弗里曼·戴森与恩里科·费米的会面：一次改变人生的经历

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#理论物理学两种计算方式

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Freeman Dyson’s Meeting with Enrico Fermi: A Life-Changing Experience

A MEETING WITH ENRICO FERMI

与恩里科・费米的一次会面

One of the big turning points in my life was a meeting with Enrico Fermi in the spring of 1953. In a few minutes, Fermi politely and ruthlessly demolished a program of research that I and my students had been pursuing for several years. He probably saved us from several more years of fruitless wandering along a road that was leading nowhere. I am eternally grateful to him for destroying our illusions and telling us the bitter truth.
我生命中的一个重大转折点是 1953 年春天与恩里科・费米的一次会面。在短短几分钟内，费米以礼貌而无情的方式摧毁了我和我的学生们多年来一直从事的研究项目。他可能使我们免于在一条没有前途的道路上继续徘徊数年。我永远感激他粉碎了我们的幻想，向我们揭示了残酷的真相。

Fermi was one of the great physicists of our time, outstanding both as a theorist and as an experimenter. In 1942, he led the team that built the first nuclear reactor in Chicago. In 1953, he was leading the team that built the Chicago cyclotron and used it to explore the strong forces that hold nuclei together. He made the first accurate measurements of the scattering of mesons by protons. His meson-proton scattering experiment gave the most direct evidence then available of the nature of the strong forces.
费米是我们时代最伟大的物理学家之一，无论是在理论方面还是在实验方面都极为杰出。1942 年，他领导了在芝加哥建造第一座核反应堆的团队。1953 年，他正在领导建造芝加哥回旋加速器的团队，并利用它来研究将原子核结合在一起的强相互作用力。他首次精确测量了介子被质子散射的情况。他的介子 - 质子散射实验为当时可用的强相互作用力的性质提供了最直接的证据。

In 1953, I was a young professor of theoretical physics at Cornell, responsible for directing the research of a small army of graduate students and post - docs. I had put them to work calculating meson - proton scattering, so that their theoretical calculations could be compared with Fermi’s measurements. In 1948 and 1949, we had made similar calculations of atomic processes, using the theory of quantum electrodynamics, and found spectacular agreement between experiment and theory. Quantum electrodynamics is the theory of electrons and photons interacting through electromagnetic forces. Because the electromagnetic forces are weak, we could calculate the atomic processes precisely. By 1951, we had triumphantly finished the atomic calculations and were looking for fresh fields to conquer. We decided to use the same techniques of calculation to explore the strong nuclear forces. We began by calculating meson - proton scattering, using a theory of the strong forces known as pseudoscalar meson theory. By the spring of 1953, after heroic efforts, we had plotted theoretical graphs of meson - proton scattering. We joyfully observed that our calculated numbers agreed pretty well with Fermi’s measured numbers. So I made an appointment to meet with Fermi and show him our results. Proudly, I rode the Greyhound bus from Ithaca to Chicago with a package of our theoretical graphs to show to him.
1953 年，我是康奈尔大学的一名年轻的理论物理学教授，负责指导一群研究生和博士后开展研究。我让他们计算介子 - 质子散射，以便将他们的理论计算结果与费米的测量结果进行比较。1948 年和 1949 年，我们曾利用量子电动力学理论对原子过程进行过类似的计算，并且发现实验与理论之间有着惊人的契合。量子电动力学是描述电子与光子通过电磁力相互作用的理论。由于电磁力很弱，我们能够精确地计算原子过程。到 1951 年，我们胜利地完成了原子计算，并开始寻找新的领域去开拓。我们决定运用相同的计算方法去探索强核力。我们从计算介子 - 质子散射入手，采用了一种名为赝标量介子理论的强相互作用理论。经过艰苦的努力，到 1953 年春，我们绘制出了介子 - 质子散射的理论图表。我们欣喜地发现，我们计算出的数值与费米测量出的数值相当吻合。于是，我约好去见费米并向他展示我们的成果。我怀着自豪的心情，带着一包我们的理论图表，乘坐灰狗巴士从伊萨卡前往芝加哥，准备向他展示。

