Oral History Transcript — Dr. Christian Moller
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Christian Moller; July 29, 1963
ABSTRACT: This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Niels Henrik David Bohr, Paul Ehrenfest, Werner Heisenberg, Lev Davidovich Landau, Christian Møller, Wolfgang Pauli, Léon Rosenfeld, Erwin Schrödinger; and Niels Bohr Institutet. Interview conducted as part of the Archives for History of Quantum Physics (AHQP) project.
Kuhn: You’re really the first person I will have talked to who is a Dane who came up through Danish schools and through the university here. The background for one’s interest in science, the nature of the curriculum and the training here, the sort of leadership which was provided, are all questions of a good deal of interest to us, as creating the background out of which the scientific movement grew.
Moller: Yes, well, I can start by saying that I started my studies in 1923.
Kuhn: Tell me how you happened in the first place to come to physics. I take it by the time you started your studies at the university you knew you were going to do physics.
Moller: I must say that I was oscillating between mathematics and. physics. I didn’t know exactly. The first years at the university it doesn’t matter, because we had to go through mathematics and physics and chemistry and astronomy anyhow, so it took really at least a year and a half before I decided it should be physics.
Kuhn: How much physics and mathematics had you been able to get in school before you actually started to the university?
Moller: In the gymnasium we had, well in mathematics we had differential calculus and integration, a little theory of numbers, and analytical geometry. Of course not very far. I mean after all we had to learn things in more detail when we came to the university, but we had a quite good foundation in the elements of mathematics. In physics it was not very much. I mean we knew about mechanics (sound fades) and that was about all. A little in theory of heat, a little in electricity, very little. But in mathematics it was not too bad, really.
Kuhn: Would that, do you think, have been typical of the Danish school system at this time, the mathematics fairly good, but physics not very much?
Moller: I think it was, yes, I think it was. I don’t know why this came about really, because it’s perhaps accidental that there were some good mathematicians who also at that time took the care to write textbooks for the gymnasium, while in physics it was really rather vague. Chemistry was very little. Astronomy we learned a little, just the apparent motions of the stars and also the Kepler’s laws and some things, but not very much. When I came to the university in 1923, I just started on the usual thing one has to go through the first two years, or actually at that time, the first three years. One had to take these four different subjects, mathematics, physics, chemistry, and astronomy. At that time these first years were taken at the technical high school. The professors there were often also professors at the university, and there was an agreement that we heard the same lectures as the engineers these first years. This has changed now.
Kuhn: There was no contact at all with the Institute?
Moller: No contact at all with the Institute at that time.
Kuhn: Excuse me for interrupting and bringing you back still a little bit. I take it you were thinking of mathematics or physics because of the interest you had acquired in school.
Moller: That’s right.
Kuhn: Did this presumably mean that you thought very likely you would be a teacher?
Moller: Well I didn’t particularly like the idea of becoming a teacher, but that was what most ended up becoming. There were very few positions, very few possibilities at the university at that time. I also thought for a short time of becoming an engineer, because there the prospects were somewhat better. But I soon decided that this would not be sufficiently interesting for me. We had a very good teacher in mathematics who by the way also taught us physics in school, and it was his influence which made me tend to both mathematics and physics. I think it was one and a half years after I started at the university that it became clear to me that it had to be theoretical physics.
Kuhn: What was it, do you remember, that convinced you?
Moller: I was very much interested in thermodynamics at that time. This was in a way the most exact subject we had in these first years. We had a very good teacher there, Professor E. S. Johansen. I don’t think he ever did real science, but he was an extremely good teacher, and wrote excellent textbooks and so on.
Kuhn: Was this course in thermodynamics one which used a more or less phenomenological approach, or was it through statistical mechanics?
Moller: No, it was the old thermodynamics, not statistical mechanics; we had practically no statistical mechanics. But it was a fascinating thing to see how one could use mathematics to get the relations between the different thermodynamic quantities and ho the whole thing could be formulated in these very few simple laws, the first and the second laws.
Also we had a course in what we called “rational mechanics”, that is the old tradition in Europe, “mécanique rationale” from the French school, and that was taught by a mathematician actually. Well this fascinated me of course very much, because it was the first time that one could calculate something in nature by using differential geometry. So I think it was “mécanique rationale” and thermodynamics which awoke my interest in physics. I had no idea of quantum theory at that time.
Kuhn: To a student in your position, either at school or beginning at the university, was Bohr a great name for you at that time?
Moller: Yes. Of course we had beard about him; we had not yet had any contact with him in these first years. That came after we had taken the first part at the technical high school. Then if we decided to study physics, we would come to the Institute on Blegdamsvej.
Kuhn: I suppose what I’m fishing for is some indication of the extent to which, particularly for a Danish student, the existence of Bohr or the work he had done would be an attraction to physics.
Moller: Certainly, certainly yes. Although we didn’t know very much about it, we had heard about it, and already in school I remember that our teacher told us about Bohr. Actually he was about his age, and. they had been studying together, so he had met him when they were students. I remember also that in my school days I got hold of a book on Einstein’s theory of relativity which also fascinated me very much. It was a popular book.
Kuhn: A Danish book?
Moller: No, it was a Norwegian book, written by a man called Schjelderup. Of course one didn’t understand it completely, but it was very fascinating.
In September 1926, I came for the first time to the Institute. At that time Heisenberg was a lecturer there. I remember he was talking about electrodynamics. It was quite surprising to us to see such a young man, hardly older than we were, giving lectures, and we also had heard a little about what he had done already. That was just the year after he had published his first papers.
Bohr himself did not give any lectures. I met him for the first time probably at the end of September, 1926. This made a great impression on me. I was sitting in the library and studying one of Einstein’s papers when he came around; he looked into what I was reading, and then he started a private lecture, walking around as he used to do. It was very hard to follow, because first of all, well, he talked about a difficult subject, and also as you remember, it was acoustically hard to hear all he was saying. And he was walking around, so one had to rotate on one’s axis, following.
Kuhn: Was this an Einstein relativity paper?
