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In footnotes or endnotes please cite AIP interviews like this:
Interview of Eugene Wigner by Thomas S. Kuhn on 1963 December 3,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes ard transcricts of oral history interviews conducted with ca. 100 atomic and quantusl 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, arid 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: Richard Becker, Niels Henrik David Bohr, Max Born, Gregory Breit, Richard Courarit, Paul Adren Maurice Dirac, Freeman Dyson, Albert Einstein, Enrico Fermi, Ferdinand Georg Frobenius, Werner Heisenberg, Walter Heitler, David Hubert, Friedrich Hund, Ernst Pascual Jordan, Max Theodor Felix von Laue, Fritz London, Herman Francis Mark, J. Robert Oppenheimer, Wolfgang Pauli, Michael Polanyi, Ratz, Riemer, Erwin Schroedinger, G. Schur, Leo Szilard, John Neumann, Victor Frederick Weisskopf, Hermann Weyl, Wigner (Eugene’s father), Enos E. Witmer; Berlin Technische Hochschule, Princeton University, and Universitaet Goettingen.
When we stopped last time, we were talking mostly about Berlin and particularly there about the earlier years in Berlin which I’d like to go back to. But before doing that, there is one other range of issues in the earlier period that we did not explore at all and that I’d like to persuade you to talk at least a little bit about. Remember, we left open the question of whether there was a 'Hungarian phenomenon' but were at least trying to explore the background of a Hungarian like yourself who did come into the sciences and who was clearly part of some group in Hungary that was coming into the sciences.
Not in Hungary; in Hungary I was not part of a group. In high school there were two of us who were particularly interested in mathematics. The other one was a fellow called Riemer. I just got a telegram fron him congratulating me on the 1963 Nobel Prize ]—-from Australia, in fact. I can’t answer it because I don’t know his address. But the two of us often were working together. The teacher, Dr. Ratz, treated us very much alike and when he gave eaminations to the class, he gave different problems to us than to the rest of the people. That’s quite natural. Perhaps it interests you that his political views were very different from mine; he was a very leftist-thinking person. I don’t know whether he is now—I don’t think so—but this may have diverted him from natural sciences and physics. I really don’t know.
You don’t know whether he is now doing mathematics or physics?
I doubt this. I saw him once about twenty-five years ago. He came to my office. You know, somebody’s suddenly coming to my office, somebody whom I haven’t seen for twenty—five years, sort of baffled me. I went up to him, introduced myself, and he introduced himself and of course from his voice I at once recognized him. We had a pleasant few hours together but he had to go on. Excuse me, this is probably of no significance.
You said there were just the two, but one class behind you was Johnny von Neumann.
Right, right. I did see him occasionaily. About once a month, I would say, we took a long walk; I think I may have mentioned that to you. He was inexhaustible on such occasions in telling me about set theory, number theory, and other mathematical subjects. It was really wonderful. He never thought of going home. (And I could say something just once in a while), but I thought it was first rate. He was phenomenal, also in his desire to talk.
Did you know Leo Szilard in this period?
Not before Berlin. Were there other Hungarians that you knew before Berlin? Remember, you told me how many of the group in that Einstein seminar, for example, had been Hungarian.
The great man to get acquainted with somebody, to walk up to the President of the United States or the President of the USSR, is Szilard. He is what many people would call “brash”, but I think that is a wrong idea. He is unpreoccupied; he doesn’t mind if somebody tells him, “I am busy now.” He got all these people together in Berlin.
It was a group then that very much revolved around him?
It didn’t perhaps revolve around him, but I am convinced he got us together. Three people whom I remember are first of all the brother of Szilard who is now an engineer in New York, then Gabor, whom I mentioned, and a M.Kornfeld, who I think became more or less a politician in Hungary.
These people are all Hungarians; are they also all Jews?
You know, I am not sure of that. Kornfeld is a Jewish name; about Szilard himself I don’t know.
I believe, though I don’t know, that he is Jewish. Von Neumann was.
Yes, about von Neumann I am sure, entirely sure. But about Szilard I am not. Gabor is not a Jewish name; on the other hand, the mere fact that they were in Berlin is sort of an indication that they may have been Jewish.
Tell me about that. This, you see, is the issue that I suddenly realized had never come up when we talked about the Hungarian background.
There was a Communist government in Hungary in ‘18 and ‘19—again I am not sure of the dates—which was overthrown, I think, in the summer of ‘19. Many Jews participated in the Communist government; in fact, it is embarrassing that in the high positions there were almost only Jews. What the reasons for this were I cannot tell and it may not be entirely true. In any case, there was a very strong reaction after it and the rights of the Jews were very much curtailed. In particular, they were not allowed to register at the University or the Technical University; or at least few of them were allowed to register there.
You must realize that the Hungarian intelligentsia was a much higher percentage Jewish than the general population because most of the people lived in a semi-feudal state and a peasant, which was the majority of the people, was a peasant. The number that is in my mind is that eighty percent of Hungary was employed in agriculture; they had very little reason to enter academic occupations. The Jews were all merchants or something of that sort until they were emancipated and then, naturally, they expanded into the professions—-this is my interpretation—-which were able to absorb people. Those were of course law, medicine, and also engineering and the sciences.
How about teachers in the universities and in the schools?
Very few of them were Jews, first because they were appointed before the Jews really became interested in these occupations, and second because there always was a certain prejudice against Jews and they were not given high positions. I remember that the population of the city of Budapest was about forty-five percent Jewish and there was only one Jewish congressman in parliament and that was a miracle, so to sreak. There was a certain—not repression but discrimination against them. There were some exceptions. I believe that Fejr was Jewish—the mathematician Fejr—and so perhaps there were a very few of them.
You mentioned last time the fact that a brother of the man who owned the factory and whom your father knew had been in the university but had never been promoted beyond Dozent. He was a Jew, wasn’t he?
So this was part of the reason in your own case for going to Berlin, was it? To get into an environment where there were more intellectual opportunities for Jews?
Actually, I do not know what the reason was. I think once it was clear that I would finish engineering school, my father said, “Why don’t you go to a German university?” He felt probably that they were better and that they taught more, and,as it turned out, they did.
Was there any place besides Berlin that you thought of then?
