Hendrik Casimir - Session I

Casimir:

I had very little in the way of documents. I am not that sort of a man; I don't keep files; I usually don't keep letters very long and so I'm afraid, — I had one or two letters written by Pauli, but they were much later; I sent them to Mrs. Pauli. I don't think I have any letters of Ehrenfest left, with the exception of a letter Ehrenfest wrote to Bohr to introduce me. At that time, of course, I wasn't allowed to see it but then did see it much later. It naturally wasn't very relevant to the development of quantum mechanics. So I don't think that I have any concrete material; the only thing I could have is certain recollections, certain indications — perhaps I could indicate some sources where, I think, you might find something.

Kuhn:

I would be very grateful for anything of this sort. I think that we might very well sort of go through it roughly chronologically. Could we start with how did you get into the sciences in the first place, with respect also to interest in this sort of work in Holland in general?

Casimir:

First of all is the question of why I chose theoretical physics. It is a little bit difficult to say; some people have a very pronounced gift in one direction, but during my school years I often hesitated between different subjects, not being "outstandingly good" in one particular field. Sometimes I thought that I would study languages; and sometimes I thought that history would be interesting, and then I veered toward science and mathematics. I had, first of all, a very good physics teacher at school, and that always helps. There were a few other factors. One thing was that my father, who was a rector of a large secondary school in The Hague, had a very great admiration for Lorentz, and also knew Ehrenfest personally very well. It was a rather progressive school and Ehrenfest was very much interested in modern methods of education. Also my father was appointed as a part-time professor of education at Leiden. Now, this was an unheard-of-thing at Leiden, because one didn't consider education at all a subject for a university. And when you have these part-time or extraordinary chairs, a small board of what we call 'curators' or supervisors has to be formed for this particular chair. Lorentz was so kind as to cover this enterprise with his authority,so he was in the first committee dealing with the special chair for education and psychology at Leiden, for which my father was extremely grateful, because he was a little bit regarded as an outsider at Leiden University. And the fact that he was, so to say, somewhat protected by the authority of Lorentz, which was unassailable, of course, helped him a great deal. So he always 'held up to me' that to be a theoretical physicist would be about the best thing you could do. Another thing was that I felt attracted toward physics and also that I was not very practical and not very good with my hands, so it had to be theoretical physics.

Kuhn:

Did you see anything yourself of Lorentz and Ehrenfest?

Casimir:

Lorentz, no. I met him later but we will come to that later in the story. Ehrenfest mainly came to our home when I was still very young; later he lost interest or perhaps the school my father vas running was going a little bit too much into a conservative pattern for his taste. I remember him from when I was a child. One of the things was that he would always drop in unexpectedly and if there was no one at home he would collect my sisters and myself around the piano and start playing children's songs and would have all the children singing with him. This I remember very distinctly: Ehrenfest hammering away on the piano, Dutch children's songs and all of us singing with him. That is an early recollection. I don't remember much afteward, although he may have been there occasionally. Then, when I intended to go and study physics, the first thing I did was to go and see Ehrenfest who, of course, received me well, knowing my father well. I also remember our first conversation. He said, "You should not study theoretical physics but become an architect." I was rather surprised, but it was one of his pet theories that special gifts and aptitudes should reveal themselves early in life. He said, "I remember you as a kid, and the one thing you were always playing with was little bricks and wooden blocks, building towers and houses and so on. It was obvious to me that you should become an architect." Then he started inquiring whether I had done anything in physics. And I said that I really hadn't, apart from what you had to do in school and always getting high marks without much trouble. But that wasn't sufficient; he said "I don't think you're going to be a theoretical physicist, in any case not with me. But you better talk with one or two of my people." So he introduced me to Goudsmit and Uhlenbeck. I remember going to Uhlenbeck who started to explain a little bit what theoretical physics was about; and I went to Goudsmit who told me a little bit about the recent success of Uhlenbeck and himself with the spin of the electron. This was 1926, summer of 1926; the final examinations of secondary schools are always in July and when I had passed that examination, and, so to say, before deciding whether I would go to Leiden, my father said that I had better talk with his old friend Ehrenfest and he sent me to Uhlenbeck and Goudsmit, and that was that. I said that I should like to try anyway, and so that was the beginning. The choice you make of your subject at Leiden comes only after a first examination, the so-called candidates so it was not particularly urgent. — And that was how I started studying physics at Leiden.

Kuhn:

Apparently you had a variety of interests of which physics was only one; did you think seriously of not doing physics after you had this initial discus sion with Ehrenfest?

Casimir:

No, no. I thought that in any case I would do physics. I also thought that I would be able to do it. Also, coming from a school-teaching family in those days, the possibilities for a physicist were not extremely great but you could always get a teaching position at a secondary school, and at that time I thought I would be quite satisfied with that. I liked the subject and I had no objection against becoming a school-master. So "I'll take physics anyway and we'll see how it will work out" and so that was that. It was two or three years at Leiden. before you took the first examination. I took it in the summer of 1928, two years later. And until that time mainly you had just fairly element work — fairly elementary mathematics and all that sort of thing — which kept you more or less busy. However, the number of students then was very limited; let's say that the number of mathematics, physics and astronomy students together was in my year perhaps 12 or so. Ehrenfest, although his teaching duties only started when people had passed this first examination, always took a keen interest in the young people. He was pretty well the only professor who really took an interest in them; he always kept his assistant quite busy keeping an eye the young people, giving informal lectures to them, which were not in the curriculum, on recent advances in physics, having the young people themselves give talks on fairly new things, having them look at the journals and see what was appearing, and all that kind of thing. There was an institute of theoretical physics and since there were so few students there, the library and reading room was a kind of center for all the students in the department who would come there and read things there and have a look at new books and new periodicals coming in and so on. The first year I was there, uhlenbeck was Ehrenfest's assistant. You know Uhlenbeck, of course, and you can understand that he did this remarkably well, organizing small informal discussion groups, and all that sort of thing. I remember that he himself gave talks on, I think, spectroscopy and the vector model, if I remember rightly, but I wouldn't know for certain. In any case, one was brought into contact with new things; Ehrenfest himself would from time to time give this sort of very informal talk to young people to get them interested. I remember that I had not been there very long when I myself gave a talk, in one of these discussion groups, on collisions of the second kind, which was then a fairly new phenomenon. It was rather well recieved, and after that, I was admitted to the famous Ehrenfest colloquium. I think that this was in the middle of my first year already. I was, of course, highly flattered. It really was a most interesting center, where you got to see, I would say, most of the prominent physicists of the day and could listen to discussions and so on. And Ehrenfest always managed that colloquim in such a way that everyone got something out of it. It was really a quite remarkable institution, you, Léon, will remember also, in the early days. As a colloquium it was quite unique. It was of course very much a creation of Ehrenfest's personality; he could make life very tough for his speaker — he disliked any form of bombast, you see — and if he felt that a man was covering up his ignorance with big words, he would just tear him to pieces. With younger speakers, if they spoke badly, he would just take the job away from them and he would tell the story. Certainly it was always extremely fascinating. You had to attend every time; if you didn't, then you were taken off the list. Well, once or twice it could be done, but you would have to have a pretty good excuse.

