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In footnotes or endnotes please cite AIP interviews like this:
Interview of Leon Rosenfeld by Thomas S. Kuhn and John L. Heilbron on 1963 July 1, Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA, www.aip.org/history-programs/niels-bohr-library/oral-histories/4847-1
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This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Harald Bohr, Niels Henrik David Bohr, Max Born, Léon Brillouin, Louis de Broglie, Paul Adrien Maurice Dirac, Th. de Donder, John Ray Dunning, Paul Ehrenfest, Albert Einstein, Enrico Fermi, Otto Robert Frisch, Gruenbaum, Werner Heisenberg, Ernst Pascual Jordan, Oskar Benjamin Klein, Hendrik Anthony Kramers, Lev Davidovich Landau, Nevill Francis Mott, Wolfgang Pauli, Rudolf Ernst Peierls, George Placzek, Edgar Rubin, Erwin Schrödinger, John Von Neumann, Eugene Paul Wigner; Universität Göttingen, Université de Liege, and Université libre de Bruxelles.
As we generally do with people whom we plan to spend more than two hours with, we usually start out quite early in your life, how you got interested in science, how much of it there was in the educational system, how your friends, family felt about this, what were the careers that seemed to be open — some sort of sociological background for the scientific career, as you experienced it yourself. In the first instance, I don’t want you to write the history or the sociology of a scientific education, but really talk fairly personally about how you encountered this as a child, as a young man.
You see I was Belgian. I prefer to throw a veil about it because it is really a very pitiful story when you look back on it. I was a school boy in the secondary school; we had a rather good secondary school in Charleroi, which is a mining town with democratic traditions. It was very good — I’m rather pleased with the education I got there as a general background, especially history. But with regard to science it was, of course, on a very poor level. The humanities were much more developed than the sciences, with the exception of pure mathematics. But this was pure mathematics in a very peculiar sense. We had a teacher who was a really remarkable man, because his devotion to the children was remarkable. For instance, the regular lessons started at eight o’clock in the morning, but he arranged for those of us who were interested to come at seven o’clock. He himself came and gave us a course of geometry much more advanced than the regular course, so at that time we knew all about projective geometry and also the so-called geometry of the triangle, the triangle in which there are so many remarkable lines with six or seven points, that kind of thing, and circles, too. So we knew all this and we were very eager; we regarded it as a kind of sport.
How many of you were there in this special group?
About a dozen or more.
How many would there have been in the regular course?
Forty or so.
Then that’s a remarkably large proportion.
Yes. But physics was extremely poor, physics was absolutely disastrous. Then we got a chemistry teacher who was more — and also chemistry is more stimulating because you see things happen in chemistry. We did a bit of glass blowing and experiments; I did experiments in the cellar of our house and so on. But remarkably enough, this chemistry teacher, when I was about to leave the school, took me aside and said, “I want to give you an advice, don’t go into science because it is the worst possible profession. Go into engineering.”
When he said this, did he have in mind the lack of career opportunities in science?
Yes. He said, “You are up for a miserable life if you go into science.” And another teacher also took me aside and he, on the contrary, wanted to persuade me to go into philology. But I resisted both, and decided to go into science. At this time I had lost my father. My mother had had no experience herself so didn’t know what to do, and was rather distressed. Everybody said that this was the worst idea that could happen, because in Charleroi at that time, there was a big tradition, since it was one of the industrial centers of the country, to regard the profession of engineer as the top that you could aim at.
What had your father done?
He was an engineer himself, and he died of an accident. He had invented a kind of electrical oven and in the experiments that he was making, through a false maneuver, the molten metal fell into a bucket of water and, of course, there was a terrible explosion, and he was —. All the others were also thrown on the floor by the shock wave and nothing happened to them. The foreman was rather badly burned, but he recovered; my father, however, fell, knocked his head against some metal object, and fractured his skull and died within a few hours. That was during the First War. At that time the Germans had occupied the electrical factory and all the engineers had resigned in order not to work for the Germans. So they had plenty of time and they started inventing a new system for an electrical oven.
Had he been an inventively inclined [person) throughout his life?
Oh, yes. He had received a prize for the invention of electrical traction; that was the beginning of electrical traction. He had a tramway system with magnetic transmission of energy. A very complicated system. When the carriage went along the rails, there was a circuit attached to the carriage and it went over a magnet, a magnetic field, and in that way a current was induced which served to push it to the next magnet, so there were a series of magnets all going. But it was never applied because very soon —. The idea was to avoid aerial wires, and then another system was introduced with ground wires, and that was much more practical.
Were you an only child? Or had you brothers and sisters?
I was an only child. Then I went to the University and —.
I don’t want to let you get to the University yet. Here you’re clearly disobeying everybody’s advice; your physics course is lousy —.
Yes, yes! It’s a wonder to myself how I came to decide that I would do theoretical physics because I had heard very little about it. But I had gotten the idea that it was so wonderful that you could get this correspondence between mathematics and physical phenomena, and that to look for those relations was the most interesting thing that you could imagine.
Had there been some applied mathematics in this special math you had been doing?
Just the elementary physics when you saw the law’s of motion. I read very little outside the schoolbooks, so I did not read any science books at the time. Of course I had the example of my father, because electrical engineers are those who are most scientific among the engineers. But I never really got into what he was doing. I just noticed that he could calculate how thick a wire should be in order to carry a certain current and that seemed to me so wonderful. I thought it was rather romantic.
Do you know what kept you away from engineering?
My father tried out whether I had any mind for engineering, but he very soon saw that it was hopeless.
What couldn’t you do?
No imagination, you see. He tried first with mechanical things, but I had no imagination, for example, for kinematic connections and so on. When I was shown I could understand quite clearly, but I couldn’t find out. He asked me how to transform an oscillatory motion into a continuous one [but] it was quite beyond me.
You weren’t clever enough to become an engineer, so you went into theoretical physics.
Yes, of course! But when I began to think about theoretical physics he had already died. I was about fourteen when he died and that is about the time you begin to start thinking about what you are going to do.
In this mathematics curricula at school, how far had that actually gone?
It was very literally in algebra and analysis. At that time the programs did not include any differential or integral calculus, but plenty of algebra. But then there was a bias toward geometry, especially because the teacher was interested; we went very far in geometry, especially in projective geometry.
You had a good geometric imagination but no kinematic imagination; there’s something odd about that combination isn’t there?
