George Uhlenbeck – Session III

Kuhn:

One of the things we haven’t talked about is education, curriculum, and books. Another one is this whole question, and you’re in just the right period for it, of how people felt about the state of physics — the problems and the pressure on the problems.

Uhlenbeck:

Only for Leiden I can tell you… Let me first tell shortly a little bit about education, because I don’t think there is very much to say about that. In one respect, I was a little bit different because of this period in Italy. Which of course the usual student did not have. That was just very good luck that I got that. And the other point was that I started to be a chemical engineer only out of a kind of desperation, because I was at that time not allowed to study in Leiden because of the law. It was a law that everyone who wanted to study at the University needed a classical education, must have gone to the gymnasium. I had gone to what Germans call “Reale Schule”… There we had no classical languages. And these people were only allowed to go to the technical universities and not to the University. My parents were also much more inclined that I would become an engineer, because it sounded much more safe as a profession. So I started in Delft as a chemical engineer. Then, however, this first fall the law was changed, and that was the famous law (“limbo”). Everybody was waiting for it. And then at last also the people from the Reale Schule were allowed to study the exact sciences, and I think also medicine — that I am not sure of — at the University. However, they could not yet study law. That was after a semester, roughly, in Delft.

I was rather unhappy there. That was a typical technical university grind education. Lots of lectures, laboratory and what not. I was finally allowed to go to Leiden. And there with regard to the education, I found it quite heavenly. Mainly because there were practically no lectures, you had nothing to do. There were only lectures in mathematics, analytic geometry and calculus and analysis and so, and they were only about four hours a week altogether. Two hours geometry, two hours analysis. Then there was physics. The general lecture, precisely as in Germany. There was the big lecture with demonstration, which I thought was quite dull and I didn’t go to that. I didn’t have to. I mean there was no attendance, nobody took any kind of responsibility for the student.

Kuhn:

Who gave the big physics lecture?

Uhlenbeck:

Kuenen, who was a very good physicist. As a general lecturer he was a little bit slow. The only other thing he gave — but that was already the next year — was thermodynamics. That I attended, and that I liked much better. In that he also did much better, I think. Then you had to do this practical, set up experiments. But since I was a first-year student, I was allowed to do that only one afternoon a week, which was just fine for me. Just one afternoon, there was no more. So I had an enormous amount of free time. There was this library which Ehrenfest had started. I didn’t get in touch with Ehrenfest at all. But I studied for myself Boltzmann’s gas theory, I remember, and mechanics as much as I needed. It was quite heaven.

Kuhn:

This was still first year?

Uhlenbeck:

First. And then the second year the question of the exam began to dawn. You see, there were no exams.

Kuhn:

What level of the sciences had you reached before you went to Delft?

Uhlenbeck:

Quite a bit. The physics and so in high school was quite good. In fact my teacher in high school was quite a good physicist. He had a Ph.D. and had also published things. He was a very shy man. I had the greatest admiration for him as a boy, and he partially determined my direction. He seemed so learned, and that attracted me. Anything which seemed learned. He also gave me the first calculus while I was still in high school. That was not taught, but I studied it for myself during the summer before the last year, so I knew calculus when I came to Leiden. But the general level was not so high. One learned in mathematics, elementary mathematics, geometry and algebra, trigonometry. And physics also, I would say, was just about equivalent with the first year physics, or sophomore year’s physics in Michigan. That we got in high school.

Kuhn:

But not with as much mathematics as the sophomore year?

Uhlenbeck:

Well, in Michigan there was also no calculus in the general course. Now perhaps, they have introduced it, but at that time there was no calculus. There were problems, but no practical work. The only practical work in high school was in chemistry. Otherwise not. And all the languages, we had three languages, which everybody at the end of high school could read fluently. So then the calculus was, of course, taken up again at the University… Analysis and infinite series and so. But no theoretical physics except this thermodynamics. That was a little bit theoretical. But then after two years, or in the third year, I finally did it — … I was a very dutiful boy. I did my exam in fine in the third year, and the last three months of that period I had to work. The examination consisted only of oral examinations. All separate topics. On analysis you went to the professor, made an appointment, and talked for half an hour while he asked questions. Same in geometry. Same in physics, for this general course and thermodynamics. So that was a little bit of the pressure; when one was under pressure. Because then one has to know everything at the same time… You see the whole method of education consisted of doing two exams. One was called “Candidates” which you did after two or three years. And then again two or three years later you did the doctorandus examination. In between there was never any examinations, never! And also no attendance, in courses or anything. Of course one knew what one had to know, because that was essentially the content of the lectures. Whether you had gone there or not gone there, there, there was always someone who took notes. Notebooks, notebooks.

Kuhn:

How about problems?

Uhlenbeck:

No problems… There were problems in class, but never assigned problems.

Kuhn:

How do you feel about that now?

Uhlenbeck:

I love it. I never did it myself very well, except if I am forced to, because that is so schoolboy like, you see. And that was, of course, what I liked. They treated us completely as grown-ups. You could take the responsibility. You made your own problems…

Kuhn:

Did the teacher suggest that one do this?

Uhlenbeck:

Not at all! They lectured and went away… Ehrenfest always didn’t believe in problems. He always said the only problems which are good to do is those you could do yourself. He never wanted to make a problem course in which the problems are assigned, that he never did. He was very much against it, in my opinion, so far as my memory goes. Anyway, I did this exam, and the second year was more of the same. We went on with calculus, and we learned a little bit more of geometry.

Kuhn:

Did you begin to get some special subjects?

