式 ——夸克并不比反夸克更多的状态下产生的。地球上的物质主要是由质子和中子，从而由夸克所构成。除了由少数物理学家在大型粒子加速器中产生的之外，不存在 由反夸克构成的反质子和反中子。从宇宙线中得到的证据表明，我们星系中的所有物质也是这样：除了少量当粒子和反粒子对进行高能碰撞时产生出来的以外，没有 发现反质子和反中子。如果在我们星系中有很大区域的反物质，则可以预料，在正反物质的边界会观测到大量的辐射，该处许多粒子和它们的反粒子相碰撞、互相湮 灭并释放出高能辐射。
为 什么夸克比反夸克多这么多？为何它们的数目不相等？这数目有所不同肯定使我们交了好运，否则，早期宇宙中它们势必已经相互湮灭了，只余下一个充满辐射而几 乎没有物质的宇宙。因此，后来也就不会有人类生命赖以发展的星系、恒星和行星。庆幸的是，大统一理论可以提供一个解释，尽管甚至刚开始时两者数量相等，为 何现在宇宙中夸克比反夸克多。正如我们已经看到的，大统一理论允许夸克变成高能下的反电子。它们也允许相反的过程，反夸克变成电子，电子和反电子变成反夸 克和夸克。早期宇宙有一时期是如此之热，使得粒子能量高到足以使这些转变发生。但是，为何导致夸克比反夸克多呢？原因在于，对于粒子和反粒子物理定律不是 完全相同的。
直 到1956年人们都相信，物理定律分别服从三个叫做C、P和T的对称。C（电荷）对称的意义是， 对于粒子和反粒子定律是相同的；P（宇称）对称是指，对于任何情景和它的镜像（右手方向自旋的粒子的镜像变成了左手方向自旋的粒子）定律不变； T（时间）对称是指，如果我们颠倒粒子和反粒子的运动方向，系统应回到原先的那样；换言之，对于前进或后退的时间方向定律是一样的。
1956 年， 两位美国物理学家李政道和杨振宁提出弱作用实际上不服从P对称。换言之，弱力使得宇宙的镜像以不同的方式发展。同一年，他们的一位同事吴健雄证明了他们的 预言是正确的。她将放射性元素的核在磁场中排列，使它们的自旋方向一致，然后演示表明，电子在一个方向比另一方向发射出得更多。次年，李和杨为此获得诺贝 尔奖。 人们还发现弱作用不服从C对称，即是说，它使得由反粒子构成的宇宙的行为和我们的宇宙不同。尽管如此，看来弱力确实服从CP联合对称。也就是说，如果每个 粒子都用其反粒子来取代，则由此构成的宇宙的镜像和原来的宇宙以同样的方式发展！但在1964年，还是两个美国人——J·W·克罗宁和瓦尔·费兹——发 现， 在称为K介子的衰变中，甚至连CP对称也不服从。1980年，克罗宁和费兹为此而获得诺贝尔奖。（很多奖是因为显示宇宙不像我们所想像的那么简单而被授予 的！）
有 一个数学定理说，任何服从量子力学和相对论的理论必须服从CPT联合对称。换言之，如果同时用反粒子来置换粒子，取镜像和时间反演，则宇宙的行为必须是一 样的。克罗宁和费兹指出，如果仅仅用反粒子来取代粒子，并且采用镜像，但不反演时间方向，则宇宙的行为于保持不变。所以，物理学定律在时间方向颠倒的情况 下必须改变——它们不服从T对称。
早 期宇宙肯定是不服从T对称的：当时间往前走时，宇宙膨胀；如果它往后退，则宇宙收缩。 而且，由于存在着不服从T对称的力，因此当宇宙膨胀时，相对于将电子变成反夸克，这些力更容易将反电子变成夸克。然后，当宇宙膨胀并冷却下来，反夸克就和 夸克湮灭，但由于已有的夸克比反夸克多，少量过剩的夸克就留下来。正是它们构成我们今天看到的物质，由这些物质构成了我们自己。这样，我们自身之存在可认 为是大统一理论的证实，哪怕仅仅是定性的而已；但此预言的不确定性到了这种程度，以至于我们不能知道在湮灭之后余下的夸克数目，甚至不知是夸克还是反夸克 余下。（然而，如果是反夸克多余留下，我们可以简单地称反夸克为夸克，夸克为反夸克。）
Aristotle believed that all the matter in the universe was made up of four basic elements – earth, air, fire, and water.