Yes, I don’t know. In projective geometry there is little imagination actually, because in fact, it is more algebra and concepts than representation, because you argue always with anharmonic ratios and with correspondences of points and lines and so on. It is very abstract; you don’t care about the figure. You argue that the intersections of two bundles of lines would form a conic section, but you don’t care how this conic section looks; it may be an ellipse, it may be a hyperbola, and so on. So this is that part of geometry which is least geometrical.
What things other than mathematics and physics were you interested in?
Oh, everything in history, and Greek and Latin, and natural history. I collected insects and flowers. I collected also postage stamps. I was always a big collector.
What sort of school was this? Was it a state school?
State school, yes.
Did you acquire enough Latin there to be able to communicate subsequent1y with the Vatican?
Yes, sure. If you know it, you can read Latin like any other language. I did not follow the Greek course to the end because it would have left me with too little mathematics, so I went over to the mathematical section for the last two years.
About how did the school divide up between those who followed the classical curriculum and those who followed the more mathematical? About half and half? I mean, it was not a school notably biased toward either the humanistic gymnasium or toward the Realschule?
No, it was not.
And those who followed the mathematical section were inclined to become engineers or schoolteachers?
Engineers, most of them. Schoolteachers — that was regarded as very inferior. In fact, when I came to the University — if you’ll allow me to say so now — the situation was that in the section which was a propaedeutical section for mathematics, physics and chemistry, the upper ‘layer’ of the students were the future engineers. Those who were studying pure science — we had lectures in common during the first two years with the others — were regarded as the scum. In fact I very soon noticed — I couldn’t help noticing without having any high idea of myself — that those who were doing the same science course were just those who could not afford to give up the idea of doing the engineering course, which was regarded as much more difficult. So it was rather depressing.
I asked you not to write the book but to speak personally, but for just a minute now, let me withdraw that. I think that the situation you describe here, with the very best people being headed for engineering, and with the ones with interest in science who might then be going into teaching as the definitely lower level, is something I have not encountered in Germany, in France, or in England. Do you have any notion what accounts for that strong and marked a situation in Belgium?
This results from the conscious policy of the government. The government was then in the hands of the clerical party, the Catholic Church. So they have the conscious policy of debunking science, but they could not, of course, afford to debunk engineering because that was the life of the country.
They had very little conception then I take it from this, of the importance of scientific training and the keeping up the population of able teachers in order to produce good engineers.
Not at all, no. It was a very miserable situation. In the middle of the 19th century there was a liberal government, very broad-minded people, and they wanted, just because the primary education was so poor in the hands of the [clerical orders] to introduce state primary schools. But that costs money, and so they had to levy a special tax in order to start the system; and that was the end of it. At that time, the people were so greedy and narrow-minded that they revolted against the extra tax. With the result, that there was a famous election in 1884 which swept away the liberal party practically and gave an absolute majority to the Catholic party. So the country since that time until the First World War in 1914 was in the hands of the clericals, a very narrow-minded capitalistic party. At that time it was so easy to make money without much effort, and therefore they cultivated engineering, not with any broad-minded aims, but just to keep up a sufficient technical level to run the factories and the mines — in a very primitive way, without any idea of perfecting things. In fact, after the First World War, the situation in the Belgian mines became extremely critical; the mines were so antiquated, there had never been any innovation introduced, that they could not compete anymore. Even now they are still handicapped.
You speak of your own school as a state school.
Oh, yes. Of courses it was not so bad; something remained of that effort. The clericals could not completely suppress those things. What they did was to put their own men in those state schools, and even into the universities, so they treated the state schools as an appendage of their own schools. I remember in my own town there were two competing schools, the state school and a Jesuit college, and in our state school we used the school books written by the Jesuits.
Was it also staffed, at least in part, by clerics?
No, it was staffed by laymen but most of them were Catholic; in fact, it was very difficult to get a job if you did not profess to be a Catholic at that time.
Were most of the students also Catholic, or did Catholics generally go to the Catholic school?
No, just in those mining districts. At that time a labor movement began and the bourgeoisie itself was anti-clerical; the clergy made a mistake in the fight against the schools. They excommunicated the liberal party, which before that time, like the conservatives, were Catholics. They were all Catholics; they all went to church. Then when the liberals were in power and started to introduce the schools, the clergy made the big mistake of excommunicating them, so that made half the population anti-clerical — mathematically.
Did they remove the interdiction when the —.
No. It was not removed.
When did you actually then go to the University?
In ‘22 The University was just as bad as the schools. There was one teacher of mathematics, who was a distinguished one, but he was very old already when I was there; still, I got good influence from him in analysis. He insisted especially on rigor and was very entertaining and stimulating. But he is the only one that I remember who was a really strong personality.
What was his name?
Deruyts. He worked on the theory of algebraic forms in the (line) of Cayley and those people, which was not a very popular subject, but he was a very deep thinker. He did not publish; except for this big work in his youth about algebraic forms, he did not publish anything.
Now, just in terms of straight curricular work for the examinations, what subjects did you learn?
The curriculum was, either way, rather sensible because it was very broad. You got a bit of everything, and I think that is good for students because then they know at least that the subject exists, but nothing was done very deeply. One got a general survey of analysis — that was the best of all. Then geometry was a terrible shock for me because the first two years I knew much more geometry from my special class than was taught there. Physics was very poor because the man who gave the lectures in physics was not a physicist himself; he was an engineer, but too bad an engineer to have made a career in engineering. That was the situation.
What was the pattern of lecturing in physics? Was there a practicum? Was it pretty much the German model?
Yes, it was rather like the German model, but on a very low level.
Was there just one man who lectured in physics?
There was one man lecturing and then another directing the practicum.
And that went on for how many years?
We had two years of physics; or rather, we had four years of physics but two were spent in a big course in elementary physics, while the next two years were supposed to be advanced physics. But unfortunately, the teacher giving advanced physics ended his life as a madman; he went completely crazy, and in my time he had not yet reached that stage, but he was not far removed from it. In the last years, my wife, for instance, had him also as a teacher and in her time he was also a little crazy, but there was no possibility of —. Nobody dared to remove him.
What sort of subjects did he, in your time, at least introduce you to?
The whole thing was very vague. Just a survey of atomic physics without any line in it. I suppose he took any textbook, like the French one of the old Chwolson, scanned one or two chapters, and put them together. There was no [continuity].
You were then able to work for yourself, on your own?