The Technische Hochschule Charlottenburg [Berlin] was an important concept, and I don’t think I thought of anything else.
I notice von Neumann went to Zuerich.
Yes, well, Zuerich was very good, but Zuerich also was very expensive, I don’t know whether that played a role, but it may well have.
Was being Jewish an issue with this group that you knew in Berlin?
No. In fact, as I told you, I did not know and I still don’t know. I never thought of wondering, “Are they Jewish, or are they not Jewish?” It just didn’t enter my mind.
How much of an issue was this for your family? Were they religious Jews?
Oh, no. I know very little about my father’s family; there are all sorts of things which I don’t know end which he never told me, but my impression is that his family was not Jewish. But I am not really positive on anything of this. My mother was.
In general I’ve been surprised at how many of the people involved with quantum mechanics at all were Jewish; but in the group of Hungarians they seem to be almost uniformly Jewish.
Yes, but I think that was principally because they were brought into contact with it by being sort of pushed out of Hungary. Even the United States should erect a monument to Hitler and one possibly to Stalin for both have advanced by probably a number of years the American natural sciences.
In the case of Hitler it’s extraordinarily clear. Well now, coming to Berlin I’d like you to start out by telling me bow you lived there. Did you live with other students?
No, I rented a room. For the first two years I went early in the morning to the chemical laboratory, worked there, ate luncheon there, worked even in the afternoon until five o’clock, and went home rather tired. This I did six days a week. I went to very few classes because there was an awful lot to do in the laboratory; the number of analyses that you had to complete before you could take your examination was awfully high. On Saturday afternoons in later days we had that little conference which I mentioned; on Sunday very often I went to a museum or a library or occasionally, in the spring, out into the woods. That I did often with friends who were not too deeply involved in science.
Tell me more about this group, the Saturday group. You’ve mentioned it before, but I’m not really clear who was in it, how it was—.
Just three of us—two in addition to myself: Johnny von Neumann and Szilard. I don’t know how often we met, but I have the impression that we met very often, almost regularly. Szilard had a group at his room; he also rented one room. But I think he was on good terms with the family so we used the living room on these occasions, and there was Gabor, Kornfeld, the two Szilards, and occasionally other people. Szilard was and is outgoing—not at all shy and retiring as most scientists are.
Was this run as a seminar?
We just collected. This was essentially in connection with that Einstein seminar on statistical mechanics and we discussed whether we understood what happened, how it was, and so on. That was essentially the subject.
Did this go on for a longer period of time than the Einstein seminar?
I don’t know. You see, the whole period of Berlin wasn’t very long. The first year I don’t think I knew Szilard. This again is uncertain, as these things unfortunately are. The second year I knew him, but then, you see, the whole study was three years from then on and I think in the third year I began to work at the Kaiser Wilhelm Institute on my engineering dissertation. Polanyi—how did I meet Polanyi? In the factory where my father worked there was a very able chemical engineer—I don’t know whether you have ever heard of him—Paul Beer. He wrote to Polanyi and sort of introduced me by letter. Polanyi invited me to their house and there I met Mark. I must say that was a wonderful experience for me. Polanyi and Mark had a discussion in the evening and I sat by; I don’t think I opened my mouth.
This was Ernst Mark?
No, no. Hermann Mark. Do you know him?
Just as a name, yes.
He is now a polymer chemist; at that time he was a physical chemist and Polanyi was also. It was a wonderful experience for me. Even now I am quite impressed with how they discussed one thing after the other, how they understood each other, how they knew all physical chemistry, how close their contact was. I remember after a little while Mark sort of got up indicating that he wanted to leave and I sort of made some motion [betraying my disappointment] “Oh, isn’t that terrible!” Mark sat down again, and I stayed on—rather embarrassed, of course, but I appreciated it just the same. I did my dissertation with Mark and at the same time Szilard. collaborated with Mark. I don‘t think the two were terribly close humanly, but they worked together and I think published one or two papers together.
This is Szilard and Mark now, or Polanyi and Mark?
Szilard and Mark.
Being in chemistry as you were in Berlin, to what extent did this separate you from the physicists or the mathematicians in Berlin? To what extent were all of these one group?
I knew very few people; I was and still am shy. I don’t introduce myself to people; I am often unnecessarily afraid that I impose on people, and so I knew awfully few people—awfully few people. I went regularly to the Wednesday afternoon colloquium and for that purpose I dropped analysis. I understood at the beginning awfully little, but got along.
Was the Wednesday afternoon colloquium also in any way a social occasion?
Not during my student days. I went there—it was always in the room—I sat down, or if there was no seat I stood up, and I listened. There were about four or five reports on papers, and Einstein, Planck, Nernst, and Laue, of course, sat in the first row, hardly ever giving a review themselves but listening to the reviews, discussing them a little, and then going on to the next. Laue was in charge of it; he read titles of papers and asked people who would be willing to renort on them.
Were the reports usually given by students?
By assistants. Pringsheim, Czerny, and Hettner, I think. I don’t remember it all, but usually it was that way.
Did you ever report to the colloquium yourself?
No, not in these days. I did not even really understand what it was about.
I gather from what you said last time: that to a great extent you felt that what you had learned of the old quantum mechanics, [i.e. quantum theory] in this period you had picked up . . . from the colloquium, plus Szilard, the Einstein seminar—-.
Yes. I now remember that I occasionally went to the so—called Staatsbibliothek and read books and papers there. I also remember having read some books; for instance, one by Reiche, I still have most of these books. I don’t throw away many books which I have read to profit. And the quantum condition—.
Do you remember other books besides Reiche that you read?
I read of course both ‘little’ books, I read Einstein’s Einfuehrung in die Relativitaetstheorie and Wassmuth's Statistical Mechanics which I mentioned. I’m sure I read others too.
But not Sommerfeld you thought?
I don’t think I ever read Sommerfeld.
That’s interesting because it was of course for so many people in these years the Bible.
Yes. Well, you know, my time was badly broken up and in some ways I was equally interested in mathematics and in theoretical physics.
What did you read in mathematics in these years?
I am terribly sorry, but I don’t really remember, And maybe I did not read very much; I had a very full schedule. I took two classes; I mean, I registered for many classes in order to be able to take the examination, but I really took only two classes. One was ‘differential equations’ by Rothe who was a teacher of mathematics, and the other was ‘organic chemistry’ by Pschorr. You lived in Germany at one time?