These elements were acted on by two forces: gravity, the tendency for earth and water to sink, and levity, the tendency for air and fire to rise. This division of the contents of the universe into matter and forces is still used today. Aristotle believed that matter was continuous, that is, one could divide a piece of matter into smaller and smaller bits without any limit: one never came up against a grain of matter that could not be divided further. A few Greeks, however, such as Democritus, held that matter was inherently grainy and that everything was made up of large numbers of various different kinds of atoms. (The word atom means “indivisible“ in Greek.) For centuries the argument continued without any real evidence on either side, but in 1803 the British chemist and physicist John Dalton pointed out that the fact that chemical compounds always combined in certain proportions could be explained by the grouping together of atoms to form units called molecules. However, the argument between the two schools of thought was not finally settled in favor of the atomists until the early years of this century. One of the important pieces of physical evidence was provided by Einstein.
In a paper written in 1905, a few weeks before the famous paper on special relativity, Einstein pointed out that what was called Brownian motion – the irregular, random motion of small particles of dust suspended in a liquid – could be explained as the effect of atoms of the liquid colliding with the dust particles.
By this time there were already suspicions that these atoms were not, after all, indivisible. Several years previously a fellow of Trinity College, Cambridge, J. J. Thomson, had demonstrated the existence of a particle of matter, called the electron, that had a mass less than one thousandth of that of the lightest atom. He used a setup rather like a modern TV picture tube: a red-hot metal filament gave off the electrons, and because these have a negative electric charge, an electric field could be used to accelerate them toward a phosphor-coated screen. When they hit the screen, flashes of light were generated. Soon it was realized that these electrons must be coming from within the atoms themselves, and in 1911 the New Zealand physicist Ernest Rutherford finally showed that the atoms of matter do have internal structure: they are made up of an extremely tiny, positively charged nucleus, around which a number of electrons orbit. He deduced this by analyzing the way in which alpha-particles, which are positively charged particles given off by radioactive atoms, are deflected when they collide with atoms.
At first it was thought that the nucleus of the atom was made up of electrons and different numbers of a positively charged particle called the proton, from the Greek word meaning “first,“ because it was believed to be the fundamental unit from which matter was made. However, in 1932 a colleague of Rutherford’s at Cambridge, James Chadwick, discovered that the nucleus contained another particle, called the neutron, which had almost the same mass as a proton but no electrical charge. Chadwick received the Nobel Prize for his discovery, and was elected Master of Gonville and Caius College, Cambridge (the college of which I am now a fellow). He later resigned as Master because of disagreements with the Fellows. There had been a bitter dispute in the college ever since a group of young Fellows returning after the war had voted many of the old Fellows out of the college offices they had held for a long time. This was before my time; I joined the college in 1965 at the tail end of the bitterness, when similar disagreements forced another Nobel Prize – winning Master, Sir Nevill Mott, to resign.
Up to about thirty years ago, it was thought that protons and neutrons were “elementary“ particles, but experiments in which protons were collided with other protons or electrons at high speeds indicated that they were in fact made up of smaller particles. These particles were named quarks by the Caltech physicist Murray Gell-Mann, who won the Nobel Prize in 1969 for his work on them. The origin of the name is an enigmatic quotation from James Joyce: “Three quarks for Muster Mark!“ The word quark is supposed to be pronounced like quart, but with a k at the end instead of a t, but is usually pronounced to rhyme with lark.
There are a number of different varieties of quarks: there are six “flavors,“ which we call up, down, strange, charmed, bottom, and top. The first three flavors had been known since the 1960s but the charmed quark was discovered only in 1974, the bottom in 1977, and the top in 1995. Each flavor comes in three “colors,“ red, green, and blue. (It should be emphasized that these terms are just labels: quarks are much smaller than the wavelength of visible light and so do not have any color in the normal sense. It is just that modern physicists seem to have more imaginative ways of naming new particles and phenomena – they no longer restrict themselves to Greek!) A proton or neutron is made up of three quarks, one of each color. A proton contains two up quarks and one down quark; a neutron contains two down and one up. We can create particles made up of the other quarks (strange, charmed, bottom, and top), but these all have a much greater mass and decay very rapidly into protons and neutrons.