Uhlenbeck:

No, thermodynamics was the only special subject. I was, at that time, unsatisfied with the mathematics, mainly because of the lack of rigor. I was so extremely attached to rigor at that time. I am not at all anymore, but at that time I thought that everything should be precise. There was one man (Proster) who gave a special course on the foundations of analysis. And that I thought was marvelous. I still have the notes of it, because it was straight forward business — Bolzano-Weierstrass and the Dedekind cut, and all that sort of thing. But I thought all that was wonderful, because it was so rigorous. Anyway, that was only a special course and no exam was required in it.

Kuhn:

Did the general physics course go on in the second year?

Uhlenbeck:

Yes. It was a two year course. Then there was also thermodynamics. Optics only in the general course, and of course in the practical. That I remember. The second year you had to work at least two or even three afternoons to get ready, because there was an assigned number of these experiments which you had to do before your exam. You had to give reports on them, written reports on the results. These experiments were quite interesting, for me, mainly because there was lots of formulas in them. You had to check and see whether you could put in experimental values and it would come out. All about diffraction, and all kinds of things. Then I wanted, always, to derive these formulas too. I still remember that the reports of my experiments were simply, for three-quarters of the time, small dissertations which I started. Kuenen was then very much impressed that I gave all the derivations. It was not required, but it was my hobby to do that. But otherwise I learned a lot for myself at these times. A remarkable amount, really. Maxwell theory I did by myself, optics, lots of diffraction theory.

Kuhn:

What books did you use?

Uhlenbeck:

I had a little book. I think it was Clemens Schaefer. It was not a big book, it was a thin one. I still remember, it had such a red cover. Of course, for myself, I pored through books. The gas theory of Boltzmann I practica1iy copied! Complete excerpts. And I began with Gibbs, already, at that time.

Kuhn:

This was before you knew Ehrenfest?

Uhlenbeck:

Well, I knew him in the second year. I saw him, we talked, but I did not know him well. After this exam, which was so far as I remember around Christmas in my third year, I started with Ehrenfest. I had already started, that third year, to follow his course, I think.

Kuhn:

What subjects were you examined in?

Uhlenbeck:

I was examined only in analysis, geometry, and in the physics course — physics and thermodynamics by Kuenen. There were three people, three professors. One (???) in geometry, Kluyver in analysis, Kuenen in physics. Ehrenfest was not an examiner for the first exam. He, as I told you, gave always these two lectures, essentially. Once in a while he did, so to say, collect a group of students and then give something extra, like partial differential equations of physics. I remember that in the third year — the second semester, after my exam — he did that, and I worked for that quite hard, too. Then I began to get acquainted with him. But I did not start to work with him yet, really at all, because his method was that he always worked with one man. That was someone else at the time, you see, not me.

Kuhn:

I see. He had really just one student at a time.

Uhlenbeck:

At most two.

Kuhn:

In your first three years how many other students of physics were there?

Uhlenbeck:

When I arrived, which was in ‘18, just five of us were starting, of which after a while I think one dropped out. One was an experimental physicist; two were mathematicians, of which one, Grosemann, is now professor at Leiden — a very well-known man. I was the only one who wanted to do theoretical physics. Already when I arrived I knew that. Somehow or another, that was the most learned subject, I thought.

Kuhn:

And these five were all in the same class. You were all the same year?

Uhlenbeck:

Yes. Of course, because it was always a collection of various years, I would say that in the mathematics courses there were certainly not more than twenty. In the big physics course there were more, because chemists and so had to follow that, and there were many more chemists. So it was a very relaxed sort of education. I think it was very fine. Mainly possible because the numbers were small.

Kuhn:

Did all of the people, or most of the people, work as hard, do as much that they were not being asked officially to do? Did they just take it for granted that you did this?

Uhlenbeck:

Well, it was not taken for granted, but most of them did. Most of them had certain special interests. Sam, already before the first exam, I’m sure, started to read Sommerfeld’s book, Atombau. I am sure that even at that time when he did his exam, he was younger than I was, two years younger, so I then hardly knew him. He was still a beginning student, but I know that in his second or third year he published his first paper. He was so good in seeing equivocal relationships. He had found that the alkali doublets followed this Sommerfeld fine structure law for relativistic doublets. And that shouldn’t be so… Ehrenfest was so conservative he thought it shouldn’t be published, so he let him publish it in a very obscure Dutch journal. Then of course two or three years later it was rediscovered by Lande. Now we know that it has to be so. But he did the purely empirical. He was very much, I think, under the influence of a high school teacher from (Lohuyzen), who was also a spectroscopist. So he was there very much interested in everything which had to do with empirical regularities.

Kuhn:

We had really just gotten you then through the first exam.

Uhlenbeck:

And then we had that seminar. Then in that semester I got, suddenly, an offer to become a high school teacher. That was my fourth year. I was a high school teacher at the gymnasium in Leiden for about 12 hours a week. Mainly I did it for money, because I kind of hated it. I taught only mathematics, nothing but mathematics. At the same time I followed, of course, Ehrenfest’s lectures, and those also of Lorentz. I told you about Lorentz. That was the Monday morning lecture, the famous Monday morning lecture, 11:00 every Monday. He talked on the recent literature which he worked out in his own way. It was told, and it may be true, that what he always did was to look at the literature and see what it was about. Then he closed it and did it his own way. That he presented in lectures. And the lectures were really quite remarkable. At least my memory of them was that they were so clear that at the end of the hour you didn’t know any more what it was all about. Nothing went wrong, so to say. In one of these things I was able to really pin it down only by making careful notes. You went already quite early to it. Ehrenfest was absolutely insistent that you went. That was one thing that he looked that everybody was there! But for the first time, since it was of course not a required thing, I just listened to it, made a few notes. I don’t remember, even, from the beginning years what a doublet was. I had this tendency that you forgot it again.

