文章来源：DECEMBER 1995    PHYSICS TODAY。个人兴趣翻译，请合理使用。

The role ofsymmetry in physics has evolved greatly during this century. Eugene Wigner madeprofound contributions to this development.

David J. Gross (is the Eugene Higgins Professor of Physics at Princeton University inPrinceton, New Jersey.)

Until the twentieth century, principles ofsymmetryplayed littleexplicit rolein theoretical physics. Conservationlaws, especially those of energy and momentum, were considered to be offundamental importance. But these were regarded as consequences of thedynamical laws of nature, rather than as consequences of the symmetries thatunderlay these laws. Maxwell’s equations, formulated in 1985, embodied bothLorentz invariance and gauge invariance. But these symmetries ofelectrodynamics were not fully appreciated for 40 years or more.

     Einstein’s great advance in 1905 was to put symmetry first, to regardthe symmetry principle as the primary feature of nature that constrains theallowable dynamical laws. Thus the transformation properties of theelectromagnetic field were not to be derived from Maxwell’s equations, asHendrik Lorentz did, but rather were consequences of relativistic invariance,and indeed largely dictate the form of Maxwell’s equations. This is a profoundchange of attitude. Lorentz must have felt that Einstein cheated.

     Ten years later this point of view scored a spectacular success withEinstein’s construction of general relativity. The principle of equivalence, aprinciple of local symmetry (the invariance of the laws of nature under localchange of the space-time coordinates), dictated the dynamics of gravity, ofspace-time itself.

     Yet even after this magnificent success, Einstein’s message had littleimpact on theoretical physics, except in the study of general relativity. Thiswas partly due to the unfamiliar and rather new mathematics that was involvedin exploiting symmetry principles, namely group theory. As Wigner noted in theintroduction to his monumental opus, GroupTheory and its Application to the Quantum mechanics of Atomic Spectra, 1published in 1931, “There is great reluctance among physicists towardsaccepting group theoretical arguments.”

     Even four years later, in 1935, Edward Condon and George Shortley, intheir tome on The Theory of Atomic Spectra, 2proudly state

We wish finally to make a few remarks concerning the place of thetheory of groups in the study of quantum mechanics of atomic spectra. Thereader will have heard that this mathematical disciplines is of great importancefor the subject. We manage to get along without it.

     That this attitude has changed sodramatically over the last 60 years, so that today principles of symmetry areregarded as the most fundamental part of our description of nature, is in nosmall part due to the influence of Eugene Winger.

图片

EINSTEINAND WIGNER (second from left) both considered symmetry principles to be offundamental importance. Einstein’s theories of special relativity (1905) andgeneral relativity (1915) are classic example of symmetry principles constrainingand even dictating dynamics. Wigner’s great contribution in the late 1920s and1930s was to discover the fundamental role symmetry plays in quantum theories,from explaining atomic spectra to classifying types of elementary particles.Pictured here at Einstein’s 70th birthday celebration in 1949 at theInstitute for Advanced Study in Princeton are (from left to right) HowardRoberson, Wigner, Herman Weyl, Kurt Gödel, I. I. Rabi, Einstein, RudolfLadenburg, J. Robert Oppenheimer and G. M. Clemence. FIGURE 1


物理学中对称性的地位在本世纪有了很大的提高。尤金·维格纳（Eugene Wigner）对此做出了影响深远的贡献。

David J. Gross（新泽西州，普林斯顿大学的物理“尤金·希金斯教授”）

直到20世纪，对称性原理在理论物理也没有一个明确的角色。守恒定律，特别是能量守恒和动量守恒，被认为是最根本，也是最重要的。但是这些都被认为是自然动力学法则的结果，而不是这些法则背后对称性的结果。1985年发现的麦克斯韦（Maxwell）方程组，包含了洛伦兹（Lorentz）不变性和规范不变性。但是这些电动力学中的对称性在长达40多年的时间中没有得到完整的认识。

爱因斯坦（Einstein）在1905做出的巨大贡献就是把对称性放在了第一位，他将对称性视为自然的基本特征，而它约束了所有允许的动力学法则。于是电磁场的变换性质不能再从麦克斯韦方程中导出——正如亨德里克·洛伦兹所做的——而是作为相对论不变性的结论，而且它确实在很大程度上决定了麦克斯韦方程的形式。这是一个将会带来深刻变革的想法。洛伦兹肯定认为爱因斯坦在骗人。

十年后，这个认识在爱因斯坦的广义相对论构架下取得了惊人的成功。等效原理，即定域对称性原理（在时空坐标局域变化下的自然法则不变性），取决于时空本身的重力变化。

就算在这巨大成功之后，爱因斯坦的想法对理论物理也没有多少影响，除开广义相对论的研究。这个部分是由于我们运用对称性原理时使用的不熟悉、甚至是全新的数学，而我们现在把这些统称为群论。维格纳在他1931年出版的著作《群论及其在原子光谱的量子力学中的应用》中写到“在接受群论观点这点上物理学家中有着很强烈的抵制情绪。”

甚至4年之后，在1935年，爱德华·勒康登（Edward Condon）和乔治·索特利（GeorgeShortley）在他们关于原子光谱理论的著作中，自豪地宣称：

在研究原子光谱的量子力学时运用到了群论，我们最后还是在其旁边做了一些标注。读者应该早已听说这种数学对这个研究至关重要 。我们设法在不需要它的情况下继续叙述。

    这个态度在过去的60年里发生了戏剧性的变化，以至于在今天，对称性原理被认为是我们描述自然中最基本的部分，而且在尤金•维格纳的影响下我们不认为还有比它更为基本的存在。 

图片

爱因斯坦和维格纳（左二）都认为对称性原理的重要性是最根本的。爱因斯坦的狭义相对论（1905）和广义相对论（1915）都是对称原理约束的经典范例，对称性原理在其中甚至支配着动力学。维格纳在19世纪20年代晚期和30年代做出的贡献则是从解释原子光谱以及基本粒子的分类中发现了对称性原理在量子力学中所起作用的根本性。照片摄于是1949年在普林斯顿高等研究所举办的爱因斯坦70大寿聚会，（从左至右）分别是：Howard Roberson, Wigner（维格纳）, Herman Weyl, Kurt Gödel, I. I. Rabi, Einstein（爱因斯坦）, Rudolf Ladenburg, J. Robert Oppenheimer and G. M. Clemence. 图1