We now know that neither the atoms nor the protons and neutrons within them are indivisible. So the question is: what are the truly elementary particles, the basic building blocks from which everything is made? Since the wavelength of light
is much larger than the size of an atom, we cannot hope to “look“ at the parts of an atom in the ordinary way. We need to use something with a much smaller wave-length. As we saw in the last chapter, quantum mechanics tells us that all particles are in fact waves, and that the higher the energy of a particle, the smaller the wavelength of the corresponding wave. So the best answer we can give to our question depends on how high a particle energy we have at our disposal, because this determines on how small a length scale we can look. These particle energies are usually measured in units called electron volts. (In Thomson’s experiments with electrons, we saw that he used an electric field to accelerate the electrons. The energy that an electron gains from an electric field of one volt is what is known as an electron volt.) In the nineteenth century, when the only particle energies that people knew how to use were the low energies of a few electron volts generated by chemical reactions such as burning, it was thought that atoms were the smallest unit. In Rutherford’s experiment, the alpha-particles had energies of millions of electron volts. More recently, we have learned how to use electromagnetic fields to give particles energies of at first millions and then thousands of millions of electron volts. And so we know that particles that were thought to be “elementary“ thirty years ago are, in fact, made up of smaller particles.
May these, as we go to still higher energies, in turn be found to be made from still smaller particles? This is certainly possible, but we do have some theoretical reasons for believing that we have, or are very near to, a knowledge of the ultimate building blocks of nature.
Using the wave/particle duality discussed in the last chapter, every-thing in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin. One way of thinking of spin is to imagine the particles as little tops spinning about an axis. However, this can be misleading, because quantum mechanics tells us that the particles do not have any well-defined axis. What the spin of a particle really tells us is what the particle looks like from different directions. A particle of spin 0 is like a dot: it looks the same from every direction Figure 5:1-i. On the other hand, a particle of spin 1 is like an arrow: it looks different from different directions Figure 5:1-ii. Only if one turns it round a complete revolution (360 degrees) does the particle look the same. A particle of spin 2 is like a double-headed arrow Figure 5:1-iii: it looks the same if one turns it round half a revolution (180 degrees). Similarly, higher spin particles look the same if one turns them through smaller fractions of a complete revolution. All this seems fairly straightforward, but the remark-able fact is that there are particles that do not look the same if one turns them through just one revolution: you have to turn them through two complete revolutions! Such particles are said to have spin .
Figure 5:1 All the known particles in the universe can be divided into two groups: particles of spin ., which make up the matter in the universe, and particles of spin 0, 1, and 2, which, as we shall see, give rise to forces between the matter particles.
The matter particles obey what is called Pauli’s exclusion principle. This was discovered in 1925 by an Austrian physicist, Wolfgang Pauli – for which he received the Nobel Prize in 1945. He was the archetypal theoretical physicist: it was said of him that even his presence in the same town would make experiments go wrong! Pauli’s exclusion principle says that two similar particles can-not exist in the same state; that is, they cannot have both the same position and the same velocity, within the limits given by the uncertainty principle. The exclusion principle is crucial because it explains why matter particles do not collapse to a state of very high density under the influence of the forces produced by the particles of spin 0, 1, and 2: if the matter particles have very nearly the same positions, they must have different velocities, which means that they will not stay in the same position for long. If the world had been created without the exclusion principle, quarks would not form separate, well-defined protons and neutrons. Nor would these, together with electrons, form separate, well-defined atoms. They would all collapse to form a roughly uniform, dense “soup.“ A proper understanding of the electron and other spin-. particles did not come until 1928, when a theory was proposed by Paul Dirac, who later was elected to the Lucasian Professorship of Mathematics at Cambridge (the same professorship that Newton had once held and that I now hold). Dirac’s theory was the first of its kind that was consistent with both quantum mechanics and the special theory of relativity. It explained mathematically why the electron had spin-.; that is, why it didn’t look the same if you turned it through only one complete revolution, but did if you turned it through two revolutions. It also predicted that the electron should have a partner: an anti-electron, or positron. The discovery of the positron in 1932 confirmed Dirac’s theory and led to his being awarded the Nobel Prize for physics in 1933. We now know that every particle has an antiparticle, with which it can annihilate. (In the case of the force-carrying particles, the antiparticles are the same as the particles themselves.) There could be whole antiworlds and antipeople made out of antiparticles. However, if you meet your antiself, don’t shake hands! You would both vanish in a great flash of light. The question of why there seem to be so many more particles than antiparticles around us is extremely
important, and I shall return to it later in the chapter.