Kuhn:

Did those lectures range over a large range?

Uhlenbeck:

Oh yes. It varied from month to month, because it was all recent stuff. Quantum theory, so far as it was. Not all this spectroscopy. That Lorentz never did, though he knew it, I think, very well. Everything with regard to the crystal structures. I remember that the papers of Born and Lande were discussed, and various other things. Relativity theory some. But anyway, I followed of course mainly Ehrenfest’s lectures, and I went to the Wednesday colloquium. That was also a famous institution. The Monday Morning lecture of Lorentz, and the Wednesday evening colloquium. This lasted from about 8 to 10.

Kuhn:

Ehrenfest organized a colloquium?

Uhlenbeck:

Yes. That was his colloquium, and he even made notes. He had a book in which he took attendance; he had notes on the lectures. And there was always much discussion, mainly from Ehrenfest. He always asked questions, and he did it really marvelously, because he often simply interrupted the speaker, and especially one of the younger ones. He said “Now you stand aside. Now I will talk.” And then he summarized it, you see. I know it has happened with me and certainly with many people, that at that time you understand it all! How precise it was. And many of the things in the colloquium I still remember; certain points I will never forget. Of course in the beginning you didn’t understand much. But by a kind of diffusion process you got finally what Ehrenfest also called the “jargon”, the jargon of modern physics. That you began to pick up, so to say, and then in later years you asked questions and took part. There was much discussion, always much discussion.

Kuhn:

Were the presentations usually from students?

Uhlenbeck:

Students sometimes, but there were also always guests. There were also experimental results from the low temperature laboratory which were presented. It was not just theory, but also not just experiment. There were no experimental details. That was never discussed. But always, so to say, the point. “What’s the point?” “What’s the point?” And always recent literature too. He himself talked. Not very often, but he talked once in a while. Those were also always hard points. I remember the lecture on the Nernst theory. For the first time I understood it. That was every Wednesday, religiously. It was never omitted. Wednesday by Wednesday. They drank tea beforehand, and then there was the colloquium. You sat around in a room. In the middle of the room there was always the recent issues of all the leading journals, new books which had appeared were there — all just to let the people see what the recent stuff was. That was the task of the assistant I did that later, I was not yet assistant, of course. That was a marvelous colloquium. That was also the year that I was a high school teacher, and for the first time I lived in Leiden. Then I had the money to have a room. Before that I commuted to the Hague, and lived with my parents. I still remember that then also in that fourth year Ehrenfest suddenly came in and said, “Well, he was inquiring about someone who wants to go to Rome, to be a teacher.” The remarkable thing was that nobody reacted except me. I thought it was wonderful, and so I put my hands up. I got this job which was at my fifth year, and then I was there for three years, until ‘25. That fifth year was the year that I should do my second exam. Of course I followed Lorentz and Ehrenfest, then also further mathematics of the same people. That was differential geometry; theoretical mechanics, given also by the mathematicians; and so-called higher analysis, by De Kluyver. Again, in each of these topics you had to do an oral exam. I did them in my fifth year, partially by coming back from Rome — once at an Easter vacation — and then also early in the summer. We came back always in June, and then I could still do some of these exams.

Kuhn:

But how did you do the lectures?

Uhlenbeck:

I didn’t do the lectures. Well, I had the lectures so far as … my fourth year. I got notes from people, and I studied then for myself out of some books. I don’t even know which, precisely… I studied a bit in Whittaker, I remember — Whittaker and Watson. I studied this book on differential geometry, of Eisenhart. That was for the other exam. For the theoretical mechanics, I studied Appell. But that was really when I was in Rome. Of course at that time books were mentioned a lot, but not a single course followed a book at all. So it was only meant as collateral readings. Neither did Ehrenfest, of course, follow a book, but he was always very insistent that you looked at books. He says he thought it was terrible, since the invention of the printing press, that he would say something before the blackboard which was in a book. He says, “Everybody can read!” “So why should I parrot what is in a book.” “All that I can teach you,” he said, “is everything in between the books. In between the books. That’s what I must tell you.” But he certainly hoped and required that you looked at books, in various portions. So I looked at very many books, really. But, then, I was a bookish fellow. Very bookish in contrast to Sara. So I remember still that I studied even Kirchoff’s lectures, which Reiche mentioned. They’re very difficult, but I studied them anyway, especially optics. At the end of the fifth year I more or less squeaked through the second exam…

Kuhn:

I want to interrupt before you get into the frame of mind of the fifth year. In your fourth year, before you went to Italy, when you were going to the colloquia and to the Lorentz lectures, what seemed the big problems?

