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Interview of Walter Heitler by John L. Heilbron on 1963 March 18, Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA, www.aip.org/history-programs/niels-bohr-library/oral-histories/4662-1
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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 circa 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: Hans Albrecht Bethe, Patrick Maynard Stuart Blackett, K. Böhm, Niels Henrik David Bohr, Max Born, Georg Bredig, Louis de Broglie, Paul Adrien Maurice Dirac, Paul Ehrenfest, Albert Einstein, James Franck, Karl Ferdinand Herzfeld, Karlsruhe Technische Hochschule, Ralph de Laer Kronig, K. Loewner, Fritz London, G. Rumer, Erwin Schrödinger, Arnold Sommerfeld, Otto Stern, Gregor Wentzel, Hermann Weyl, Wilhelm Wien, Hideki Yukawa; Universität Berlin, University of Bristol, Copenhagen Conferences, Deutsche Physikalische Gesellschaft meeting (Freiburg), Universität Göttingen, Universität München, Zurich Eidgenössische Technische Hochschule, and Universität Zurich.
Well, how shall we do it?
Well, I shall proceed roughly according to this outline if that’s all right with you. We could begin perhaps by your telling us, if you would, how you first became interested in science.
Yes. Yes, I think I’ll tell you just my early scientific life and interests. Well, my interest in science awoke rather early, at the age of 10 or 12 or so. I don’t think it was stimulated by a special home atmosphere or by school. My father was a professor for engineering, and so the atmosphere at home was certainly not unfavorable, but it did not particularly stimulate interest in science. I was first interested in astronomy; at the age of 12 or so I made myself a telescope from an old camera lens and the objective of an old microscope. I was very happy then that I could see the ring of Saturn and so on. Well, later at the age of 14 or 15 I became interested in practically everything scientific — mathematics, physics and chemistry, even geology. I installed a chemical laboratory in the bathroom which was perhaps not always to the pleasure of my family, and so on. My school education was mainly classic, Latin and Greek. And for this I’m very grateful, in fact. Especially I derived a great deal of pleasure and interest from Greek — Greek philosophy, Greek poetry. Plato was my favorite philosopher, and perhaps he still is. The science, teaching in school was rather poor; my mathematics teacher was a kindly old man, but as I usually was far in advance of his lessons, I used the mathematics lessons for preparing the next Latin lesson or so, and he didn’t object. The physics teacher’s main concern was to be against Einstein and against relativity. Well, I was not on very good terms with him, or he was not with me, to put it more precisely, especially since he once discovered that I was reading a book by Einstein secretly under my desk.
What was his particular objection?
That I can’t really remember, but I know that he was an opponent of Einstein and the theory of relativity. Well, chemistry did not exist at all, nor biology; but I think it is a good thing that I had a broad classical education rather than a scientific education of which I would have enough later on. Philosophy was very good also. Later while I was still at school, I was privileged to attend a course of lectures by Professor Bredig; that was the first introduction I got to quantum theory. It was a sort of an evening course, and I received special permission to attend although I was not yet at the Technische Hochschule in Karlsruhe. Well, of course, he represented it from the point of view of physical chemistry, thermodynamics and statistics, which was also historically the origin of quantum theory. I believe that this course and the lectures I heard later on by Planck did in a way stimulate my interest in these subjects — statistics, and so on. They gave me the idea at first, that quantum theory was rather a subject of thermodynamics and statistics that it was at the border line between physics and chemistry. Well, when school came to an end I still didn’t quite know what to do. It was clear that I would go to the University and study something scientific, but I still oscillated between mathematics and chemistry. I didn’t really know that physics could be a career of its own. Then one day a friend of our family came from Munich — he had just finished his studies in Munich; he was a chemist—and I discussed the question with him. It was he who told me that what I really wanted was theoretical physics. There was a department of theoretical physics in Munich under Sommerfeld. Well, from that time on I was more or less settled to do physics. I think that should cover my time before the University.
I wonder if you can remember at all what Bredig had to say?
Well, I don’t remember very well, but I remember it was something about the structure of the atom and about Bohr’s model. Of course, the atom was introduced from the side of chemistry, which, of course, historically was also correct. And, I think, there was something about Planck’s idea of the quanta of light and this sort of thing. But I don’t really remember any details.
It wouldn’t have included what Sommerfeld had been doing, or anything so recent as that?
No, no, that did not come in at that time yet. I began at the Technische Hochschule in Karlsruhe, and I was inscribed as a student of chemistry. Physics as a subject of its own didn’t exist in Karlsruhe. Well, I stayed three semesters in Karlsruhe, and the lectures I mainly attended were those of Bredig and some mathematicians of which I want to mention especially Professor Boehm. He was really a very fine mathematician, and a very fine man, too. He had a very profound influence on me since it was he who taught me first how really to think, to think exactly and to think properly. There was a seminar by him which was attended by only perhaps two or three students, and this was really delightful. In fact this connection with Professor Boehm was to be a connection for life; later on we became close friends and remained so until he died, a few years ago near here on the other side of Lake Constance. There was also a seminar in Karlsruhe on the theory of knowledge in which I was greatly interested. It was more philosophical; all together I had great philosophical interests at that time, and later on, too, of course. And, as you asked before, my interest in science was always a desire for knowledge only, and it was never an interest in the practical side of science.
Of what did that seminar with Boehm consist?
Theory of Knowledge? Well, that was the philosophy of science, more or less, how to get a knowledge of nature through scientific research. I don’t remember in detail which philosophers were discussed. Kant was certainly one of them. Well, the other names you mentioned here were not really very interesting for me. Gaede was the physicist, but he was interested in vacuum pumps, and that did not interest me very much. You mentioned Professor Heun, and perhaps I may say a word about him. He was retired at that time, but nevertheless I knew him very well because he happened to live at the same house with us. I frequently talked to him, and he encouraged me in my scientific, career. Also he would put in now and then a nice word to my father, who was, at the beginning, of course, a bit skeptical about my scientific intentions.
That you couldn’t make a living out of it?
Yes, it was more or less that. Well, and it’s true, of course that at that time science was not a subject with which it was easy to make a living. That is perfectly true, and especially physics was not a very good subject. There were very, very few physicists at that time employed in industry, and the only possibility would be to become a school teacher. I was always clear for myself that what I wanted was the University career, but that was in Germany at that time notoriously difficult, especially if you had no financial resources, or not a great many financial resources. Well, I think that covers Karlsruhe.
You were still in chemistry all this time though?
I was officially in chemistry, but students were very free; you could go to any lectures you liked. I did, of course, attend the lectures by Bredig and some chemical laboratory, but you were not obliged to take this or that subject; you could do what you wanted, as long as you passed your examinations later on. Well, is there any more about Karlsruhe you would like, to know?
At that time, if I remember, Schur, who worked on group theory, was at Karlsruhe for some time.
That was Berlin.
He was at Berlin.
Schur was in Berlin. Well, you asked, “Was there any feeling that Karlsruhe was past its prime? Probably you mean the glorious time when Heinrich Hertz was at Karlsruhe. Well, surely it wasn’t like that anymore, but still it was good, and especially in chemistry. Bredig was regarded as an outstanding physical chemist. Mathematics was not too bad either, although I believe Boehm must have felt a bit out of place there. He was not a bit interested in the practical side of mathematics, but that, of course, was what he had to teach at the Technische Hochschule.