Never really lived there, no.
Well, there is a Pschorr Brauerei, a brewery, and it’s a very good beer I must say. He was a member of that family and he was an organic chemist. I took those two classes, I probably read some book on differential equations to supplement—.
But you don’t have the impression that you were reading abstract mathematics or more advanced subjects less related to science.
I am almost sure that I did not read algebra, for instance. I read a small book on set theory. I have practically all these books so if it is in any way important I could look at that though some of iry books were left in Hungary. I made every effort to get them out but unsuccessfully.
It would be worth at least looking at these. I also of course want to talk to you about papers and correspondence and things of that sort.
I have a great deal of that saved up; much of it was left in Hungary but I did not throw away terribly much. But that was later, that was much later. I don’t think I even have the calculations saved which I did in those days.
Would you have correspondence from those days?
I doubt it.
You think all the correspondence you have is probably from the time after you first came to the United States?
No. When I returned to Berlin [as a Privatdozent, 1928] then I had correspondence. But I don’t think I had correspondence——in fact, I am as sure as I can easily be——on scientific matters. Now I remember some other books that I read and much of it I read under the influence of another friend, Popper, who was also a Hungarian and Jewish. He was also a chemical engineer, my classmate, and not terribly interested in science——more interested in business, but felt that it was good thing to have a technical education. However, he advised me to read a number of books although I don’t know whether he himself read them. Among them was Nernst’s Theoretical This is a very indefinite statement because Nernst’s Theoretical Chemistry grew from a thin volume to a very thick one. I read it when it was about two or three centimeters thick.
One of the later editions.
I now have the last edition—the one which was the last when I was in Germany (in ‘20) which I did not read. I remember that these books all mentioned quantum theory with a somewhat condescending attitude as some sort of a “Zukunftsmusik”; that it was a very important thing and some people knew it but in practice it wasn’t necessary. It was a great eye-opener for me that in the colloquium they constantly talked about that. Then I read Herz’s Physical Chemistry; of course I read K. A. Hofman’s Anorganische Chemie from cover to cover and I knew it thoroughly and I still know large parts of it. Excuse me, I ramble a little.
This is as it should be. When do you suppose you began to follow the journals systematically?
I subscribed to the Zeitschrift fuer Physik when I went to Hungary because I knew—.
When you went to Berlin?
No, no. When I returned to Hungary—-in that period which may have been very short or may have lasted two years. I read the Zeitschrift fuer Physik rather systematically then. Eucken has an article there on the chemical constant. . . . That I reviewed for Volmer’s collo-. quium, and it would also be interesting for me to look up whether I reviewed that for Volmer’s coiloquium before I returned to Hungary or after. I think before.
I think before.
I think before, as you say. Yes, when I was Polanyi ‘s student—you know I did my doctoral thesis with Polanyi—I was reasonably seriously interested in it, and I read then also a great deal of serious quantum theory inasmuch as there was serious quantum theory at that time.
How did Polanyi himself feel about quantum theory? Was he well acquainted with it?
No, nobody was. Nobody in Berlin was. It was all a little dilettantish in Berlin which was not bad because everybody felt that this was not it, but of course real quantum theory in Heisenberg’s sense grew out of the ‘not it’.
This is a question which I had raised here with you and. I realize that in a sense I have raised it mistakenly because I had suggested that in some sense Berlin had ceased to be a leading place in physics; I realize it isn’t true, but it is in quantum mechanics.
Yes, in quantum theory.
I mean, before the first war it was terribly important for quantum theory; from Bohr on, after the war, it never achieves the same place until about the time of the new quantum theory again.
I now realize that in some ways I was more self-taught than I thought I was, My interest in quantum theory was my own,I worked in Polanyi’s laboratory, but nobody there was interested in quantum theory. Polanyi himself, and I’m sure he would not contradict me on this, felt that quantum theory was too mathematical for him.
When you say that people did in the colloquium talk a lot about it, what sort of problems do you remember?
Oh, the determination of the ionization energy of mercury was one of the many things. The Reststrahlen of sodium chloride, the second excited state of thallium, and so on. The Bohr-Kramers-Slater must have been—
That was the summer of ‘24.
Yes, I remember that very well and it was a very memorable occasion. I forget who reported on it; I remember that on the Bose statistics Einstein himself reported. You knew that.
Well, I didn’t know that he reported but I knew that he was deeply interested in and involved with its transmission at that point. It would have been natural for him.
He reported on that. I also remember that there is a factor of two: the density of black-body radiation is twice greater than one would first think because of the two degrees of polarization. Einstein made the joke, “This is a somewhat weak point which we will take into account by creating a two,” and he put on a factor of two. It was a joke of course, Altogether I think he convinced everybody in those days that there is some wave nature to matter. Fermi is most famous for the Fermi statistics, but nobody in Berlin was surprised by that. That appeared quite obvious. Fermi has made many wonderful contributions; in particular, the beta decay theory, and many others. But this, for which he is most famous, everybody took for granted in Berlin and many people discovered it independently. One element which was very much missing in Berlin was positive encouragement. Einstein was very nice to young people and very wise, but he never encouraged them with, “Well, look here; this is quite a nice idea. Why don’t you work it out and publish it?” This was missing, and that would have been quite important.
And really among senior figures in this area there was almost no one else, was there? How about Laue?
Szilard did his doctoral thesis with Laue, but he said that in the present sad state of physics Laue did not give thesis subjects in physics. If you wanted to work for him you could do it, he would accept the work, but he felt that he didn’t want to give thesis subjects because the problems were too difficult. Planck never had a student as far as I can tell; Nernst was not interested in these matters.
Do you mean that Laue did not give thesis topics at all, or that he gave them on classical problems?
Not at all, and as a result very few people did their theses with Laue.
You must have been in Berlin when one of the quantum mechanical developments that might have been quite exciting to the people in your field came out; that was the Bohr—Stoner periodic table.
Yes, I remember that was reported. They talked about the Tauchbahnen. Those who reported, however, reported without enthusiasm; they said," Well, we have to know this; this is what people talk about,” but impression was that there was very little enthusiasm about it.