Well, the man who gave theoretical physics was also very poor in every respect, but, at least, he just copied; he could choose good books to copy from. For instance, he copied Abraham’s book on electricity, and a bit of Lorentz; so from that point of view we had a very good grounding in electricity and electron theory in the sense that we got the material, but without any explanation. He just read out his notes. I tried once or twice to ask him something but it was quite impossible; he was unable to give any explanation. In mechanics, it was very good. He also chose good books by Painleve and so on. For instance, in celestial mechanics, we got quite a bit, for instance, a whole book on planetary perturbations with all the details and all those tedious series expansions. If there was any line in it we had to find it out ourselves. It is very difficult for you to get an idea of what the level of that teaching was.
How many people were there?
A dozen, not more. Those people were going to be teachers in the high schools, so you can imagine. So the attitude of the student who was not interested in the subject was simply to find out how little he had to cram and to get into his memory in order just to pass the examination, and it was very easy to get it. After a few years you knew the standard questions.
When did the examination come?
At the end of each year.
You had examinations annually. And was that a general examination for the teaching certificate?
Just for the degree itself.
Well, you had to have four diplomas from the four annual examinations; then you got the final one. At that time you had to do your thesis and you got a degree of Doctor with a thesis at the end of four years. So in the last year actually, you still had some lectures, but most of the time was employed in writing a thesis. So I had to write a thesis without any help whatsoever. It was not a very good one!
Just on the subject, you clearly had a prolonged exposure to electromagnetic theory, electron theory, and to analytical mechanics, presumably including Hamilton-Jacobi techniques and so on.
Yes, very, very, detailed.
What about thermodynamics, statistical mechanics?
Optics, yes, we had some optics in astronomy — the theory of telescopes. But this course was also given by a man who hardly knew what convex and concave meant.
With this formidable background, how did you go about selecting a thesis topic? How did one proceed?
Obviously I had to pick up a problem, so in this long course there was a work about magnetic hysteresis, and especially magnetic viscosity, and in the course it was said that this was a very obscure phenomenon which was not understood. Now we do know very well why. So I said, “Oh, well, that’s something then.” So I tried to understand magnetic viscosity without having the faintest idea what it was about. But, you see, once you get into such a subject, then you find some side issue, and finally what I did was to study in great detail the precession of a magnetic atom — I mean a sphere of electricity which had a magnetic moment, and then how it precessed in a magnetic field — with finite amplitude. Then you get elliptic functions and it was a beautiful mathematical exercise! There was very little physics in it.
In all of this, at the time you reached your thesis, to what extent had you been exposed to relativity, to quantum mechanics?
Not at all, not at all. I had not heard a word of quantum theory, not a word.
This is ‘25 now?
In the last year I started myself. I looked at the papers and, I think, the first idea of the quantum of action —. Oh yes, of course, I had read some popular books in which there was some talk of the quantum of action.
And relativity, very little more?
Hardly, I think. There was an old professor who was retired and was, as you would imagine, an opponent of relativity. Then he gave a course of lectures, just for the fun of it, on relativity, but just to speak against it. That was my introduction to relativity.
What were you doing for yourself in these years in the sciences? Were you reading other books?
I was reading a bit, yes. I started reading. I think my first contact with quantum theory was through reading’s papers. You can imagine how much I understood of them
Possibly more than you —
Possibly more than if I had followed all the —. [laughter] I don’t know.
You think, for example, that as of the time that you read Schrodinger’s papers, you had never read Sommerfeld’s Atombau?
No; I read all that in Gottingen. Well, wait a minute. No. When I left the university, I went to Paris for one year, and there I started reading. There I realized how little I knew and then I started reading Sommerfeld, Courant-Hilbert, and —.
How did you go about getting to the Ecole Normale in Paris?
Well, this astronomy professor was a very poor astronomer, but he was at least a liberally-minded man who understood that the only way to get out of the morass was to send young people abroad. There was an agreement between the two governments reserving a few places at the Ecole Normale for certain foreigners; there were Belgians, Rumanians, and Serbians, or Yugoslavs, after the war. I think there were two places for the Belgians, mostly for literary people. [My astronomy professor] heard about this, but somehow I came too late; nevertheless the French were generous enough to allow a third one, so there were three Belgians that year: one historian, one philologist, and myself.
I want very much to hear about this year in Paris, but I’m still uncomfortable about your account of your four years at the University of Liege. Somehow or other this doesn’t sound like a full time job. You clearly were not, I gather, spending very much time outside the courses doing a lot of reading in physics and mathematics for yourself. The program itself was not terribly consuming.
Yes, it was, because I was a very conscientious student and did not miss a single lecture even though they were so dull; so most of my time was spent in those lectures and practical [courses]. There was a practical astronomy, practical historiography; there was mathematics, physics, chemistry, crystallography, astronomy, and geodesy. It was an all-around education.
And you had to take all of these subjects?
Yes, with practical exercises in all those [courses] so that this system consumed a lot of time. If the professors had been reasonable, it would have been a very good grounding in general physics; only they were just men who had been put there mostly for political reasons, and the government did not care about the state universities. They had their own Catholic university in Louvain and that was, of course, very well organized. It was a private one and not the government’s job so the government saw as its aim rather to leave the state universities in a state of rigidity, but they were not at all interested. There were a few liberal professors, very eminent men, but not in my time; in Liege, for instance, there was a chemist, (Spring), who was a very liberal man but he had a hell of a time; he was in conflict with the government at all times, he got no credits, no money for developing —. Then as soon as he died, he was replaced by an absolute nonentity.
As you worked on these courses, did you work directly from the lectures or were there also books that you were supposed to have?
No. The system was that each professor had his own course and you had to take notes or even dictation sometimes. No books were indicated to you. (???) It was a practical question, too, because at the examination it was running a risk which no one was willing to take to try to be independent. You had to repeat what he wanted to hear, whether you believed it or not.
It’s a harsh story you tell.
Was the situation the same at Brussels?
In Brussels it was at that time a bit better. I say (at that time) because now the situation has changed quite a bit. Brussels was an anti-clerical university which was founded against the Louvain University, and it was also a private university, but they were very poor, they had no great means. Therefore, although they wanted to do the job properly, they were handicapped by lack of means. Their professors were either well-to-do people who [taught) just to help and were not concerned much about getting an extra salary, or they were engineers who could not make a career in industry, or doctors who could not get a private practice. Nevertheless, it is a fact that the University of Brussels, because it was in a liberal state, was the best one.
Did you go to Liege rather than to Brussels simply because it was nearer to home?