Uhlenbeck:

It’s difficult to say, because I was still just a school boy. The only thing which was clear is the quantum theory, because that was always at the end of the Ehrenfest lecture. He talked about some of the quantum theory things, that that was the new thing and that was what people were interested in. That was, of course, also discussed at the colloquium very often. But I don’t think that in my fourth year I had already impressions of what the central problem was. Everything seemed interesting to me at that time. Relativity theory was also touched upon by Ehrenfest — always at the end of the Maxwell theory — but only just to the Lorentz transformations and all these paradoxes. He had all kinds of models that tried to explain. Ehrenfest had of course the tendency to do everything as “anschaulich” as possible — his models. On the other hand, therefore, he didn’t hope that you even knew everything. There were only a few things that you had to know. That was Hamilton theory, Maxwell equations, some portions of statistical mechanics — these you learned very well. There was not the feeling — at least I didn’t have the feeling — that there was, so to say, a frontier, except that it was quantum theory and atomic structure and so on. One knew that everything was very mysterious. As a student you know that was mysterious, of course. I myself didn’t work at all on anything at those times, except learning the books. And already from my early days my main interest was still kinetic theory and statistical mechanics. Especially Ehrenfest’s encyclopedia article made a big impression on me. It was so clear, and I was just ripe for it, which was very good… Sam was much more specialized, and I’m sure that he knew at that time already much more. Not at that time, but at the same period of his development — he was two years after me. He knew already much more about atomic structure, because he had studied Sommerfeld’s book.

Kuhn:

You got a good deal of relativity also from Lorentz?

Uhlenbeck:

Well, Lorentz, once in a while, discussed problems in relativity, and even general relativity. I then did not understand really, although I thought I understood when he explained it. In the Lorentz lecture, of course, no holds were barred. Everything was discussed, everything! And he computed everything.

Kuhn:

Did Lorentz himself have any feelings about his own version and earlier work toward relativity, as against the Einstein formulation?

Uhlenbeck:

I think he had, but I certainly don’t know that of my personal experience. The contact with Lorentz at that time was non-existent. You went to the lecture, but he was, so to say, the god. He gave his lecture and then he went home again to Haarlem. Of course he talked with Ehrenfest, no doubt. He did not come to the colloquium, of course.

Kuhn:

What about the aether?

Uhlenbeck:

He never talked about that.

Kuhn:

What about the rest of the students, just getting it through Ehrenfest? Was the aether physical for you?

Uhlenbeck:

I can’t say. Ehrenfest’s inaugural address was about this. I still remember having read it. He talked about it a little bit, but we certainly did not have strong convictions one way or another. But relativity was for me, and I think for most of the students, on the horizon of our attention. The thing which we had to work on, if there was anything, was statistical mechanics and quantum theory…

Kuhn:

So special relativity was not yet classical?

Uhlenbeck:

Oh no, no. And it also was not so known, you see, that one felt that it was a kind of an instrument. Nowadays, of course, all people know it so well, but at that time we knew it just a little bit.

Kuhn:

Well, I think there are some schools in Germany, where it was much more closely built into their curriculum.

Uhlenbeck:

I suppose so. Ehrenfest was the opposite of a systematic man. He was not systematic. He always wanted to have the points “at was the point? As soon as it became so to say technical machinery, then he left it. He just left it. He told me later. This is now neither here nor there, but he told me later that both with regard to the quantization of the rotator and also with regard to the Langevin formula for magnetism, that he did it all first, years before! Some of it was published, I think. But he did it only on the plane, because there it was easy! And he never did it even for three dimensions, you see, because then he saw the point. He saw immediately the point that it was discrete, and that you then have also an effect on the specific heat. Then later on it was of course done much better, by Reiche especially, and so he is never even mentioned… And that was typical of him. As soon as it became a longish calculation, then he didn’t do it. He just didn’t do it.

Kuhn:

Now I’ll let you go to Italy, or come back from Italy — whatever you like.

Uhlenbeck:

Let me talk one bit about Italy. That was my fifth year. I then did the exam, and I did not do, very much else. I learned Italian.

Kuhn:

Oh, you did the exams the first year you were in Italy? I see.

Uhlenbeck:

The second exam, the doctorandus. Ehrenfest always said he had a kind of faith in me which was based on nothing, he said. I didn’t do even an exam with him, although he was my principal man. He was then, of course, present. The only thing he let me do, which was also required. The exam at that time was then divided into two parts. One of them was just very short, an hour at the most, in which one was again formally a little bit quizzed… A little bit on analysis, and a little bit (???). There I did pretty well, so he was all in favor of — In analysis I didn’t do so good. Ehrenfest asked a little bit about Maxwell equations — oh, very little. That you have to get two what they call (“scriptions”). It was not quite a problem. You had to write part of it as a problem and part of it as an essay. I got one in mathematics and one in physics… You were simply given a problem and told you had three days to write it. And you could have access to books, and even friends of course. It was very important that you have! Everybody helped, you see, everybody helped!... And then you wrote it out — the physics. Mathematics — it was a tough problem that even with my friends we only solved half. And the mathematician Kluyver, who had his doubts about me, let it go at that. But he was not quite content, really. Ehrenfest gave me for a scription something on which I had talked in the colloquium, so I wrote it out a little bit further. I still remember what it was. It was on the dynamical theory of x-ray reflection which I had studied a little bit at that time. And that was perfectly okay.

Kuhn:

On the dynamical theory of x-ray reflection — you mean what?

Uhlenbeck:

Ewald’s stuff, you see. The question that the reflection could not simply be done geometrically by the Bragg reflection, but that you must think of partial waves. That had certain consequences which Ehrenfest was at that time interested in. And I wrote about it. Then the second half of the exam was then a short discussion of these scriptions, and then it was through! I was through and I got my diploma. Without doing an exam with Ehrenfest, no oral exam!

Kuhn:

What was the point of the scriptions? If you could bring in all your friends and so on?