In quantum mechanics, the forces or interactions between matter particles are all supposed to be carried by particles of integer spin – 0, 1, or 2. What happens is that a matter particle, such as an electron or a quark, emits a force-carrying particle. The recoil from this emission changes the velocity of the matter particle. The force-carrying particle then collides with another matter particle and is absorbed. This collision changes the velocity of the second particle, just as if there had been a force between the two matter particles. It is an important property of ' the force-carrying particles that they do not obey the exclusion principle. This means that there is no limit to the number that can be exchanged, and so they can give rise to a strong force. However, if the force-carrying particles have a high mass, it will be difficult to produce and exchange them over a large distance. So the forces that they carry will have only a short range. On the other hand, if the force-carrying particles have no mass of their own, the forces will be long range. The force-carrying particles exchanged between matter particles are said to be virtual particles because, unlike “real“ particles, they cannot be directly detected by a particle detector. We know they exist, however, because they do have a measurable effect: they give rise to forces between matter particles. Particles of spin 0, 1, or 2 do also exist in some circumstances as real particles, when they can be directly detected. They then appear to us as what a classical physicist would call waves, such as waves of light or gravitational waves. They may sometimes be emitted when matter particles interact with each other by exchanging virtual force-carrying particles. (For example, the electric repulsive force between two electrons is due to the exchange of virtual photons, which can never be directly detected; but if one electron moves past another, real photons may be given off, which we detect as light waves.) Force-carrying particles can be grouped into four categories according to the strength of the force that they carry and the particles with which they interact. It should be emphasized that this division into four classes is man-made; it is convenient for the construction of partial theories, but it may not correspond to anything deeper. Ultimately, most physicists hope to find a unified theory that will explain all four forces as different aspects of a single force. Indeed, many would say this is the prime goal of physics today. Recently, successful attempts have been made to unify three of the four categories of force – and I shall describe these in this chapter. The question of the unification of the remaining category, gravity, we shall leave till later.
The first category is the gravitational force. This force is universal, that is, every particle feels the force of gravity, according to its mass or energy. Gravity is the weakest of the four forces by a long way; it is so weak that we would not notice it at all were it not for two special properties that it has: it can act over large distances, and it is always attractive.
This means that the very weak gravitational forces between the individual particles in two large bodies, such as the earth and the sun, can all add up to produce a significant force. The other three forces are either short range, or are sometimes attractive and some-times repulsive, so they tend to cancel out. In the quantum mechanical way of looking at the gravitational field, the force between two matter particles is pictured as being carried by a particle of spin 2 called the graviton. This has no mass of its own, so the force that it carries is long range. The gravitational force between the sun and the earth is ascribed to the exchange of gravitons between the particles that make up these two bodies. Although the exchanged particles are virtual, they certainly do produce a measurable effect – they make the earth orbit the sun! Real gravitons make up what classical physicists would call gravitational waves, which are very weak – and so difficult to detect that they have not yet been observed.
The next category is the electromagnetic force, which interacts with electrically charged particles like electrons and quarks, but not with uncharged particles such as gravitons. It is much stronger than the gravitational force: the electromagnetic force between two electrons is about a million million million million million million million (1 with forty-two zeros after it) times bigger than the gravitational force. However, there are two kinds of electric charge, positive and negative. The force between two positive charges is repulsive, as is the force between two negative charges, but the force is attractive between a positive and a negative charge. A large body, such as the earth or the sun, contains nearly equal numbers of positive and negative charges. Thus the attractive and repulsive forces between the individual particles nearly cancel each other out, and there is very little net electromagnetic force. However, on the small scales of atoms and molecules, electromagnetic forces dominate. The electromagnetic attraction between negatively charged electrons and positively charged protons in the nucleus causes the electrons to orbit the nucleus of the atom, just as gravitational attraction causes the earth to orbit the sun. The electromagnetic attraction is pictured as being caused by the exchange of large numbers of virtual massless particles of spin 1, called photons. Again, the photons that are exchanged are virtual particles. However, when an electron changes from one allowed orbit to another one nearer to the nucleus, energy is released and a real photon is emitted – which can be observed as visible light by the human eye, if it has the right wave-length, or by a photon detector such as photographic film. Equally, if a real photon collides with an atom, it may move an electron from an orbit nearer the nucleus to one farther away. This uses up the energy of the photon, so it is absorbed.