Moller: It was the famous paper on general relativity from 1916 I was studying, and he told me about the importance of Einstein’s work, how it had changed our notions of space and time. But then he said, “Well, you see, all these things are now cleared up, and you should start to study quantum mechanics, because there are many things to be cleared up yet, and probably the transformation of our thinking, I mean the revolution in our epistemology, will be much deeper in quantum theory than in relativity theory.” So I followed his advice, and started to study (quantum mechanics). I knew about his own papers at the time, I mean the first 1913 papers and had even seen them. He recommended me to read a paper by Klein in which he applied the Schrodinger equation in order to calculate transition probabilities in accordance with the correspondence principle in a way which was quite different from the way Schrodinger himself thought about his equation.
Maybe I should mention also that Schrodinger himself came to Copenhagen in the fall of 1926. He gave a talk in the Fysisk Forening here about his equation. This was also a marvelous experience because he was a very good speaker, and could make things very clear. Also the Schrodinger way of attacking the problem of the stationary states of the atoms was so much easier to grasp for us than the Heisenberg way because the mathematical tool was a well-known thing. The theory of partial differential equations had been used for a long time in physics of course. So this was very exciting.
Kuhn: Do you remember, was there much discussion at the Fysisk Forening?
Moller: Well there was some. But this was a rather big audience. It took place in the technical high school and I think the big auditorium was filled. But I know that the next day there was a colloquium at the Institute. I was not present at this, but I wrote about it in this little article in Fysisk Tidsskrift after Bohr’s death. Bohr told me later that there was a discussion between Schrodinger on the one side and Heisenberg-Bohr on the other side. They tried to convince him that one could never get away from the notion of the stationary states, and that transition and probability notions should be used in order to describe these transitions. Then Schrodinger said, in German: “Wenn wir zu dieser Herumspringerei wieder zuruckkehren mussen, dann bedaure ich, dass ich mich in diesen (Dreck gemischt habe).” And then Bohr answered, “Well it may be that you regret that you have mixed into it, but we are very glad that you have mixed into the subject.” [chuckle] So Schrodinger’s point of view was of course quite different from the one which finally has been the accepted point of view. He thought that now we could do away with this “irrational” way of describing nature, and get back to a more classical way of describing the atom.
Kuhn: Did you yourself at this time, as you were beginning to learn the newer quantum theory, try, to do the Heisenberg approach also?
Moller: Well, I studied the Heisenberg papers, but soon, of course, Schrodinger himself showed that the two ways were identical, that is equivalent. Then Dirac with his transformation theory showed quite generally that there were many ways of formulating the quantum mechanical laws, not only the Heisenberg and the Schrodinger ways, but an infinite number of ways. But that came a little later. The paper by Klein was very illuminating in this respect, because it was really the first use of the Schrödinger equation which was done in a way which we would still today recognize as a correct way.
Kuhn: Were there other things that Bohr suggested that you read or that were being generally used to help people at your level?
Moller: Yes, well it was mostly his suggestions for giving colloquia, at the students’ colloquia. The students had now and then to give colloquia on a subject; Bohr gave the subject and one should study the paper, and then give a talk on it. We were very few students, so it happened rather frequently to us. I think I had to give 4 or 5 colloquia during my study years. The first was a classical one; it was on the Zeeman experiments on the velocity of light in moving bodies, but the next I think must have been on Dirac’ s equation. It was quite new then and, well, Bohr also used us young people to tell him about things.
Kuhn: How many of you were there who would have been required --
Moller: Oh, I think we were only about five Danish students in this subject. In this connection I remember that I came to talk with Nishina about the Dirac equation. He had not studied this paper yet, and I told him about what I had got out of it. Soon after, he and Klein started to make the famous calculations on the Klein-Nishina formula. And there I also got a little job in checking the things.
Kuhn: Not a little job!
Moller: [chuckle] No, it was a hard job, because the calculations were much more involved than they became later. There were some techniques which one didn’t know then, especially the summing of all these spin states, which was a hard job before Casimir invented his method to do it very easily. A little later I remember I had to give a colloquium on Dirac’s radiation theory. Really that was a first attempt to get a rational description of the radiation phenomena.
Kuhn: Is it possible that those two were done in opposite order? That is, they were published in opposite order. The radiation theory is older than the electron one.
Moller: Yes, right, right -- but I think my colloquia were the other way around. That’s right. Oh yes, I remember that now, because I was in the hospital, and I took this book with me to read in the hospital. That was later, because I had moved from one college to another, from the Regensen to the (Bock) Kollegium.
Kuhn: Is it probable that you were the first one to report to the colloquium on the Dirac radiation theory?
Moller: Yes. That’s absolutely certain.
Kuhn: Would that mean that it had not been taken so seriously immediately?
Moller: No, but it was so new. The paper had just arrived in the library. I am speaking now about the Dirac electron. No, about the other thing I do not know. Maybe it had been talked about earlier, that is quite probable, that is very probable of course. No but I think I was the first who talked about the Dirac theory of the electron.
Kuhn: Right. What sort of reactions did people have?
Moller: Oh, I mean, any paper of Dirac at that time was like an –- abenbaring -- what do you call it?
Kuhn: A revelation.
Moller: A revelation, yes. It was so exciting. Already the first paper in which he really came to the transformation theory -- it was called “Physical Interpretation of Quantum Mechanics” -- it was a very strange situation. One had a formalism there, and one really didn’t quite know what it meant. It’s a very strange thing, it’s really a thing which still puzzles me, how it is possible that one could come to a formalism which turned out to be exactly right even in different ways and could come to the correct theory which was not just an empirical description of what one knew, but went much farther than that. One didn’t quite know what it meant physically. And then this paper by Dirac cleared this up.