What was the seminar in which he influenced you so much? What was the subject?
I remember that was on the Poisson equation, Gauss and, the Poisson equation. We read some papers of Gauss, old papers by Gauss, and studied them very carefully.
Were you able to pursue your philosophical, interests in Karlsruhe?
And then you decided to go to Berlin?
I decided to go to Berlin, and I could persuade my father that it was the right thing to do. Especially I wanted to see and hear these great men in Berlin; Einstein, Planck, von Laue, von Mises, Nernst, Haber and Schur I met there, and a few others. Well, at Berlin it was a bit of a shock to me because I found that I didn’t know much, that here what I learned in Karlsruhe was not nearly good enough, especially in mathematics. I felt a bit lost with all these highbrow mathematicians there using what one called the “epsilontics” — you know that? — a great deal. But very soon I got into it. On the whole I can say that the professors were rather remote from the students, but remember I was still in my second year when I came to Berlin, and they were rather unapproachable. But still I had a few words with Planck and Einstein now and then. I remember a very impressive colloquium in which Einstein took part, and there was one remark which I think you would be interested in. It brought home to me the difficulty of quantum theory. I don’t remember in what connection the remark was made, but Einstein said, “Already in l905” — that was the date when he wrote his famous paper on the photoelectric effect and the light quanta –- “I realized what a” — I must use the German expression –- “Schweinerei the quantum theory was.” So it is true that already in Berlin, and also in Karlsruhe, I was perfectly aware of the fact that profound difficulties existed in quantum theory.
Was there much being done in Berlin? Was there much interest in the difficulties?
Oh, yes. Well, a few years later Einstein wrote his famous paper on Bose’s statistics. Von Laue was perhaps more interested in relativity and x-rays, but still there was a general atmosphere of excitement and of impending new discoveries; so much I can say. Of course I was not advanced enough to appreciate all the difficulties and to appreciate the progress that was made.
How long were you there?
I was there one year, two semesters, Well, I heard Planck’s lectures, and that was one of the few lecture courses which I really attended from beginning to end. And I was lucky; Planck lectured on thermodynamics and then on statistics and radiation theory, which were the subjects where he was at his best—I mean that was his own subject. Von Laue didn’t lecture; then there were lectures by von Mises on applied mathematics, vector calculus and so on, which were excellent lectures. Then there were the mathematicians Schur and Lowner; I attended some lectures there. With Lowner I had a special connection because he is a very distant relative of mine; that was also one of the reasons why I went to Berlin.
And you were exposed to group theory at that time?
Yes, but I wasn’t particularly interested. I heard the lectures more or less as a matter of duty, but it didn’t seem that it had anything to do with physics. The point of view which was, later on, reversed by 180 degrees. Well, then the reason why I went to Munich was this: in Berlin there would have been little chance that I could get help with a Ph.D. thesis. The attitude of the professors was more or less this: “All right, if you have an idea, work it out and write a thesis; we will either accept it, or we’ll refuse it.” But you could get no help from the professors; nor could you get a suggestion for a subject. Well, I didn’t feel that I was such a great man that I could afford to embark on this line.
Were there many people who were brave enough?
Very, very few were lucky. I don’t know anyone who did. And especially my financial resources were not too great; I had to finish within a certain period of time, and so I thought it would be better to go to Munich where you could just ask for a subject for a Ph.D., get a subject, and you could get also help. It was very well known in Berlin that Munich was the place if you wanted to get your Ph.D.
What was the reputation of Gottingen in that respect?
Rather similar, but somehow I preferred Munich because of its natural beauty. I was keen on mountaineering and skiing, and Munich was the place for it. That was the reason why I went to Munich and not to Gottingen.
And by this time you had decided to go into quantum physics, or at least into physics?
Yes, physics; theoretical physics. That was decided by that time, and I told my father I could always become a school teacher if nothing else. Well, so I went to Munich; and with the influence from Professor Bredig in Karlsruhe and Planck in Berlin, my chief line of interest was statistics and thermodynamics, a sort of border line between physics and chemistry. So it was quite natural that for the Ph.D. thesis I attached myself to Herzfeld rather than to Sommerfeld, but I was in Sommerfeld’s department and accepted as a research student.
Did you participate in the seminars?
Of course, yes, in all the seminars. I heard Sommerfeld’s lectures, of course, they were excellent lectures, mainly on what one calls now applied mathematics, that is differential equations in physics, and so on. Also, Wentzel gave very interesting lectures. He lectured on fluctuations, those statistical fluctuations, which, of course, again strengthened my early interest in these subjects. Now, I studied about one year, and then asked Herzfeld to give me a thesis. All together I stayed two years in Munich.
Was that a remarkably short time?
Well, it was rather short, but not perhaps excessively short. Physics was much easier at that time than it is now. The standard university course in physics ended with classical theory, Maxwell’s theory; that was the end. Quantum theory was not included in the general course, except in Berlin where Planck lectured on it. But only on the theory of radiation. Well, then you asked a question which I like to answer: “It has been said that in Wien’s Institute most students were Nazi sympathizers.” That may very well be true; it is certain that Wien was a Nazi. There was a great tension between Wien and Sommerfeld; in the colloquia they both sat on the front bench, but at opposite ends.
Were there arguments between them?
Not before the students. And it was well-known that Sommerfeld’s students usually did badly in Wien’s examinations. He was I think quite anti-Semitic. This was true enough in my own case, and my own examination was quite unfair really, but still I passed it, so really it wasn’t —.
What particular incidents were there?
Well, he hurried down some questions, and when I answered, he at once had the next question ready. I really answered all the questions, but he gave the appearance of crossness and unsatisfaction every time, and he made the candidate just simply nervous. You couldn’t give a quiet answer without his interrupting and so on. Then he asked me a question, “How do you measure that?” I answered him, and [he said] “Yes, but there is another method; I want to know the other method.” And I didn’t know that, and so on; but I passed it and it’s not worthwhile talking about.
I wanted to ask then more or less the same question about the other schools you attended, whether there was any difficulty at Berlin or Karlsruhe.
Not in Karlsruhe and in Berlin I didn’t feel it. I didn’t feel it, but there may have been such difficulties. In Karlsruhe the difficulties came later on; and, in fact, Professor Boehm, whom I mentioned, resigned shortly after the Nazis came to power, and retired. He retired to a little place in south Germany. But when I was in the University both in Karlsruhe and in Berlin, there was nothing to be felt yet, nothing openly to be felt yet. But after all Bredig was a Jew, or half-Jew, and also Einstein, Schur, Mises, Haber, and so on. But then Sommerfeld’s department was entirely free from that; I must say that Sommerfeld was an exceedingly decent man for whom I had the highest admiration. Now shall we go into physics? You asked a number of questions about physics, and then I’ll tell you later on about my own work. Well, when I first came to Munich, that was in 1924, of course I had not really an overall view of the situation. And not all the discussions were just on the level at which I could understand everything. But I can tell you the following. In Sommerfeld’s department the emphasis was, as you know, about atomic models and atomic theory, and the classification of spectra and so on. One of the great discoveries — or what was hailed as a great discovery — was the exact formula for the multiplet spectra — spectral intensities — which were discovered and then the classification of the iron spectrum and so on. So, such models as Heisenberg’s Rumpf model that was the sort of thing that was discussed. The theory of Bohr, Kramers and Slater was mentioned, but nobody, I think, took it very seriously in Munich.