No. I could have gone to Brussels just as well or even better. But my father came from the engineering school of Liege and my mother always had this idea in the back of her head that my craze of wanting to be a scientist would pass, so I would at least have two yrs in the engineering school to make up my mind. She had the quiet hope that I would then decide to continue in engineering. Then surely Liege was the best engineering school at the time.
It seems to me terribly surprising that you really stayed with this program against all the obstacles and with as little encouragement as you got. You clearly had some idea that it was going to be different later.
Yes. At the beginning I worried quite a bit, but then I suppose I settled down to the idea that something would turn up. In the last three years of the university I was very much encouraged to continue by this astronomer who had spotted a few of us. He told me that he would try to send me abroad and so on, so I was quite pacified.
Were you pretty thoroughly conscious throughout this time that what you were being exposed to was backward?
That helped also. Of course I did not realize it fully; I had some idea that it was not quite up-to-date, but I knew so little of what was going on. It was only in the last year that I started reading the literature and then realizing that there was a gap between what those people were talking about and what was written in the papers. There was nobody to talk to, either.
I tremendously admire your pertinacity.
I don’t know; it’s difficult to think back. I think it was more resignation — no, ‘resignation’ is not the right word; it was lack of realizing how bad it was that helped me out.
But you discovered that in Paris?
In Paris, yes. I discovered that in Paris immediately and it was rather a shock. But then I found very good people to talk to. (Laure) was one of my comrades there.
How then did you go about obtaining what you had missed?
But I must say that in Paris I met with very little help from the professors. When I went to the professors of physics there the only one who was a bit amiable was Fabry, but he was just polite rather than particularly interested. Another one was Bloch, and then the mathematicians. There was Langevin, of course, but that was quite different.
Did you go to lectures regularly in Paris?
Yes. Langevin was the only one —. You see, I immediately went to de Broglie who was then quite unknown. [In fact] when I asked for the name “de Broglie” I had to repeat it several times and finally write it out before the people understood whom I wanted to see and could direct me to his office.
How had you known, coming from Liege, that de Broglie was somebody you wanted?
That was through reading.
You read Schrodinger after you got to Paris or before?
Before, just by chance; I opened the Annalen der Physik in the library and there was this paper by Schrodinger.
How did you know it was important?
Because he said so, you see! You couldn’t get away from that impression because of his style.
Not with the second Mitteilung at least.
I hit upon the third, and since I knew so much about Hamiltonian mechanics — it was not so unfamiliar — so it appealed to me directly. As you say, I was not corrupted by any —.
Knowledge of what the problem is worth! So really, when you went to Paris, you already had it in mind to try to find de Broglie and to begin to work on wave mechanics?
Oh, yes. (???) I knew at least that that was a problem that was being discussed.
While you were still in Belgium before, had you been at all involved with de Donder?
No, not at all. I got to know de Donder at the end of my Paris year because in Paris I spent most of my time learning what I had missed at Liege. I learned quite a lot from Langevin’s lectures at the College de France; that was really wonderful.
What was he lecturing on?
On statistical mechanics. That was really wonderful, and then of course de Broglie also, but de Broglie was very queer. His course was very interesting because he just described his work, his whole idea, but at that time he was absolutely groping around. He ignored [i.e., did not know about] Schrodinger — well, not quite, but he ignored at any rate the Copenhagen school — so he was groping around; he asked me to —. I remember, just as one example, that J.J. Thomson, who must have been quite senile at that time, had published a note in Nature about some model of the electron, rotating electron. De Broglie asked me to study it to see whether that was not a way of getting (around). At that time one was preoccupied with the spin problem, but de Broglie had no idea even of how the problem had to be formulated so the wildest things were (???). So you could not get any guidance from anyone. But then —.
He must either have just published or been working on the book on Des Mouvements which was the second round of the thesis but written after Schrodinger —.
Yes. In fact that was the climate. Then Brillouin helped me also quite a lot. He did not give any lectures, but he had a seminar which was very instructive because there, at least, one discussed the latest publications and so on.
How did you go about getting de Broglie just to set you this problem?
I was the only one talking with de Broglie. He gave a course which was followed by a dozen people who went there, sat down, took notes, and then went away. I was the only one who approached him. He was so shy — and I was shy too — that the first contact was rather difficult, but then, as it happens with shy people after the first contact has been established, [we became] very intimate. For instance, when he had finished his lectures I followed him and we walked together down the street and discussed things; on one of those occasions he mentioned, “Have you seen this last paper by J.J. Thomson? This may be something to look at.” Brillouin was the one who was most alert in following these things.
Did you now, with this guidance, do a good deal of reading by yourself?
Yes, of course.
What sort of books and articles were particularly helpful? How much of it was books and how much of it was the literature in the journals?
At that time it was mostly books because I had to catch up.
What books did you then find?
Sommerfeld, Courant-Hilbert, and some others too, and some on relativity. Of course on relativity I read Eddington.
Weyl came later.
How about Born’s Atommechanik?
No, that I only got to know when I came to Gottingen.
How about any writings by Bohr? Did you encounter those at all in Paris?
Hardly. I read very little of the preceding periods because I was also anxious to do some research, and then the only research I did was in just combining my freshly acquired knowledge of relativity with wave mechanics and developing the wave equation in five dimensions. That seemed to me a very handy formalism to get at the same time the electromagnetic field — combination with the wave mechanics had not yet been done. That put me in contact with de Donder. I published a note which I sent to him to be presented to the Belgian Academy. De Donder was the least critical person you can imagine, be was enthusiastic about it. So he asked me then to come to Brussels, be wanted to have me in Brussels; I wanted to go abroad a bit more, but I worked for a month with him in Brussels.
In the summer?
How much was de Broglie involved with you in this five-dimensional relativistic formulation?
Very much, because, in fact, I was the one who called his attention to it because he did not know about it. Then he wrote a paper about it which was very like Klein’s — Klein’s paper appeared at the same time. De Broglie made a modification which made it a bit more elegant.
You had begun before Klein’s work came out?
Yes; I don’t know how I was led to Kaluza.
But you did know Kaluza?
Yes, I started from Kaluza, but I suppose it was in a paper by Einstein himself that I saw by chance in the Berliner Bericht that I got a hint about it.
You learned tensor manipulation and so on from Eddington?
Yes. That was a very good example to learn with manipulations, Christoffel symbols, and so forth.
Were there others besides de Broglie interested in this five dimensional business; for instance Langevin?