Uhlenbeck:

It was tradition. Had been done for fifty years like that. Everybody did it, so this was the way it was done. Two scriptions, you had always the scriptions. One in your major subject and one in one of the minors. My other minor was theoretical mechanics. Mathematics and theoretical mechanics. Then on your diploma, which was the thing which was required by law for anyone who wanted to teach in high schools, it was then indicated that you had taken these minors. And so I was allowed to teach in all the high schools and gymnasiums. I was allowed to teach physics, mathematics, and theoretical mechanics, which were always separate subjects, even in high schools.

Kuhn:

Did theoretical mechanics by that time definitely include Hamilton-Jacoby theory?

Uhlenbeck:

Yes. Not very much of it. We had contact transformations and so on. That was done by a mathematician.

Kuhn:

What did you learn those out of?

Uhlenbeck:

Really out of his lectures. Since I had to study most of it for myself, I studied most of it out of Appell, which was the book which also Van der Woude recommended, and I still have the book… I studied those volumes — much of it, not all of it. But then it was interesting. I did this exam early in September, as soon as school was over. I was really expected to be back in Rome already, but the ambassador gave me then a little bit longer so that I could do this exam.

Kuhn:

Tell me now what the job in Rome was.

Uhlenbeck:

This was the ambassador, von (R____) was his name. He wanted his two sons to have a Dutch education, but he wanted them also with him. So he hit upon the scheme to hire two people. He had plenty of money because of his American wife. He hired two people, one for the classical languages, Latin and Greek. This was always half the time of the curriculum… And the rest of the time was everything else. I was hired for everything else. And so I taught this boy mathematics, and some physics. Of course the older boy was already quite through. He is now an ambassador in Washington. But this younger brother was the one whom I had mainly. I taught him everything else, except modern languages, because for that he had again his own tutors. Furthermore he knew the modern languages much better than I did, because the boy spoke fluently Italian, French, English. The only language he was not so good in was Dutch! Because he was never in Holland. He always made mistakes in Dutch, which I had then to correct. And that was a wonderful job. I did not live with him. The last two years — two and a half years in fact — there was only one boy, and he can take only so much. And we had to divide it in two. So it amounted really to about every morning or every afternoon, and then the other part, the other fellow came.

So I had, again, an enormous amount of free time in Rome. Then after this exam, Ehrenfest said that I should look up Fermi. He gave me a letter and also a series of questions. That was typically Ehrenfest. This was in connection with the paper of Fermi on the proof of the ergodic theorem… Ehrenfest was so impressed by that paper, he wrote a paper himself, which is also in the Collected Works, and sent a copy of that with some questions. I was supposed to look up Fermi, who was then what they call “littera docente” in Italy. And of course in this whole physics building, I still don’t know precisely where it is. Anyway, I looked him up, of course, and Fermi was clearly very alone. He had two people who were at least about his own age, and with whom he could talk. Those two were Pontremoli and the other was the man who is now professor at Torino, Persico. I talked a lot with Fermi. I remember that he walked home with me and talked, and I have, even, the memory that he talked with me about the Fermi statistics. And so that is where I really learned to know Fermi. I told him about Leiden very much, and that, I am sure, made him decide to use the half a year of his fellowship that he still had. That was, of course, an international Rockefeller fellowship, of which he spent one half year in Gottingen and had quit.

Kuhn:

What did he say about why he quit Gottingen?

Uhlenbeck:

He never said. I know only indirectly that he was not happy there. And then we said we should have a little seminar, because then I talked about the Ehrenfest colloquium and how fine it was. But I was of course, compared to him, a complete beginner. He was younger than I was, but he was in a sense a wonder child, like Pauli. At Pisa he wrote about general relativity and what not. He knew everything. And as I said, I think this must have been before he began to tell me something about these electrons in a harmonic oscillator field, and then, of the exclusion principle. I didn’t quite understand. I may have been mistaken, maybe it was later. But it must be about that time though. Anyway, we had then a little seminar, with Pontremoli, Persico, and me, in this old building. Of course Fermi always talked. It was really a little lecture that he gave us. And what we talked on was the classical perturbation theory, three-body problem, analytical mechanics, all applied to the quantum theory. You see, all these things which one now finds in the first volume of Born. Fermi knew everything, and he talked about these things… This was the topic of our seminar. He was so much ahead of all three of us, that he was the one who talked all the time. That was also the only year, really, I think the only year, that I followed lectures in Rome. I followed the lectures of Volterra and of Levi-Civita. But that was all in mathematics… This was the second year. And then I came back in June again, and of course I went to Leiden to see Ehrenfest. Ehrenfest said, “Now you’ve got to come back, now this should be over.” But then I didn’t want to really, I liked it so much. The boy had still one year to go, and this ambassador wanted very much not to change. I just stayed over, and that was the third year. And then the third year I didn’t do any physics at all… Fermi was gone now, because Fermi got then this job in Florence. It may be that he went to Leiden first, but the last year in Rome I never saw Fermi. I think he was a semester in Leiden, and then went to Florence as a professor of something. He didn’t get any money in Rome so far as I know.

Kuhn:

You said the other day that there was no physics in Italy.

Uhlenbeck:

There was Corbino. He was the professor, and he was only an experimentalist. There was certainly, except for Fermi, no one who knew anything about physics.

Kuhn:

Do you have any notion what the curriculum was like?

Uhlenbeck:

No, not at all, because I never met any students. I don’t think there were any students! To tell you the truth, in physics. There were certainly some in mathematics. The second year there was also Stark — or was that the third year? Stark — from M.I.T. We came then to Rome to study with Levi-Civita. Of course all these people then I got to know. I mean there were always so few, and if there were Dutch people I knew then through the Dutch Institute… There were always other Dutch people, but mainly art historians and what not. I knew them all; I still remember some of them.