About the spectroscopic models, that there was interest in them we know; but what we’re curious about is whether or not they were taken as literally as they would seem to be in the published record?
No. Certainly, not as literally true. It was quite clear, also in Munich, that what was wanted was a new mechanics to account for atomic phenomena; and that mechanics was not there yet. But the hope was that by studying atoms — studying spectra, studying intensities and so on — you could gradually get nearer to it. That was simply the idea; nobody thought that any such model would be final.
What was understood by ‘a new mechanics,’ or the hope for a new mechanics? Was there any indication at all?
That the mechanical laws had to be changed and that they are different in an atom from what they are for macroscopic bodies.
Was there any vague notion of how it was to be done?
No. Well, later on we shall see there was; but there was, at any rate in Munich, no notion of how it was to be done. We shall discuss a few attempts later on. Then you ask about the Correspondence Principle. Well, of course, everybody knew about it, but it was taken — and I remember that I personally took it — as a principle which stated that the new mechanics, which was not known yet, would be such that it contained classical mechanics as a limiting case. That at a certain limit it would go over into classical theory. But it was not the idea that the Correspondence Principle would be useful in establishing the new mechanics, so the interest in the Correspondence Principle was not nearly as great as I believe it was in Copenhagen, or perhaps in Gottingen; I don’t know. I didn’t know anything about the state of mind of people in Gottingen at that time.
It’s a little bit peculiar that Sommerfeld occasionally says that the requirements of the Correspondence Principle seem to be in fact contradicted in atomic physics. From what he says it’s not clear that one should expect that one would even have the classical physics contained in the new mechanics.
Well, I don’t remember any such remarks by Sommerfeld; it’s possible, but I don’t remember them. But if I look back now in my own memory, the idea was, or at least my idea at that time was, “All right, there will be something very, very new to come; but somehow there must be a connection with classical theory; and that we’ll discover by the Correspondence Principle.”
And that was its entire content then for —
That would be its essential content, yes, and not much more. Well, as you ask, I was perfectly aware of the great difficulties in contemporary physics; and, in fact, I did not expect these difficulties to be solved so soon as was in fact the case. My teachers did represent the difficulties as fundamental, always, in Karlsruhe, in Berlin, and in Munich.
And then what was thought of the Gottingen program, once it came out? The Heisenberg paper and the papers of Born and Jordan …?
Well, that was toward the end of my study in Munich. Now I must mention one thing. These papers, Heisenberg’s paper as well as Schrödinger’s papers soon afterwards, appeared just at the time when I was preparing for my Ph.D. examination — very unfortunate. This was one of the factors which really delayed my entry into theoretical physics. The papers were read with great excitement in Munich, and there was a great deal of discussion. I’ll tell you also in a moment about de Broglie’s paper; that, too, was discussed a very great deal. And all this was a great excitement, but I personally had to postpone the thorough study of this for a few months, half a year, simply, I had to do my Ph.D. There was another delay through another reason; I’m coming to that. But I would like to tell you about de Broglie’s paper a little later in connection with my own work. I’ll put the question aside until a little later. You asked, also about the Pauli principle. Well, I can’t share your impression that little attention was paid to the Pauli principle until after wave mechanics. When it appeared, it was considered as correct because it explained the periodic system of elements, and the time interval between Pauli’ s paper and wave mechanics was rather short.
It was about a year.
Was it? I thought Schrodinger’s paper —
‘25 and ‘26. Pauli was early ‘25 and Schrodinger was the beginning of ‘26.
In late ‘25; we had proofs, manuscript in Zurich. Well, at least in my memory it was about the same time, or at least at short intervals. Yes, it was also clear that Pauli’s exclusion principle was a new discovery connected with a new mechanics, which was not known yet at the time.
And what about the spin? That came at the end of ‘25.
The spin came at the end of ‘25, and perhaps we’ll also discuss that a little later.
You did mention, and perhaps it’s appropriate here, that the Heisenberg and the Born, Heisenberg and Jordan papers were much discussed at Munich. Although you said you couldn’t get involved, I wonder if you could elaborate a bit on that statement. For instance, we have the impression that the Schrodinger papers were received much differently than the Gottingen ones.
Yes. In Munich I think the Schrodinger papers were received better because first of all they were so clear; secondly, they were so understandable; and thirdly, they had to do with differential equations which was Sommerfeld’s favorite subject. Sommerfeld could understand them at first go, whereas Heisenberg, Born and Jordan were using mathematical methods of a more abstract kind which perhaps were not quite so much to the liking of Sommerfeld. But I may be quite wrong; I mean they may have been discussed and read eagerly.
Did anyone try to apply it?
Not as far as I know in Munich; not at the time when I was there. It was all very new; people were studying it; and, of course, it took some time before you could learn it. Sommerfeld was always rather slow himself; I’m coming to that point later on again. I started preparing for my Ph.D. in the spring, at Easter, 1926; and then Schrodinger’s papers came in. I only had a few more months in Munich before I had to finish, you see, so I can’t give you a very accurate account of how this work was received in Munich.
Well, shall we proceed then to your work?
How did you like the suggestion that Herzfeld made for your thesis topic?
I was rather, pleased, but this was not the first piece of work I did. The thesis was the last of my Munich papers. I wrote these two papers on statistics, Numbers 2 and 3 [on your outline bibliography], before I started on my thesis. So shall we take them in historical order? You realize that I was interested in radiation problems all that time; and especially I was very much interested in Bose’s paper, in Bose’s statistics, when it came out. I was asked to give a seminar about it, two seminars in fact, on Bose’s paper and on the Einstein papers on Bose’s statistics. There was a great deal of discussion about it. Sommerfeld was not usually very fond of statistics, but still he was very interested — Herzfeld, too, Wentzel also — and, well, it was discussed. At the end of Einstein’s paper, you know, there is this remark about de Broglie’s thesis. Well, as a consequence of this seminar talk I gave in Munich, de Broglie’s thesis was read; it was not easy to get because the relations between Germany and France were not so very good yet — there were still after-war effects. Still we got it, and everybody read de Broglie’s thesis. Nobody took it very seriously because it was so simple to make objections.
What kind of objections were made?
Well, I don’t remember all the objections, but I remember an objection I made myself in a discussion with Sommerfeld and Herzfeld. The objection was this: de Broglie attributes a frequency to each body proportional to its whole internal energy, that is to say, to its whole mass. Now take a macroscopic crystal; you have a certain frequency attached to it which is proportional to its mass, divide it in two, and the frequency would be half. Now this de Broglie frequency was thought to be something thoroughly atomic, something belonging to atomic physics, and not belonging to macroscopic bodies, and both Sommerfeld and Herzfeld agreed with my objection and thought it was ridiculous. But as far as I know, and that is the impression I gained in Munich, there was really nobody, no physicist in Germany or elsewhere, who took de Broglie’s thesis seriously — not even in Gottingen. That was what I heard; whether it’s true or not I don’t know — except by one man and that was Schrodinger.
Had you seen that note of Elsasser?
That was later; that was a bit later.
At the end of l925.
Was it? Yes, perhaps; perhaps you are right; I hadn’t thought of it. Well, then Einstein certainly took it a bit seriously.