What did de Broglie think one could eventually get out of it? Did he think that the answer to —.
At that moment, the preoccupation was how to treat the interactions and it looked as if there were a possibility of having a closed formalism, a unified formalism, including the interactions. I think de Broglie wanted to avoid the configuration space of Schrodinger because he said it wasn’t sufficiently physical; he thought of the waves as something real, and. therefore, didn’t like the waves in configuration space. Then he thought that perhaps by introducing such a general field, the gravitational field, and especially the five-dimensional formalism which included all the electromagnetism, that you could get closed equations that included the interactions.
Were there discussions while you were in Paris with de Broglie or with Brillouin or others about the statistical interpretation that begins to emerge in that period?
Yes. Brillouin took it for granted. There was not the slightest contact between Brillouin and de Broglie — no, not at all; they were in two different worlds. De Broglie was quite isolated. Brillouin took it for granted because he only refereed current literature. It was there that I learned about Born’s Stosstheorie and so on, and de Broglie of course knew that too — he read the literature. So we had talks about it and de Broglie only expressed his distaste for those things, again coming back with the objection that “it’s all very abstract, it’s in configuration space, it may be right, but it’s not a physical description, it’s only a formal description and you must have some underlying reality which can only be described in ordinary space.” That was a worrying problem.
How did you yourself feel about it at that time?
I just was under the influence of de Broglie and the first months I was in Gottingen I still tried very hard in that same line, making models of wave packets in ordinary space and trying to find interactions. But Born discouraged me. Born put me on a complete problem of optics. It was very fortunate for me that Born was writing his book, which was perhaps not a very good book, but anyhow, he asked me to help him.
This is the book that is ultimately Born-Jordan?
Elementare Quantenmechanik, by Born-Jordan; there was very little of Jordan in it. But that really gave me an opportunity to get deep into questions and also into history; it was then that I learned about the preceding periods. There was a very good lecture by Jordan at that time which I followed. Jordan was Privatdozent, and he gave the lecture in which he showed the correspondence between the old —. He treated the problems in the old quantum theory, the correspondence principle, and then the new theory, and showed how the new quantum mechanics had given a rigorous expression for the correspondence principle. That was extremely interesting.
You’d used mostly matrix techniques to do it?
I want to ask another question or two about Paris. You mentioned that the spin was the most discussed question of the day; was there an actual opposition to it?
No. No opposition. The arguments of Goudsmit and Uhlenbeck are very clear —.
But theirs of course is relativistic.
But there the problem, for de Broglie at least, was how to incorporate the spin in a realistic wave model, so I tried to construct a wave packet which would have a magnetic moment and that kind of thing.
The Darwin paper must have come out while you were still there. Possibly even the Pauli.
Yes, I don’t remember exactly when I read this paper, but I think it was in Gottingen.
You don’t refer to Pauli in your little note on —.
No, I remember that I saw Pauli for the first time at the Solvay Congress in ‘27. I was then in Brussels working with de Bonder. Of course I was not admitted to the Congress itself, but de Bonder took me —. In the first place, I wanted to see Born, because I had gotten the idea that the best place for me to go was to Born, to Gottingen.
Did you think of staying in Paris longer?
No, I had had enough of Paris. First of all it would have been difficult because this place in the Ecole Normale was only for one year. I felt that —. Langevin was very kind and so on; he was not —. He was the first to tell me, when I went to see him at the beginning, “Well, I am very glad you are here, but you will find yourself very isolated here and you will not find anybody to take care of you.” He realized the situation. Also I realized that there was more activity and more flowering in Gottingen; Gottingen had struck me as more active at that time than Copenhagen, and, in fact, it was perhaps true because at that time there was Jordan, Nordheim, Heitler, and all the mathematicians. I also wanted very much to see Hilbert and that famous mathematical school, so I was very eager to go to Gottingen. So I waited outside the door where they were discussing, and when they came out, I went to Born and asked him whether he would deign to have me next year; he accepted immediately.
What sort of financial arrangement did you have? In Paris you had a fellowship.
Yes. Then this astronomer, Dehalu, was the administrator of the University [of Liege] and he got me some money. So there was no financial problem, no worry at all.
When had you begun your writing of a history of science?
That was already when I was a student.
Already at Liege?
Yes, I had a very great interest in that.
How did that start, do you know?
I was always interested in history, even as a schoolboy. I had a very good history teacher who really presented the problem; he had a method which I find very interesting. He said, “Suppose you are the King of France in the 15th century and explain what politics you would follow in the situation that you would be confronted with.” He was a pupil of Pirenne so he was very good and I was very interested in history.
At the University did you do this entirely by yourself, or were there also —?
Oh, yes. I was also discouraged from doing it. I published a small thing and immediately this mathematician called me in and, expressed his dissatisfaction with my wasting my time.
You published something already while you were a student at Liege?
Yes, that was about (de Sluis). There was a periodical, a small bulletin edited by the engineering students and I published a few things in it, among which was a small study of (de Sluis).
And you later published that?
Part of it, with some manuscripts which I found in Paris. While I was in Paris I used the opportunity to go to the Bibliotheque Nationale and look at those manuscripts, the existence of which I had learned from those preliminary studies.
Was this ‘waste of time’ frowned upon in Paris too, or did anybody care enough —?
Nobody knew about it! In Paris, nobody at all cared about me, how I spent my time.
Did you find that aspect of the situation quite different at Gottingen?
Was there a sort of individual attention?
Yes. Sure. In Paris I had some possibility of talking to people, but it was very limited. I spoke with (Lauret) at the Ecole Normale just because I chanced to be sitting in the same room, and I had a few others. But I made a point at the Ecole of not conversing with the scientists, but with the literary people, because that would widen my interests. And so nor best friends at the Ecole Normale, apart from (Lauret), were literary people. At the dinner table, you see, you had on one side the literary and on the other the scientific, but I went with the literary.
What was the state and nature of your interest in political questions at this period?
That of course was when I got interested in politics.
It was in Paris then?
Yes. The Ecole is very very —.
But you had not had particular interests already in Liege?
Very little. There was very little political activity at that time in Liege. The only political activity concerned those linguistic squabbles because it was the time when they transformed the Ghent University into a Flemish University and that was very much resisted. We had a strike and so on at Liege, but that was not very much.
In Paris, did your political interest take the form of activity?
In Paris I got the first glimpse of social problems and international politics.
Was this mostly discussion that you were engaged in, or did you also take a more activist role?
Only discussions, no militancy.