The third category is called the weak nuclear force, which is responsible for radioactivity and which acts on all matter particles of spin-., but not on particles of spin 0, 1, or 2, such as photons and gravitons. The weak nuclear force was not well understood until 1967, when Abdus Salam at Imperial College, London, and Steven Weinberg at Harvard both
proposed theories that unified this interaction with the electromagnetic force, just as Maxwell had unified electricity and magnetism about a hundred years earlier. They suggested that in addition to the photon, there were three other spin-1 particles, known collectively as massive vector bosons, that carried the weak force. These were called W+ (pronounced W plus), W- (pronounced W minus), and Zo (pronounced Z naught), and each had a mass of around 100 GeV (GeV stands for gigaelectron-volt, or one thousand million electron volts). The Weinberg-Salam theory exhibits a property known as spontaneous symmetry breaking. This means that what appear to be a number of completely different particles at low energies are in fact found to be all the same type of particle, only in different states. At high energies all these particles behave similarly. The effect is rather like the behavior of a roulette ball on a roulette wheel. At high energies (when the wheel is spun quickly) the ball behaves in essentially only one way – it rolls round and round. But as the wheel slows, the energy of the ball decreases, and eventually the ball drops into one of the thirty-seven slots in the wheel. In other words, at low energies there are thirty-seven different states in which the ball can exist. If, for some reason, we could only observe the ball at low energies, we would then think that there were thirty-seven different types of ball! In the Weinberg-Salam theory, at energies much greater than 100 GeV, the three new particles and the photon would all behave in a similar manner. But at the lower particle energies that occur in most normal situations, this symmetry between the particles would be broken. WE, W, and Zo would acquire large masses, making the forces they carry have a very short range. At the time that Salam and Weinberg proposed their theory, few people believed them, and particle accelerators were not powerful enough to reach the energies of 100 GeV required to produce real W+, W-, or Zo particles.
However, over the next ten years or so, the other predictions of the theory at lower energies agreed so well with experiment that, in 1979, Salam and Weinberg were awarded the Nobel Prize for physics, together with Sheldon Glashow, also at Harvard, who had suggested similar unified theories of the electromagnetic and weak nuclear forces.
The Nobel committee was spared the embarrassment of having made a mistake by the discovery in 1983 at CERN (European Centre for Nuclear Research) of the three massive partners of the photon, with the correct predicted masses and other properties. Carlo Rubbia, who led the team of several hundred physicists that made the discovery, received the Nobel Prize in 1984, along with Simon van der Meer, the CERNengineer who developed the antimatter storage system employed. (It is very difficult to make a mark in experimental physics these days unless you are already at the top! ) The fourth category is the strong nuclear force, which holds the quarks together in the proton and neutron, and holds the protons and neutrons together in the nucleus of an atom. It is believed that this force is carried by another spin-1 particle, called the gluon, which interacts only with itself and with the quarks. The strong nuclear force has a curious property called confinement: it always binds particles together into combinations that have no color. One cannot have a single quark on its own because it would have a color (red, green, or blue). Instead, a red quark has to be joined to a green and a blue quark by a “string“ of gluons (red + green + blue = white). Such a triplet constitutes a proton or a neutron. Another possibility is a pair consisting of a quark and an antiquark (red + antired, or green + antigreen, or blue + antiblue = white).
Such combinations make up the particles known as mesons, which are unstable because the quark and antiquark can annihilate each other, producing electrons and other particles. Similarly, confinement prevents one having a single gluon on its own, because gluons also have color. Instead, one has to have a collection of gluons whose colors add up to white.
Such a collection forms an unstable particle called a glueball.
The fact that confinement prevents one from observing an isolated quark or gluon might seem to make the whole notion of quarks and gluons as particles somewhat metaphysical. However, there is another property of the strong nuclear force, called asymptotic freedom, that makes the concept of quarks and gluons well defined. At normal energies, the strong nuclear force is indeed strong, and it binds the quarks tightly together. However, experiments with large particle accelerators indicate that at high energies the strong force becomes much weaker, and the quarks and gluons behave almost like free particles.