His enthusiasm wasn’t contagious though.
Yes, quite. Well, paper Number 2, which you mentioned, was sent to Einstein and he was very pleased with it, though, of course, it probably was rather trivial if you look at it from our present point of view. So I proceeded on with this statistical work towards Paper Number , which was rather unfortunate. Well, I think the statistical part was perhaps all right, but not the part on the intensities of spectral lines, which was pure nonsense. This was pure nonsense; apparently neither Herzfeld nor Sommerfeld, who both saw the paper, saw that this was nonsense, for they permitted me to publish it. But the nonsense soon, of course, became apparent, and as a consequence, I fell a bit into disgrace with Sommerfeld. At that time the standard of publication was rather higher than it is now, and a paper which contained really out-right mistake, or which was altogether wrong was a minor disaster for the author. Well, at any rate, Sommerfeld did take it seriously and this had consequences. Perhaps I’ll mention this now; it had the consequence that later on when I got this Rockefeller Fellowship from the International Education Board, Sommerfeld thought it would be better if I stuck to the subject of my thesis, which was somewhat between physics and chemistry. He sent me to Bjerrum in Copenhagen — physical chemistry. I was not in Bohr’s institute, and this delayed again my entry into theoretical physics proper. I was really delayed by about one year. You see first I had this preparation for the Ph.D.; I had to do it properly because of Wien. If I hadn’t done it properly, Wien certainly would have [prevented] my promotion. This delayed everything further. Well, I’ll come into this then when we go to the other work.
What did Sommerfeld feel was his own share of the blame in this?
Well, he didn’t say anything about it, but that was then perfectly honest; he simply thought that I would be better placed in a department where I could do the same sort of work as I did with my thesis. This was more the line of physical chemistry and physics, statistics and so on, but not theoretical physics proper.
What did you consider at the time that the most important contribution of that paper was?
Well, it isn’t important at all, but I have looked at it now again. It may be that the purely statistical part is all right, that you can represent it — well perhaps; it could be made all right. But at any rate it’s old.
No, I mean what did you consider at the time was the most important part of it; did you consider that its most important part was contributing to the question of the spectral intensities?
No, no, I thought the statistical part was the more important.
The other part was just tacked on at the end?
Yes, it was tacked on at the end. Of course I was happy to be able to do it; or I believed I could do something that would interest Sommerfeld — he was interested in the intensities of spectral lines. And he was interested at first.
You mentioned before that it was Honl who had done most of the work on the intensity, the Sum Rules, although the paper is signed Sommerfeld and Honl.
Yes. Well, I think Hön1 did a great deal of work on it, but he will tell you.
What was the policy of publishing? When did one publish with Sommerfeld, and when did one publish alone?
Well, Sommerfeld decided that, I think. In general he was very generous; he allowed people to publish alone, but in this case I think he joined because he had really some part in it. I don’t quite know how it was, but you can see the policy in connection with my thesis. Herzfeld stated the problem; I asked him for a problem and he gave it to me. I worked it out, and he gave me advice. The result was that we published a short paper together on this, the liquids. We published the short paper together, and afterwards I wrote the thesis alone, a detailed paper. That was the sort of thing that was quite usual. Well, this thesis was regarded generally as good. I remember that O. Stern remarked favorably about it to Herzfeld, at least [regarding] the part on the mixability of fluids; the other part I think is uninteresting. And so Sommerfeld thought I would best continue on that line.
May we come back for one moment to the paper that I have called Number 2, about your first work on the statistics. You quote a paper of Lande’s about the light quanta and coherence; I wonder what sort of impression that paper of Lande’s had made, the attempt to understand the Bose statistics physically?
Yes. Well, it was, I think, regarded: as just one attempt to understand things better, but certainly not as final.
You’re the only one I have ever seen even mention that paper of Lande’s, which I have found to be a rather interesting paper.
Yes. Well, I don’t think it was regarded as a very great discovery.
Oh, no, but t meant rather how hard people were striving to obtain some sort of physical idea of the Bose statistics.
That was one example of many; there were papers by Herzfeld, too. There were many attempts somehow to (name) things and to put them together, but I think it was always clear that they wouldn’t lead to, the final solution. Well, then you have asked also about the Compton effect, and how one regarded the Compton effect. I think there were several ways of looking at it, and I think it was clear to me at least that since Einstein’s paper of 1905, one could regard the Compton effect simply as the absorption of one photon and the emission of another. This is an interpretation which I rather liked, and I adopted it in preference to come of the considerations Schrodinger later on put forward. Altogether my liking was more for particles rather than waves, for particles and discrete things rather than continuous things like waves.
Well, you must have liked this paper by Herzfeld then, his particle treatment of the dispersion problem
That’s another paper that one doesn’t see mentioned very often.
Yes. Well, I looked at it again recently, a few days ago, and I thought it was putting the situation that prevailed at the time rather well. I mean you have to connect something like phases to a light quantum; you couldn’t help it.
Was the wave and particle problem much discussed at Munich?
Well, yes. I mean, of course, it was the fundamental problem. I mean there wasn’t any need for discussion; the problem was there all the time and in the mind of everybody all the time. Only when somebody made a fresh contribution was it discussed.
It was felt that the thing to do was to introduce, as Herzfeld does, the phases into the particles or as Bohr was more inclined to do, to introduce the particulate properties into the waves? In short, were the particles —?
Well, I think they were both regarded as being on the same footing. There was no quarrel over what one should prefer — the waves or the particles, but the problem was how to combine both. Well, there is a question on the Correspondence Principle; I think I have already answered it.
Yes. In that paper though, you do suggest that one might try experiments to distinguish, or at least to decide, whether your approach was correct. Did you have any experiments in mind?
I don’t remember what I had in mind. Probably it was experiments on spectral lines, and so on, on intensities. But I had nothing special in mind. Well, perhaps I had something particular in mind, but I certainly don’t remember it. Well, I think that covers Munich.
Well, you have already explained that you didn’t go to Copenhagen to see Bohr? When you were there, did you —?
Yes, I did. So I went to Copenhagen, and Sommerfeld arranged it. He arranged for me to go to Bjerrum, who suggested a problem to me somewhat on similar lines to my thesis, and, well, I had to work on it. But, of course I frequently went to Bohr’s institute, and I was quite welcome there, but more or less only as a guest and not as a member of the institute. It wasn’t a very happy time because of that. You see, I wanted —. I mean what I really would have liked to do was to change to Bohr, but I couldn’t very well do this. Bjerrum was an awfully nice man, and he helped me a great deal, so I couldn’t possible say I would leave him and go to Bohr’s institute. Still I had some discussions with people there — with Bohr, of course, and Heisenberg, who was there for a time, and especially with Klein. There was one paper which I started there in addition to this paper on physical chemistry; that is the Paper Number 4 [on the outline], “Freie Weglange und Quantelung der Molekultranslation” [Zs. f. Phys. 46, (1927)]. I want to tell you the story of this paper later on. Well, as I said, I wasn’t too happy about the situation and the work which I did with Bjerrum—it was never published. I don’t know if it was worth anything; at any rate it was never published.
How long did you work with him?