Did you also begin to read along more sociological and political lines?
What sort of things?
At that time I began to read the newspapers attentively. I always read the newspapers, but only superficially and just in order to know what was going about but without having very clear views. It was the period just after the First World War when everything was in turmoil. The people who were prepared for that, the people who already had some political education before the war, would find that a very interesting period; but for a newcomer who had no preparation and no idea on his own, it all seemed utter confusion without any clear line. So I couldn’t get a hold of it, get a hold of any interesting point. It was only in Paris by listening to the animated discussions of the people that I realized that there was a problem there that was worth thinking about.
This sort of discussion would consume a considerable amount of the time of the people at the Ecole?
Yes. Of course [as a result of] or whole environment I had a keen sense of what was then called the “social question,” the state of the workers, class differences, and so on.
Had you concerned yourself with those already?
No, but you couldn’t help noticing the miserable state of the workers. In fact, we lived on a boulevard full of posh houses and then, from the back yard, we had a view of the slums. And one hundred yards from these bourgeois dwellings was a coal mine where you could see the coal miners going home without even a wash, black faced, because washing installations were not provided in the mine: you had to do that kind of thing at home. Our maid was the daughter of a miner’s family, and in the patriarchal spirit this maid was considered part of the family. So it happened sometimes, when I was a small boy that my mother went to the miners, to give them old clothes or something, I suppose, and I went with her, so I have recollections of that very poor environment. That leaves impressions; also I have recollections of the big strikes and demonstrations and the banners flowing, but that did not crystallize to any conscious thinking about those problems until I came to Paris. During my student years I always had the feeling that there was disharmony and confusion, but I thought it was too complicated and hopeless. But I did not read Marx until I came to Germany and then I read it. When I opened the book and read the first chapter, it struck me that I had [here] a man of genius, just as when you open Darwin and read it, you feel there is something there which is a really superior grasp of the questions.
Was there this same sort of interest in political questions at Gottingen, or was the fact that you read Marx when you got there really a carry-over from Paris?
That was more because at that time I was concentrating on learning German. I knew a bit of German, but in perfecting my knowledge of the language I was beginning to read German literature, and it occurred to me that that also was the moment to start reading Marx.
Coming to Gottingen from Paris, did you again get this same sense of having been in a backwater even in Paris?
Yes, very much so. That was really an overwhelming impression — the life and this active exchange .in the discussions that were going on all the time in Gottingen.
Where did they mostly go on? In the seminar colloquium, or —?
Everywhere, all over the place: in the street, in the library, in the corridors. Whenever you met someone you were sure to be involved [and asked], “Have you read the last number of Naturwissenschaften?”
And were you able to participate in those discussions when you arrived?
No. At the beginning I felt myself so green. This was another shock again, so I spent a great part of the night eagerly reading things that I had noticed I ought to have known and did not know of or had not understood, even in relativity. When I came there I was more or less regarded as an expert in relativity just because of that note, but I soon found that when somebody asked me a question, I was unable to answer it. So I spent nights reading relativity more attentively.
What would you describe as what was missing in your knowledge of relativity?
Well, as you would expect, the physical interpretation. It is very easy to learn the technique of tensor calculus and even to apply it, but when you come to the finer points such as “what is ‘x’, (“do you write f(x) or g(x)”) — ‘x’ or ‘g(x)’.
Good. This is now in the fall, October of ‘27, that you get to Gottingen. What are the problems of particular concern?
At that time the greatest stir was caused by Dirac’s papers on radiation theory — at the beginning at least — and then the efforts to make a relativistic theory of the spin. Wigner and Jordan found the method which was then called second quantization,” a very bad name, but four Fermions as we would say now. And right at the beginning, even before that, there was the transformation theory. I always remember how depressed Jordan was when Dirac’s papers came out.
All those papers came out before you got there.
Yes, you’re right, but I remember a conversation with Jordan in which he told me that he had been depressed because Dirac’s paper had come out, I think, a bit before his own, and especially because he saw that Dirac had done it better than he had with his Delta function.
You got there after the transformation theory, after the Heisenberg paper on the uncertainty principle, after Bohr’s Como paper. To what extent was —?
Not after Bohr’s Como paper; that was ‘29 or ‘28. No, I’m sorry, you are right; but it was published while I was in Gottingen.
To what extent were those issues still wide open for discussion? The issues of the statistical interpretation, the issues of duality, the issues of uncertainty, measurement problems —.
The Gottingen people were looking down on the others about it because they thought that they understood the whole thing. There was a characteristic remark by Wigner after the Como lecture: “This lecture will not induce any one of us to change his own meaning [opinion] about quantum mechanics.” In fact they did not appreciate the problems raised by Bohr.
Would it be fair to say that in some sense they were settling for the Heisenberg paper without the Bohr?
Without the Bohr complement, yes.
Were they much interested in it at all?
No, no. At that time I was still a bit heretical and I still insisted on the possibility of giving mere reality to the waves and so on. Then Jordan took the trouble to explain the details to me, or rather, to point out the arguments; that contributed a great deal to make me abandon them completely.
What arguments were particularly effective?
Not any particular argument, but the whole consistency of the thing. I had spent several months vainly trying to do anything with those waves in ordinary space and getting nowhere at all, whereas I saw that the others could really apply these things and develop a consistent interpretation and so on.
But you did continue on these real space — this was part of the five-dimensional formulation?
The five-dimensional formulation was more of an accident; I did not go on. But I still used general relativity because it gave a general formal framework which is helpful, because in this formal representation with tensors and so on, you write the formula in a more compact form. I was out for closed expressions, not for any expansions or practical calculations, but more trying to find a compact expression.
You say it was Jordan who particularly went over the arguments with you. I have the feeling, which is tentative and I advance it so that you will knock it down, that in some sense or other Jordan himself took the wave function, the probability amplitudes, more seriously physically than most people in the Gottingen group, and that in this sense also he may have been a little closer to Copenhagen in certain respects at this time. Was that apparent at all in your own dealings with him? Or does this make any sense to you that he’s in a slightly special position vis-a-vis the physicalness of wave function.
No, I cannot say that. That doesn’t mean that it wasn’t so, but it did not strike me simply because I was so confused in my mind at that time and I couldn’t possibly have noticed such subtle differences. In fact, my own view of the Como lecture when I read it was that Bohr was just putting in a rather heavy form things which had been expressed much more simply by Born and which were current in Gottingen at the time. I did not see, I did not feel, any of the subtlety that was in it, and. I suppose that this was the general feeling in Gottingen. This complementarily business was just a way of putting in words the situation that every-one knew. I suppose if you look at it now, the Como lecture did not yet clinch the argument; all this question about defining the concepts came later.