Kuhn:

Then it was then you got so interested in history?

Uhlenbeck:

Then I had so completely lost touch, you see. And I read all these things. I was shaken. That third year shook me, so to say. I didn’t know what I should do. I had, thank God, my uncle who was professor of linguistics at Leiden, a very fine old gentleman. He was in sympathy with me. I knew him so well. He was one of the men for whom I had such an admiration. And he said, “Yes, well maybe that is so, maybe you should do —” But then there was this difficulty about the classical languages, I had to learn. And he said, “But why don’t you anyway first go with Ehrenfest and see whether you can write a dissertation. You’ll have, at least, your Ph.D.” The future was always high school teaching, that frightened me too. There was no future except high school teaching. And I had done that a year and I didn’t like it at all.

Kuhn:

Would that have been less true — in history?

Uhlenbeck:

No, also true. But in history you had other possibilities. You could get into institutes like the Rome Institute, which I liked very much. A man there made me write this first paper. He was a Dutch man who was one of the founders of (???). So I did it. I went to Ehrenfest, and Ehrenfest said, “All right, let us try.” And we started to work on these problems in wave equation — one of the first papers. And he told Sam to get me acquainted with what’s going on.

Kuhn:

Is there more that you could say about that time with Fermi? About Fermi’s state of mind, his interests, things he felt or expressed about the state of physics?

Uhlenbeck:

I don’t think that he felt strongly — at least he never told — that there was such great difficulties that something had to change. He never said something like that. He may have held that though.

Kuhn:

Are there other things that you remember about him? What sort of a person was he?

Uhlenbeck:

Extremely mild. As I said, the impression was that he was lonely. I was a young student, clearly not his intellectual equal, but he really went out with me and talked with me. Of course, there was nobody he could talk to, you see. Here was somebody at least who listened and tried to understand — that was my Ehrenfest education. So I told him about Leiden. My impression was that he was kind of intellectually lonely at that time, which was ‘2l. You know, I mentioned that in this lecture. It made a big impression on me that Fermi apparently said to people that he found himself in Leiden, and that there he got a confidence to work so completely for himself. And that was due to Ehrenfest. And that was the thing which he did not get in Gottingen… Of course, I knew Fermi much better in his American period, because he came to Ann Arbor a couple of summers, and I even worked together with him. I wrote a paper together with him, but that’s another story, so to say. In my Rome period I had not much intellectual contact because I didn’t know enough at that time to really appreciate. I have this vague memory that he told me about the Fermi statistics. I think that is a topic for a paper, of early ‘25… I have the memory that he told me. But otherwise, golly, we talked about all kinds of things and also about the Italian situation, in which he was also not happy. There was so little future for him at that time, you see. On the other hand, of course, one must remember that this was the revolutionary period in Italy. I mean I saw the march through Rome. I was there. And I listened to Mussolini’s first speeches in Rome. And I saw all these black shirts in the streets of Rome… It was very exciting, those revolutionary times. Well, so that’s my education. Afterwards, of course, after this summer and the spin, everything about history was forgotten. Then it was so clear that I should go on.

Kuhn:

Well you had gotten a good deal of material that was relevant to what you did with Sam, hadn’t you, from the Italy seminar with Fermi?

Uhlenbeck:

Not much, no, no. Because you see with Sam we mainly talked on these empirical regularities in spectra. All the coupling schemes. Russell-Saunders coupling and how the vectors — always the vector models we talked about, and the various experiments related with it and so. That was the main thing that started us off. And also, you see, the Pauli papers were all of this formal and numerological way. Some physics, some numerology. You had, so to say, to smell your way through it. It was very strange business for me. I never really quite learned it. Sam was of course very good at that.

Kuhn:

Did Ehrenfest do any of that?

Uhlenbeck:

No, it was also not an Ehrenfestis, but he always wanted to hear about it.

Kuhn:

Did Sam do it for Ehrenfest?

Uhlenbeck:

No, no. Sam did it all originally on his own… He got his degree with Ehrenfest, yes, but he was never a student of Ehrenfest in the sense that he went through this period that they worked every day together. You see that was the Ehrenfest method. I told you of that already. And that of course I did. I did that for two years — worked practically every afternoon with bin. That of course made an enormous difference for me. Sam talked a lot with Ehrenfest when he was in Leiden, but he was never his assistant. Then he also went to Tubingen, although his dissertation was of course with Ehrenfest. We got the degree the same day. Ehrenfest wanted that. He said, you must do it on the same day, because at the dissertation the professor is always supposed to give a speech about the students. And he says he did not want to give two speeches. He wanted to modulate it a little bit, first the one and then the other. This was also not quite kosher for the Dutch tradition. They didn’t like it. Ehrenfest, of course, was so un-Dutch in many respects. And I remember that our dissertations — the dissertation is always defense of thesis… You have always these assertations, at the end. That’s typical Dutch method. And that gives really maybe something to talk about. And that lasts only about half an hour or forty minutes… Then, the faculty goes out and afterwards they come in again. It is given to you with the speech. So I think Sam was the first. No, I was the first. And then Ehrenfest said, “You go out, you go out, and we take Sam.” And then at the end, I still see us sitting next to each other in front of this whole row of professors. And then Ehrenfest made the speech to both of us. We had at that time already the job to go to Ann Arbor. That was already settled, that was settled in the spring… Ehrenfest was responsible that we got it.