Would that be true generally of all of the technical quantum theoretical developments, of the more theoretical as against the more experimental?
I remember the theory of the hydrogen molecule was reported.
Which hydrogen molecule?
The old-fashioned one which did not work. I remember the eight orbits forming an octahedron was reported—a great many papers. But I think the trouble was that they appreciated the significance of those papers correctly; and it is better perhaps to be a little under the illusion that the papers are important and very little is missing to proceed to the correct picture.
What about things like the spectros copy and the Lands g-factor, for example?
You are right. They reported the sum rules; I don’t quite remember whether they reported the g-factor. I remember one of the books I read was Hund’s little book on spectroscopy.
That’s already later, that’s '26.
Is that so? After quantum mechanics?
Yes. It doesn’t really use it; I mean, it’s the last gasp of the old quantum theory.
A beautiful book. But then I am wrong on that. But the sum rules I knew, and in fact it was partly because of the sum rules that I felt that reality was very much simpler than the theory of that time. . .
Was there much talk about the Correspondence Principle?
No, very little. I remember another interesting discovery: the Stern-Gerlach experiment; everybody was enthusiastic about it . I remember that Stern, after quantum mechanics was discovered, said, “This [i.e. the Stern-Gerlach experiment] clearly shows that it is not true that there is zero angular momentum; now of course they want to blame it on the spin." But Ehrenfest’s paper in which he showed that there is no way to get the angular momentum into the system was reported in much detail and that was taken seriously. This was probably the reason for my thinking that the angular momentum was always and invariably an integer. Anyway if you have a chemical reaction, you should assume that it is an integer, that there is no problem about the angular momentum.
So you think the ease with which you shove aside the angular momentum problem in your thesis is really related to this background of frustration with it in the case of the Stern-Gerlach experiment.
That is very interesting. What about the whole series of issues that come out with the Pauli principle: before spin now, but the question of the duplicity of the two values for the electron?
I don’t think I learned that. I may have heard it. The spin, you know, I learned first from the Born-Jordan paper.
Heisenberg and Jordan?
You remember there is a paper by Born and Jordan and then one by Born-Heisenberg-Jordan. I think the Born-Jordan paper already mentions the spin.
They mention it but they don’t do anything with it.
No, but they say that this “puts a different light" on the problem. I think that is their expression.
I forget whether that’s Born-Jordan or Born-Heisenberg-Jordan, but it isn’t until the Heisenberg-Jordan paper that it is introduced into quantum mechanics. Not even then; I think Pauli introduced it.
Well, wave mechanics, but they solved—. It’s not as neat a treatment; it’s still an ad hoc treatment.
It was also my luck that I did not understand that part of the paper.
In 1924 and ‘25 there are a whole series of attempts, of which in a sense the Heisenberg matrices without matrices paper is the last, to introduce a new quantum mechanics, to replace differentials with differences, and this sort of thing.
My impression is that it was hardly mentioned. I knew vaguely that Heisenberg had used half quanta. I. thought until I returned to Berlin that Heisenberg was an old professor, about fifty-five, in Muenchen. And once he studied some exprimental data and found that half quanta fit it better. I was quite out of touch with many things.
That’s very interesting. Do you know that that happened to him in his first semester at the university? Sommerfeld gave him the problem. That was never published, but his very first semester at Munich was where the half quantum numbers started with. I was fascinated to hear that.
Is that right? Oh, Heisenberg is a great man.
Certainly one of the people who from the beginning was again and again associated with important things. You speak now of returning to Berlin and we have to take it that this must have been '25-'26.
You know, I remember that I came to lunch at the Kaiser Wilhelm Institute and I told Polanyi about having read the Born-Heisenberg-Jordan paper and so on and he said, “Oh, Born-Heisenberg is a good beginner but Schroedinger really discovered things.” Of course I had no idea of that because I subscribed to the Zeitschrift fuer Physik and not to the Annalen der Phsik, so that was that! So I had no idea. I may have heard the name Schroedinger before, but probably not. He said, “What? What?” Soon enough I started to study Schroedinger’s paper and read it and that I discussed with Szilard again.
Now were you yourself much more impressed with the Schrdinger things... You had clearly been very much interested in the Born-Jordan, Born-Heisenberg-Jordan papers because you have a very clear recollection. Now was it sort of clear to you from the very beginning that this was the right way?
I felt that there was a very good chance that on this something useful and really informative could be obtained. I was more impressed with the Schrdinger approach, as most people were, because it was in a way clear to me that this could form a transition to classical mechanics.
Had you tried to do anything with matrices yourself before you were aware of the Schroedinger papers?
I doubt it, I doubt it. I think I left Budapest not long after I finished reading the Born. You see, I also had another occupation. I don’t know whether that hindered me much, but anyway I did not work on it in the day time certainly but in the afternoon on Saturday. The whole paper was very difficult. But Schroedinger I at once took to; it was more natural to me. We did not have the background and mental preparation for this complicated mechanics but we did have the idea of the Fuehrungsfeld and Schroedinger’s ideas were very close to the Fuehrungsfeld.
How about that mathematics? Had you had the sort of mathematical background to handle the Schroedinger equations, second order partial differential equations?
Differential equations and even partial differential equations I did know reasonably well, and then everybody started to read Courant Hubert and I read it too. It was very easy.
You’ve already told me where you first heard of spin; did you follow that up immediately?
No, not in the least.
When do you suppose you began to take the spin seriously?
When I found that without the spin you cannot obtain the even splitting of spectral lines.
Let me pin this down; I've wondered about this. In this two part paper, the first of which is without group theory, and the second—- these are late papers, late '26—
I don’t remember the dates.
They were both in 1926 at which point you were clearly in Berlin.
Yes, but that was very soon after I arrived in Berlin.
There was an address given by Heisenberg in Hamburg. There was a Physikalische Gesellschaft meeting in Hamburg to which I went. Heisenberg spoke at that meeting on the Mehrkoerper problem. I remember that by that time I understood that the anti-symmetric wave functions lead to Fermi statistics and the symmetric ones to Bose statistics. I even mentioned this in the discussion of Heisenberg’s paper. Szilard constantly told me, “See to it that this remark is printed.” But they did not print it because they did not print any discussion. But when I went back to Berlin the first thing was to try to work this out in a concrete case—
Do you think you had seen Dirac’s paper already?