Kuhn:

How many were there at the colloquium?

Casimir:

At that period I would say perhaps 20, 25, something like that. You certainly learned there how to give a lecture, even how to use a blackboard. There was one thing there; if there was a famous invited speaker, then he had to write his name on the wall; therefore on that wall there was a beautiful collection of famous names: Bohr, Einstein, Schrodinger, Max Plank, Dirac, and Heisenberg. Now that whole institute has been torn down ; it is a pity. But the wall has been well preserved. Incidentally, but that's a bit later, on that wall among the great names you find one deep scratch which is still there. And that deep scratch in the wall has a curious history. It was made by a rather poor student of physics who had failed an examination or pre-examination with Ehrenfest. The student was also rather given to drinking; when he had to come to Ehrenfest he thought he had better get some courage so he came reeking of Bohls at 9:00 o'clock in the morning.Ehrenfest was very strict teetotaler and also a man with a very sensitive nose and so the student, also not having answered the first two questions to Ehrenfest's liking, was kicked out of the room and told that he might try again next year but not before. The man was so mad that he went to that wall and among Bohr and Einstein and the others he wrote his name, which was (Mirlo), and then made a very deep scratch below it with his pocket knife. I was Ehrenfest's assistant at that time, and I found his signature there. It would have been just too bad to have Ehrenfest see that his sacred collection of names had been defiled in this way so I very carefully wiped off the name. But after all, I didn't have anything like plaster of Paris so I couldn't fill up the scratch, and I don't think that anyone did afterwards. The name disappeared but the scratch —. Afterwards the man went to Amsterdam and I understand that during the war he did rather well in the resistance movement and was shot by the Germans. So the scratch on the wall is kind of a monument to an unknown soldier. You should get a photograph of the wall of names. It is interesting because the dates are always added on which they gave their colloquium lecture so therefore it is a certain time scale: 'when did Dirac come to Leiden? when did Max Planck lecture in Leiden?' Einstein came very often. Of course, or fairly often. Einstein was even a kind of honorary professor at Leiden, you see, being a great friend of Ehrenfest. And I think there was a period when he came a few days every year to give lectures. I remember having seen him at Leiden at least on two occasions. one thing I remember, it was either in the winter 1926-27 or the next year,when Planck came to leiden as a visitor and Kramers gave a lecture. I don't remember if Planck gave some lectures also, but Ehrenfest thought it would be a nice idea to have some discussions on new quantum mechanics. That was then still very new, of course, and the interpretation was very new at Leiden, so he asked Kramers to give a lecture. I think that Kramers was then still at Copenhagen, but he was, more or less, in the process of moving from Copenhagen to Utrecht. Do you remember exactly when Kramers was appointed at Utrecht?

Kuhn:

Heisenberg came here [Copenhagen] to replace him in, I think, 1926-1927; late in 1926 would be about the last that he was here.

Casimir:

Maybe then he had just arrived at Utrecht, although I have a feeling that he had not yet settled down at Utrecht, but I don't know for certain. Well, Kramers started to explain the ideas about wave-packet and about probability and the first discussion of uncertainty principles and that sort of thing.

Kuhn:

That's not 1926-1927, because the uncertainty principle itself comes well along in 1927, so it would have to be 1927-28.

Casimir:

Right, so it would be 1927-1928, my second year at the university. Then he must have been at Utrecht already but still in very close contact with Copenhagen. There are a few things I just remember. I remember Kramers' opening sentences: "Ich fuhle mich heute wie ein Kind, das seinem Vater sein Spielzeug zeigt. Ich warte schon, er wird schon horchen (eben weil er ein Vater ist.) Kramers had his misgivings about the quality of the work and so on. I think it was also on that occasion that Ehrenfest asked Planek whether he didn’t regret the more deterministic theories of classical physics. And Planck very courageously said, ‘No, because I cannot regret things which I have seen to be wrong.” I don’t remember whether he said, “Sachen von denen man eigesehen hat, dass sie falsch sind, kann man nicht bedauern,” or whether he said, “Sachen von denen man eingesehen hat, dass sie falsch sind, soil man nicht bedauern”; perhaps it was the second thing, I don’t know for certain. Incidentaily, in my first year, I also went, a little bit brazenly, to a few of the famous “Monday Morning” Lectures of Lorentz. I remember that Lorentz then was lecturing on the classical theory of the spinning electrons. I think that there is even something in his collected works about that, where he had taken up the work of Uhlenbeck and Goudsmit. I don’t think I could really follow it in detail then, I was a very young and very shy student, so I was slightly taken aback when I went to the lecture and Lorentz had the habit in that lecture of always introducing himself to all the people who came to that lecture, and it was a bit of a shock to me. He was very kind and referred to my father, whom he knew well. It was remarkable; I think that even later in life, Lorentz, if he had become acquainted with someone in that way, would never forget him afterwards. He had apparently a prodigious memory and always knew everyone he had seen once without mixing them up. That must come in very handy. I wish I had that kind of memory. I'm terrible at remembering people. Now let’s go back to quantum mechanics.

Kuhn:

Let me throw in one question before we turn more particularly to quantum mechanics. Clearly, if you were in the colloquium by the middle of your first year, you were learning an awful lot of physics very fast?

Casimir:

Fairly fast, yes, skipping a lot.

Kuhn:

I take it then that you were doing a lot of reading of physics on your own. And I wonder what sort of books that Uhlenbeck or Ehrenfest would have sent a student in your position to in order to learn about physics and particularly modern physics fairly rapidly?

Casimir:

Yes, well, I didn’t really start on quantum mechanics, of course. What did I read?

Kuhn:

If you yourself gave a paper in your first year on collisions of the second kind, you were doing something with quantum mechanics.

Casimir:

I think I got that from Franck and Jordan’s book, Anregung von Quantenspruengen durch stoesse, which Rosenfeld will remember from his Goettingen days.

Rosenfeld:

Yes.

