Leon Rosenfeld - Session II

Kuhn:

We had been talking about Gottingen. I think we had run out of questions on Gottingen. If you have other thoughts about it I’d be delighted, otherwise we can proceed and talk about how you got to Pauli.

Rosenfeld:

The only things I remembered as perhaps rather characteristic are one or two anecdotes concerning Ehrenfest. I think the first time I saw Ehrenfest was at a seminar in Gottingen where he had come just for a visit, and where the man had explained some problem treated according to the new wave mechanics of Schrodinger. Then Born sprang up and said, “That can also be made with matrices,” and then he started scribbling, repeating the same calculations but with matrix formalisms. Then Ehrenfest said, “But why do you want to do it like that? It’s much more ‘anschaulich’ with those waves.” Born said, “Well, the two treatments are equivalent. Es ist nur eine Frage der Gewohnheit.” “Ja,” said Ehrenfest, “aber es gibt schlechte Gewohnheiten.” Born was rather piqued! Then I don’t remember exactly what happened; perhaps I may have had a conversation with Ehrenfest at that time, but sometime afterwards I got a letter from Ehrenfest, asking me to instruct him about von Neumann’s theory which had just appeared — his axiomatic treatment. At that time in Gottingen I had studied those papers by von Neumann very carefully so I sent something as a sort of resume of von Neumann’s ideas to Ehrenfest. In my files I found his answer on a post card, in which he seemed very pleased with the exposition which, he said, was quite clear. But I remember from his answer — I don’t remember what I wrote — that I had explained that von Neumann’s axioms allowed one to get away with this “beruchtigte Interferenz der Wahrscheinlichkeit,” because the superposition principle is not formulated explicitly. It was hidden in the axioms but not formulated explicitly. At that time, — of course, I’ve changed since then — but at that time I regarded that as an advantage. In the answer of Ehrenfest there is a remark on that; he says, “You call this interference “beruchtigt”, but how do you imagine that one could have dealt with the Davisson-Germer and other experiments without that concept?”

Kuhn:

How could you have answered that question? I mean, I take it that you were not the only one at that time who didn’t like the idea of the interference of probability waves.

Rosenfeld:

I was very pleased at that time, thought, of course, it was rather shortsighted, but I thought that this axiomatic formulation of von Neumann, in which it does not come explicitly but which comes as a consequence of the axioms, was a help; that is, you started from more general axioms about probabilities which did not seem to introduce such hard-to-visualize concepts, and then you got them from those axioms as a consequence. However, I did not realize the obvious thing — the thing which now looks obvious — that, of course, you had hidden the thing in the axiom. In fact, one of the things that poor Lande is up against now is exactly the same fallacy; he imagines that he has gotten rid of the conceptual novelties, not to say difficulties, of quantum theory because he has introduced this ‘axiom of continuity’, as he calls it, this graduation of probabilities, without realizing that it’s just equivalent. It’s only an indirect way of saying the same thing. That is the danger of axiomatics.

Kuhn:

On this story of Born and Ehrenfest and in connection also with your own work on the Born-Jordan Elementare Quantenmechanik — I’m still puzzled. Born, in the chapter of the autobiography that we’ve seen, laments the fact that they did the whole thing matrix-mechanically and agrees now with Pauli that it was a mistake and so on. Rather, he says, Jordan persuaded him to do it this way. On the other hand, both Jordan and you point out that there was to have been a second volume which would have taken the other approach, which makes better sense. And also it just doesn’t seem to me terribly likely that Jordan would have pressed him; Jordan was doing much more with waves from the beginning. Do you remember if it was Born who pretty clearly insisted on doing it that way?

Rosenfeld:

I have that impression, though I cannot vouch for it absolutely, because when I came into the project I was just a helper, so I was not let in on the secrets of the gods. I don’t know what deliberations there were. The only thing I remember about Jordan is that Born was terribly angry about him because he did not contribute his part, and I think the whole manuscript had to wait for a month or two before Jordan’s chapter arrived. Jordan had gone to Hamburg at that time. I knew Jordan rather well at the beginning of my stay in Gottingen when he was still there, and in fact, I attended a lecture by him which was extremely good, a very illuminating lecture about quantum statistics. In spite of his stuttering, it was a very stimulating and really a very good lecture. Then he went to Hamburg just about the time I started this work on the book, so that, in regard to the book, Jordan didn’t enter my horizon as a — except as a man who does not fulfill his duty. But I had the impression that it was just an experiment, a pedagogical experiment that Born was making to see how far one could go with this matrix thing. In fact, I think, what he had in mind was something which Dirac did very much better at the same time; namely, in Dirac’s book, he starts with an operator algebra and he carries out that (formalism). This matrix formalism was just an encumbrance to special representation, but it was Born’s pet idea. After all, it was Born who noticed the identity between Heisenberg’s concept of quantum mechanical variables and. matrices. Then Born fell ill; that must have been the winter semester of ‘28-‘29. So Heitler and I had the task of giving his lecture on quantum theory, quantum mechanics, and we shared the job. We each took the things which we liked best; I took just this von Neumann business, just this axiomatic part. On that occasion I got to know the eldest daughter of Ehrenfest who was then studying mathematics at Gottingen, and she came to those lectures, as did several other mathematicians, just because they were interested in this mathematical aspect. As I think of it, that must have been the occasion for Ehrenfest to ask me more about that.