Well, I stayed half a year, and well, I must have worked with him perhaps three or four months. I don’t even remember the subject; it was something about ionic solutions; that’s all I remember. Well, probably not much did come out of it. At any rate I didn’t publish it. Well, then to change the situation I wrote to Schrodinger and asked him if he would accept me for the second half of the Rockefeller time, and he reluctantly did agree, and I went to Zurich to work with Schrödinger. Well, then, of course, in Zurich I met London, which was to be a decisive turning point in my career. I must say that I did not get much response in Copenhagen or much favorable response. Klein was interested about the Paper Number 4; perhaps it wasn’t entirely clear yet, and perhaps people were interested in other things. But then I received a great deal of interest later on in Gottingen with that paper. Well, I’ll tell you that a little later. I may tell you now perhaps what it is about — no, it has to come later; I’m sorry. Well, then during that time I acquainted myself thoroughly with Schrodinger’s papers; not so much with the Gottingen papers yet. As I was to go to Zurich to work with Schrodinger, the Schrodinger papers had to be studied first, and I think I can say that by that time at least I had understood Schrodinger very well.
Did you have to have some sort of program when you wrote to Schrodinger? Did you suggest something?
No, no. There was no program at all. And, in fact, in Zurich it was like this; Schrodinger was interested in everything we told him, but again there was no idea that he should help us; we had no help from him. He was interested in his own problems; we discussed things together; we frequently had a seminar, of course. There was a seminar, and we frequently went with him on excursions in the countryside, practically every Sunday. These usually ended up in a country park with a great deal of wine; Schrödinger was very fond of wine. But we were left entirely free for our work, both London and I, and we worked together without any help from anybody.
So these are mainly “pro forma” acknowledgements at the end of the papers?
Rather, yes. Well, then we come to the Zurich period.
However, anything you could tell us to help us understand the development of the interpretation question would be much appreciated.
Well, I must answer this question from my own point of view. In Copenhagen I had no clear view about it, and I don’t think the question —. When did Born’s paper on the statistical interpretation come out?
Yes. You see, that was later, so this question was not yet in the foreground in Copenhagen. As far as I can remember, I have the feeling that people there were not at all clear about it. The statistical interpretation was not found yet. Of course, the papers by Schrodinger were also studied in Copenhagen, and the connection with the Gottingen version must have been discussed, but I think things were at that time not very clear yet. I would like to discuss the problem of interpretation later on from the Zurich angle. I’m coming to that then. But at any rate in my memory there is nothing clear about the fundamental aspects of quantum mechanics from this period in Copenhagen. It may be my fault; it may be that I didn’t understand it yet, but at any rate there is nothing clear in my memory dating from this period. There is a great deal clear from later periods, but not then. I may say perhaps this: when I came to Zurich both London and I were very enthusiastic about Schrodinger’s papers; everybody was. And it was only at a later stage. I mean towards the end of our time together in Zurich, that we discussed the probability interpretation and altogether the problem of interpretation. Perhaps we were wrapped up too much in wave mechanics; our purpose was to understand it better, to apply it, and to see about exploring the full contents of wave mechanics. We did not worry very much about the probability interpretation until the very end; that is to say, until we had finished our paper on the hydrogen molecule.
Which would be about the time that was preparing the drafts for the Solvay Congress, I should think.
Yes, yes. Well, later on, of course, when I did become acquainted with the problem as well as with Born’s papers on collisions where ha first stated the probability interpretation, I became convinced at once that this was the correct interpretation. And I disagreed with Schrodinger when he objected to it. That was quite clear, so towards the end of my Zurich time and at the beginning of my Gottingen time the question of the interpretation was perfectly clear to me, and to London, too.
To London also?
To London as well, yes, quite so. But it was only when I came to Gottingen that I really studied thoroughly the matrix mechanics; well, I simply didn’t know enough of the mathematical tools which were required for it. The mathematics was simply beyond me and especially the later work on the transformation theory by Dirac and by Jordan I only studied in Gottingen. That was really then the final point in the understanding of quantum mechanics; and this convinced me then at once; there was no hesitation about that.
Were there discussions with Schrodinger? Did you try to convince him?
No, we didn’t think that the discussions would have been very appropriate. We avoided discussions on hot subjects with Schrodinger; we were youngsters and Schrodinger was the great man, so even if we didn’t believe him we avoided [telling him so].
Would he accept such a discussion, if you had been interested in precipitating it?
Oh, yes; oh, yes. But then it would have been easy for him to talk us out of it.
I had asked about the attempts to introduce the spin into the formalism, and had wondered whether or not you could recall other attempts before Pauli’s — there was some work of Darwin — but I wonder if you recall discussions of attempts to work in the spin
We did discuss Pauli’s paper when it appeared, and we discussed the problem a great deal before that time. You see, with our work, which I’m going to describe later on, on the hydrogen molecule — the chemical bond — we did come across the problem of spin, and we did come across the problem of the Pauli principle. We did discuss it a great deal; we were aware of the fact that the spin was the problem which we couldn’t solve, that it was just attached to the wave equation of Schrodinger or superimposed on it, but there was no natural amalgamation between wave mechanics and the spin. We worried a great deal about it. We worried a great deal about it, but we were unable to solve it. When Pauli’s paper then did appear, and it did appear during the time we were in Zurich, we of course greatly appreciated it; but we still did not think it was final because we felt it was also a sort of hybrid between a wave equation and some matrix mechanics superimposed on it. It was, so to speak, glued together, but not naturally combined together; we did not think that this was final. Well, I suppose the reason why we could not think on similar lines as Pauli in fact did, was that we were both insufficiently acquainted with matrix mechanics and with the technique of matrix mechanics. It would never have occurred to us that you could combine the wave equation of Schrodinger with some matrix mechanical ideas; it would have been too far from our minds.
I think we were probably about to talk about the history of this Paper Number 4. [“Freie Weglange und Quantelung der Molekultransation”]
Yes. Well, this Paper Number 4 had quite a different origin from what it appears to have. In the old quantum theory there was a certain problem which I think so people at least considered to be a profound difficulty. Namely, in the old quantum theory periodic motions are quantized, whereas a periodic motions aren’t quantized. Now you can easily construct examples which are something between periodic and non-periodic motions, and one example which I had heard about was given by Ehrenfest. It was the following: consider a rotator — that’s periodic motion. Now, say after 20 rotations the sense of direction is changed, and so on, again and again. Or perhaps at random intervals the sense of rotation is changed. Now this is not strictly speaking periodic motion, and it is not strictly a periodic and so you do not know whether it is quantized or not. Now, this problem was on my mind for quite a time. I always knew about the difficulty; and the motion, as Herzfeld brought home to me, of a molecule in a gas, has some similarity with this. Especially in a dense gas it is more or less periodic, but not quite. Now when Schrödinger’s papers on wave mechanics appeared, I was very much interested in whether this problem could be solved now in wave mechanics. Well, in fact it could; and that is the origin of this paper; that is the reason why I wrote this paper. I started it, as I said, in Copenhagen, continued a bit in Zurich when I was not occupied otherwise, and finished it in Gottingen. And in Gottingen, Hilbert very much agreed with it and thought it was very nice; I gave a colloquium talk about it. You asked when I acquired the necessary mathematics; well, that’s simple. With Schrodinger’s papers it was imperative that I should get acquainted with the mathematical tools essentially as they are so very nicely put down in the book of Courant and Hilbert, and of course I read that book. That contained all I needed for this paper also.