Casimir:

I don’t think I read the whole book, but I read chapters of it; I remember studying Goudsmit's doctoral dissertation which came out a little bit later, and also Hund's book on spectral lines I remember studying rather carefully. I got my Maxwell theory from a very small German book by Clemens Schaefer which is a nice little book, and I read the first chapter of Lorentz’ theory of electrons, which is a wonderful introduction. I couldn’t date all the things exactly, of course. I worked through most of Jeans’ kinetic theory of gases, I remember, and then of course there was a little bit of outside reading; the first thing I read was Sommerfeld’s Atombau und Spektrailinien, during the summer vacation of 1926. That was in many ways an eyeopener to a young student and it must have had great influence on many people. I think also that I began reading Weyl’s Raum-Zeit-Materie rather early, and although I wasn’t able to understand everything, still I got something out of it. And, of course, when one had to prepare such a thing on collision of the second kind, one had Franck and Jordan’s book, but they always encourage you to read at least some original papers. Sometime in ‘27, I think, or it may have been ‘28, Pauli came to Leiden and gave a lecture on his theory of the spinning electron. I remember especially that Ehrenfest very much emphasized — that must have been in ‘28, but the date can be inferred from the wall in Leiden — the question: ‘How is it possible that you have these equations and that they are invariant? I have always been taught that the only possible equations in physics are tensor equations.’ That was then this question of the two valued representations of the rotation group in which Ehrenfest was always very much interested and which played such an important part in the whole development of the formalism. I remember that Pauli said that you can show that they are invariant, “und das stimmt schon; es gibt so ein Art (von Blaettkrusten); das hat Weyl mir irgendwie erklaert.” Pauli himself had not perhaps at that time —. Or else he didn’t want to speak about it. But it was before Weyl’s book appeared, I think, or at least still very early in the days of group theory. For Ehrenfest this was extremely important and I think the work that van der Waerden, for instance, later did on spinors was really directly under pressure that was brought to bear by Ehrenfest who was fascinated by this formal question, and I think it came up for the first time during this Pauli lecture in the coiloquium. During my second year at the University Elsasser became Ehrenfest’s assistant and that didn't work out too well; Ehrenfest and Elsasser didn’t get along well together. He had admired Elsasser’s suggestion, concerning these interference effects very much, but the two of them didn’t hit it off too well and Elsasser didn’t do as much, I would say, for students and so on, as Uhlenbeck had done, although he could have been very useful in many ways. One weakness of Ehrenfest’s way of doing things was that people didn’t get much training in mathematical and computational techniques, and also he very often looked at the formal structure of the formula rather than at quantitative things. He had a famous habit of writing 4π in quotation marks and that could be 4π or 1/4π or perhaps 4π/c².

Kuhn:

Now that’s an Ehrenfest story I hadn’t heard before; that’s quite leading and interesting.

Casimir:

Yes, the 4π in quotation marks. And, as a matter of fact, I don’t think that he himself had a very outstanding feeling for orders of magnitude. When I came to Bohr, one of the things which impressed me so much was that Bohr had an almost uncanny feeling for possible orders of magnitude and whether a certain effect might become important or would be small, and also how that would be related to experimental possibilities. I remember Ehrenfest' s saying, “As for myself, I’m not an experimentalist, but I should like to have more feeling for what you can do and what you cannot do.” And he said: “I was so surprised the other day when someone had to measure a very small current, and I think that man said, ‘I think I will measure it with a quadrant electrometer.’ I was completely surprised because I hadn’t realized that very small currents are best measured with such an instrument.” That is quite remarkable. Elsasser, from the Sommerfeld school, might have been very useful in running a seminar where people would have learned to work out problems quantitatively a little bit more and to do some more mathematical physics, which was not Ehrenfest's way of doing it. What was important from his point of view was formal and logical structure. I remember, but that was in my third year, Ehrenfest said, “Well, you are wasting your time; you are listening to my lectures on electricity and magnetism, so I will examine you.” So he examined me in Maxwell theory, walking up and down the corridor without paper or blackboard, and I had to recite formulae; he would say things and I would answer, and he would catch me on some paradoxes and so on. He said, “Well, there are a few things there you still don’t know,” but I think he said something like, “Die Musik hast du schon verstanden.” [The music] of Maxwell’s equations, yes! That was in the old Institute of Theoretical Physics in a very small corridor and he was partly sitting on the bannister, talking about Maxwell’s equations. It was also during my second year that Lorentz died. When I had passed this first examination in June ‘28, Ehrenfest took me along with him to Goettingen just to listen to a few lectures and to learn German a little bit better. I remember a little bit of the atmosphere there, and I listened to lectures by Born and by Franck. I think it was the next summer that Ehrenfest began to talk with van der Waerden on the spinors.

Kuhn:

Where did he talk with van der Waerden?

Casimir:

At Goettingen, I think. Ehrenfest liked to go to Goettingen every year at the summer semester and I was there twice, once in the summer of ‘28 and, I think, also the next year. An interesting period in leiden was when Dirac was there; Dirac spent quite some time there. That must have been the spring of ‘28. When did the first edition of his book appear?

Kuhn:

1930.

Rosenfeld:

Yes.

Casimir:

Dirac spent quite a few months at leiden working on his book and, as a matter of fact, the first chapters were then presented as lectures at Leiden. I remember these lectures and that I was still very much at the beginning of the game, although I had read something on quantum theory. In a way I was perhaps not supposed to go there. I remember definitely that Rutgers was there and that he taught Dirac to ride a bicycle, which Dirac hadn’t done before.

Kuhn:

This would be before your time in Copenhagen?

Casimir:

That was definitely before my time in Copenhagen.

Rosenfeld:

I remember Dirac in Goettingen later, in either ‘28 or ‘29; he was working on his book.

Casimir:

He went to Goettingen after he had delivered these lectures at Leiden, I think, and I would almost think that it was ‘28 and not ‘29.

Rosenfeld:

No, it could not be 1929. In the summer of ‘28 we went for a tour with Rutgers, Dirac and Tamm.

Casimir:

Yes, because Tamm was also at Leiden then, so it must be ‘28. Before that he spent quite some time working on his book, giving lectures and so on. I also recall that they were very beautifully presented and that Ehrenfest's attitude was quite amusing because Ehrenfest was always interested in seeing how people’s minds worked. Now in the case of Dirac, he had worked on these chapters in the book and then it was presented in perfect form. You know the habit of Dirac: if you wouldn’t understand things, he would not offer any explanations but would very patiently repeat exactly the same thing, and usually it worked, but it wasn't quite Ehrenfest 's way of doing things. I remember that once Ehrenfest put a question to Dirac to which Dirac had no immiediate answer and so Dirac began to work it out on the blackboard; he covered the entire blackboard with very small things. And Ehrenfest was right behind him trying to see what he did and exclaiming, “Kinder, Kinder! Schaut jetzt zu. Jetzt kann man sehen, wie er es macht" That was very typical. Now it must have been ‘28 because I know that I went to these lectures with a somewhat bad conscience because I had to read for this first examination and this was quite outside the range of the subject, of course. Then later, in ‘28 I started really working with Ehrenfest — I had been to Goettingen and then in September I really started working on theory. I was one of the few students Ehrenfest had. Rutgers was one, and there were one or two others besides me. During that winter Oppenheimer spent quite some time at Eindhoven, becoming quite great friends with Rutgers but not hitting it off too well with Ehrenfest — not too badly either. Perhaps Oppenheimer himself was not exactly what I would call “on top of his form” that winter.

Kuhn:

By the time that you really began to follow the work in quantum mechanics closely quantum mechanical theory — did problems like the interpretation of the Schrodinger equation seem pretty well solved?