It’s a very strange thing, isn’t it, don’t you feel also, that mathematics is so --, well as Wigner has put it once, is so useful. There’s something weird about it. It is not just collecting the data and trying to make an empirical formula. One gets something which is so extremely accurate quite strange. Well then I talked with Rosenfeld about this some time ago, he said “Well, yes, one should remember that it’s something like the development of the species.” I mean, it’s a little surprising that the development goes the right direction. But of course there are many many many generations and he said, “Try to imagine how many theories are thought out and bow few of them work.” It may be the natural select ion which -- but still, there is something. Probably of course the laws of nature do not exist at all by themselves, but they are created by men, and therefore the mathematics is the language which we use, and also the way we think about the thing. But still there’s something there which I always feel is a little mysterious.
Kuhn: Did you ever talk to Bohr along these lines?
Moller: No, I don’t think so. Well Bohr did not I think, believe in the Laws of Nature. I mean he spoke always about ‘regularities’ and said we can make a picture of the things only in small pieces. Of course his first work, the 1913 paper, all those 3 papers, he started really from something very concrete, I mean what we knew about the spectral lines and so on. He was closer to the facts than when the later quantum mechanics was developed. I mean there one certainly had a scheme which combined an enormous amount of things. No, I don’t think that he felt it was so mystical. That’s my private feeling.
Kuhn: And perhaps not mathematical either.
Moller: No, he was not so mathematical. That is right. But do you think it is a little surprising?
Kuhn: Yes. And I think of course the thing that makes it most surprising at all, and strikingly so in this case, is the two virtually simultaneous approaches from quite different directions, reaching apparently quite different systems, that then prove to be equivalent in so many areas.
We’ve jumped here, or at least said very little about ‘26 to ‘28. You come to the Institute in ‘26, you talk in ‘28 on the Dirac electron. There’s an awful lot going on in these periods that must have been discussed a great deal around the Institute and I’d like not to go past that any more quickly than we have to.
Moller: Well, of course there were constantly colloquia going on in the Institute and we students also had the opportunity to follow these discussions. Well there of course Bohr always was the man who made these discussions so exciting. It was extraordinary how he could go on for hours and hours to try to clarify things.
Kuhn: Do you remember particular discussions that excited you, particular topics that he, or you, pursued at this time?
Moller: Well, I think I have to go up to ‘28 to -- of course when he started to speak about complementarity and all the discussions of Gedanken experiments, that was always very exciting. When, oh I think about many hundreds of times we heard him speak about the holes, the two holes in the screen and so on, and the shutter. He never got tired of speaking about these things, because he rightly thought that we had not understood them completely. He also said once that if somebody said, “Well this is clear,” then he could say “Well, I think that if a man says it is completely clear to him these days, then, he has not understood really the subject.” He said once, I think he said it in German, “If you do not get (schwindlig) sometimes when you think about these things then you have not really understood it.” [chuckle] In these years, of course there were a number of people coming, and some of them of course stayed for a long time. Heisenberg as I said was here when I started to hear lectures at the Institute, but the year after I think he left, and then Klein became the lecturer, and we had the regular lectures from him.
Kuhn: Was there at any time at the Institute just one set of regular lectures going on?
Moller: Yes, there was a course of lectures we had to go through. But these again were mostly courses on classical physics.
Kuhn: Was there a regular sequence of topics that you had to cover?
Moller: Yes, yes, yes. There was electrodynamics and statistical mechanics, relativity theory, and well, with mechanics I mean also analytical mechanics. But the quantum theory was so new that there were no textbooks, we had to read it out of the papers from the journals. This was quite fascinating but it also took some time to come into it. Well, then a little later Gamow came, that was in ‘28 I think; he had just done his paper on the alpha decay of the nucleus, I mean the tunnel effect. And Landau came here, which was very exciting. He was a remarkable chap. He was quite young, very young, and a very clever boy -- very aggressive also in his remarks about things. Of course Pauli was here very often also. He stayed in Copenhagen I think before I came to the Institute for a whole year. Later he came on visits, especially during the conferences which Bohr called every year; small conferences of about 10-15 persons only. Ehrenfest came also to these meetings and this gave rise to many nice remarks during the meetings because Ehrenfest and Pauli always were teasing each other. I suppose you have heard these.
Kuhn: Some of them. But not by any means all of them, and I like to hear about them, because they’re both fascinating figures and it’s an interesting relationship.
Moller: You must have heard the story about when they first met. Both Ehrenfest and Pauli had written a Handbuch Artikel in the Encyklopadie Ehrenfest on statistical mechanics and Pauli of course on relativity. And when Ehrenfest saw Pauli he said “Ihr Handbuch-Artikel gefallt mir viel besser als Sie selbst.” And then Pauli immediately, without thinking answered, “Wie merkwurdig, mit Ihnen geht es mir gerade umgekehrt!” [Laughter]
Kuhn: You know, it‘s a strange thing, I have heard this before, but with the response ‘I take that as a compliment’, or something like that. But up to the point of the line I gave you, the two stories are identical. I like this much better.
Moller: Well, there is also the one -- that was during conference. I heard that. Pauli was giving a lecture, and was walking up and down parallel to the blackboard as he used to. In the old lecture room to the right of the blackboard there is the entrance door, and so Pauli had walked up and down while he was talking for a long time, and suddenly Ehrenfest jumped up and said “Nein, ich halte es nicht mehr aus! Jedesmal glaubt man dass Pauli zur Tur hinausgeht, und dann kehrt er um.” [Laughter] This disappointment of course.
Kuhn: You also spent some time at Hamburg during this period, didn’t you?
Moller: Yes, well that was actually before I came to Bohr’s Institute. I went to Hamburg when I had finished at the Polytekniske Laereanstalt.
Kuhn: How long were you there?
Moller: Oh, only for a term, in the summertime of 1926. Well, Pauli was then lecturing there, but I didn’t get much contact with him, I just spoke with him a few times. He had then been in Copenhagen already. I was very interested in some lectures by Artin on mathematics. It was still the time when I didn’t quite know whether I should study mathematics or -- but I think I knew it was physics. He was giving excellent lectures on modern algebra. Also on mechanics of continuous matter, I mean theory of elasticity.
Kuhn: Did you go to Pauli’s lectures also.
