Years ago, Sebastian White of Brookhaven National Laboratory planned to write the book series "Fermi in America: Fermi's Memories as a Teacher at Columbia University and the University of Chicago." To this end, he interviewed former students and colleagues of Professor Fermi, including Tsung-Dao Lee, Richard L. GawinGarwin), Freeman Dyson and Willis Lamb, among others.
Lee Tsung-do became a doctoral student at Fermi in 1947. In the interview, he provided a personal feeling of contact with Fermi back then. Although this interview has been written for many years, Mr. Tsung-Dao Lee's recollection of how Fermi taught students still has a certain significance for how we run a good university and how we educate students. It is hereby published for the benefit of readers.
Interviewer |Sebastian White.
Interviewee |Lee Tsung-do.
Translation |Wang Chuilin.
In 1948, Fermi and Tsung-Dao Lee collaborated to make a special slide rule to calculate the internal temperature distribution of main-sequence stars.
White: You're a graduate student in Fermi's 40s, how does it feel to have Fermi as your teacher?
Tsung-Dao Lee: It was a very exciting experience. Of course, in those days, the overall level of professors and students at the University of Chicago was quite remarkable, plus Fermi joined. I came directly from China in the autumn of 1946. This started my professional career.
White: You knew Fermi was there, and that's one of the reasons you came to Chicago?
Tsung-Dao Lee: Yes, that's one of the reasons. Another reason is that I only have two years of college degree, and the University of Chicago is the only school that can admit me directly to graduate school.
Wright: How did you come to agree with Fermi on the topic of your Ph.D.**?
Tsung-Dao Lee: Actually, Fermi and I had a few topics back then. The first topic had less to do with Fermi and was more influenced by the progress of physical research at that time.
It was in 1948, and Jack Steinberger was my classmate. He did an experiment on the decay of musons (now known as musons) and found that they had a continuum. Chen-Ning Yang, Marshall Rosenbluth, and I analyzed three processes: muon decay, muon capture, and decay. We were very pleased to find that their coupling constants were about the same. At that time, I was already a student of Fermi, and it all happened so fast. Jack Steinberg had come to the experimental conclusion that there was a continuum, but he didn't know how to calculate it, which is why I was involved. He came to me and asked me that I had made it using the three-body decay theory (naturally, this calculation was also based on Fermi's weak action theory).
On this basis, I worked with Yang Zhenning and Rosenbruce, and together we calculated these three processes. After that, I told Fermi about the results of these calculations, and he was very interested. He said, "You have to write these out." I say the question is why they have to have the same coupling constant. I think there must be a fundamental principle like general relativity hidden in this. I was very conscious of applying Fermi's theory of decay. I asked him why his original decay theory used the letter g to represent the decay coupling constant, and he told me that, indeed, he had the idea of general relativity in his head.
After that, several months passed, because there were several difficulties. For example, an intermediate boson must have mass, but how is this mass created? Around Christmas 1948, Fermida asked me to go to his office. He said he had just received two articles from Tiomno and Wheeler.
They also analyzed all three processes and found that they had the same coupling constant. But they did not speculate on the middle boson. I mentioned to Fermi that I was considering the possibility of an intermediate boson, but I couldn't figure out the invariant principle. At that time, it was not known that there could be a unified weak interaction, because there was only Fermi's decay theory. But once we take the three roles of decay and muon decay and muon capture, we study them together: these three different processes lead us to think further and further. So we speculate that there must be an intermediate boson that is heavy and has a universal coupling constant. The question is how to make the decays of V and A have a choice rule that couples to the same intermediate boson: because in 1948 it was accepted that the cosmos must be conserved.
I mentioned this issue to Enrico Femi, and he felt the same way. That's why we didn't write it down right away. But by Christmas, Wheeler's article arrived, and Fermi said, you have to write it right away.
At the same time, Fermi told me that he would write to Huiqin and tell them that we had done this work a few months ago. That Christmas, Mr. Yang and Mr. Rosenbruce were away on vacation, so I hastily wrote a short essay signed by the names of the three men. That was my first post. In the journal Physical Review, it takes up only half a page. In the text, there is a paragraph dedicated to the intermediate boson, universally coupled, which is heavy and has a very short lifespan. Years later, Yang and I called it "W", which stands for weak.