Kuhn:

Do you have any recollection what he asked you? Because he’s the sort of person who was not repelled by axiomatic formulations.

Rosenfeld:

No, not at all. But he did not feel like plodding through those very obscurely written, though very clear in substance, papers by von Neumann, and when he heard that somebody had done that job, he thought, “Well, let us pump him’.” I think it was just that. He thought that he could be spared the task of reading the papers. Von Neumann as a whole has been partly clarified, but mostly through confusion when one looks at it in retrospect. There is always a danger, as, for instance, on this point of the Schnitt. Many people, especially young people, find it helpful because it is put in symbols, it is formalized. But the danger of formalizing is that you lose the physical content of it, or at least you are in danger of losing it so it’s always a double-edged sword.

Kuhn:

How did this work out at the time? You were deeply interested in the von Neumann thing, but who else was interested in it?

Rosenfeld:

Well, Wigner, of course, and Jordan, too. Those were the two who dealt with it most in conversation. I was also a close friend of Heitler, but Heitler was not at all interested in those things.

Kuhn:

Was Born interested?

Rosenfeld:

Yes, surely. In his book there is an effort, as he thought, to popularize von Neumann’s ideas, to put them in a simpler form. Whether he succeeded is another question, but at least he had that idea. Anyway, I’m glad to have had that grounding in “Neumannistics” because when it is corrected by the influence of Bohr, then it is a sort of skeleton which helps to get a precise expression for the ideas. I think one of the main difficulties in understanding Bohr’s ideas for most people is that they are formulated in such a subtle way that they are difficult to grasp. Bohr himself always said that what he said was meant as an invitation for the reader to think along that line, but not as an apodictic statement. And I think that’s very true, but most people do not like that kind of exercise.

Kuhn:

How did Pauli feel about the von Neumann approach? Was this just more “Formalismus” for him?

Rosenfeld:

At that time I had hardly any contact with Pauli, and when I later came to Zurich, there were other problems, so that it never came up in discussion. The stage was past and axiomatics was done. I suppose people were happy with it, but there it was. At that time, of course, von Neumann went on with Goedel’s theorem and Pauli was very interested in that, but that was a quite different question. The only encounter I remember between Bohr and von Neumann was rather disastrous. Von Neumann came to Copenhagen once for a short visit and he was invited, as always, to give a colloquium in which he took up those questions of measurements and so on. Bohr didn’t interrupt very much; I don’t remember if his verdict was “sehr, sehr interessant”, but surely his comments later were very disparaging. After the war, Bohr met von Neumann in the United States and I don’t know exactly what conversations they had, but again, when Bohr occasionally mentioned von Neumann it was always with this mixture of admiration for his formal genius and quite different expressions for his insight into the questions. On the whole, I think that Bohr was rather annoyed by von Neumann’s presentation.

Kuhn:

Now we might deal with the transition from Gottingen to Zurich.

Rosenfeld:

Yes, but I wanted perhaps to describe my visit to Ehrenfest. Ehrenfest invited me to come to Leiden; that was a great stir because that was the first time that I was asked to come to give a colloquium in such a famous place as the Ehrenfest Hochpult. He received me in an extremely cordial manner, inviting me to his house for both lunch and supper, perhaps because he wanted to analyze me to the core. Anyhow, it was, as I look back on it now, a very exciting conversation. But at the time, I made a very poor showing because I was terribly shy, so I could hardly formulate any replies to his questions, partly from shyness and partly from ignorance. So I answered very abruptly and I must have given the impression that I did not care much for what he was saying, which was not at all the case. I remember when I came in his room he was sitting in an armchair and he jumped up. He did not come to me, but he jumped up to his book shelves, picked out a volume, opened it — the volume opened mechanically at that page — and, putting the volume before my nose, he said, “Haben Sie das verstanden?” It was a page in Planck’s Warmestrahlung, in which occurs this famous division by N factorial. Not only had I not understood it, I was also not even aware of the problem! So that was a very inauspicious beginning.