Moller: Oh yes, he gave some lectures on relativity. Oh yes.
Kuhn: Was it fairly usual for a Danish student to go elsewhere for a semester or two?
Moller: No, it was quite unusual. I felt that I should go away a little; I think that there were several reasons why I wanted to go away for a little time, and I think it was quite good. No, it was not so usual, at least not at this early stage; I mean later people would go away for some time. I went a little later, in 1928, to Berlin. There was a Ferienkurs course in theoretical physics going on there in 1928. Of course Berlin at that time had a number of quite good people. Einstein was there, Planck, von Laue and --
Kuhn: Schrodinger was also there.
Moller: Schrodinger of course, yes Schrodinger was there. Oh that was the main reason why I went to this. He was announcing some lectures on wave mechanics. Einstein was also expected to give lectures, but he was a little ill that summer I think; he had something with his heart. Although later I don’t know if he --. It may also have been an excuse, I don’t know.
Kuhn: In ‘28, do you remember from that summer, was Schrodinger still insisting upon something like his original interpretation?
Moller: Yes, yes he was. Although he -- well he still was not quite satisfied with his own equation, because he didn’t like the i, I mean the imaginary unit appearing explicitly in the time-dependent Schrodinger equation, and he thought that this was something which should be removed after some time.
Kuhn: Ah, did he!
Moller: Oh yes, oh yes. And he also was not at all satisfied with the complementarity ideas of Bohr which just had come up then. He said “Bohr will alles wegkomplementieren.” But he had about that time, I think, found the connection between the Heisenberg way and his own way to formulate the thing. He had just written this paper I think where be proved that it was equivalent.
Kuhn: That paper actually came out already in 1926.
Moller: No -- is that true?
Kuhn: Yes. It comes between the “Zweiten-” u. “Dritten Mitteilung”.
Moller: But the first paper was in ‘26 wasn’t it?
Kuhn: Yes, but there were in fact about five papers, one right after the other in ‘26, almost once a month. There’s the “Erste Mitteilung” then the “Zweite-” then there’s this intervening piece on the equivalence, and then there’s the third and fourth parts, and then I think one of the unnumbered parts still comes in ‘26.
Moller: Yes, you’re right. Annalen der Physik 1926, that is the one, yes, that’s right. Yes, but I think he still thought about it really as wave mechanics, and he didn’t like the introduction of probability notions.
Kuhn: How did other people in Berlin --. I mean did you talk with other students about this?
Moller: I talked with some Russian students who were present --. I don’t think they had a very firm conviction about this. No, but in Berlin at that time even Planck and also Einstein of course were somewhat reluctant in admitting that quantum mechanics already was complete. They hoped for a later development which would make it unnecessary to use the probability notions. Also von Laue for a long time was -- I think the Berlin school was a little in opposition to Bohr’s ideas.
Kuhn: I think that’s quite true, and I wondered what effect this had really on the student body. On the one hand I take it that the faculty was somewhat resistant, but that on the other hand both von Neumann and Wigner come out of that environment.
Moller: Yes, yes. Well also of course Planck was the first to introduce the idea of quanta, and Einstein was the first really to use the probability notion in deriving the radiation formula of Planck. And I remember also that Schrodinger, about that time also, after Born’s paper on the statistical interpretation, wrote a paper, in Naturwissenschaften I think, which was an old talk he had given some years before where he had said something about how it might be necessary in the atomic theory to use, in principle, probability notions. And when he published that, I remember Bohr saw this paper, and then he said, “I think Schrodinger wants to emphasize that be once has been willing to admit these wild things.” Something like that. But I must admit, I didn’t come into very much contact with students in Berlin. I mean it was a Ferienkurs and it was mostly foreigners who were there. Well, how far have we come now?
Kuhn: Well we have certainly come to ‘28, unless you can remember other things that happened in this first period. You’ve spoken on a couple of occasions, of the impression made by the Dirac transformation theory paper in ‘27. But at much the same time there are the Jordan papers on the “Neue Begrundung” and the derivation of the wave equation from statistical postulates. Now I wonder what the impact of those papers was--in retrospect of course they’re classics -- and just what their role was around Copenhagen at the time. Do you remember any particular discussions of them?
Moller: No. I think I only remember the time when Jordan was here himself, and that was a little later. He did this paper together with Klein on the so-called double quantization; I remember very well, that they “quantized” the Schrodinger equation, so to say, and in this way got the particles out of it, and put down these commutation relations of the amplitudes.
Kuhn: There’s a very curious thing that goes on with respect to that paper -- I’ll ask you first, did that seem brand new to you, that idea of quantizing the amplitudes?
Moller: Well of course Dirac had done something like that in the radiation theory, really. I mean there he also introduced the amplitudes as q-numbers and put down some commutation relations for them. I mean, also the light quanta are Bose particles. Jordan and Klein did that for electrons as if they had been Bose particles, I mean the electrons without spin, and introduced the interaction. That was a nice thing, they introduced Coulomb interaction and showed that if you reverse the order of some factors, then you can make the infinite self energy disappear. As a matter of fact, that was a procedure which later quite generally was given by Wick. One always had to have the creation operators to the left of all the annihilation operators.
Kuhn: I ask this, and you’re speaking to the point except that I’d like it if one could be still more concrete about it. This is I think a perfect description of the differences at the technical level with this procedure as it exists in the Dirac paper, and as it exists in the Jordan-Klein paper. I also have the feeling that for all of the mathematical equivalence of the two procedures Dirac himself at least and some of the people who read the Dirac paper saw this as a transformation to a new set of q-numbers, but not as a quantization of the wave function. With Jordan it is a quantization of the wave function in order to generate particles. That shift in the way one looks at the same mathematics, is, I think, quite important in this development here, and it’s really that which I had in mind when I said, ‘was that new with the Klein-Jordan?’ I don’t think Jordan thinks it was new. I think he thinks what they were doing was extending the generality of the Dirac approach.