This was my first direct (one-on-one) contact with Fermi for a long time. He was very patient. In both of the Tymno and Wheeler essays, there is a proofreading note thanking Fermi for pointing out that three of his students had previously had the same idea independently.
I don't think this is a suitable Ph.D. topic, because I don't know how this universal interaction is based. So, my first article was not suggested by Fermi, he acted like a good friend, giving me support and encouragement.
My second topic is related to Maria Mayer's shell model. This also happened in 1948. At that time, there was an article by Eugene Feenberg that discovered a potential energy that could be applied to the nucleus of a complex atom. It gives these energy levels. But there is a problem with this potential energy, which is that it violates the principle of adiabatic.
Maria discussed her article at an academic presentation, and there was a bunch of objections. At the end of the presentation, Fermi asked, why not consider spin-orbit (L-S) coupling?
After that, I noticed that the next week, another symposium was held, but the speaker was again Maria, and the topic was the same. This time, I listened to it again, and Maria's report had improved a lot, and she already had a final shell model, a very beautiful model. In Maria's article, she thanked Fermi for his contribution in asking accurate questions. In her Nobel Prize speech, she once again affirmed Fermi's vital contribution to asking accurate questions. However, on this occasion, she said that she had already considered spin-orbit (L-S) coupling and happened to meet Fermi in the hallway, when they stopped to discuss the magic number. In this version, Fermi asks the spin-orbit (L-S) coupling question, which she has already answered and answers right away. Obviously, it's been a long time since this incident, and she may have different memories.
Now, let's talk about the next question I got from Fermi. He was thinking about a problem, because the average free path of a nucleon in a heavy nucleus is only about one nucleus radius or less, and it is very difficult to understand how keeping an orbit makes Maria's analysis meaningful.
At the time, Fermi had his obsessive thoughts. In his early work, in argon atoms or other noble gases, he noted that it is possible to have many other electrons in an electron orbital. Fermi uses his effective scattering length and delta function model so that he can obtain orbits in a medium provided by other electron clouds. This fits very well with the experiment. So he was thinking about whether the same line of thought could explain Maria Meyer's magic number.
I remember saying at the time that it was indeed a very good topic. He explained it to me. I thought about it for about a week or two. Later, he asked me if I had figured it out, and I said, "No progress yet." Building on what Fermi has already done, I can't forge a new path. Later, I understood that the real difficulty comes from the complexity of the problem, which is not as simple as Fermi electron gas, it has to do with a strongly coupled medium.
Professor Fermi was patient and said, "It's a bit tricky. Well, how about we switch roles? ”
He said that there were always physics questions that puzzled him, and he wanted to seek answers and learn more. He suggested that I give him a lecture. I said, I'll give it my all.
At that time, Fermi was mainly experimenting. When he admitted me as his student, I was his only theoretical student. When I first made the request, he said he didn't want to bring any theory students. Because at that time he was not working on the theoretical side, he was building a particle cyclotron. He's measuring neutron-electron interactions, and so on. After that, he said, "Okay, he took me." But it seems, this student is a bit picky.
He asked me to read the literature and then gave him lessons. So, we meet once a week and spend an afternoon together. I went to his lab to find him, and then we went to his office together. Normally, we discuss a topic that he raised last week. At that time, he was interested in astrophysics, such as the problem of protons colliding with stars, and the correlation with cosmic rays.
At first, he asked me what the temperature of the center of the sun was. I gave him a report: it said about 10 million degrees. He asked me if I had done the accounting myself. I said that there are two correlation equations between the light intensity and the energy generation due to convection in the core, so it is more complicated. At that time, he asked me again, how do you know that this answer is correct. I wrote the equation and showed him the law of energy conversion and the 3The 5th power is proportional. Whereas, the energy production is proportional to the temperature to the approximately 16th power. Fermi said: You can't rely on other people's calculations, you have to approve them yourself before you can accept them.