Where did this problem of Ehrenfest’s appear? Did he ever publish anything on that?
That I do not know, but I heard about it, and it was somehow described as weak quantization — the problem of weak-quantization. Well, I showed in this paper that there was no difficulty anymore in wave mechanics or quantum mechanics.
At the end of that paper you mention that you could go further working out the equation of state and so forth.
Yes, but I did not have the intention to go into the theory of conductivity; and I only mentioned that it would be useful there — whether I gave the reason or not I don’t know. Well, London used it later on for his theory of liquid helium.
But you had no intention of getting back into that?
No, I had no intention to — with the fundamental problem now cleared up I had no intention to go further. Well, then you ask questions about quantum electrodynamics and the Klein-Gordon equation and so on. I think I can answer this very briefly. Well, quantum electrodynamics was not really much discussed in Zurich at that time. It was not until I came to Gottingen that I read the papers by Heisenberg and Jordan and Klein and so on. Well, the question will later be repeated in connection with Gottingen, and then perhaps I’ll say a little more about it. At any rate it was not dominant in Zurich; neither was the relativistic wave equation very much in the foreground. The Klein-Gordon equation, of course, was discussed; the main objection to it was that the charge density was not positive; and so it was not really considered correct. The problem was left until later on — quite unjustly so, of course, because the Klein-Gordon equation is really correct for particles with zero spin. Well, I think we have come to Paper Number 5, or is there anything before?
Let us go to this famous paper.
Well, I think the best would be if I would describe for you, as well as I can remember, the history of it. The other original intention — London’s and mine — was not as ambitious as that. We thought just as small ‘by the way’ problem to consider the question of the van der Waals’ forces, and we thought this would be answered by calculating just the interaction of the charges of two atoms. So we set out to calculate the interaction of two hydrogen atoms and their charge densities without thinking even of the exchange. Well, the result was not very encouraging; we got what we later on called the ‘Coulomb integral’, which was much too big for the van der Waals’ forces, although it gave some attraction. So we were really stuck, and stuck for quite a while; we didn’t know what it meant and didn’t know what to do with it. Heisenberg’s paper on the exchange had appeared, but somehow the exchange was there mixed up with resonance — with the resonance of two electrons in the same atom, one excited, one in the ground state. And. Heisenberg himself represented it in such a way that the two things seemed inseparable, so we did not think that the exchange played a role. But still we couldn’t go on and for a few weeks we had to believe it, although we frequently discussed it. Then one day there was a very disagreeable day in Zurich; I don’t know if you know what is meant by the Fohn. It’s a particular weather situation which is most disagreeable; it’s coming on now I think. It’s a very hot south wind, and it takes people different ways.
Some are very cross — my landlady was very cross then — and some people just fall asleep. I belong to the latter category; and I slept till very late in the morning, found I couldn’t do any work at all, had a quick lunch, went to sleep again in the afternoon, and slept until five o’clock. When I woke up at five o’clock I had clearly — I still remember it as if it were yesterday — the picture before me of the two wave functions of two hydrogen molecules joined together with a plus and minus and with the exchange in it. So I was very excited, and I got up and thought it out. As soon as I was clear that the exchange did play a role, I called London up; and he came to me as quickly as possible. Meanwhile I had already started developing a sort of perturbation theory. We worked together then until rather late at night, and then by that time most of the paper was clear. That is to say, we knew how to treat it; we knew that —. Well, I’m not quite sure if we knew it the same evening, but at least it was not later than the following day that we knew we had the formation of the hydrogen molecule in our hands and we also knew that there was a second mode of interaction which meant repulsion between two hydrogen atoms — also new at the time — new to the chemists, too.
Well, the rest was then rather quick work and very easy, except, of course, that we had to struggle with the proper formulation of the Pauli principle, which was not at that time available, and also the connection with the spin. We had a little trouble with the evaluation of one integral; we were not very good mathematicians really; and one integral led to the integral sign or integral number or whatever it’s called; and, well, we had some trouble with that. But that wasn’t very serious and essentially the paper was finished in that one evening and the short time that followed. Now you ask whether we interpreted the (Ψ) function as charge density. Well, in fact we did interpret it in this way; but, if my memory is right, we did not really think it had to be true literally. In our minds we left it open whether this was literally true, or whether some interpretation like Born’s was perhaps the true one; it wouldn’t matter for this particular problem. Now you ask also whether we were agreed [whether] the problem on non-polar binding was due to Herzfeld. Well, I think that the non-polar binding was something that presented a problem outside the old-fashioned physics. I think that was always clear to me — probably even since the days of Bredig. I think I always knew at any rate; I don’t remember any time when I thought that non-polar binding was solvable in terms of the old physics. Well, there is a minor question about perturbation energies.
I don’ t really remember much about it — about orthogonality and so on; but I think we made it clear for ourselves that the situation was not very different from ordinary perturbation theory; I really can’t tell you if we had a great deal of headache about this question. I don’t remember it. But I do remember that there was a very great deal of discussion about the Pauli principle and how it could be interpreted. Now you also ask how the paper was received when we read it at the Freiburg meeting of the Deutsche Physikalische Gesellschaft. Well, I think it was received favorably as far as I remember. Especially a chemist I knew called (Mark) — I think he’s in Canada now — remarked very favorably about it. But I don t think many people really saw the full significance of it; they were probably too much concerned with other news in physics which was perhaps more exciting. We sent manuscripts of proofs to both Sömmerfe1d and Born. Born showed it to Franck and he replied immediately and very enthusiastically. That had some consequences for me — personal consequences. Sommerfeld was as usual slow in the uptake; that is one of the most laughable qualities of Sömmerfe1d. He was always very slow, but when he had then accepted and understood a thing, then he also did know it. He didn’t write immediately but later on, when my time in Zurich came to an end, I went to see him, also for the simple purpose of finding a job. Then he asked me to explain it to him personally, or explain a few points; and he was then immediately enthusiastic, too.
He changed his former opinion?
He did change his former opinion, and quite openly said so. He was not only great mathematician and physicist, but he was also a great man who could admit his mistakes. I mean he said so quite frankly to me. Well, that was Zurich. I think that covers Zurich, or have you any more questions?
Yes, of a very general nature. What can you tell us, for example, about London and his approach to physics? He had some deep philosophical interests, too, didn’t he?
Yes, yes. He really started as a philosopher; he studied philosophy first before he changed to physics. And his interest was, even more than mine, on philosophical lines. I remember that his interest in theoretical physics was also perhaps broader than mine; I was quite content in Zurich — later on of course I changed my mind — to really understand wave mechanics thoroughly before I would go on to study the more general aspects of quantum mechanics. But London always urged me on to it; I think it was he who brought up these discussions on the probability interpretation and so on, rather than me. When this paper with London was finished, of course, we both went on to work on similar lines; and you have here a paper on your list — Paper Number 6 — which initiates the group theory approach to quantum chemistry and so on. Well, London did not join into that; he thought it was too complicated. He didn’t join in my studies of group theory. Wigner’s papers had appeared by that time, and I saw immediately that they would be useful for further development of this theory of chemical bonds, but London wanted to get on in his own more intuitive way. Well, he also was away from Zurich for a time, so I wrote that paper alone. But I’d like to discuss it in connection with the Gottingen papers, if you don’t mind. Now about London; yes, in a way [his mind was similar to mine]; he was very, very fond of Greek. He was very much interested in philosophy, and he took physics, perhaps even more than I did, as a tool to a more philosophical outlook on the world.
