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这个题目在有些学科看来很荒谬,很“唯心”,但它似乎真的伟大光荣正确。今儿重复一遍,是因为在无意间找到了一个“传说”的源头。
我经常传达老爱对日食观测的态度——学生问他,假如观测结果与广义相对论不符,怎么办?“我将为亲爱的上帝感到遗憾——理论是正确的。”这个故事是真的。老爱的学生伊尔莎(Ilse Rosenthal-Schneider)在1957年7月23日写了篇《回忆与爱老师的对话》(“Reminiscences of Conversation with Einstein”)。莎莎姐说,有一次,她和老师读一篇文章,里面有很多反对老师理论的东西。一会儿,老师突然打断她,拿出爱丁顿的电报来,很淡定地说,“我就知道理论是正确的。”莎莎问,假如没证实他的预言呢?老师就提出了那个著名的回答:
Da konnt' mir halt der Iiebe Gott leid tun, die Theorie stimmt doch.
(Then I would have been sorry for the dear Lord - the theory is correct.)
这句似乎有点儿大不敬的话,不是老爱个人的信念,也是那一代很多物理学家的信念。1963年5月,狄拉克在《科学美国人》发表了“散文”《物理学家的自然图景的演化》(The Evolution of the Physicist’s Picture of Nature, Scientific American 208 (May 1963), 45-53),讲了薛定谔的故事。薛老师从德布罗意(de Broglie)的物质波得到一个漂亮方程——狄老说,他是通过纯粹的思想得到方程的(Schrodinger got this equation by pure thought),而不像海森堡那样贴近实验——他把方程用于氢原子的电子,结果与实验不符(那会儿不知道电子有自旋)。老薛郁闷了几个月,然后发表了近似的方程——就是我们熟悉的那个没考虑相对论的“薛家方程”——因为它的计算结果与观测一致。其实,如果考虑自旋,老薛的相对论方程本来就没问题。老狄从这个故事得到的启示是:方程的美比方程符合实验更重要(it is more important to have beauty in one's equations than to have them fit experiment)。假如老薛更自信一些,他会早几个月就发表更精确的方程——现在那个方程叫Klein-Gordon。
狄老师总结说,如果真有了深刻的思想,那么走方程美的路线肯定会进步的(if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress)。即使不能完全与实验一致,也不要太沮丧,因为偏差很可能来自某些小问题,以后会明白的。量子力学就是那样发现的……
I might tell you the story I heard from Schrodinger of how, when he first got the idea for this equation, he immediately applied it to the behavior of the electron in the hydrogen atom, and then he got results that did not agree with experiment. The disagreement arose because at that time it was not known that the electron has a spin. That, of course, was a great disappointment to Schrodinger, and it caused him to abandon the work for some months. Then he noticed that if he applied the theory in a more approximate way, not taking into ac count the refinements required by relativity, to this rough approximation his work was in agreement with observation. He published his first paper with only this rough approximation, and in that way Schrodinger’s wave equation was presented to the world. Afterward, of course, when people found out how to take into account correctly the spin of the electron, the discrepancy between the results of applying Schrodinger’s relativistic equation and the experiments was completely cleared up.
I think there is a moral to this story, namely that it is more important to have beauty in one’s equations than to have them fit experiment. If Schrodinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. That equation is now known as the Klein-Gordon equation, although it was really discovered by Schrodinger, and in fact was discovered by Schrodinger before he discovered his nonrelativistic treatment of the hydrogen atom. It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory. That is how quantum mechanics was discovered.
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