Casimir:

I think they were still being debated. I listened in on the “fringes” during these first two years at the university and I remember when the first results from interference were told in the colloquium and so on. I also remember discussions where people, even Uhlenbeck, were not quite certain that these waves which you use mathematically would really behave as normal waves and show normal interference patterns when scattered by crystal lattices and so on. So the thing was still being debated and certainly was not in every way clarified, but I think the thoughts were gaining ground very rapidly. We youngsters, as I recall, did not quite understand why people of the older generation thought these things so hard to work with, because we found it in a way easier. It’s the same thing you have nowadays with modern field theories and what not. When I started to work with Ehrenfest in '28, he was then very much interested in applications of group theory; that was just becoming important in those days. And I think on various occasions he invited Wigner and also Heitler to Leiden to explain things; of the two, Wigner of course being the greater physicist and Heitler being a much clearer lecturer in explaining group theory on, let’s say, a relatively elementary level. Ehrenfest's way of working, by the way, was often to take a paper that he thought important, for instance, older papers like Dirac’s transformation theory papers, and to say to his students, “Now we are going to read this paper together and see whether we can understand it and whether we can understand all the steps involved.” So you would sit by yourself and study it; perhaps you would see him for a few hours a day when he was really interested, and sometimes you wouldn’t see him for quite some time. His idea of studying physics was especially to read what he considered the important papers and if you got stuck, then you could look at a text book or a handbook or something and see what was there, or refer to older papers; but the best thing was to try to read this fairly advanced paper, which in those days was still quite possible. Of course, then you would skip a lot of things and there would be terrific gaps in your knowledge, but it was a way to get people to the front of science rather rapidly. Another recollection I have of these days was when Weyl’s book on Gruppen theorie und Quantenmechanik came out, which I studied rather carefully. And I think I not only learned a certain amount of group theory then, but also a lot of quantum mechanics; that has been an extremely valuable book to tue. But I also remember that Rutgers and I read the first papers of Wigner on the application of group theoretical method, and so on, together. I remember how beautiful I thought this was, particularly in Weyl’s book where it is well written down, because I had not studied spectroscopy in great detail but sufficiently so to appreciate the vector model and all that sort of thing, and then to see how that came from the theory of representations gave me a great kick.

Kuhn:

Do you remember particular papers that you worked through with Ehrenfest that he thought were worth doing this way?

Casimir:

I think we worked together on some of the papers on the transformation theory and Wigner’s early group theoretical papers; those are the ones I remember, but there must have been others.

Kuhn:

Was there any concern still at Leiden with matrix mechanics as an alternate to wave mechanics, or was the approach pretty much dominated by wave mechanics throughout?

Casimir:

In my recollection, it was pretty much dominated by wave mechanics, and matrix mechanics, so to speak, only came back through group theoretical arguments, if I may put it that way. Of course, there were not many people who were actually working out concrete problems with quantum mechanics at Leiden in those days. Early in ‘29 Ehrenfest took me along with him to a Copenhagen meeting —

Rosenfeld:

That was the first meeting?

Casimir:

Of this somewhat extended type, yes. I remember travelling with Ehrenfest to Copenhagen very well; I also remember Ehrenfest's words which I put in my letter to Mrs. Bohr after his [Bohr’s] death: “Das wichtigste Erlebnis, das es fuer einen jungen Physiker geben kann, ist Niels Bohr kennen zu lernen.” Ehrenfest had suggested that I might stay some time, but Bohr didn’t know whether that would be a good idea or not; in any case, however, I went to that first meeting, which was an interesting one.

Kuhn:

What was the general subject?

Casimir:

[To Rosenfeld] Would you remember? Was it at that meeting that Heitler spoke about the theory of the chemical bond?

Rosenfeld:

Yes.

Casimir:

That was one thing, and the magnetic moment of the electron was another. The Dirac theory of the electron existed already, of course, because it was published in ‘28 and in Weyl’s book, which was out at this time, there was the Dirac theory of the electron with four-dimensional spinors and so on.

Kuhn:

It would have been out perhaps a full year at that time.

Casimir:

Those were a few of the subjects. There was the most remarkable incident of Heitler’ a lecture on chemical binding, which you will remember. You haven’t heard it? It’s really a remarkable story. I had already heard from informal discussion with Pauli and so on that Pauli didn’t like this approach to the theory of the chemical bond. Heitler gave his lecture, and then, somewhat tired, he sat down on a chair; now you know that Heitler is a little man, and as he was sitting there, Pauli came at him with rather violent remarks. His argument was roughly this: We know that this particular approximation is wrong in the case of large distances, for then there is always a an der Waals attraction, no repulsion, no saturation. We also know that this particular approximation is quite wrong when the two nuclei are very close together, when we get repulsion. And Pauli, as usual, walked up and down, and then approached Heitler rather threateningly, saying, “Nun gibt es eine an die Gruppen glaubende Physiker appeilierende Aussage, die behauptet, dass trotzdem in einem Zwiscbengebiet diese Annherung wenigstens quantitativ das Richtige geben soll,” and at this particular moment, the chair on which Heitler was sitting collapsed under him and Heitler fell over backwards. The audience roared with laughter and said, "Pauli effect!" I don’t know whether anyone engineered that; it would, of course, not have been beyond Gamow to do it, but I don’t think he had an opportunity. But it was also characteristic of Pauli who was very much against a lot of mathematics on uncertain foundations. We know that he was not against mathematics nor against hard work; he even told me later that if he were younger, what would interest him would be to develop numerical methods for calculating atomic and molecular spectra, but he wouldn’t do it now, he said, though it might have interested him when he was twenty. He didn’t like this sort of mathematical thing where you have no idea about the approximations involved; that was why he also disliked much of solid state physics: Ich mag diese Physik des festen Koerpers nicht; zwar hab’ ich damit angefangen.” Then, of course, Gamow was there who had just published his theory on alpha radioactivity that winter. He paid us a visit in Leiden that winter also, and I remember showing Gamow the Rijksmuseum at Amsterdam where we ran into Oppenheimer and exchanged a few words. Oppenheimer was also at Leiden then, but he was having a day off. Well, the result was that I stayed in Copenhagen until the summer and came back to Copenhagen again the next September, I think.

Rosenfeld:

I do remember that at that meeting Goudsmit put to you the problem of calculating —

Casimir:

Yes, that is certainly one of the things that is interesting because Goudsmit wanted to calculate the hyperfine structure or S states or hydrogen-like atoms or — no — of the alkali halides [alkali metals], so you had only one electron. There is a difficulty because if you write interaction between magnetic dipoles, you get a divergent result. I had read Weyl’s book carefully, and Dirac's paper too, so I knew that you could have a current associated with a spin; in fact I remember that it struck me as a very important sort of thing that one should not think of an electron as a little magnet, but that a hydrogen atom in its ground state had such a beautiful current distribution extending over the whole of the wave function and going around like rotating spheres. Now if you take that, it’s very easy to calculate the magnetic field at the center and then, applying normal ideas, to calculate the interaction; so during that meeting I derived this formula with 8π/3 times Ψ_o² times for the interaction, and Goudsmit provided an estimate for the Ψ_o² with the n³ and the Z_i and the Z_external squared. This is a well-known kind of Landé formula ... That was my first original work in physics. The fate of that was that I wrote a paper, which was probably rather badly written, and sent it to Goudsmit who left it on his desk for a year or so. In the meantime Fermi had published this theory, but I think I had it not quite a year before; and I’m still proud to say that, although the paper was badly written, I had it in a more general form at once for arbitrary l and j and so on, and I think that in a way, using group theory methods, I had a rather more elegant derivation. That was the origin of the certain interest I always kept in hyperfine structures, and it also made me aware of this difference between dipoles and currents about which a lot of nonsense has been written in physics, because it’s always a slightly tricky point. That summer I was again in Goettingen and that was the summer when Ehrenfest got van der Waerden to write about spinors. Or perhaps that was a year later. Yes, he got van der Waerden talking about spinors then, but the paper was later. At this time there was Bohr's question about the measurement of the electron; I stayed at Copenhagen and I remember that Bohr sometimes used me a little bit as a kind of “reverberator’ or listener.