Because Dirac had that one right.
Absolutely right. Dirac made few mistakes in his life. No, I don’t think I had read Dirac’s paper, because then it wouldn’t have been surprising, But you know, Dirac’s papers were considered extremely difficult to read.
They still are, but beautiful.
Very beautiful. But the people thought, “Oh, there is a queer man in England who works on these things and he has his own language and he is probably a very great genius, but for us down-to-earth people this is not quite so useful.” This was the attitude. But I am sure soon enough I found out what he said in his paper.
Do you remember how lleisenberg reacted to that? He now speaks of being ashamed of not having understood that.
I don't think he took it very seriously when a young man who spoke German with an accent said in a somewhat shy fashion that he was mistaken. I would be greatly surprised if he remembered. When I went back to Berlin I at once started to work on it, and worked out the three particle ease. And there of course the surprise, which I found very soon, was that there are always degeneracies which cannot be resolved. Dirac did have a slight mistake on that; he gave the impression that there are symmetric and anti-symmetric wave functions and nothing in between.
When you heard Heisenberg at Hamburg was this perhaps the early summer of 1926?
His paper was out before.
His paper was submitted in June.
My recollection is that this meeting was sometime in September.
But you were already working on this problem when you were there.
In the sense that I knew that anti-symmetry leads to Fermi statistics, or rather to the exclusion principle. Fermi statistics I really did not know about. Pauli wrote to me about Fermi’s paper. But I wrote to somebody that I thought the Bose statistics was a mistake because it followed from the exclusion principle that just the other statistics were right; and Pauli wrote back, “Don’t be so proud of that, because Fermi has a paper, an ante-diluvial paper, in which he points this out.”
But this whole question of relating: you say you knew already that the anti—symmetric functions corresponded to the exclusion principle, yet so far as I know, in the published literature the first mention of this sort of thing is in Heisenberg’s paper.
You see, I had at that time already read Heisenberg’s paper.
The paper was already out when the meeting was held?
At least I had seen it. I may have seen a manuscript, but I had seen it. I did not invent that. Yes, the paper was out, the helium paper was out, and I studied it. It was on the basis of that paper that I arrived at the tiny correction to it that the anti-symmetric wave functions lead to the exclusion principle and not the way be implied it, That’s all I did.
As one looks at those two papers, the papers of yours submitted in November, this is a brand new thing for you to be doing. It doesn’t in any apparent way relate to anything you’ve done before.
Well, you know, that’s not quite true. I was always convinced that the symmetry is much greater and those relations of the sum rules and the intensity rules, more generally, are somehow related to spherical harmonics, to groups. That the spherical harmonics are related to groups I think is obvious on the surface. I planned right then to work out the spectroscopy on the rotation group, but Heisenberg’s paper came and I wanted to understand it so I slithered into the permutation, or symmetric, groups. However, I always considered that to be an interim problem: “Well, let me do that first so that I understand this part.”
This is terribly interesting, but where had you known about groups at all? Groups were something that nobody knew about.
I knew about groups because of Weissenberg and possibly a little because of Johnny von Neumann, Weissenberg told me, “Here is Weber’s read that and then you will prove to me that stable positions in crystals are symmetry points, or that symmetry points are stable.”
You think that you had done nothing with algebra before this?
Very little. I read a book of algebra, a very excellent book. I still possess it. It’s Denes Koenig’s, a Hungarian algebra book and and splendid one.
Did you read it at this time or had you read it earlier?
No, long ago, long ago. Perhaps in high school, I think, or perhaps early in college during the summer vacation. Probably the first year of chemical engineering. I remember that I forgot for awhile the derivation of the small Fermat theorem, which is a group theoretical derivation, and when I asked Johnny to repeat it because I had forgotten, he said, “That is too bad if you forget that.” He was right of course.
In those first papers, those first group theoretical papers, or in the first one [paper 2a] you do without groups at all; Part I—.
The three particles. There was unresolvable degeneracy; that’s what I learned.
But in Part II you say immediately that Johnny von Neumann has pointed out to you and has actually predicted what the general result will be and has pointed out to you that group theory is applicable here. What I’m not clear about, you see, is where that suggestion enters in view of the fact that you had had for some time these thoughts about the relation of groups to—.
Well, I went to Johnny and said, “Look, Johnny, this is evidently a symmetry problem.” I don’t know whether I said group or symmetry; I think probably I said: “This is evidently a symmetry problem. I think the mathematicians must have considered this; and look, there is symmetric, anti-symmetric, but then there are others, and it ‘s evident that in the case of four particles there will be even more, and so on. The mathematicians must have thought of this before.” I don’t know how long Johnny thought, but probably not more than half an hour and possibly only five minutes, and he said, “Yes there is representation theory and Schur and Frobenius.” He went to Schur, borrowed a reprint, gave that reprint to me, I read it and of course it was clear that that was the solution.
Schur was the first thing you read?
Yes, on representation theory; I had no idea that representation theory existed. Johnny said, “Oh, you must read that; you could perhaps work it out but this is one of the things on which old Frobenius made his reputation so it cannot be so easy,” and of course it is not, I knew some group theory but I knew no representation theory.
But you read the Schur and then back to Frobenius?
The article which was decisive is by Frobenius and Schur; in 1905 they published an article, Neue Begruendung der Theorie der Gruppencharakter. I think I still have the reprint; I keep such things out of—what do you call it—emotional, or—
You call it “piety”.
Yes, piety reasons; and it was so easy to read. Of course I was in a sense ready for it because I had thought about it. It’s a beautiful article.
Then you would say that when you began to take up the problem that it was presented to you by the understanding of the Heisenberg paper. But even before the Heisenberg paper, though, you were looking for group characters.
Group character of course means something very technical; what I was looking for were group—like things. And that was to a considerable extent due to Heisenberg.
Plus, I take it, this even earlier idea that there’s something wrong about the whole notion of orbits, that it’s more like a shell, that it’s got properties—
Of course it isn’t a shell actually. But I always thought of it as a transparent or partially transparent sphere—spherical surface or spherical shells.