But there was no real attempt at Gottingen in these periods to argue these natters out further?
Did people do measurement problems?
There was a fight between the matrix addicts and the wave mechanics people. I remember people joking a bit about Born and also about me, since I was involved in his book, [accusing us] of trying to make simple things complicated. It was not a quite unjustified criticism; in that book Born tried to write down the Schrodinger equation as if it were a matrix equation, glossing over all the difficulties of those (continuous) spectra. So people said, “Why all this effort, since we have the wave mechanics which is much simpler and much more handy to deal with?” and so on, but there was not much deep thought behind it. I think it was just an argument of useful, practical problems. One had a developed formalism of differential equations and therefore it was much more powerful than this cumbersome matrix algebra.
Who lined up on which side?
At that time most people swore by wave mechanics; Born was the only one [on the other side], although he himself had contributed to wave mechanics. But at that time for some reason in writing this book he was emphasizing the matrix formalism.
You speak of there having been arguments and discussions of these, and it doesn’t sound as if it were just Born versus the group.
Yes, actually it was. Born did not take much part in those. It was I, if you like, as representative of Born, but I was not very warm either. I only said that the matrix formulation had the advantage of being more compact, allowing one to use all the ideas of classical mechanics, [for instance] the Hamilton formalism which was also very useful. I was always inclined to emphasize a general aspect, general formulations, whereas the others were anxious to solve practical problems. So they got at me [by saying], “Well, you have a beautiful set of Hamiltonian equations and a beautiful formalism of perturbation theory, but try to give the answer to calculated transition probabilities with your formalism.”
In this period the matrix formalism looked like a more complete formalism than the Schrodinger formalism? And even with operators —.
Yes. We knew they were equivalent, but more compact, which allowed an easier survey of the general relations. To write a set of Hamilton equations gives you a certain insight into the structure and relations between the time variations of the momenta and coordinates that you do not get in the Schrodinger equation. You only get it in the Schrodinger equation when you construct the matrix element from the wave function; I think there is something in it. They are two formalisms adapted to different aspects, the matrix formalism — what we would now call, in Dirac’s language, the Heisenberg representation — being more adapted to describe the particle aspect, and the Schrodinger representation being more adapted to represent what we call the wave aspect, or distribution in space.
Did you discuss this with Born at all? Anything you could tell us about Born’s own or other resistance to embracing and arguing —.
Born had the idea that this book, Elementare Quantenmechanik, would be the first volume and then there would be a second volume in which the same things would be discussed in terms of waves. That was the reason actually. Born did not want to put one above the other, that was not his intention at all, but then he got discouraged about that by two things: First, the review of his book by Pauli, and then the fact that Weyl’s book appeared. I still remember Born telling me, “I’ve just gotten Weyl’s book and I’m quite discouraged because I see that in forty pages he has put so beautifully all the things I was going to put in a book of two hundred pages.” So there was no use in writing [that second volume] and he gave it up.
Were his lectures arranged the same way, that is, first of all a general matrix mechanical presentation, and then, next semester or something, wave mechanics?
No. In his lectures he mixed up the two, or rather, he presented the two aspects for each problem. In so far as he did that, I think, he very soon came to the equivalence of the two formalisms and then he chose the one or the other for discussion.
You say that, close to the beginning, at least, of your time, there was a good deal of excitement about the Dirac emission and absorption of radiation papers.
Yes, because that seemed to give just the answer to that puzzling problem about the abstractness of the configuration space. There we, Jordan and Wigner in particular, saw the possibility of formally considering the wave equation in ordinary space and yet treating a system of interacting particles. That was the answer to that problem.
Yes, that’s what Professor Klein said, you recall, about what converted him to —.
There’s almost a year that goes by between the Dirac paper and the Jordan-Wigner paper, and I’m curious in part about earlier reactions. Again I see perhaps no way out of saying too much about what’s on my mind. It’s perfectly clear that one can read the Dirac paper, as Jordan does read it and then goes on with it, as a paper in wave quantization of Schrodinger functions, as second quantization. To me, I think, it’s also clear that you don’t have to read it that way and I don’t think it was quite written that way. My own feeling is that for Dirac, this is a transformation of variables and that this whole business of seeing this as a one electron problem which is now quantized in order to give you more and more electrons — as a field theory then — comes quite rapidly, but is not there in the beginning. And it’s just in your period at Gottingen that this transition occurs. There must have been some people, I suppose, who were pretty bothered by this technique of Dirac’s at the beginning; there must have been a while before this way of looking at it —.
Oh, yes. It looked like a wonder. I think the first difficulty was to understand correctly the technique of it and then it was so that it was a transformation, as you say, from one set of variables to the other. It was very unfamiliar in the beginning to work with those occupation numbers as variables, but then one noticed — especially Jordan for whom it was very easy because it was his transformation theory — that by unitary transformations one could get from the one to the other, only it was infinite. And that was it. I don’t know how the second quantization originated, but I don’t think it corresponds to a very deep expression of something new, but rather it was more jargon invented for quick communication without any deep meaning in it. It was a very unfortunate choice of words, surely.
Jordan himself says that in an important sense, he had this idea from the time he first saw the Schrodinger equation. He had been the person who was really responsible in both the Born-Jordan and the Born-Heisenberg-Jordan for those last sections in each paper on the quantization of the electromagnetic field. From the time he saw the Schrodinger equation he felt — and nobody would take him seriously — that now the way to handle multiple electron problems was by quantizing the Schrodinger equation just the way you would quantize the electromagnetic field earlier and in this way generate —. In fact he thought initially that the way to do the helium atom was to take the one electron solution and quantize it to get two electrons, which was wrong. I think Dirac had no such thoughts in mind about what he was doing when he did this sort of thing. Furthermore, I think there must still have been problems in Gottingen in ‘27 and ‘28; it was one thing to take the Dirac paper and to understand it and to use occupation numbers as variables, but it’s another thing to get this notion of quantizing the wave function for handling multiple electron problems. And even if people learned to do one of these, there must still have been discussions about this rather different physical view of the situation that Jordan took.