Moller: I think it was a very important paper, because it also gave the clue to the quantum electrodynamics of Heisenberg and Pauli. I mean in between came the Jordan paper on how you should treat the thing if the quanta were not Bose particles but Fermions: just change the commutation relations. But I think, one hoped for a time that one could remove the infinities from the Heisenberg-Pauli quantum electrodynamics, since it had been possible to eliminate the infinities at least for the static Coulomb energy by interchanging the order; in fact one hoped that one could do it also relativistic ally.
But it turned out of course not to be true. The Heisenberg-Pauli quantum electrodynamics contained these infinities. Only after renormalization and these things can one get them away. But I think this paper by Klein and Jordan was a very important step, on the way to the general quantizing of fields.
Kuhn: Was this whole idea of quantizing the wave function one that Bohr was interested in and sympathetic with?
Moller: Oh I think so. Yes, I think so. As far as it went in the paper by Jordan and Klein, it was of course nothing else but the Schrodinger configuration space treatment of many particles. I mean it was completely equivalent to that. But it showed that the Schrodinger equation was not a classical equation. I mean one couldn’t --. Schrodinger himself had exactly the same thing by treating a many-bodied system in configuration space, which also showed that one was far away from having a field like hydrodynamics -- that was what I think Schrodinger hoped, that these things were a little like hydrodynamics. I mean he hoped that the particles would come out as small packets of matter somehow. And he was so unfortunate in this paper to choose the harmonic oscillator because this really moves like a particle. It’s the only field where it would. In all other fields the particle would spread out, not keep together. But then it was interesting that by quantization of this Schrodinger equation for the one particle system, one could get out the system with many particles. I think that was a very important step forward.
But Bohr I think, at least for a long time, and we, too, all thought that the quantum electrodynamics was not of so terribly much use, because most of the things could be done by correspondence methods. For instance in the Klein-Nishina formula the field was not quantized. I mean it was a c-number treatment; also the way I treated the collision between fast particles was a correspondence treatment, and the field came in only as an intermediary thing, as a c-number.
Kuhn: I wanted to ask you about that. There were these two alternate approaches in this period. I take it that to Heisenberg and Pauli at least, the field theoretical approach looked like the more fundamental one. To what extent, in your own mind, and that of people with whom you talked, in Klein’s mind also say, was the correspondence principle approach thought of as an approximate substitute in view of the infinities, and to what extent did it look like just as fundamental an approach?
Moller: No, no. I don’t think so. I think one looked upon this as a preliminary thing. I mean something like the Heisenberg-Pauli theory would always appear as something more fundamental. But it didn’t give so many new results, Schwinger and Feynman came along, and there you really got something new, which you could not get by simple correspondence methods. But, otherwise, all these formulas, I mean the Delbruck scattering and the Klein-Nishina formula and scattering between fast particles and between electrons and positrons, as Bhabha did, could be done by these correspondence methods. But certainly, I think we all had the feeling that the field is something real and must also be treated like a quantum mechanical system by means of q-numbers end with commutation relations and so on. It was the way to go. First, it was a straightforward generalization of ordinary quantum mechanics of a finite number of degrees of freedom, and second it was a system which had an infinite number of degrees of freedom. The infinities which came in simply could not be avoided. One sees now that as long as one has a Hamiltonian scheme, these infinities will come.
Kuhn: There must have been, one guesses, a certain amount of opposition, not of principle but of values, between those who said, early, “All right, but I can’t get results from the field theory; therefore instead of breaking my head over it I’m going to do correspondence argument”; and those who said, “No, the fundamental thing to do is to work out the field theory.” I’m curious to know when you would say it becomes clear that the infinities are really fundamental, one is not going to get rid of them by better mathematics or something of this sort.
Moller: Well, as a matter of fact, my point of view is that even the renormalization theory is not quite satisfactory, and that one really has to go away from the Hamiltonian description. I think it can be done. We have a recent paper by (Paul Christiansen) in Aarhus who has been able to formulate the whole thing in such a way that no infinities ever come up. But he cannot do other things. He does get the same result as the renormalization procedure, which is good of course, because these are in good agreement with the experiments. But you can avoid, I mean it is really possible --. At times one said in these years, ‘Well maybe it is not possible, we will have to have quite new principles coming in. Maybe it’s connected with the fact that electrodynamics is not alone in the world. We have other fields, the meson fields, and they will all change the whole thing.’ And there I remember that Dirac always said that electrodynamics has to be solved first. One has to solve one problem at a time, he said. He wrote, in fact, a paper himself, as you remember, where he thought that he had formulated things in such a way that the infinities would not come in anymore.
Kuhn: This was the ‘32 paper, the one that Rosenfeld answered?
Moller: Yes. And, well there is an anecdote which I think you probably know, that when Dirac gave a lecture on this, he said, “I think we have to solve one problem at a time.” And then afterwards Bohr said, “Yes, but I’m sure that Nature solved them all at once.” But at that time one very often thought that maybe the difficulties in quantum electrodynamics were connected with the existence of other fields.
Kuhn: Still, when you start talking about the meson field and other fields, this is getting fairly late in the development, and I’d be particularly curious for any material that will illuminate the early developments. Certainly by the time of your thesis, but even before this in the case of Klein, here at least in Copenhagen, my sense of the situation is that the correspondence approach has become a basic approach in this area.
Moller: Yes, yes. I’m not quite sure about it, but I think we all felt that something like the things Heisenberg and Pauli had done were the natural thing to do.
Kuhn: Did you really work on that approach yourself?
Moller: No, no, I only remember that I had the tedious job of filling in formulae in a copy of this paper by Heisenberg. Pauli came on a visit here and I asked him if I could read it and be said, “Well you can fill in the formulae. In this way you will also be able to read it.” So I did that. No, no, I studied these papers of course, but that was actually, let me see, when was the Heisenberg-Pauli?
Kuhn: That’s ‘29.
Moller: As early as that? Yes. But they were difficult, very difficult to read.
Kuhn: From my point of view they’re still difficult.
Moller: Still difficult, yes, but it’s easier now, for a student, because you can read in textbooks. I don’t know if I can say anything useful in that connection.