This is the first group theory paper but still restricted to three particles and still no groups; you put the condition for no radiation in a form that now seems to me rather odd. [Showing a copy of the formulation in outline for interviews] . . . You take as the condition that there shall be no radiation between two separate states the condition that this cross product shall be simply zero [see outline]; there is nothing in here about polarization or anything of the sort. It works out very nicely on straight symmetry grounds, but it‘s rather unclear what you’re thinking of when you do this.
I must admit that I don’t remember.
Later everything goes as it should.
This formulation is correct I think because it proves that not only the dipole moment but all higher moments vanish. In fact, every single particle operator vanishes. So it is correct, but whether I would have been able to say this when I wrote the article, I have no idea. I just don’t remember.
It suggested one possibility to me. There would be one terribly good basis for doing this with some people in this time, which is very shortly afterwards discarded, and this would be people who were reafly fond of the Schroedinger interpretation and who would think that this was a physical interference between these two states.
Yes, I think that probably was on my mind. ‘Does the probability distribution of a single electron change in time, can it have this frequency when it changes in time?' You see, I take an arbitrary wave function: 'Can it have this frequency when it changes in time?’ I probably learned that from reading Schroedinger’s paper carefully.
Now Schroedinger himself does not call these probability functions.
Well, you know that was axiomatic for me and many others and I don’t know how we learned that but I believe everybody knew it. Certainly I knew that they are probability functions. It’s evident from the derivation; it’s evident from the analogy between light and matter which Einstein always pressed; it’s evident from everything that is a probability. The thing that became clear, and I think that did become clear to me first—. It’s very difficult, to discuss this.
I speak to you almost as if I were speaking to myself and that is a little dangerous because naturally everybody remembers much better what he thought about than what somebody else thought about. If you listen to me you may come to the conclusion that I discovered gun-powder, which I did not. Very definitely not. But I think the wonderful thing in the Schroedinger theory is the many—dimensionality which makes it possible to have statistical correlations. Among the people whom I knew I was the first who saw that. That is the explanation, for instance, of the Bothe-Geiger experiment. But I am quite sure I explained that to Szilard, to Johnny von Neumann, and so on.
And very early?
Yes, and very early.
So you think that there was no time, even reading Schroedinger, when you did not quite readily see that what he was saying about this as a physical wave, would not do.
No, nobody to my knowledge believed that.
When you said you felt at home with it because it somehow led back to classical things again, what does that mean?
I felt that this now explained why the wave packets moved as the configuration point moved in classical theory, that the fuehrungsfeld explains the motions of classical theory.
And you did think of the function as a Fuehrungsfeld?
Yes, definitely so. But the wonderful thing that I felt at that time was that the Fuehrungsfeld is not in ordinary space but in configuration-space so that it can describe statistical correlations and in particular, for instance, the Bothe-Geiger experiment is not a contradiction to it.
That’s a terribly nice point and it’s a way I had not thought about this before.
As you say, this is an important thing. Why is it now, suddenly, that the Ftihrungsfeld is good? The Fuehrungsfeld is suddenly good because it's not in ordinary space but in configuration space.
That’s very very interesting and it’s a new way of looking at that time.
It’s not new.
No, but I mean it’s new to me now; I have not heard it put this way before. At the time you were doing these papers, you say you were explicitly leaving out spin; now at this point, you still hoped that one might be able to do it without spin?
Well, I realized very soon that you can’t; the 2l + 1 and the fact that one had only l as a quantum number, and no j, showed it clearly, However, I did not know how to introduce spin.
It’s not clear from the papers how sure you were—. You have these first two papers [2a, 2b] and then a little while later you have the more general paper  from May, 1927, “Einige Folgerungen aus der Schroedingerschen Theorie fuer die Termstrukturen,” in which there is still no spin. This is the first paper in which the problem of the 2l + 1 and only getting odd Zeeman patterns becomes clear, and it’s not entirely clear whether you knew at the time you did this paper that if you could handle spin, that would give the answer.
I did not know. I knew that without spin you can’t, that the way it is you can’t get the experimentally correct answer, but I did not know how to introduce spin.
Were you pretty sure that spin was going to be the answer?
I think so, but I am not sure.
How closely at this point were you in touch with Pauli?
Not at all. Pauli’s article I read in the—
In the same issue of the Zeitschrift Fuer Physik?
Of course I had my own article much before that.
Yes, but in the beginning of your article on the Schroedinger equation you make the remark that if we are to introduce spin here we will have to have an additional variable in the Schroedinger equation.
Yes, that was my mistake. I thought it would be a continuous variable because I thought of the spin as pointing into a direction and I tried to think of an equation in terms of Θ and Φ, I mean, in terms of polar angles. And of course I got nowhere, exactly nowhere.
And you knew nothing of Pauli’s work at that time?
Nothing. When Pauli’s work came out I at once thought, “Now aren’t you stupid not to have thought this way.” But also my time was also considerably taken up with writing that paper, correcting—I was assistant to Becker—.
To whom were you assistant?
Richard Becker. He gave me very little work, but just the same
This was really the beginning of your publication except for the thesis and a few chemical papers earlier; you published quite a lot in that year and it’s difficult.
Well, it was difficult for me. I don’t know; that’s not an objective measure. But I did think about introducing the spin, I did think of it very much but not enough, and not well enough.
And as an additional variable in the Schroedinger equation?
Yes, and that of course I could easily see wouldn’t work, I discussed that with Johnny Neumann and he also said, “No, no, it can’t be done.” So Pauli’s paper was a real revelation.
Did you and von Neumann then go immediately to work on the extension to the spin terms as soon as the Pauli paper came out?
Yes. Incidentaily, I worked that out [papers 5, 8, 9] practically by myself. We published it together because I had a bad conscience about not having published the first two papers with Johnny. These two papers of three, I think, which I published with Johnny have of course no significance; it’s a routine matter.
After the first one.
Yes, but the first one, or at least the second one, I should have published with him.
No, when I said the three I was thinking of the three that you do together—that big paper, the series of three papers.
He had very little to do with that. That he understood it there is no need to say, but he did very little on it. I asked him to correct the proofs but he didn’t do it and sent it back as it was, which ended in a catastrophe because the first paper is full of misprints. But I had a bad conscience because I felt that I should have published the second paper on group theory with him.