Figure 5:2 Figure 5:2 shows a photograph of a collision between a high-energy proton and antiproton. The success of the unification of the electromagnetic and weak nuclear forces led to a number of attempts to combine these two forces with the strong nuclear force into what is called a grand unified theory (or GUT). This title is rather an exaggeration: the resultant theories are not all that grand, nor are they fully unified, as they do not include gravity. Nor are they really complete theories, because they contain a number of parameters whose values cannot be predicted from the theory but have to be chosen to fit in with experiment. Nevertheless, they may be a step toward a complete, fully unified theory. The basic idea of GUTs is as follows: as was mentioned above, the strong nuclear force gets weaker at high energies. On the other hand, the electromagnetic and weak forces, which are not asymptotically free, get stronger at high energies. At some very high energy, called the grand unification energy, these three forces would all have the same strength and so could just be different aspects of a single force. The GUTs also predict that at this energy the different spin-. matter particles, like quarks and electrons, would also all be essentially the same, thus achieving another unification.
The value of the grand unification energy is not very well known, but it would probably have to be at least a thousand million million GeV. The present generation of particle accelerators can collide particles at energies of about one hundred GeV, and machines are planned that would raise this to a few thousand GeV. But a machine that was powerful enough to accelerate particles to the grand unification energy would have to be as big as the Solar System – and would be unlikely to be funded in the present economic climate. Thus it is impossible to test grand unified theories directly in the laboratory.
However, just as in the case of the electromagnetic and weak unified theory, there are low-energy consequences of the theory that can be tested.
The most interesting of these is the prediction that protons, which make up much of the mass of ordinary matter, can spontaneously decay into lighter particles such as antielectrons. The reason this is possible is that at the grand unification energy there is no essential difference between a quark and an antielectron. The three quarks inside a proton normally do not have enough energy to change into antielectrons, but very occasionally one of them may acquire
sufficient energy to make the transition because the uncertainty principle means that the energy of the quarks inside the proton cannot be fixed exactly. The proton would then decay. The probability of a quark gaining sufficient energy is so low that one is likely to have to wait at least a million million million million million years (1 followed by thirty zeros). This is much longer than the time since the big bang, which is a mere ten thousand million years or so (1 followed by ten zeros).
Thus one might think that the possibility of spontaneous proton decay could not be tested experimentally. However, one can increase one’s chances of detecting a decay by observing a large amount of matter containing a very large number of protons. (If, for example, one observed a number of protons equal to 1 followed by thirty-one zeros for a period of one year, one would expect, according to the simplest GUT, to observe more than one proton decay.) A number of such experiments have been carried out, but none have yielded definite evidence of proton or neutron decay. One experiment used eight thousand tons of water and was performed in the Morton Salt Mine in Ohio (to avoid other events taking place, caused by cosmic rays, that might be confused with proton decay). Since no spontaneous proton decay had been observed during the experiment, one can calculate that the probable life of the proton must be greater than ten million million million million million years (1 with thirty-one zeros). This is longer than the lifetime predicted by the simplest grand unified theory, but there are more elaborate theories in which the predicted lifetimes are longer. Still more sensitive experiments involving even larger quantities of matter will be needed to test them.
Even though it is very difficult to observe spontaneous proton decay, it may be that our very existence is a consequence of the reverse process, the production of protons, or more simply, of quarks, from an initial situation in which there were no more quarks than antiquarks, which is the most natural way to imagine the universe starting out. Matter on the earth is made up mainly of protons and neutrons, which in turn are made up of quarks. There are no antiprotons or antineutrons, made up from antiquarks, except for a few that physicists produce in large particle accelerators. We have evidence from cosmic rays that the same is true for all the matter in our galaxy: there are no antiprotons or antineutrons apart from a small number that are produced as particle/ antiparticle pairs in high-energy collisions. If there were large regions of antimatter in our galaxy, we would expect to observe large quantities of radiation from the borders between the regions of matter and antimatter, where many particles would be colliding with their anti-particles, annihilating each other and giving off high-energy radiation.
We have no direct evidence as to whether the matter in other galaxies is made up of protons and neutrons or antiprotons and anti-neutrons, but it must be one or the other: there cannot be a mixture in a single galaxy because in that case we would again observe a lot of radiation from annihilations. We therefore believe that all galaxies are composed of quarks rather than antiquarks; it seems implausible that some galaxies should be matter and some antimatter.