Kuhn: At the meetings, people kept looking back and pointing to the Weisskopf paper as the paper which proved the infinity problem.
Moller: But that was also a little later.
Kuhn: The infinities certainly exist already in the Heisenberg-Pauli paper, and they’re very much aware of them. I’m curious to know to what extent it really is historically, I mean as things happened, correct to say that the Weisskopf paper had a crucial role in the infinities question. You point to them yourself in the beginning of your thesis, where you point out this as a reason for taking the correspondence principle approach. There must have been other steps in this development of the attitude toward the infinity problem.
Moller: There was a paper by Heisenberg where he -- [telephone interruption]… About that time also in ‘29, probably ‘30, there was a paper by Landau and Peierls who believed, that these difficulties were very essential and connected with relativistic formulation of quantum mechanics. But then I think that the paper by Bohr and Rosenfeld showed that this was a little beside the point.
Kuhn: Do you remember discussions that went on over the Landau-Peierls paper or in the course of the development of the Bohr-Rosenfeld paper?
Moller: Oh yes, I remember many discussions there, but I’m not sure that I really can tell anything about it.
Kuhn: Landau-Peierls’ objections, if one took them seriously, seemed very fundamental indeed, and I wonder to what extent people did take them seriously, or did say, “Look I don’t know the answer, but it can’t be like that.”
Moller: Well, I think that the paper by Bohr-Rosenfeld, which came as a consequence of these discussions, showed that it is not true that there is an inconsistency, I mean that this --.
Kuhn: But there’s a two-year period in there really.
Moller: Oh yes, but it took a very long time to write this paper. I mean I think there were, I don’t know, 14 proofs to this paper. No, this went on for a long time. There was a paper by Heisenberg -- oh yes, that’s what I was going to tell you -- there was a paper by Heisenberg in which he tried to avoid the infinities by introducing a Gitterwelt --
Kuhn: A minimum length?
Moller: No, earlier than that, but it is connected with that, I think. He introduced instead of the continuum a space-time lattice, but this of course made difficulties with the relativistic invariance. Such a lattice would not be a re1ativisticly invariant notion. I think in this paper the idea was that the difficulty was due to the infinite number of degrees of freedom you have in the field, so one takes at least --. Well, it will also be an infinite number, but countable.
Kuhn: Well now, come away from this direct approach to the quantum electrodynamics. How did you get on to your thesis problem? Where did that problem come from?
Moller: Well, actually it was Landau who mentioned that probably one could do such a calculation by a purely correspondence treatment. He mentioned also Bethe a treatment of the non-relativistic case. Bethe had treated the collisions and stopping phenomena in the non-relativistic case. He had written the matrix element for the transition in such a way that it looked as if one particle in its transition creates a charge distribution which then acts on the other through a Coulomb potential. And then the rather obvious idea came to do it relativistic ally; instead of using the Coulomb static potential, to introduce a retarded potential corresponding to the charge and current which corresponds to such a transition. This is very close to Klein’s treatment of radiation -- the correspondence treatment of the radiation from an atom in making a transition from there to there. This transition corresponds to a certain charge and current distribution, and then one calculates by classical Maxwell equations the radiation which corresponds to this. So now here it’s only one step further to make this radiation work on the other particle. It was not Bohr who gave me the idea to do this, it was actually this remark by Landau. When one finds then that the expression for the transition is, as a matter of fact, symmetrical in the two particles, then it is very probable that this should give the right result. And then a year later it was shown by, I think first by Bethe and Fermi, that using the Heisenberg-Pauli quantum electrodynamics, one gets exactly the same result.
In this same year, when I had published the first paper in the Zeitschrift fur Physik, which was more or less a preliminary thing, I got a letter from Cambridge from an experimental man, who was doing experiments with scattering of beta particles in a gas, and he asked me about this paper in Zeitschrift fur Physik. Unfortunately he didn’t sign the letter, I didn’t know who it was. I wrote to Delbruck who was in Cambridge and asked him who was working with such things in Cambridge. He wrote back -- I just looked up this letter -- that he couldn’t say for sure, but there was a student of Blackett who probably was doing this. Then a few months later, I got a letter again from the same man. He said, “A few months ago I wrote you a letter, but I never got an answer.” It was Champion. He did these experiments. So in the following year, while I was preparing this thesis, we had correspondence with each other, so in the thesis I also had his experimental results.
Kuhn: To what extent did this problem at the time seem important because of the possibility of an experimental check, or because it was important to develop the theory this way, for a sort of completeness? One could be driven to this for various reasons.
Moller: There was the big paper by Bethe on the non-relativistic stopping and it was very natural to try to generalize it to very fast particles. One had the cosmic radiation already, of course, and it would be nice to treat these things in a consistent relativistic way. It had also some connection with Bohr’s very earliest papers, because Bohr also treated the classical stopping. But of course the stopping thing could be treated in a somewhat different way. This way of doing it as I did was more important for the direct scattering between two electrons. And so far it seems still that it holds. We have not been able to come up to these high energies, although in Stanford of course they have now the monster which probably can show us if there are some deviations when you come to very small distances. One would think it probable, but one doesn’t know really. At that time also, a little later perhaps, Heitler’s paper on the Bremsstrahlung at very high energies came out, and it was also a little doubted if this formula would hold up to these very high energies, but it seemed that it was completely correct up to the very highest energies, this of course was very important for the development of the shower theory, of the soft showers.
Kuhn: In that same period in which you are at work on your thesis and bringing it out, I take it that interest at Copenhagen is also now beginning increasingly to turn to the nucleus.
Moller: Yes. With Gamow’s arrival in ‘29 already of course one became --. It was so interesting to see that quantum mechanics could be used also inside the nucleus.
Kuhn: Was that really initially surprising? Hadn’t one ever taken it for granted.