That was marvelous, because as a result we didn’t have to do high school teaching. You see we had immediately a place where it was at least a university. The way that came about — I still remember. Colby, from Ann Arbor, was then in Europe, looking around really for people for Ann Arbor to succeed Oscar Klein, who was also two years in Ann Arbor, I think. There he discovered the wave equation. Colby came to Ehrenfest, and we were also present. Ehrenfest gave him an impassioned speech, in which he said that this was a very bad idea, to try to get one man to Ann Arbor. Because that was — nobody there — that was just wilderness — you must at least have two, he says, otherwise they have nobody to talk to. Even better, more than two. And he was very serious. He could talk so seriously about how science develops. He made an enormous impression on Colby. We walked home with him, and he says “Yes, he’s a great man. He’s really a great man.” As a result, two or three weeks later, we got both an appointment to Michigan as an instructor. And we both accepted. I accepted immediately. Sam had still a little bit of hesitation, but he did it too. And we went to America on the same boat in August. And then began the Michigan period for me, which was ‘27. But of course then the quantum mechanics was already there… You see the first Heisenberg paper, we knew about, but it was completely — at least to me — completely strange.

Kuhn:

Did you know it was to be taken seriously?

Uhlenbeck:

Everything which Heisenberg did had to be taken seriously, because Heisenberg, Pauli, and, of course, Bohr were the gods. They were the people who knew everything.

Kuhn:

But this was already clear about Heisenberg?

Uhlenbeck:

Oh yes. Sure, sure. Absolutely. Of course in a minor sense also Lande, but still not like Pauli, or Heisenberg, or Bohr. So we knew that this paper was probably very profound. And I remember having looked at it, but I couldn’t make head or tails of it really. And my impression, and I think also Sam’s, was that this was just some more of the same thing, funny rules about the unmechanischen Zwang, and this and that. We did not understand really, but since it was always written by Bohr or Heisenberg, we knew somehow that it should be taken seriously. But it never, so to say, sank in, this sort of thing. I don’t know the precise order, but I think the Born-Jordan paper came before Schrodinger, but not much before. I remember studying that a bit, and also with Ehrenfest. Ehrenfest then began to see a little bit about matrixes and so on.

Kuhn:

Had he known about matrixes?

Uhlenbeck:

Yes.

Kuhn:

Had you had them?

Uhlenbeck:

Yes. I’m sure that we learned that very quickly then. What you had to know was so little. We studied it, but it was so clear that you couldn’t make any problems with it, even for yourself. Everything became these infinite numbers of equations that you had then to solve, and so nobody knew exactly how to do it. One had the impression that there was a real advance, all right. I think that was clear. But it was still so strange that one couldn’t do very much with it. And that changed with Schrodinger. Because that was ‘26, yes, it was in March ‘26. And then with Ehrenfest we studied every paper, and made little problems. We did the perturbation theory even before the next paper appeared where the perturbation theory was done. We made little problems, and I told you about the hydrogen atom and the intensities. There for the first time I learned to handle a little bit all these special functions. It was so good that I was so dutiful. I had studied those things out of Whittaker-Watson. And so I became the expert on special functions. I just knew what a spherical harmonic was and so on. And that was wonderful, that was very wonderful. And that lasted, I think, about six months. It was the whole second semester, or the first semester of ‘26. Then — that was very important — was when Klein came. He was also a Lorentz Fellow. Through the Lorentz funds, of which I have already told you about, Oscar Klein was brought to Leiden. And I stayed with him. We stayed in the same rooming house… He had come back from America. He was, I think, in Copenhagen, and then Ehrenfest invited him to stay.

I have the impression that it must have been at least a month, maybe even longer, but it was certainly a month. We had, all the time, these discussions with Klein. Every afternoon. And Klein of course had in Ann Arbor found a wave equation too. He knew De Broglie. And he had written down what now is called the Klein-Gordon equation. He did it of course immediately relativistically. I think he had also the non-relativistic form. But he had not solved it. He did not have the hydrogen atom. And furthermore he was in Ann Arbor, so that was really the wilderness. I think that was one of the reasons why he wanted to come back to Europe. Then he had also these ideas about five-dimensional relativity, and we discussed about that. It was very interesting… The fifth dimension had something to do with the mass I think, at that point. I wrote a paper with Ehrenfest on this five-dimensional stuff, typical Ehrenfestian paper. He was then also working on the Compton effect, and on the radiation theory — what now is called the korrespondenzmassige interpretation of the radiation phenomena. He wrote that at that time, also, two of his well-known papers about it. Very soon he had of course the formula for the intensity of the Compton effect.

Well later on he did what is called the Klein-Nishina formula. But that was not done in Leiden, that was later. But he did it for the thing without spin too, I’m sure of that. The connection with dispersion theory became then clear to me — how they hang together. That was a very, very interesting time. I had two good friends in Leiden, with whom I always had dinner together. Both of them experimentalists, (Neyroff and Meersma). And I still remember one time after these discussions with Klein in which he had told about his five-dimensional relativity and how out of that quantum conditions could come. You see, from the periodicity condition in the fifth dimension you got the quantum conditions. And I was so excited. I told them, “Very soon we had the world formalized. We will know everything! Everything will be known at that time.” Well, it was a beautiful exaggeration. That was a little bit the feeling — that somehow maybe we know everything now.

Kuhn:

Did you all feel that way? Did Ehrenfest and Sam?

Uhlenbeck:

Well, Sam did not take part much in that. I think he must have been at Tubingen then. Ehrenfest of course took part. But Ehrenfest was always much more skeptical than I was. He was a complete skeptical man about these things. He was very excited about it, and interested.