How hard was it to get to the idea of a multi-valued representation?
When the Pauli paper was out I think Pauli even mentioned some of the different representations. It was not at all difficult.
I’m not sure.
I don’t know for sure either.
That whole way of treating it, which is immensely ingenious when one first sees it, of considering the rotation in which the spins are not rotated and then talking about that part of the rotation which is multi-valued, but pinning down the part that is not multi-valued as a way into it.
I worked hard on it, wrote it down, and so on, but I don’t think it took me much energy.
Had you basically done the first part of that before you went to Göttingen? It’s submitted when you’re already in Göttingen I think.
Yes, I think so; I think I probably wrote it in Göttingen and submitted it from there. I don’t remember. Do you know when it was submitted?
Actually it’s submitted later than I thought; it’s submitted on the 28th of December, 1927, this first of three with von Neumann, so that by that time you were surely in Göttingen.
I remember when I found the error. You know, there is an error in “Einige Folgerungen” that I found in the summer when my parents and I were taking a summer vacation somewhere, perhaps in Bad Gastein and it slowly dawned on me, “That can't be right, that formula.” Then I worked out the formula correctly.
Did it just come to you or had you been working on related problems, scribbling or something?
Probably I had worked on related problems.
Now your own paper must have initially come out late in the spring or early in the summer. It was submitted in early May.
When was it submitted?
The “Einige Folgerungen” is May, 1927.
Then it must have come out in August.
It would be as late as that?
I can’t understand this entirely because I remember that when Pauli’s paper came out I read it, I understood it quite readily, and I went to Johnny and told him now we could work out the rest of the theory. Johnny said yes, we could. He realized probably more clearly that we could, but I was more interested in doing it than he was and so I was the one who worked it out. I think we corresponded on that probably.
Do you think some of that correspondence still exists?
I could look.
It would be worth it.
You know how it is—one files away correspondence and one does not look at it. I don’t know; that may have been taken back to Hungary, but certainly it is worthwhile to look.
You told me of a letter from Paul Dirac that you thought you had.
And I did not give it to you.
You looked a little bit, I think, but you had not found it when we last talked. It is at some point going to be important to see what really is there from these years into the early ‘30’s or so. Those are not the last important years except for this project. You were in Berlin presumably for about a year as an assistant?
It was one or two years; I don’t know.
Yes, possibly even three semesters. I think perhaps not longer than that.
No, it was either one year or two years and not three semesters.
There would be no chance that you would come back from Budapest in the spring?
Yes, but that wouldn’t have been a semester because I would then have been working for Weissenberg. I don’t count that a semester.
You were there for a semester for Weissenberg and then perhaps two more.
But of course Weissenberg was not at the Technische Hochschule or anything, so that semesters did not play a role in that.
Then you were two semesters with Becker.
At least two semesters. Maybe more.You don’t think four?
Again we run into trouble because ‘27-’28 you were in Goettingen, or at least I think you were.
Yes, sure. I was in Goettingen a year, a whole year.
‘26— ‘27 would be the preceding year; if it were two years it would have started back in ‘25—’26 and then we have no time for Weissenberg or for the tannery. What took you to Goettingen?
Becker came to me and said: “I already know what you are going to do next year. Sommerfeld wrote to me and told me that you should become Hubert’s assistant while Nordheim is away in England.”
Sommerfeld knew of you through your papers?
Yes. He never read them. I believe he wrote to me later on that he never read them, but he took it upon himself to look out for me. I don’t think I was introduced to him except for a few minutes. He was somebody who had a deep sense of responsibility for young people, whether or not his students.
Do you want to talk about Goettingen tonight? Shall we stop now?
Whatever you wish. *** [Discuss engagements, necessity of writing Nobel address, etc.]
Why don’t we go on for a bit?
I came to Goettingen and for several weeks I didn’t even know anybody. As I said, I am not a person who goes and puts his nose into things, but I rented a room, of course, and I went to the auditorium where there was a mathematics library, sat around there and read journals and books and worked reasonably hard. Courant once came to me. He’s a wonderful person, but of course he was very busy and he told me, “Mr. Wigner, I have very much to talk to you about but right now I am very busy.” I never saw him, we never had a discussion,and I don’t think that he was interested in those things in which I was interested. But soon I met Jordan.
You were seeing Hubert, however?
Five times altogether.
Yes,he was not interested in physics.
In some of the earlier periods I think that he had given his physics assistants quite a lot to do.
I explained to him a number of times what was happening. Once I remember he said, “Oh, then one doesn’t have to learn any more of this theory” which was an obvious sign that he really did not want to learn it.
Which theory was that?
I forget it—some theory. I hardly saw him; he was not in good health anymore and surely he was not interested in physics. You know Hilbert is a towering person. I had a good deal of contact with Heitler. I don’t know whether you have come into close contact with Heitler.
I have not seen him myself. My colleague John Heilbron talked with him last year.
I think it was very stimulating to see Heitler and to be in contact with him and I saw him a good deal. I saw many other people in Goettingen, but with the big shots I had very little contact.
You saw very little of Born, for instance?
Very little. Born was very busy. Born instituted a seminar on group theory.
Immediately, while you were there?
Yes, and Heitler and I spoke mostly; he was quite interested and a little irritated that this new thing might have to be learned but he at least took the trouble of wanting to learn it.
The Heitler-London paper was already out at this point.
Yes, and everybody recognized that at once as one of the very important contributions—and so did I. Frankly I always thought that london, whom I knew from Berlin, had the greater share in it. I knew him as a very thoughtful, very industrious, thorough, imaginative person.
Had he been in Berlin when you were working on the group theory paper?
I think so.
So he may really have been started on that even before those came out?
Oh, yes. Later on he became interested in group theory and the papers he wrote in connection with that were very nice, but at that time I don’t think he was yet interested. Well, I worked along at a number of things then and several papers which I wrote were the direct outcome of that seminar, in particular, the paper on the conservation laws in quantum mechanics [No. 7], which has the parity conservation in it, which I thought was quite obvious. I did not consider that a discovery.
How was it received? Did anybody make a fuss about it at the time?