Moller: Yes. I think one thought it was very likely that it should be so, and it was very satisfying that such a typical quantum mechanical effect as the tunnel effect was important for the description of the alpha decay. But still you see, one did not quite know, because there were other things which seemed to make it difficult. The beta emission was so extremely strange that it seemed that the energy was not conserved. I mean this experiment by Ellis and Wooster where one directly measures the energy which is coming out in the form of heat, and one finds that it does not correspond to the total energy which is released in these transitions. Only about half of it. I remember Gamow was writing a book on this, and he had a stamp -- I don’t know if you’ve heard about that -- of a Totenkopf, and every time there was something with beta theory he made this stamp! One really didn’t know if this was a sign that after all quantum mechanics does not hold inside the nuclei, until Pauli of course came with this very simple explanation of the existence of the neutrino which carries away the energy.
Kuhn: Well now how did people originally feel about the neutrino which circulated I think in discussion for some time before it appeared in print?
Moller: Yes Well, I think the thing which made it seem very probable that something like this should exist was that it was not only a question of non-conservation of energy, because after all -- but it was also the conservation of spin. And this I think gave a very strong support for this. Of course Bohr I know was for some years still playing with the idea that energy might not be conserved in these processes. But at least after Fermi’s theory came, the first papers of Fermi, which I read with great enthusiasm, then I had the feeling that it was rather evident that something like a neutrino existed. After all, how does one prove the existence of a thing? For instance when the neutron was discovered, it was by the reverse process, I mean the effect of this thing on something. One could just as well say, “Well, the very fact that beta spectra show a lack of energy, shows that something has come out with these and these properties.” So I think the theorists during the ‘30’s mostly were inclined to say that this is quite certain. The experimentalists still were a little doubtful about it; they want to be able to find the effect of a thing. I was very nice of course when one could find the effect of the neutrino.
Kuhn: Were the Fermi papers also fairly decisive in Bohr’s attitude towards the neutrino?
Moller: I think so, yes, I think so. Well, first of all it’s rather striking that such a simple thing as merely seeing how much phase space there is, one nearly gets the right form. The phase space of a particle, which we cannot see, but which is there. It is rather convincing that there must be something. And then of course also the conservation of the spin. //Without the neutrino there’s// there’s not only loss of energy but also something wrong with the spin.
Kuhn: I understand from what several people have said that the positron, and perhaps here unlike the neutron, did make real trouble for a bit.
Moller: Well, in Dirac’s first paper, he thought that the holes could be protons, because these were the only positive particles we knew of. But then Pauli showed, I think it was Pauli who showed rigorously that the holes must be a particle of exactly the same mass as the electron because of the symmetry. And then, well Pauli was very critical to Dirac theory for many many years because of the negative energies and the whole ideas of filling up this sea was so monstrous, which it is, of course. Nowadays we don’t need to do it anymore, but even in the Handbuck-Artikel of Pauli on quantum mechanics, he said there’s still something fundamentally wrong with this equation. Pais told me when he was here the story about somebody who was in Ann Arbor giving a colloquium in which the Dirac equation played a role; be started to write the Dirac equation on the blackboard. Pauli was present. Pauli went up, and crossed it out: “Das ist falsch!” [laughter] I don’t know what he meant.
Kuhn: How late would that have been?
Moller: I don’t know, I should have asked Pais about that. But, when was Pauli in the United States for the first time? It was at the end of the 30’s I think.
Kuhn: He may have been there before that.
Moller: Maybe, yes. During the war he was there. No it’s probably earlier, it must be earlier.
Kuhn: Most of the people who had achieved similar attention had at least had the opportunity to be in the United States by then. And particularly Goudsmit and Uhlenbeck started bringing people over with some regularity, but I’m not really sure. [Interruption] You say the interest in nuclear physics, I mean the increasing transition to it really dates from the Gamow work.
Moller: Yes. But I think one couldn’t do so very much with it before the neutron was discovered in ‘32.
Kuhn: I take it also that in ‘29 still, Bohr himself was still deeply concerned and giving most of his attention to measurement problems.
Moller: That’s right, that’s right. Those were the years when he was doing all these Gedanken experiments. Yes, yes, that’s right. But, I know how excited he was about the neutron. Of course this immediately helped quite a lot, because the existence of the electrons inside the nucleus was a very mysterious thing. To think that the thing should be a collection of protons and electrons in order to give the right charge, that was a very very difficult thing.
Kuhn: Do you remember discussions about that problem here?
Moller: Yes, yes, oh yes. I mean already from the uncertainty principle it was clear that if electrons really should exist inside the nucleus, then it must require extremely big forces to keep them inside, which was rather unlikely. And, at one time I remember that Bohr said, “I think the electrons are rather a kind of ‘lime’ [mortar] which helps to keep together the nucleus.” This is a little in the direction of saying that the electrons really do not exist as electrons, they are a kind of ‘lime’, and this is really then what went into the Fermi formulation and the Heisenberg formulation of the nuclear forces. It’s really the same. But Heisenberg’s came after one had discovered the neutron, and one could say that the proton and the neutron are the same particle in two different states; you have an exchange of this thing which gives the nuclear forces. At that time of course one didn’t think of the meson yet.
Kuhn: Prior to the neutron, did Bohr take the electron to be an argument that perhaps really the quantum mechanics didn’t apply to the nucleus?
Moller: I think that was what was behind it. I mean it may be that something really new was there which could not be described by quantum mechanics. As I said, for a long time he had the idea that maybe energy is not conserved in these processes, which would clearly be in contradiction with quantum mechanics.
Kuhn: That idea of energy non-conservation comes up again and again and again in Bohr’s life.
Moller: Yes, that’s right. Oh it was of course much earlier in the paper by Bohr-Kramers-and Slater, where they stated explicitly that probably the energy is conserved only statistically, but not in each process. But then, that was a direct experiment. I think it was Bothe.
Kuhn: Bothe and Geiger, and Compton and Simon.
Moller: Yes, right.
Kuhn: Reading some of the letters, one finds again and again that there are repeated occasions on which things go wrong and Bohr suggests energy non-conservation. It’s curious, one almost has the feeling on occasions that he really thought that science had to go in this direction, that we would ultimately see that energy was not conserved. I’ve always been curious as to why that was.