Kuhn:

When you say skeptical do you mean he was very skeptical about the world formula or that he was skeptical about wave mechanics?

Uhlenbeck:

No, no, he was not skeptical about wave mechanics. He knew that this was really an enormous advance. But the feeling that one knew everything, that of course I am sure he didn’t have. I mean that was more the younger generation which got this feeling.

Kuhn:

Had you felt before that things had to break, loose?

Uhlenbeck:

Not really, because again I was just not up to it, you see. People who feel that there is something going on must have been people who really completely knew how the situation was. I would think those would be people like Heisenberg and Pauli and Bohr, especially, and perhaps Dirac. I didn’t know that Dirac had this feeling. But people like me — we knew that it was very confused. In discussion with Sam, I was very scathing about all this unmechanischen Zwang, which I didn’t understand what it all was, you see. But I wouldn’t have dared to say that! That was what fools said. If you didn’t understand what you were told, clearly there must be something to it. But that — in the summer during the spin period — that it was very confused was very clear. And that, therefore, something in the future had to be verified, that was of course also clear. But that this would imply a revolutionary change in the foundations — that for me was far too specific. I think only a few people had that, and these were the people who finally did it. All the others thought it’s all very difficult, and maybe you just go on with what there is. The usual people only think the next step. But I don’t think it was general.

Kuhn:

The Compton effect must have been your fourth year.

Uhlenbeck:

The Compton effect we knew, that we knew. That was also discussed by Ehrenfest.

Kuhn:

Did that come as a big surprise?

Uhlenbeck:

Oh, it was very interesting, but one knew that sometimes one has to work with photons. That we learned in a colloquia — these things like photoelectric effect and so on. That there were photons, that one knew.

Kuhn:

There was no question whether the photon aspect was fundamental? You knew the Einstein paper on the energy fluctuation?

Uhlenbeck:

I don’t know whether I knew it, but surely Ehrenfest knew this sort of thing backwards and forwards. No, no, no! I remember even that he talked of one aspect of this fluctuation paper in his lectures. You see, when you take the Wien formula, then it becomes just independent fluctuation of particles. And that I remember Ehrenfest did in his lectures… The other term was too complicated to do. And that was, so to say, the classical interference theory, which Ehrenfest knew too, of course very well, but I don’t remember that we ever had that. The notion that there were photons, that there was what we now call duality, that was hammered into us, as being the situation at present. Maybe not satisfactory, but these facts were there. So the Compton effect was also discussed, and I certainly studied it. Of course there was this basic question of the conservation laws of momentum and energy that were there applied… It was, of course, quite new really, but it didn’t strike us as extremely new. So we took it more or less in our stride, I would say. The Compton effect we took in our stride in Leiden. One aspect of that period which I can probably reconstruct if I think longer about it, is the effect of the visitors. There were always so many visitors who lectured. And that was also due to Ehrenfest. He was in a certain sense a central figure. People came, or he invited them. Bohr — I told you already about Bohr, in ‘25, at the Lorentz festival — and Oppenheimer, and we had a little conference with Dirac. That was later, of course. Pauli came, I think probably also Heisenberg. Then the long visit of Klein.

Kuhn:

Did students come from all over Europe also?

Uhlenbeck:

No. There were always foreign students, but they were mainly people who worked in the low temperature laboratory. There was (???), for instance. I remember that I talked with (???) in Leiden. He was then working at the low temperature laboratory. And there were sometimes foreign students. Yes, while I was there there was always one or two, but nobody whom I really remember, except Oppenheimer. He was there for a period, but never for very long. I knew younger students, I remember.

Kuhn:

Did you know Kramers in that period at all?

Uhlenbeck:

Yes, I knew Kramers much better later on. But he came, and gave a speech — in which connection I don’t know. This must be ‘26 or ‘27 — I was still assistant to Ehrenfest. In it he talked about the WKB method. He made the impression, so to say, that he knew everything which there was, so to say. This was the first impression that he always made; he was a little bit pedantic. But it was only a first impression. I mean, just the way he talked, you see. He always talked so (???). But I can’t say that I learned to know him very well in this Leiden period, because he was of course at Copenhagen. He was then in Copenhagen, except towards the end. He became professor in Utrecht, and I think I was still in Holland, when that happened, although I am not certain. It may have been when I was already in Ann Arbor. But then we got him to this summer school in Ann Arbor. He gave one of the early summer schools. And then I learned a lot from him. Later of course we were colleagues for four years in Holland. I succeeded him in Utrecht. You see, after the death of Ehrenfest, Kramers went to Leiden. And then after a long — it was about a year of interregnum in which nobody was there — finally it was offered to me. And after a long discussion with Kramers whether I should do it or not, I finally did it, of course. I was four years there. I saw him very often during those four years. We also had a colloquium; we called it the “K” Club, Planck club. All the professors, theoretical physics and all, came together at each others’ houses.

Kuhn:

How many of you were there then?

Uhlenbeck:

About five or six, because also the assistants came. Each one had an assistant. So the people who were there were always Kramers, Kronig, Fokker, myself, plus assistants — Kahn, Belinfante, and some other people. — Pauli was also present several times at this “K” Club. That was every month. And then we went to the different towns. I was in Utrecht, Kronig was in Groningen, Fokker was of course in Leiden, Kramers was in Leiden. And that was very fine. But that was ‘35 - ‘39, which was much later. Then I knew Kramers very well; I know his family also very well.