Kuhn:

When you say the ‘problem of measurement of the electron’ do you mean to determine the spin of a free electron?

Casimir:

Yes, whether you can determine the spin of a free electron. And then to discuss all kinds of contraptions and so on.

Kuhn:

Do you know if that problem begins for Bohr only after the Dirac electron?

Rosenfeld:

Of course.

Casimir:

Yes.

Kuhn:

There’s a problem one can formulate before, but there is suddenly a much better reason for formulating it afterwards.

Rosenfeld:

It was directly an outcome of Dirac’s paper; it was then that the question came up.

Kuhn:

Yes, that makes very good sense, but it would not have had to be the way it happened. In particular, one could have begun to wonder after the Pauli paper, though, of course, then Dirac gets this without putting it in, this question has a new forcefulness. So this problem was one with which Bohr was working very actively?

Casimir:

Yes, very actively.

Kuhn:

What else was particularly concerning him at this time? Was he, for example, at all concerned with the developments that were going on quite rapidly in quantum electrodynamics?

Rosenfeld:

That came a bit later, I think.

Casimir:

I think that came a bit later.

Kuhn:

The whole issue of second quantization which was very alive in just the years you were there was not one that —?

Casimir:

I don’t think it was one that played a great role here at Copenhagen. I must get these periods straightened out a little. I came here in the spring of ‘29 and stayed until the summer; then I was again in Copenhagen some of the academic year 1929-1930 following; but I also had to prepare my second examination at Leiden, so I wasn’t there the whole time. I passed that second examination at Leiden in the summer of 1930. Then I joined Ehrenfest on a trip to the United States, to Ann Arbor, where I also had the privilege of being present when Fermi came to America for the first time in his life and delivered his famous lectures on the quantum theory of electromagnetic fields, about which I might have a few things to say later. Then after that summer, I went again to Copenhagen and spent most of that academic year there working on my thesis which was published in the subsequent academic year, which would be ‘31-'32. I got my Doctor’s Degree in the autmn of 1931 and then worked for one year at Leiden. The summer of ‘32 I spent some time at Berlin-Dahlem with Lise Meitner; just to get the thing fixed, I also got into contact there with the spectroscopist Schuler, a wel1-known hyperfine structure spectroscopist. And I still had my old interest in hyperfine structures, slightly frustrated because of my first publication. Schueler had some rather curious things, perturbations of mercury lines, which I helped him unravel, developing a theory of interconfiguration interactions in hyperfine structures. I remained somewhat in correspondence with him and later, he was the first to find clear indications of quadrupole effects, of cosine square effects, in hyperfine structures. And I then worked out the theory for the interaction of electrons and quadrupole moments and derived the formula for hyperfine splitting due to quadrupole moments, but that was quite a few years later, in ‘36 or so when I was already back in Leiden; and that was about the end of my relations with hyperfine structures.

Kuhn:

Was it after that that you went to Zurich with Pauli?

Casimir:

Yes, that was later. I worked at Berlin in the summer and then I got a letter from Pauli asking whether I wanted to become his assistant, so I was with Pauli in '32-'33. Then I went back to Leiden after Ehrenfest’s death and stayed at Leiden until ‘42. So that is just a rough time scheme, and now let us see what I remember. That first year when I spent quite some time in Copenhagen, in the season 1929-30, there were not so many visitors. I think Gamow was mainly away most of the time in Cambridge; if I remember rightly, Bohr really had introduced Gamow to Rutherford and to Cambridge, feeling that here was an important thing. After all, Gamow's little paper provided the solution to a problem which had been very explicitly put by Rutherford, because he was always worrying about how it was possible that you get alpha particles with this certain energy which would not be sufficient to surmount a potential barrier, whereas from scattering experiments you knew that you had a Coulomb field to quite short distances, and so this turning was very important. I think Gamow himself, of course also realized the possibility of the inverse process where you could shoot electrons into nuclei. So I believe that Gamow's presence and ideas at Cambridge did a lot to interest Rutherford so that he encouraged Cockcroft and Walton to go ahead with their experiments, because without this idea it would have been ridiculous to try to get nuclear disintegration with energies as low as those Cockcroft and Walton had; and probably they even had less than they thought they had.

Kuhn:

The Gamow work had actually been done before you were here?

Casimir:

Yes, because it was very new when Gamow visited us at Leiden before first visit to Copenhagen, some time in the very early winter of ‘29. Then Gamow was also here at Copenhagen where I met him, but be went again to Cambridge. Although the things such as the uncertainty principle and so on were more or less well established in Bohr's way of thinking, he was still spending quite some time, I think, thinking about special examples, working them out, solving apparent paradoxes, and so on. Then this question of measuring the spin of free electrons was an important thing. Another thing that be was rather concerned with was the Dirac theory, how good it was and how bad it was, and with the Klein paradox which was then formulated here

Kuhn:

I take it that what particularly was on his mind, then was the negative energy states?

Casimir:

Yes. I remember when Dirac’s first paper came on what were then believed to be electrons and protons, Bohr was particularly vexed by Dirac’s remark that this infinite charge, being entirely homogeneous, would have no influence at all. Bohr said, "That's quite impossible, for the divergence is infinite then,” which, of course, it would be. And so this whole question —

Kuhn:

Dirac immediately responds to that by suggesting that one reformulates one's notions as to what Maxwell’s equations are about by supposing it’s only deviations from the average distribution that —

Casimir:

Well, I think he never quite liked the idea.

Rosenfeld:

At one time, much later, be speculated on the possibility of using that sea of negative electrons in order to get the conservation of zero point energy by arguing that one had to count all the kinds of elementary particles, each contributing self energy, either positive or negative, and all those self energies can —

Kuhn:

When was that?

Rosenfeld:

That was quite a bit later, in ‘46.

Casimir:

Well, that’s one thing. Another thing which came before that time of course and partly at Leiden already was the begining of solid state physics, electrons in solids, which wasn’t studied very much at Copenhagen. There’s one thing I remember which Ehrenfest was very interested in. Ehrenfest liked to “help out,” let us say, great paradoxes and problems which you had to solve and one of the things which was always heavy on his mind was the existence of a positive Hall effect in some conductors; that was a problem which had also troubled Lorentz a lot. I don’t know whether you have seen the address I gave at the Academy of Science at Amsterdam when Peierls got the Lorentz medal.