He changed to physics just about the time of, or just before the new mechanics?
Just about the same time; just about the same time as I entered it. He had written one or two papers before on physics — perhaps a little before I came into it. Well, with this joint paper with London I think I can say that I had made my proper entrance into theoretical physics, which was delayed by about one year, through the circumstances I have mentioned… Well, in this paper with London, of course it was clear that the exchange of two electrons was a fundamental phenomenon, a fundamental effect, and naturally many discussions arose from this fact. [There were] questions like: what is really exchanged here? Are the two electrons really exchanged? Is there any sense in asking what is the frequency of exchange? And so on. And especially experimental physicists and chemists very frequently put the question to us: “What do you really mean by this exchange?” There was Franck for example, who thought of the analogy of two pendulums in resonance and so on, and so on. And I believe that for a time I really thought it was a major and un-understood problem of quantum mechanics to explain what this exchange really means. [We were] pressed so much by the questions of other people, and always likes to understand a thing on the unfamiliar lines on the (unreadable) that is familiar with one. But this was something quite new. Well, I believe then that at that time I thought it to be a problem, but later on I think it became gradually clear to me that it has to be taken as a fundamentally new phenomenon that has no proper analogy in older physics. And that is, I think, the only proper way to describe it. One can define a frequency of exchange in a certain manner — one has to be very careful about it — by a frequency of exchange of spin directions; that is a possibility. But this does not really occur in the finished molecule; that would be a non-stationary state where the spin directions exchange at the frequency which is identical to the value of the exchange integral. There are many misunderstandings and I dare say that even today not all chemists and not even all physicists are really clear about it. But I think the only honest answer today is that the exchange is something typical for quantum mechanics, and should not be interpreted — or one should not try to interpret it — in terms of classical physics.
How did London feel about it?
The same; the same yes, we agreed on that. We discussed it of course, a very great deal. Then there is a question — “you point out that the principal problem in contemporary physics is the reduction of q-space to three or four dimensional concepts.” Well, I had no clear idea of how this could be done, nor had I any clear idea of how the description in the many-dimensional q-space could be replaced by a description of exchanges, but I think later on what I must have bad in mind at least I had a vague idea — was that this was done by the quantization of the psi-field. This is the answer to the questions which I raised here.
Well, I found that remark very mysterious.
Yes. I think it was. Well, then we are coming to Gottingen, and you ask how my appointment at Gottingen came about. Well, when the Zurich time was over, I went to Sommerfeld and also asked him if he knew of a job for me, and in fact he produced a position as assistant in Cologne with somebody; I don’t know who the professor was there. And I was on my way to Cologne, but I thought then I would perhaps stop in at Gottingen to see Born because he had written so nicely about my paper. And the result was then that Born offered me the position as his assistant. The position was just vacant, and so I stayed in Gottingen. And that was all about that. Now the next thing is all this work on the group theory which started really in Zurich; paper no. 6 then was continued in Gottingen. But the general program was to continue on the lines of the joint paper with London, and the problem was to understand — let us say to understand chemistry.
This is perhaps a bit too much to ask, but it was to understand what the chemists mean if they say an atom has a valence of two or three or four; what the chemists mean if they put down a formula with so many bonds here and so many bonds there in a multi-atomic molecule. Both London and I believed that all this must be now within reach of quantum mechanics; one must be able to understand it. And so when we separated — well, I started it even in Zurich — we each vent on somehow on similar lines. Now at that time Wigner’s papers on the group theory appeared and I saw immediately that group theory could be a tool, not only for the classification of the energy values of a multi-body problem, but also for the calculation of perturbation energies, and so on.
It was quite clear that the program which we had outlined for ourselves was essentially the treatment of the many-body problem, and it was very complicated business too. So I started to study group theory. I read first the book by Speiser, a very nice classical book on group theory, and especially on the permutation group. Later on I read papers by Schur and other people. The very nice thing about this was that the mathematicians had prepared group theory so well for the use of the physicists without knowing it that sometimes I could just copy word for word pages from a group theory paper and use them for my purposes. This has happened several times in physics; on a much greater scale, you remember Riemannian geometry was used by Einstein. Schrodinger could use Courant and Hilbert, and so on. So this subject had a great fascination for me. What was unfortunate is that it became rather complicated, and I did not see the simplification which was really possible. This simplification was brought out by a paper by Slater. Now perhaps before I go on with this — there are several papers on group theory. This one paper first is quite logically on the diatomic molecules, but with higher atoms - formed by higher atoms; and then there was still a group theory paper on multi-atomic molecules. But perhaps I’ll say a few words first about Gottingen.
Well, the atmosphere in Gottingen was delightful; it was simply delightful with Born and Franck at the head and a number of other very nice people as well. Nordheim became a great friend of mine, and there were the experimental physicists, Kuhn, who is now at Oxford and for a time Herzberg. There was a very friendly atmosphere, and everything was discussed. The atmosphere was quite favorable for my interests in chemical bond and molecules too, because Franck at that time was working on molecules — Franck and Sponer and Herzberg too. At that time I studied all that I had missed before — the papers by Heisenberg, Born and Jordan on matrix mechanics, especially papers by Dirac which I read through in one night, all of them.
All of them in one night?
All of them; they were fast-reading and very well-written too. Well, all of them which had appeared by then; there were about 4 or 5 which had appeared by then. Then it was perfectly clear to me that the statistical interpretation of Born was correct, and this was strengthened later on by very frequent visits to Copenhagen. This time I was not an outsider in Bohr’s Institute. There were a lot of conferences — at least once a year — sometimes twice a year, and I used to go from Gottingen, perhaps twice a year, for a few weeks each time. Well, if you like to say the ‘Copenhagen interpretation of quantum mechanics’, then I adopted it. I adopted the Copenhagen interpretation, and I was very well versed in what other people called the ‘Copenhagen spirit’. I had no sympathy either with de Broglie’s pilot waves, nor with Schrodinger and Einstein’s attempts to get around the statistical interpretation.
Do you remember if there were anyone who was favorably impressed by the efforts of Einstein and Schrodinger?
No, except the people in Berlin. They were all united, you see: Einstein, Laue, Planck and Schrodinger. They were all of one opinion; they didn’t believe all this, and they wouldn’t budge. But otherwise I don’t know anyone who has not ever accepted it — perhaps de Broglie, I don’t know. But there was not really much discussion about it, except about details because it was simply accepted as correct; there was no doubt about it. Then you ask about the Dirac equation. At first the Dirac equation was considered correct; everybody in Gottingen agreed with it. Then the difficulties came — the difficulties with the negative energies and Klein’s objection on the reflection of the electrons by a potential wall, or rather the penetrating of the electrons by a potential wall, or rather the penetrating of the electrons through a potential wail. That was considered a very serious objection. Then Dirac proposed the ‘hole’ theory, which was generally regarded as madness.
What about the protons first?