Why should there be so many more quarks than antiquarks? Why are there not equal numbers of each? It is certainly fortunate for us that the numbers are unequal because, if they had been the same, nearly all the quarks and antiquarks would have annihilated each other in the early universe and left a universe filled with radiation but hardly any matter.
There would then have been no galaxies, stars, or planets on which human life could have developed. Luckily, grand unified theories may provide an explanation of why the universe should now contain more quarks than antiquarks, even if it started out with equal numbers of each. As we have seen, GUTs allow quarks to change into antielectrons at high energy. They also allow the reverse processes, antiquarks turning into electrons, and electrons and antielectrons turning into antiquarks and quarks. There was a time in the very early universe when it was so hot that the particle energies would have been high enough for these transformations to take place. But why should that lead to more quarks than antiquarks? The reason is that the laws of physics are not quite the same for particles and antiparticles.
Up to 1956 it was believed that the laws of physics obeyed each of three separate symmetries called C, P, and T. The symmetry C means that the laws are the same for particles and antiparticles. The symmetry P means that the laws are the same for any situation and its mirror image (the mirror image of a particle spinning in a right-handed direction is one spinning in a left-handed direction). The symmetry T means that if you reverse the direction of motion of all particles and antiparticles, the system should go back to what it was at earlier times; in other words, the laws are the same in the forward and backward directions of time. In 1956 two American physicists, Tsung-Dao Lee and Chen Ning Yang, suggested that the weak force does not in fact obey the symmetry P. In other words, the weak force would make the universe develop in a different way from the way in which the mirror image of the universe would develop. The same year, a colleague, Chien-Shiung Wu, proved their prediction correct. She did this by lining up the nuclei of radioactive atoms in a magnetic field, so that they were all spinning in the same direction, and showed that the electrons were given off more in one direction than another. The following year, Lee and Yang received the Nobel Prize for their idea. It was also found that the weak force did not obey the symmetry C. That is, it would cause a universe composed of antiparticles to behave differently from our universe. Nevertheless, it seemed that the weak force did obey the combined symmetry CP. That is, the universe would develop in the same way as its mirror image if, in addition, every particle was swapped with its antiparticle! However, in 1964 two more Americans, J. W. Cronin and Val Fitch, discovered that even the CP symmetry was not obeyed in the decay of certain particles called K-mesons. Cronin and Fitch eventually received the Nobel Prize for their work in 1980. (A lot of prizes have been awarded for showing that the universe is not as simple as we might have thought!)
There is a mathematical theorem that says that any theory that obeys quantum mechanics and relativity must always obey the combined symmetry CPT. In other words, the universe would have to behave the same if one replaced particles by antiparticles, took the mirror image, and also reversed the direction of time. But Cronin and Fitch showed that if one replaces particles by antiparticles and takes the mirror image, but does not reverse the direction of time, then the universe does not behave the same. The laws of physics, therefore, must change if one reverses the direction of time – they do not obey the symmetry T.
Certainly the early universe does not obey the symmetry T: as time runs forward the universe expands – if it ran backward, the universe would be contracting. And since there are forces that do not obey the symmetry T, it follows that as the universe expands, these forces could cause more antielectrons to turn into quarks than electrons into antiquarks.
Then, as the universe expanded and cooled, the antiquarks would annihilate with the quarks, but since there would be more quarks than antiquarks, a small excess of quarks would remain. It is these that make up the matter we see today and out of which we ourselves are made. Thus our very existence could be regarded as a confirmation of grand unified theories, though a qualitative one only; the uncertainties are such that one cannot predict the numbers of quarks that will be left after the annihilation, or even whether it would be quarks or antiquarks that would remain. (Had it been an excess of antiquarks, however, we would simply have named antiquarks quarks, and quarks antiquarks.) Grand unified theories do not include the force of gravity. This does not matter too much, because gravity is such a weak force that its effects can usually be neglected when we are dealing with elementary particles or atoms. However, the fact that it is both long range and always attractive means that its effects all add up. So for a sufficiently large number of matter particles, gravitational forces can dominate over all other forces. This is why it is gravity that determines the evolution of the universe. Even for objects the size of stars, the attractive force of gravity can win over all the other forces and cause the star to collapse. My work in the 1970s focused on the black holes that can result from such stellar collapse and the intense gravitational fields around them. It was this that led to the first hints of how the theories of quantum mechanics and general relativity might affect each other – a glimpse of the shape of a quantum theory of gravity yet to come.