Rosenfeld:

No.

Casimir:

Peierls got the Lorentz medal last autumn at Amsterdam and I had to make the presentation there and then I looked up a few of the other things, and I found that Lorentz himself had been very worried about the existence of the positive Hall effect. I think it is not always sufficiently recognized in the literature, at least not in the literature on semi-conductors, that it was Peierls who first introduced the idea of a positive hole. Of course Heisenberg had worked on almost-filled shells in atoms and pointed out that they almost behaved like positive particles, but Peierls was the first to have almost-filled bands in conductors and to point out that they behaved so as to get a positive Hall effect, and were positive holes, really; and that was quite a bit before Dirac’s first publication on electrons and protons. It’s not too trivial because there are two ideas in it, of course, since you always have to have the combination of two things: namely, the particle itself in the top of the band behaves like a thing with negative mass because the energy is curved the wrong way; and secondly, an empty spot in a filled band behaves like one particle ... So there are these two elements of the negative mass and the almost-filled shell which, of course, are not in Heisenberg’s theory of the almost filled shells, and really the positive electron in an ordinary band precedes the positive electron by quite a few years. I found it rather amusing to put that straight historically; I don’t think there is the slightest doubt about it.

Rosenfeld:

The time lag must not be very —

Casimir:

No, the time lag between Dirac's electrons and protons and Peierls’ paper is perhaps something over half a year.

Rosenfeld:

Was Heisenberg’s paper before Peierls’ or was it after?

Casimir:

I don’t know, but Peierls said that his ideas had been much influenced by Heisenberg’s. But he definitely was the first one to introduce this notion, which is an interesting feature there. I think it was also that year that I did a lot of work with Bohr and Bohr had to write an appraisal of the work of candidates for a chair of theoretical physics at Stockholm, the candidates being Klein, Faxén, Wailer, and, I think, Enskog. That was terrible because you know how it is in Sweden; people apply for such a job and then official experts are appointed who must write reports; and so we got huge packets of papers written by Klein, Wailer, Faxén, and Enskog. Bohr thought it would be nice if Klein got this sort of thing, but Bohr, of course, also thought that, after all, you had to read all these papers and see what was in them and then write an appraisal, so I acted then more or less as his secretary and we read most of these papers. That was not so bad; we started to analyze them and to speak about them sometimes here end sometimes at his country house. The trouble really began when Bohr started writing his appraisals; that was when I really learned Danish, especially Danish laudatory adjectives in their different shades of approval. I remember that he spent a very long time thinking about one of Klein’s papers, saying, “Ja, det er et smukt arbejde,” and I said, “That will never do.” (“Det er et vigtig arbejde.”) “Take it away, it won’t do,” and so on. Finally it came out as "(???) arbejde.” I said," I’m afraid I don’t know the word,” and the only explanation be gave was, “(???) (???) (???).” [Casimir and Rosenfeld laugh.] I also remember that Bohr had a curious habit that things must be sent away on a Saturday evening so they could just catch the train to Hamburg; he said that if you get things away on Saturday you gain one day because they travel on Sunday, so finally we got it off and I think it was the ninth or tenth version of the manuscript. Dear Miss Schultz was also almost exasperated by that time. It was a beautiful piece of writing and Klein got the position. Whether it was worth all the trouble I have my doubts, but I remember that when I once made a very slight suggestion in that direction it was not well received. “Now don’t desert me,” Bohr said. I even have a book at home which he presented me when this work was finished, so apparently it had been very difficult for him too. I got a book with a beautiful inscription saying that it was thanking me for "..." [Casimir here says two lines of Danish.] Well, that was one thing. There were, I think, other things he had to write in that period. I myself became interested in a problem of an asymmetric top, an asymmetric rotator, which had been one of the things studied very extensively by Kramers together with Ittmann at Utrecht. They had done it the hard way, in a way, tackling the differential equation with Landé functions, adding quite a few new results about Landé functions to existing knowledge and so on. Then Huang found that you could write down this kind of matrix equation, and while I was here, Klein found that you could write down these equations quite simply by matrix methods. I then got interested in extending that a little bit more so as also to be able to calculate intensities. I also became interested in the connection of this formalism of Klein’s with group theory, because, I think, you can say that operators of angular momentum in a rotating frame of coordinates — that’s rotating with a rigid rotator — and in a stationary frame of coordinates, correspond to infinitesimal rotations of the two parameter groups — the one which you multiply on the right hand and the one which you multiply on the left hand. So you could work out the connection between the theory of the rotator and representations of the rotation groups. I started to work on that during that first winter at Copenhagen. Bohr, of course, was not so much interested in these mathematical things, but I still remember he very kindly looked at this sort of thing and even helped me get that paper, which was the first I had ever published, into shape.

Kuhn:

What sort of criticisms and suggestions was he able to make in connection with the paper?

Casimir:

The kind of things, I remember, are the way of aligning the formula, the way of stating certain things, the way of formulating an introduction, and so on, rather than the mathematics, really. I then went back to Leiden to pass that examination and that summer I traveled with Ehrenfest to Ann Arbor, Michigan, where Fermi was as well as Uhlenbeck and Goudsmit.

Kuhn:

I want very much to come back to that point, but let me emphasize one more thing before we pass away from this period in Copenhagen. This really goes back to something Professor Rosenfeld and I were talking about a day or so ago, which was on the whole the lack of any very early response after the Como meeting to the difference between the uncertainty principle in Heisenberg’s formulation of it and the elements that Bohr was adding through complementarity in his own Como paper. I think that Professor Rosenfeld has said himself that he had really not seen that there was something more and deeper than Heisenberg had gotten hold of. Many people seem to feel, on the one band, that that whole story of the interpretation is done after Como and Solvay in the fall of '27; yet clearly Bohr was still very much concerned, in the time you were there, with some of the analysis of measurement problems, and I am still very much unaware of how that deeper element enters the consciousness of physicists and the extent of Bohr’s own concern With it.

Casimir:

It was certainly always there that winter as well as the next winter when I was again at Copenhagen, as were Landau and Gamow. It is difficult; he bad been producing, roughly within that period, various articles also — one in Naturwissenachaften — and then rewriting certain things later for the university yearbook, and he sometimes gave lectures and sometimes a discussion with philosophers and so on, and I remember his always coming back to a screen with two holes. It was one of the favorite ones that was always there.

Rosenfeld:

And then it was the year in which he was tackled by Einstein; the Einstein box was in 1930 at the Solvay Conference.

Casimir:

Yes, and when was this Einstein proposal which, I think, appeared later in a modified form in a paper by Einstein, Rosen and Podolaky where gravity was brought into play?

Rosenfeld:

That was later.

Casimir:

But I also remember a colloquium when Einstein was at Leiden and I was again at Leiden; that must have been the winter of '31-'32 when Einstein spoke about his misgivings on the theory. I remember that Ehrenfest was presiding, and Einstein presented these things while I had the task of trying to defend quantum theory. Being well coached by Bohr, I could, of course, show that there was really no paradox, that it works out all right, Einstein listened very patiently and then he said, “Ja, ja. Ich weiss schon, die Sache ist schon widerspruchsfrei. Das ist schon richtig, aber sie enthaelt trotzdem eine gewisse Haerte." That must definitely have been in the winter of '31-'32 because then I was again at Leiden. We also made as a toy a box illustrating one of these paradoxes. [To Rosenfeld] Do you remember the one?