Wait a minute; first came the ‘hole’ theory. The ‘hole’ theory where the negative energy states were thought to be all filled up. This was generally regarded as madness, and I remember a very heated discussion in Copenhagen where Bohr simply described it to Dirac’s face as madness. Well, a little later Dirac came out with the idea that the holes could be protons, and he wrote a paper about it, thinking that a heavy mass could arise from interaction of these many electrons. Nobody really believed that, but then a little later the positive electron was discovered and then the problem was settled.
Do you recall what Dirac replied to Bohr when Bohr accused him of madness?
Yes. Well, Bohr called it madness, and Dirac thought it was [nevertheless] a good idea. You know Dirac never replies much; if possible, he avoids speaking, and I don’t remember that he said anything after Bohr’s remark. He just gave his lecture and finished. So that was that. Then you ask if I could tell anything about the gradual acceptance of the idea of second quantization and the quantized field. Well, I think this was accepted without much hesitation. The quantization of the electromagnetic field was considered as what really corresponded to the original idea of Planck; there were no objections. And the same was true for the quantization of the psi-field in as much as it could be shown that it was equivalent to the q-space description. I don’t think anybody objected to that. When Heisenberg and Pauli’s paper on quantum electrodynamics appeared there were also very few objections to it; I think it was generally regarded as more or less correct, but everyone knew of course, immediately that the difficulties were there — the difficulties connected with the infinite self-energy and other infinities. The divergencies were not removed and so that made the paper a preliminary paper, not a final one; the difficulties are there today as they were at that time. But gradually one thought that it was as good as could be done, and even today there is not really any essential progress on that point. The difficulties are there just the same. But it took some time before people realized that there was truth in it, and especially then I remember one of these Copenhagen conferences when Bohr very emphatically stated that the quantum electrodynamics of free fields — that is to say in the absence of electrons — must be correct. And then he wrote with Rosenfeld that frightful paper on the measurability of fields.
Do you call it frightful because of its intricacy?
Because of its complication, yes. Well, it’s very interesting; it’s one of the most elaborate and conscientious papers I’ve ever seen. It’s a wonderful paper. Well, coming back then to my own work. I have covered already the papers on group theory, and now there was a sort of a turning point in this work which was due to the appearance of a paper by Slater. In this paper it was shown that you can simplify the multi-body problem if you include the spin, in the sense that you include the spin wave function, although dynamically the spin played no role whatsoever. You see, that was the mistake, if you want to call it a mistake, we made in the beginning, both London and I. We thought the spin has no dynamical influence on the problem, so let’s leave it out all together. Then indeed this group theory treatment of the multi-body problem becomes very complicated, but if you include the spin wave function there is a certain simplification. The result of this was then a paper with Rumer which you have mentioned on the list, and which I think gave a general method for treating the interaction of several atoms. And it was really in this paper that we then could see what the chemists mean by a chemical formula, when they write down a chemical formula. And we could associate a chemical bond immediately with an electron pair with anti parallel spin in the wave function describing the molecules.
There were a few additions to this — mathematical additions by Weyl; he was very interested in this work too, of course from his group theory point of view. He gave us a few more hints and a few simplifications, but essentially I think one can say that this was the final paper in the general program which I set out to treat, to carry through. There were a few new things for the chemists; one is that to each chemical formula there corresponds a wave function, but the wave function does not correspond — well, how shall I put it — the wave function is not such that it corresponds to one chemical formula alone, but it is in general a combination of several. There are some structures which are quite important for the calculation of energy-contribution which the chemists never think of. Perhaps I’ll put it on the blackboard if you like. I think I know it. Well, it might be if you have a molecule like this, not only would a wave function come in where there are three electron pairs formed between the two C-atoms but also something, let us say, like this, and so on. Well, this is perhaps not only of purely academic interest, because that gives an understanding for what the chemists call an activation energy.
London was really the first, even a long time before this paper appeared, who showed that the activation energies in the treatment of three hydrogen atoms could be understood in quantum mechanics, and this method gave us then a general understanding for it. Later Pauling called this a resonance between several structures, which is a name perhaps not quite in agreement with the use of the word resonance by physicists, but it doesn’t really matter. And a further point, which was also violently objected to by the chemists, was that both London and I stated that the carbon atom with its 4 valences must be in an excited state, (in-between the s-state), and that was what the paper with Herzberg was about. Well, all this was later naturally accepted by the chemists, and I think now they are making full use of all these various structures. But at that time I don’t think the chemists did find this of much use for them. Well, with this one point that excited atoms also played a role for chemistry, as in the case of carbon, there was then a final paper on this subject on chemistry. It was a short note with Miss Poesch, later Mrs. Nordheim; that was really a thesis by Mrs. Nordheim on the influence of excited states, but by that time I had already then changed my subject.
I think the program which I set for myself was then more or less — at least in general — finished. But now I have to add something to your list, if you don’t mind — other papers. This concerns a short paper which historically is rather important, for the Gottingen period. Well, this paper with Herzberg [“Gehorchen d. Stickstoffkerne d. Boseschen Statist?”. Naturwiss, 17 (1929).] has a searing on quite a different aspect of physics at the time. The origin was the following. Herzberg was in Franck’s department working on molecules, but we were good friends. One day he came to me to discuss a paper which he had read by Rasetti and which was confirmed by him, I believe. This paper was on the alternating intensities of the band spectra of nitrogen. Now from the band spectrum of the nitrogen molecule you can draw conclusions as to the statistics which the nitrogen nucleus obeys. You can decide whether it obeys Bose statistics or Fermi statistics. Now at that time it was believed that the nucleus consisted of protons and electrons no other elementary particles were known — so the nitrogen nucleus had to consist of 14 protons and 7 electrons to make up the proper mass and charge. Now this paper by Rasetti contradicted this conclusion. Wait a minute I think I left out an argument. If the nitrogen nucleus consisted of l4 protons and 7 electrons, it would have to obey Fermi’s statistics, because there was a theorem which was proved by Wigner — I believe it was proved by Wigner — that a compound particle consisting of an odd number of particles each obeying Fermi statistics also obeys Fermi statistics as a whole.
Now this paper by Rasetti was in contradiction with this because it showed that the nitrogen nucleus obeyed Bose’s statistics. Now shortly before I had read the paper by Kronig in which he showed that the nitrogen nucleus also had an integral spin, and [he] came to the conclusion that the electron, once inside the nucleus, somehow loses its spin. We could now add a similar conclusion; we could say that the electron inside the nucleus not only lost its spin, but it also lost the contribution it made to the statistics of the nucleus. The two things go parallel. Now we did not go on further in speculating what all this could mean. We were too much convinced of the generally accepted idea that there are no other particles but protons and electrons. So we put our conclusion that way, that the electron inside the nucleus must apparently be something quite different from what it is outside in that it has no spin and does not obey Fermi’s statistics. Well, this paper was greatly discussed then at one of the Copenhagen meetings, and so on. But sometime afterwards — a few months later; I believe it was a half a year later — the neutron was discovered, and that solved the problem. But you see we were very near to predicting the neutron; Kronig also was very near to it.
No, I don’t know how I missed that paper; that’s quite interesting.
Yes, this is the paper. Well, of course, its interest is mainly historical, but that’s why I tell you. Yes, that’s your business, but, of course, now no physicist would quote it anymore, and there is, of course, no need to quote it any more. Well, I suppose that finishes it as far as I’m concerned. But if there are any more questions on your part, or if something occurs to me we could continue, at any rate perhaps we’ll make another appointment.