When I arrived in Fermi’s office, I handed the graphs to Fermi, but he hardly glanced at them. He invited me to sit down, and asked me in a friendly way about the health of my wife and our new - born baby son, now fifty years old. Then he delivered his verdict in a quiet, even voice. “There are two ways of doing calculations in theoretical physics,” he said. “One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self - consistent mathematical formalism. You have neither.” I was slightly stunned, but ventured to ask him why he did not consider the pseudoscalar meson theory to be a self - consistent mathematical formalism. He replied, “Quantum electrodynamics is a good theory because the forces are weak, and when the formalism is ambiguous we have a clear physical picture to guide us. With the pseudoscalar meson theory there is no physical picture, and the forces are so strong that nothing converges. To reach your calculated results, you had to introduce arbitrary cut - off procedures that are not based either on solid physics or on solid mathematics.”
当我到达费米的办公室时，我把图表递给他，但他只是匆匆看了一眼。他请我坐下，友好地询问了我的妻子和我们刚出生的婴儿儿子（现在已经 50 岁了）的健康状况。然后，他平静而平稳地宣布了他的看法：“在理论物理学中进行计算有两种方式。” 他说，“一种方式，也是我更喜欢的方式，就是对你要计算的过程有一个清晰的物理图像。另一种方式是有一个精确且自洽的数学形式体系。你两者都没有。” 我有点震惊，但还是冒险问他为什么他认为赝标量介子理论不是一个自洽的数学形式体系。他回答说：“量子电动力学是一个好理论，因为力很弱，当形式体系含糊不清时，我们有一个清晰的物理图像来引导我们。而赝标量介子理论没有物理图像，而且力太强了，什么也得不到收敛。为了得到你的计算结果，你不得不引入一些并非基于坚实的物理或数学的任意截断程序。”

In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?” I thought for a moment about our cut - off procedures and said, “Four.” He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” With that, the conversation was over. I thanked Fermi for his time and trouble, and sadly took the next bus back to Ithaca to tell the bad news to the students. Because it was important for the students to have their names on a published paper, we did not abandon our calculations immediately. We finished the calculations and wrote a long paper that was duly published in the Physical Review with all our names on it. Then we dispersed to find other lines of work. I escaped to Berkeley, California, to start a new career in condensed - matter physics.
我绝望地问费米，他对我们的计算结果与他的测量结果之间的一致性是否没有留下印象。他回答说：“你用了多少个任意参数来进行你的计算？” 我想了想我们的截断程序，说：“四个。” 他说：“我记得我的朋友冯・诺伊曼过去常说，有了四个参数，我可以拟合一头大象，有了五个参数，我可以让它摆动鼻子。” 说完，谈话就结束了。我感谢费米抽出时间和费心，然后带着悲伤的心情，乘坐下一班公共汽车回到伊萨卡，把坏消息告诉学生们。因为对于学生们来说，在一篇已发表的论文上署名是很重要的，所以我们没有立即放弃我们的计算。我们完成了计算，写了一篇长论文，该论文按照规定在《物理评论》上发表，上面有我们所有人的名字。然后，我们各自分散去寻找其他研究方向。我逃到加利福尼亚州的伯克利，开始在凝聚态物理学领域的新职业生涯。

Looking back after fifty years, we can see clearly that Fermi was right. The crucial discovery that made sense of the strong forces was the quark. Mesons and protons are little bags of quarks. Before Murray Gell - Mann discovered quarks, no theory of the strong forces could possibly have been adequate. Fermi knew nothing about quarks, and died before they were discovered. But somehow he knew that something essential was missing in the meson theories of the 1950s. His physical intuition told him that the pseudoscalar meson theory could not be right. And so it was Fermi’s intuition, and not any discrepancy between theory and experiment, that saved me and my students from getting stuck in a blind alley.
五十年后回顾往事，我们可以清楚地看到费米是正确的。使强相互作用力合理的关键发现是夸克。介子和质子是装着夸克的小袋子。在默里・盖尔曼发现夸克之前，任何关于强相互作用力的理论都不可能是完善的。费米对夸克一无所知，并且在夸克被发现之前就去世了。但他不知怎么地知道，20 世纪 50 年代的介子理论中缺少了一些本质的东西。他的物理直觉告诉他，赝标量介子理论不可能是正确的。因此，是费米的直觉，而不是理论与实验之间的任何差异，使我以及我的学生们免于陷入一条死胡同。