They were not interested. There was, first of all, a certain enmity to group theory; secondly, the parity—people did not know whether there was such a thing. Hund knew spectroscopy but Born didn’t know spectroscopy particularly well. Then I started to work on the molecular case with Witmer. Witmer is at the University of Pennsylvania now. It’s a very tragic thing because he never was promoted from Assistant Professor, but I did not know that until recently. Of course, at this stage of the game it’s not possible to do much about it.
He was involved in a number of things of some importance as a collaborator, at least during this period.
Yes. He is even more gauche than I was, and he is rigid in some ways. Well, we all have our faults. But that collaboration with him was very satisfactory. I remember there was a meeting at the end of that year that I was in Goettingen and Heisenberg and Pauli came. Pauli always was extremely derisive to almost everybody. Born and Oppenheimer wrote a paper which I consider very important on why the nuclear motion in molecules can be treated differently from the electronic motion. Pauli thought —well, “de mortuis nil nisi bene” —but anyway, the fact is that he thought he could irritate both Born and me at the same time by saying, “Well, even that paper had some good to it because it induced Wigner to work out the group theory of molecules; of course it isn’t very interesting.”
Did that paper have a real role? I know you refer to it and to some extent use it, but is that what started you on the molecular problem?
I don’t know. You see, up to that time I was not worried about molecules because I was working on atoms, and my interest in these, perhaps less fundamental, questions was reasonably confined. The Born-Oppenheimer paper showed how things are. It wasn’t that I had thought hard about that question and that then their paper was the revelation. I did not think about it, but when it came out I realized that now we could work out the spectroscopy of molecular spectra and that would be interesting because it did not then exist. One could see that we could work out something that would be new, so I decided to do that.
where did Witmer come into it?
I don’t know exactly. He was not a great group theorist. He was interested in molecular spectra, but really I could not tell you why we collaborated.
Do you think he may have come in because he knew more about molecular spectra and you about group theory?
That may be.
Was Hund involved with that paper? He was already at Leipzig, wasn’t he?
Yes. As you know, Hund wrote a reasonably similar paper; surprisingly enough even much of the notation is the same. Of course, if you try to think of a notation you naturally come to similar ideas, but the similarity really is very remarkable. I read some earlier papers of Hund; Hund’s ‘case a’ and ‘case b’ were familiar to me from his earlier papers, but that is a slightly different problem.
Toward the end of the year I started to work on two things: first, I wanted to work out the relativistic theory of the electron, and I did realize even at that time that it is a group problem. As a matter of fact I did work out the Dirac equation without interaction. I think I have a letter from Jordan on this because I discussed it with Jordan very much; then I worked with Jordan on the quantization of the exclusion principle, but that’s almost entirely his work.
Let me step back a little bit. I do want to hear you talk about how other people responded to group theory. A number of people say, “I didn’t learn it until I absolutely had to," and this was in the ‘30's for many of them. Did you find that people had great trouble reading your early papers?
Yes, but this had many reasons. First of all, I did not write well, and, for instance, I remember I wanted to say “the lambdas” and in the end it came out “lambda minus a”; such things happened. And then, you know, people don’t like new things. I remember how Schroedinger told me, “Oh, well, this may have been the first way to derive the root of spectroscopy, but surely nobody will do it this way in five years.” Becker was not this way; Becker supported me and Laue, surprisingly, supported me also, He did not learn it very well, but he supported me. Schroedinger not.
Einstein of course was not interested because this was a detail, but most people thought, “Oh, that’s a nuisance. Why should I learn group theory? It is not physical and has nothing to do with it.” People like to think of motions, which is not, in my opinion, and which even in that day was not, in my opinion, the right way to think about stationary states. Nothing moves, and this is what I think I digested much earlier than most people; in a stationary state nothing moves, but this is what they did not want to accept. They said, “Well, you see something going around,” when actually you don’t. For instance, my shells did not move, and it was evident to me that nothing moves.
That fits in also with the way you handle this non-interaction of states at the very beginning. I’m terribly interested in what you told me about Schroedinger’s reaction as against Laue’s and Becker’s, How did Pauli react to this work, do you know?
I don’t think he liked it particularly. There was a word, “Die Gruppenpest”, and you have to chase away the “Gruppenpest”. But Johnny Neumann, for instance, told me, “Oh these are old fogeys; in five years every student will learn group theory as a matter of course,” and essentially he was right.
Yes, including Pauli.
But you think the word “Gruppenpest” was Pauli’s? It’s like Pauli, Who else used that?
I think Schroedinger probably used it; I don’t really remember too well, But it was not popular, not popular at all. Even Becker occasionally blurted out, forgetting that he was a loyal supporter of his assistant!
Did Weyl’s book help? Weyl’s book was earlier than your own.
Both Johnny and I felt that that was a very unfair thing. Johnny knew what Weyl knew about the application of group theory. He, V. Neumann, said Weyl knew and saw clearly that the operators for Mx, My and Mz are the infinitesimal operators of the rotation group. But otherwise Weyl had, before the article which you mentioned, (“Einige Eigenschaften”), appeared, no knowledge of it, He says in his book that, “was implizit vorhanden war”; of course the whole mathematics is implicitly contained in the axioms. We both felt, I particularly—well, Johnny about equally—that it was, as Johnny said—he said it in Hungarian—”schwer inkorrekt”. You speak German?
Yes, Schwer inkorrekt.
But it’s in the past and it disappears in insignificance as do all these things.
Did it help make physicists acquainted with it?
No, As a matter of fact, it was awfully difficult to read, There are a few people who can read it; Bargnann can read it. I read some of it and I even found mistakes in it which, needless to say, made me very happy. It may have helped call attention to group theory because people realized that if a great mathematician, as Weyl unquestionably was, writes a book on a subject, then there must be something to it.
But basically your own book is the one that made the methods available to physicists you think?
That’s what most people say, but of course if they talk to me they won’t say, “Oh, I like Weyl‘s book much more.” Actually, though, there is somebody who told me that somebody else told him that he preferred Weyl’s book. The person who told him was Majorana; and the person to whom he said it, I thinks was Segre. Segre lightly told that to me, not by way of pointing out the characteristics of the two books but pointing out what a wonderful genius Majorana was.
Or what a strange turn of mind!
No, no. I think probably it is much more beautiful, but it certainly did not help me because I knew the contents at the time it came out.