Fermi suggested that we might be able to make a slide rule to check it out. He helped me make a 6-foot-long slide rule to solve the problem; I also have a copy of the photo taken with the slide rule. He did carpenter's work, and I carved and photographed the scale of the log scale. When we made it, we calculated it right away, maybe it took an hour. I want to describe these episodes to show that he was a very good teacher, and at that time (1948) Fermi was already recognized as a master of physics, and I was only a young student who had recently arrived in the United States from China. But Mr. Fermi spared no time and energy to guide me and educate me.
Now back to my ** topic. We started working on the topic of white dwarfs and Chandrasekhar. Back then, the Chandrasekhar limit was not what is now recognized as 14 solar masses, but 4 times or more. At the time, it was not clear what the internal composition of the white dwarf was, whether it was made up of hydrogen, helium, or other heavier nuclei. This changes the ratio of electrons to nucleons. Gravity acts on the nucleon, but the pressure to resist collapse comes from the electrons. So the problem depends on the ratio of the number of electrons to the number of nucleons (actually the square of the ratio). There was an article by Marshak (who was working with Bethe) that said that the most likely ingredient was hydrogen. The idea is that because white dwarfs are very dense, the heat flow from the core to the surface of the planet will be very fast, and if the core of the white dwarf is very cold, it will slow down the fuel burning. This is also what Gamow thinks. They claim that white dwarfs are the birth of planets, and that white dwarfs may be composed entirely of protons.
Thus, the Chandrasekhar limit was four times the number of limits now recognized, and when I tried to read Marshak's and Marshak and Bate's articles, I realized that there might be something wrong with their thinking, and that the opacity of the dense matter used in their calculations was wrong.
I mentioned these points to Fermi, and he suggested that I write them a letter. So I wrote to Marshak while he was on vacation in Wyoming. The reply was rather rude. He said, "Who are you?" At that time, Marshak was working with Bate, and he had already done a lot of work on meson theory and made a lot of achievements in his career. Of course, after that, we became good friends. Anyway, he said he would give me an answer. In my letter, I pointed out what I thought he was wrong. He wrote back to me and said I was right. At the same time, let me take it a step further: Is the main element in the interior of a white dwarf hydrogen, or helium? When I think about it, I feel that this white dwarf should be made entirely of helium, not hydrogen. Energy production is a steep function of temperature, whereas energy output is a slow function of temperature.
Marshak and Bette found the equilibrium point, but it's not actually a stable solution, because if you increase the temperature a little bit, the energy production will increase dramatically, and the whole thing will **. So, with Fermi's encouragement, I wrote an article on this topic. That article was published in the journal Astrophysics. This article, along with the correct handling of opacity, became my Ph.D. (mine was later applied by scientists in the Los Alamos lab who were particularly interested in dense matter).
Fermi is different. Not only in physics, but also in terms of his achievements, he is also very kind in dealing with people. For example, he asked me a question, and I replied that I didn't want to do it, and if I ran into a professor, he would say, "To hell with it." However, this is not the case with Fermi, who will say, "Okay, then you will teach me." "It takes a lot of patience and kindness. I remember he was very busy, he was doing experiments, building the Chicago Particle Cyclotron, and so on.
WHITE: Garwin talked about Fermi's charisma for leadership. He guides people in the direction of his work. Your relationship with Fermi seems to be a little different.
Tsung-Dao Lee: Yes, I can give some examples. During that time, I met with him once a week. And each discussion is a whole afternoon, talking together. We spend a lot of time together. I don't know if any other teacher would do that. Of course I mean, it was quite special, but I was too young to know how lucky I was and what a special teacher I met.
Shortly after I arrived in Chicago, Fermi offered an evening class that was only available to invited students. I was very lucky to be invited, which was very special. The course lasted about two years, from 1948 to 1949. Every week he assigns some questions. At the time, Fermi was measuring the interaction between neutrons and electrons, and he said that because neutrons have a magnetic moment, you can try to calculate it using quantum electrodynamics. The next week I did the calculations using the Born approximation. Before Fermi arrived, I spoke to another student, Mulford Goldberg, and we both got the same answer. After that, Fermi came and asked us about the results. We gave him our formula. "You used the Born approximation? We replied, "Of course, what else can you use?" "He explained to us that if you use the Born approximation, when the electron comes in, it rotates and so on. In short, we discuss the commonly accepted views on the validity of semi-classical calculations.