Rosenfeld:

Yes, that must have been in ‘31 because it was for the anniversary of the Institute.

Casimir:

Yes, with the photographic shutter, the little lamp, the spring balance and the portrait of Einstein. A very nice contraption-it might still exist.

Rosenfeld:

It may still exist. I hope so.

Casimir:

I also think that Bohr was always struggling writing these papers to find, let’s say, better formulations of these things, to look at the relation with other fields of physics, also to look at various examples and to discuss them, and so on. This, of course, was taken up later with Rosenfeld in connection with the electromagnetic field. I don’t think he himself was at that period very much taken up by the more technical applications of quantum theory and, quantum mechanics.

Rosenfeld:

No, I even remember a remark made by Landau when Landau first came here: “What’s Bohr doing? What’s Bohr doing?” And we said, “He’s discussing those cases of complementarity.” "Oh, yes,” said Landau, “but that’s not physics.”

Kuhn:

What year was that?

Rosenfeld:

1930 or ‘31.

Kuhn:

About the same time as the Landau-Peierls paper. Is that also wasting time? I was trying to see how it would relate to the Landau-Peierls paper. Well, it’s right in here that there’s a problem I think we probably can’t answer, but it may show some in the correspondence. The history of the battles with Einstein and with the other old hold-outs is fairly clear even if not in all its detail; it is also fairly clear that by 1930, and in some cases already by 1929, for a number of people these problems had already ceased to be physics. Furthermore, I think they had ceased to be physics before the depths of Bohr’s Como paper were at all realized, that they had ceased to be physics at a point which is really represented by Heisenberg’s uncertainty principle paper and that doesn’t include the notion of duality and doesn’t really include complementarity at all. Already at this point a number of physicists have cut off and let go of it; now somewhere in between there is the introduction and growing conviction about this extra element of Bohr and it is very hard to get any notion for the structure of that development.

Casimir:

Yes, I would say that is very difficult. You cannot attach it so easily to one very concrete paper publishing one concrete formula and so on, so that is what makes it so difficult. I think that Bohr’s own thinking about these things gradually developed; he always went round and round that sane subject, studying other examples in a slightly different way, taking new problems, looking at new things coming into physics from this point of view. Apart from those people trying to fight against it in physics — "the Einstein group” some older people who might still need some convincing, and, even worse, philosophers because they were standing outside physics, I would say that most physicists would take it for granted, whereas Bohr kept thinking and reformulating these things. And I would say that that was an important part of his thinking and his activities during most of the time I spent with him in the spring ‘29, summer of the next academic season, and most of the academic season after that.

Kuhn:

And that really gets practically up to the time when you do the paper with him?

Casimir:

Yes.

Kuhn:

Now let me get back to the time you went to Ann Arbor.

Casimir:

There were a few interesting things there perhaps. Ehrenfest perhaps did not have so many new things to give there; I remember his not being satisfied with the statement, that if you have an even number of particles obeying Fermi statistics then the composite system made of them will behave as if it were Bose particles. Ehrenfest went by car with Dieke from Ann Arbor to California, and there is a paper written later that year by Ehrenfest and Oppenheimer in which that was worked out, though perhaps not in the most elegant way. One could do it better these days. Fermi impressed everyone very much by his very clear lectures on quantum theory of the electromagnetic field; of course before that, the Heisenberg-Pauli theory and so on had been also reported at the Copenhagen Conference, but I would say that people found it difficult to work with. Then there was the Dirac theory of radiation, and I think this Fermi publication turned it into a sort of tool which you could easily solve problems with.

Kuhn:

I take it this was to some extent your first real involvement yourself with problems of quantum electrodynamics. Do you remember what people at the Conference thought of the state of the field? Was it already relatively clear that both the zero point energy problem and the self-energy problem were not going to respond to further treatment?

Casimir:

I would think so, yes. I think this was fairly clear.

Kuhn:

I would say that in the Heisenberg-Pauli paper, although they were very careful to make all these remaining problems explicit, the tone of the paper is one of great encouragement, as if to say, “And in the next formulation we may have it so that these will —"

Casimir:

Yes, optimism was probably there to a certain extent. It may be true that the ideas of self-energy were not so clear. I’m coming back to a moment later when I speak about working with Pauli. That was one thing. Fermi, of course, spoke even more Italian then than he did later, and that was very amusing. He had very great difficulty with dipthongs but he would pronounce them with great energy, saying, “Nah-oo psah-ee ees a fyounk-shun that ees kone-teen-youss and fin-ih-tah een the nay-boor-hood of the or-ee-gee-nah.” That was of course perfectly understandable once one got accustomed to it; there was a one-to-one correspondence and for us it was very easy, but for Americans it would be a little more difficult, of course. Also Onsager was there at that meeting and tried rather unsuccessfully to get Ehrenfest interested in his ideas of time-reversal and timesymmetry and irreversible thermodynamics, derivation of the Kelvin relations for the thermoelectric quantities on the basis of symmetry between past and future; and Ehrenfest didn’t catch on to that, which is remarkable. “There might be something in it,” he said, but he wasn’t really much fascinated by it. Well, that doesn’t have much to do with quantum theory. I don’t remember too many other highlights there; as I said, remember these very brilliant Fermi lectures.

Kuhn:

You don’t particularly remember any discussion about the remaining problems in quantum electrodynamics?

Casimir:

No, at that moment, no. I think that Ehrenfest from time to time extended a word of warning and said, “You will get your difficulties with the point electron,” but that was about it. After this visit to the United States I was again in Copenhagen where Landau and Gamow were also Gamow was working on the first edition of his book on the nucleus while Miss Swirls, who later married Jeffreys, was trying to brush up his English and convert it in reasonable form. Landau was working on a number of problems, not getting much in shape for publication that year at Copenhagen. He was very critical of everything. Part of the time A. H. Wilson was there, the man who started semiconductor theory and whom Landau thought a complete fool, his favorite pastime in the evening being to tease Wilson and try to make him furious, in which he often succeeded. The Landau-Peierls paper was one which Bohr didn’t like at all; he thought it was not well analyzed and I think he felt a little bit that it encroached upon his favorite field with fairly uncareful preparation.

Kuhn:

And this even at a time, from what I gather from what Professor Rosenfeld writes about Bohr’s knowledge of the field when they took it up together, when Bohr’s own preparation to work on this problem was in some sense still inadequate.

Casimir:

I remember that with Landau the question was always, ‘who is going to make quantum electrodynamics?’ So he didn’t feel that what existed then was really the answer. So at that moment it was fully realized that there were these remaining problems of infinite energies and so on and so forth. Landau always raised the problem of who was going to make quantum electrodynamics.

Kuhn:

It was Landau who raised this problem rather than Bohr raising it with him?