Moller: Well of course the development of physics has always gone in the direction that this has been one of the last things people like to give up. One always tries a different explanation -- again with the neutrino.
Kuhn: Yet in Bohr’s case, this was almost the thing he would propose first.
Kuhn: It really sets him apart.
Moller: But of course the energy conservation is something now so connected with the time displacement, it will be a real terrible revolution if it should turn out not to be possible to invent neutrinos or something like that in order to have energy conservation. This will be a fantastic thing.
Kuhn: It’s your impression then that it’s really from the neutron that intensive interest here, and the real switch to nuclear physics started.
Moller: Yes. And then of course also the experiments by Fermi in l934 on slow neutrons; this, plus all the things which came up there, the cross-section and so on, was what led Bohr to the idea of the compound nucleus on which he then worked for quite a number of years, up till the war. No, I think before the neutron was discovered it would have been very hard to come very much further there. The material of which the thing is built up is so essential for understanding how it is built up.
Kuhn: Yet, at least at some places, I suppose particularly Cambridge, one was already trying to do a nuclear theory, a quantum mechanical nuclear theory where possible. In retrospect one now forgets it because how could they have done it? But they were at least trying.
Moller: Yes, what are you thinking of in Cambridge?
Kuhn: Oh, well Mott gets involved to some extent, and Ellis would be one. There’s a group around the theory -- I know these nuclear papers considerably less well.
Moller: I know that’s it’s an old idea of Rutherford that there should be a neutral proton, so to say, and I think that was very essential. Rutherford seems to have had this idea, and this gave the clue to these experiments so that Chadwick had the courage to really say that this is a new particle, a neutral particle. Before that there were some experiments by the Joliots and Mme Curie where they -- how was it now -- interpret something as a ‘nuclear Compton effect’ but which would be -- I remember that, how was it now?
Kuhn: Yes, I know of that, I haven’t read it.
Moller: Felix Bloch was here, and we discussed it a little and we said this is completely impossible because the mass of the nucleus is so high that from the Klein-Nishina formula, the Compton effect of a photon hitting such a heavy particle would be absolutely negligible. But it was actually neutrons and not photons that were coming out. They were not able to say what it was; it was Chadwick who then cleared it up.
Kuhn: No I didn’t mean to say an attempt at the neutron, but an attempt to apply theory in some detail to nuclear processes.
Moller: Oh yes, Gamow also went over there, and his theory of the tunnel effect was very important in making the experiment of Cockcroft and Walton hopeful, because he could see that there is, after all, in quantum mechanics a certain probability that a proton will be able to come in, although classically it would never be able to come in. That is true of course. But that was not very much further than the old Gamow idea in which you suppose you have such a potential well and you have particles in here and they can go out -- that would be the alpha decay -- but you could also have the opposite, the particle being shot in although it has not the energy classically, to climb the hill. It can, it is a sort of way to get through. That’s right of course. In connection with Cockcroft and Walton’s first experiments, the energy was not very high, but still they got some transmutations. But to get a detailed kind of theory of the constitution of the nucle4s is rather impossible unless you know what it consists of. So I think the discovery of the neutron was a turning point.
I suppose you have talked with Rosenfeld about all the discussions of complementarity.
Kuhn: Well except that people remember different things. That’s a subject on which I would be particularly glad to have more information.
Moller: Well I remember of course the excitement when Bohr was able to beat Einstein with his own weapon. That was at a Solvay meeting; Einstein invented a way of showing that quantum mechanics was not consistent. He proposed to determine the energy of the photon which had come out of the box by weighing the box before and afterwards. Then Bohr could show that if one takes Einstein’s formula for the rate of a clock in a gravitational field then it comes exactly to making the thing consistent again. And Gamow even made a model of this box with a spring and clock and shutter, which opened at a certain time and closed again at a certain time.
Kuhn: Were you at Brussels for the meeting at which that interchange went on?
Moller: No, no, oh no. No, these first meetings I only heard about. The first meeting I came to was in 1948.
Kuhn: To what extent, after ‘28-29, when you were getting deeply involved with your own work, were complementarity and the measurement experiments still really deep issues for people in Copenhagen, beyond Bohr himself?
Moller: Although we listened to hundreds and hundreds of talks about these things, and we were interested in it, I don’t think, except Rosenfeld perhaps, that any of us were spending so much time with this thing. I mean, after all, when Bohr is there, it is very hard to do something better. And also when you are young it is more interesting to attack definite problems -- I mean this was so general, nearly philosophical. No, later I became involved with the meson things, and also did some work on k-capture of electrons, according to Fermi’s theory. These things are definite problems which --. Also of course it was difficult with this complementarity. One could very easily go wrong, and it required Bohr to straighten things out.
Kuhn: It a somewhat peculiar development in that in the really physical problems, somebody learns how to do them, then other people learn how to do them too, then even a graduate student can do them. But this set of problems Bohr learned to do and to do them brilliantly. There are all sorts of very skilled physicists capable of doing very stupid things with hem right now. Now presumably at one point one could have seen that happening, seen people stopping following, losing interest in this without really ever having learned it. Was that true already by ‘29 and ‘30?
Moller: No I don’t think. I mean we certainly were very interested in it, but we were already convinced that quantum mechanics was consistent. I mean Bohr had convinced us, and we thought that perhaps there is not so much more to do there. What you say about brilliant people falling into pitfalls in this field is certainly true. I mean even Heisenberg in some cases, as Bohr pointed out later, made some mistakes in such discussions. But it is also quite true that nowadays students learn quantum mechanics without really following all these difficulties which Bohr saw, and which he cleared up. It is possible to do things with quantum mechanics without understanding anything about complementarity, and most of the students now do not read anything about it I think. It is also quite strange that all the textbooks avoid these things, with the exception of Landau’s I think, and also with the exception of Kramers’ old book where there are some discussions of real experiments, how one should measure this and this. But usually one jumps over this.