Yes, it was not easy at all. First of all, you had to go over from commutation to anti-commutation and that’s already a big step, and then the construction of the annihilation-creation operators in Fermi statistics is not so easy because of those questions of signs. In fact there was a wrong paper by Jordan first in which he had forgotten about those signs and got a wrong result. That was then corrected by Wigner. They worked with this formal analogy: photons are particles and particles are waves, so they should be treated similarly; then the electro-magnetic waves follow Bose’s statistics and that corresponds to commutation; and then the others follow Fermi statistics. Then it was discovered that that corresponds formally to anti-commutation which is very near to it, so they looked at it in a very formalistic way. That may be the origin of the word ‘second quantization.’
I know their analogy and I know it demands anti-commutation. I’m merely wondering how people at Gottingen took this. This was, in a sense, — I hadn’t realized it until quite recently in preparing for Jordan — this is really a larger transformation a real turn with respect to what’s been going on, for a year and a half or so, in the whole way of looking at the way you handle particle problems. I hadn’t realized that there was a turn that big that cane that quickly, and it seems to me that there must have been all sorts of discussions of it at Gottingen and probably opposition to it.
No, it was received as great progress in formal aspects; it made things look simpler than this configuration space business, especially because it allowed you to formulate problems in what they called a more “anschaulich” way. “Anschaulich” means sufficiently vague to be misapplied to any situation. All the time they were insisting on making things more “anschaulich,” and especially making those Fermi statistics “anschaulich,” so they were very happy to have that. Of course, if they really thought so, it was an illusion, but that was the trend at least. So there was no opposition to that at all; on the contrary, it was regarded as a great (boon).
What is the connection of your work with Witmer on the larger questions of the day?
The only reason that I got involved with Witmer was that we lived in the same pension and therefore we had conversations after dinner; those works were results of those after-dinner conversations.
Did you have to inspire anybody to do those experiments?
Yes, very much so. Skinner tried some experiments, but I suppose he never got anything because of the form factors. We had taken no account of the form factors which would blur out. I think the effect we discuss there, this coherence, is a real effect, but it was blurred out by the form factors which we did not consider.
What of the second paper with the photon interaction?
That was nothing. I think it’s better to forget about that.
You were at Gottingen just for the one year?
No. At the end of the year when I was going away, Born asked me whether I would like to stay on as his assistant, primarily to complete work on his book.
Were you there then a whole second year? In our biography it’s clear that you were in Gottingen in ‘28-‘29 and the ETH was in ‘29-‘30, but what happened in between?
I was three semesters as an assistant in Gottingen, I think.
That would take up the prescribed amount of time. Then you were very definitely in Gottingen when the Dirac electron paper came out?
Oh, yes. That caused great excitement. In fact, Wigner and Jordan were very near to it, and so they were rather depressed to see that Dirac had come first. They admired his solution very much, of course.
you know what they had been doing? There were clearly a lot of people trying to work the spin — trying to take the Pauli spin matrices or something of this sort and put them into the Klein-Gordon equation.
Yes, that’s what they were trying to do.
That seems to me somehow very different from the Dirac approach which comes out with the spin matrices without having put them in.
Yes, that was regarded as a miracle. The general feeling was that Dirac had had more than he deserved! Doing physics in that way was not done!
When you say ‘more than he deserved,’ you mean he had no right to get the spin matrices out of that approach rather than that nobody ought to do that much good physics.
Yes. Surely Wigner and Jordan tried to — they went in the same direction —.Darwin who also got very near, after all — and they tried then to introduce the Pauli matrices, to build them in somehow in a completely relativistic equation. But the idea that it had to be of the first degree — that was his.
How acute was the negative energy state problem?
That was not prominent at that time; it came later.
Was there any disposition to be skeptical about the Dirac equation?
No, it was immediately seen as the solution. It was regarded really as an absolute wonder.
Did people worry at all about what that extra variable that the alphas and rhos were the operators for was? Was there any attempt to worry about a model of the electron?
Yes. It was very soon found that the velocity was always c and it was not seen clearly what that meant, the idea being that now we must cease to talk about velocity, that there was no use in it because the velocity was always c.
Was Schrodinger’s explanation —.
That came later; Zitternbewegung came later, but it came at a stage when people had ceased to worry about it. Nobody was really excited by this Zitternbewegung.
Were there attempts to apply in any sort of detail, anything like the Klein-Nishina?
Yes, of course. Then one started discussing all the possible applications. The paper by Klein-Nishina came in ‘29. Yes, it came rather early, but —.
Was there really a quite considerable attempt there to pick up the Dirac equation and do problems with it? It’s still hard to do problems with and there were a lot of problems, so the whole question as to how quickly the Dirac electron gets itself really integrated into the approaches — generally, to the problems of quantum electrodynamics. There is a lot of quantum-electrodynamics that seems to go on from this time on without really using the Dirac electron or taking any particular cognizance of its existence by people who clearly know and presumably admire it. Did you yourself try to do anything with the Dirac electron?
Yes, in fact, I did derive what is now called the Gordon decomposition of the current. I did that, but I did not publish it, and then it was published by Gordon. That was an effort to understand how the magnetic properties could be separated, whether the magnetic properties could be separated cleanly from the translation properties, and that is possible then in the current. I remember showing that to Wigner, which is the reason I didn’t publish it. Wigner looked at it and said, “Well, yes, yes; so what?” Then I have some recollection of Wigner’s discussing the orders of magnitude of the corrections you had to expect and saying that it was all relativistic effects or small effects. At that time there was not so much material that was not explained; in fact, the most outstanding difficulty was those so-called relativistic doublets in the hydrogen spectrum which were cleared up, but by Dirac himself. That was the most interesting application at that time. Then, of course, one realized that there were plenty of small effects, corrections. Perhaps even the correction to the scattering formula was mentioned, I don’t remember, but it was felt that those were small effects which could not be compared with any clear-cut experiment on materials. So from that point of view there was not much interest. I heard at that time that Wigner and von Neumann were more interested in the formal properties of the spin. Then of course, there was one very big application which was started immediately by Wigner and that was the incorporation of the spin in this group description of the treatment of spectroscopy; he discovered that the spin corresponded to the representations of half integer index. That was a big thing and was done immediately afterwards with the help of von Neumann.
What about this whole entry of group theory into quantum mechanics? Were you all busy learning group theory?
Oh, yes, of course. I learned it from Wigner and I even solved various problems. Using this “Darstellung,” this representation technique, you can do various things which do not lead, of course, to new results. You can do it by algebraic calculation, but it’s more elegant to do it with those representations, getting solutions from the Schrodinger equation, for instance.