Casimir:

Yes, it was Landau who raised it.

Kuhn:

Did Landau think that the key to it might very well lie in this sort of problem as illustrated in the Landau-Peierls paper?

Casimir:

That I don’t know. I don’t think that he thought that was the way in which you ought do it.

Rosenfeld:

No, their paper was more descriptive, I think; they wanted to show that the present approach, which is still a current one, after all, was completely wrong.

Casimir:

I went back to Leiden at Ehrenfest’s request in the academic season of '31-'32 and I first finished my thesis, which dealt with this question of asymmetric tops and rotations and representations of the group of rotations and that sort of thing; I developed some general mathematical theorems on irreducible representations which were later found to be rather useful. I don’t remember very much about that particular winter after I finished my thesis; I don’t think I did anything very important myself, and nothing very much was going on in theory at Leiden at that particular moment, As a matter of fact, when summer came, Ehrenfest sent me away from Leiden, saying that I wasn’t doing anything there. That was when he first sent me to Berlin and I already told you about this episode with hyperfine structures and so on; then Pauli asked me to become his assistant at Zurich.

Kuhn:

Whom did you succeed there?

Casimir:

Peierls. This was in a way interesting. Pauli had just finished his Handbuch article on quantum mechanics so it was in state of affairs where you could regard many chapters as closed, so to speak. This was the paper of which he always said, “Es ist nicht so gut wie die erste Auflage, aber immerhin doch noch zweimal besser als sonstige Darstellungen der Quantenmechanik,” with due modesty, because he didn’t really think it was as good as the first one. Pauli was looking a little bit for problems at that moment; he didn’t like, let us say, more applied work such as solid state physics and a number of other things, and he became interested in rather abstract formalisms. He was giving a lecture on general relativity and he played around with formalisms of quantum mechanics and five-dimensional relativity and that sort of thing. I think this occupied most of his time and effort during that period. I remember some discussions with him about this question of self-energy in which he mentioned — I think it is even in his Handbuch article — that you have, of course, an infinite self-energy. Now you may ask what happens to a bound electron. Peierls, at his request, had worked out, but I think had never published, that. He found that, if you take bound states, still the self-energy diverges in exactly the same way as it does for a free electron. I also remember that Pauli and I discussed then that it might be possible therefore to take the difference of these two divergent sums in a certain way so that they would compensate one another for the high frequencies and that you might get a finer difference which then could be interpreted as a difference in electromagnetic mass in a bound state and a free state, and that that then might have a physical meaning. I remember considering working out that problem Just for the fun of it; that would have given you the Bethe approximation for the Lamb shift and we discussed that in ‘32. Our attitude was that you could calculate such a thing, but that it was rather doubtful whether theory was good enough to give a definite meaning to such a quantity, although to speak with Bohr, “Man sollte darauf vorbereitet sein, dass Abweichungen von dieser(weisen)Abnung vorkommen koennten.” So there was just a ghost of a hint in Pauli’s Handbuch article where he says this. These five-dimensional things didn’t carry him very far, of course.

Kuhn:

Did he hope that they would do something for the quantum electrodynamics problem?

Casimir:

Yes, I think so. I also remember at one moment he said that this must be the source of terrestrial magnetism because he thought he had found some coupling terms between gravity and the electrons. I think I helped him work out the orders of magnitude. There were quite a few powers of 10, some thirty or forty, I believe, missing. And there was a rather curious episode with the two papers of Pauli and Solomon.

Kuhn:

This I don't know at all.

Casimir:

That was a very formal paper on some formulation of Einstein; Einstein had a four-one dimensional, if I remember rightly, and Solomon had written a rather formalistic paper on tensors and so on, and the first thing that I had to do when I came to Zurich as Pauli’s assistant was to check over some of the results in the second proofs, which I did. Solomon was a very good theoretician, but in this paper he had been rather sloppy, and as a matter of fact, although the general thought and pattern of the paper was perfectly all right, most of the formulae were wrong in the first edition. So Pauli said we have to write to the Journal de Physique telling them they had to stop publication and wait until we put that right. Then a terrific thing happened; a letter came that they had waited so long for the second proof, and since there had been so few corrections in the first proof, they had printed the thing. So the second paper, Pauli-Solomon number two, was written with an elegantly phrased introduction that although the general ideas and so on were all right, there were certain defects in the actual calculations in the previous paper. So Pauli took it up again from the very beginning. Pauli was really a little bit embarrassed about that: “Was muss ich noch sagen? Muss ich jetzt Ihren Namen nennen? Das ist naemlich so peinlich, aber die Formeln sind jetzt alle von Ihnen; also was muss ich jetzt?” [General laughter] So I graciously consented not to be quoted in that paper and to be a ghost writer for Pauli and Solomon Number 2. What I also remember of that Zuerich time is that Otto Stern, who was a good friend of Pauli, came there and told about his experiments with the proton magnetic moment and so on, which in a way was quite a sensation.

Kuhn:

Do you remember particular reactions to that?

Casimir:

Pauli, of course, I think, knew that you could, in a formal way, write extra terms in a Dirac equation so as to get higher magnetic moments, so that in a way consoled him. I remember that I worked a bit, apart from these things, on various problems of theory of radiation, radiation damping and damping in successive states and so on. And Pauli was much interested in mathematical problems at that time, and I remember when I came to Zuerich he said, "Now there is one unsolved problem in group theory which is a problem of the complate reducibility of representations which is not quite satisfactory because it is proven by Weyl, but only with a kind of integration over group space and not by purely algebraic methods.” So be put me to work on that and I was able to do it easily for the rotation group and for a number of other cases for other groups; then I wrote to van der Waerden who completed the proof. It was later simplified by Brouwer. The basis of it was really an operator that I had introduced in my thesis when I was working on rotators. Then there was this problem in connection with radiation which again was connected somewhat closely with these self-energy things. I did some work on the scattering of radiation by bound electrons, a correction to Klein-Nishina formula when electrons are bound, So Pauli was rather interested in these problems and always asked, “Where are the limitations? To what extent can you rely on such formalisms and where can you not?" And let’s say, as I said before, some vague ideas of renormalization were present, but one didn’t really see how to do it and how to do it relativistically, and so on.

Kuhn:

You’re there really when the problem of the negative energy state finally comes out experimentally, aren’t you?

Casimir:

I don’t know if I was at Zurich then or whether I was already back at —. When was the positive electron? When was Anderson’s paper?

Kuhn:

Anderson’s paper was ‘32. I think the Blackett-Occhialini paper is already early ‘33. I'm not sure of those dates now.

Casimir:

Of course, in ‘33 I went back to Leiden after Ehrenfest’s death. I had intended to stay one more year in Zuerich, but Ehrenfest brought much pressure to bear on me to come back to Leiden. This is again part of the Ehrenfest tragedy that his plan to commit suicide, I think, was one which he had had for a very long time; and he also knew that it would take quite some time, that there would be a gap, before a successor was appointed, and so he wanted at least to have me there, a young man, to tide things over. So I was back at Leiden in September ‘33.