Instead, he used a different way of calculating and arrived at his formula. The result is that when the validity range is correct, our formula degenerates to his formula, but, if not, only his formula is correct for the real neutron magnetic moment and electron. At that time, Fermi calculated this problem, because Fermi was also doing experiments and measurements at the same time. And it has ended his measurements. So he is thinking about new interactions (beyond the role of electromagnetism).
Normally, as soon as Fermi announces that he has done it, I don't do it anymore because he has already derived the correct answer.
Around 1952, shortly after I entered the Institute for Advanced Study, I was called by Muffoue Goldberg, who was in the physics department at Princeton University, and asked me if we could have lunch together. He asked me if I had read a Foldy and Wouthuysen article. I said no. He said, "Let's take a look and then come back and think about the electron and the neutron problem." "I read it and am pretty sure that our formula appears verbatim in their article, and that it is exactly the same as Fermi's experimental results! I learned a lesson. If you get a formula and you believe that your formula is correct, you should substitute the numbers into the formula and do some calculations, but neither Goldberg nor I did.
When Fermi says this is the result, none of us will have any doubts about whether he is correct or not, and none of us will bother to substitute the numbers and compare them with his experiments.
White: Gawin had previously told a story about Fermi's time in Rome. At the time, Fermi was working on a laboratory bench and, seemingly instinctively, replaced a block of lead with a piece of paraffin, which led to an entire series of slow neutron research work. Can you tell us a story like this about the role of "inspiration" in theoretical work, for example, in Fermi's theory of decay?
Tsung-Dao Lee: Speaking of Fermi's decay theory, in Fermi's own words, this statement has already appeared in publications, when he was trying to understand quadratic quantization. He didn't quite understand Pauli's work, and at the same time he was interested in decay.
We must recognize the peculiarity of decay, if we compare it to the case of electrons emitting photons. Electrons emit photons with one particle in (i.e., electrons) and two particles out (i.e., electrons and photons), whereas in the case of decay is one in (neutrons) and three particles (protons, electrons, and neutrinos) out. This is quite extraordinary. So Fermi realized that this had to be done with the Dirac Sea concept, and I think he realized that quadratic quantization was a tool for analyzing this new phenomenon.
The story of paraffin wax is perhaps typical of Fermi. There must be a lot of articles on this. There is no doubt that this is inspiration, but, like most inspirations, it comes from a deep understanding of the origin of physical nature. Finding this origin is like picking a grain out of a sack. That's how genius is born. However, you have to start with a sack. I think that the paraffin wax incident may have been a decision made by Fermi after he had appeared in his mind intermittently and subconsciously countless times. From an outsider's point of view, it's amazing. It's magical, but it's a miracle of humanity.
Wright: We're talking about a wide range of topics, but can I ask you a little bit about yourself?
Tsung-Dao Lee: I think everyone has their own main mode of thinking, which is to focus on what you think about and use the techniques you have learned to achieve your goals. At the same time, there will be other "by-products", which may not be very logical, but can be freely associated. It is these by-products that suddenly bring into the subject of thought, and inspiration pops up. In order to grasp these inspirations, if you are studying theory, you need to have analytical ability, and if you are engaged in experiments, you must have all the experimental tools and techniques you need. I think this experience is common to many people. When it comes to Fermi, he is special, he has a strong theoretical analysis ability to concretize abstract things, and he can design and execute extremely effective experimental proofs. In short, he possesses an extraordinary genius for the ability to translate different and extremely difficult natural phenomena into clarity and clarity. Fermi is a great giant of theoretical and experimental physics, and he is also a very good teacher who can teach and understand.
This article was originally published in China Science Daily (2012-01-18 b4 people).