Then he turned the conversation to all kinds of subjects, mostly quantum mechanics, of course, but it glided on all kinds of subjects. I remember that he asked me if I had understood the cause of the French Revolution, because that was one of the problems that he had never been able to get to the bottom of. He had read all kinds of books, he said, all kinds of expositions from various points of view, but he had not understood the motives behind the French Revolution. Ehrenfest managed, in a very friendly way, to give me one more day of hospitality and asked me what I wanted to do. I said I wanted to go to the Museum to see the famous paintings and so on, which I had never seen. Then he said, “Well, do you want to do that because it is something that has to be done, or is it because you like paintings?” I told him it was because I liked paintings, I had no preconceived ideas about that. So that was all right and he explained to me how I should go, where I should go, and what I should see. I met his younger daughter, who was an artist, for the first time there. I don’t know what she is doing now, but she was already studying art then and later made extremely nice educational books and games for children.

Heilbron:

Did you mean literally that Ehrenfest tried to analyze you?

Rosenfeld:

I suppose so, but it’s a pure guess, of course. He was always very interested in people in general, so I was a new subject of investigation. At that time Casmir was one of his most brilliant pupils, as well as Rutgers who is now a professor in Ghent. I got rather friendly with Rutgers on this visit; I suppose that Rutgers was more or less assigned to take care of me, so we went out in the evening and so on.

Kuhn:

What exactly was your colloquium on?

Rosenfeld:

It was on the work that I had done on optical activity.

Kuhn:

Had this subject been specified on the invitation, or were you simply asked to come give a colloquium on something of your choice?

Rosenfeld:

It was specified. He was interested in this curious phenomenon, this resonance between the mirror symmetrical forms, which, in fact, was not my invention but Hund’s, but in this optical activity it played a fundamental part. So he was interested in that treatment and again he wanted to understand it thoroughly.

Heilbron:

What were the other issues he was particularly interested in at the time, other quantum mechanical problems? Was he interested in Dirac’s theory and so forth, electrodynamics —

Rosenfeld:

Yes, at that time, everybody was still interested in the very principles of the thing; that is, the connection between the wave mechanics and the matrix formulation — transition probabilities — was of course formally understood because one had the formula to pass from the one to the other, but the transformation theory was then very new and not yet quite digested, so to speak. And then all the consequences of wave mechanics, such as the tunnel effect and this resonance phenomenon, looked very strange, so Ehrenfest was keenly interested in those new phenomena which were completely foreign to classical theory.

Heilbron:

Had he completely accepted the —?

Rosenfeld:

Well, I’m not absolutely sure, I’m not absolutely sure that he didn’t have the idea in the back of his mind that the Schrodinger point of view and the primacy of the wave might not have something in it. Then I suppose that when he saw those strange phenomena with waves which were not explainable in terms of particles, he may have thought that Bohr’s complementarity had something in it. It was after I had done these optical works, so it must have been early ‘29. It must have been in the spring of ‘29.

Kuhn:

By the Spring of ‘29 were you already in Zurich?

Rosenfeld:

No. I came to Zurich before the summer semester, but it must have been after Easter because in Easter ‘29 I came to the conference here. It was my first meeting with Bohr. I came from Gottingen where I was still at that time. I had already corresponded with Pauli, and, in fact, I had first corresponded with Bohr, asking him whether I could come to Copenhagen. But it was not convenient [to him], because he was busy then writing the Danish translations of his essays for the university Festschrift, and he had other obligations, the eternal obligations of things that he had to write up. So the answer came that it was not convenient and I had better postpone this, and so I wrote to Pauli then to ask whether he would take me up. Unfortunately I’ve lost that postcard, but I remember the contents very well. He was very friendly and he said: “With pleasure, because we have just completed a scheme of quantum electrodynamics with Heisenberg; ‘das ist ein Gebiet, das noch nicht abgebrochen ist.’” So he was eager to have people brush up the details and explore the consequences and that’s what I did at Zurich actually.

Kuhn:

What sort of financial arrangements were there that enabled you to live in Zurich?

Rosenfeld:

That was done through Liege University and by this man, this curator, Dehalu, whom I mentioned. There was a fund called ‘patrimoine’. You see, during the war, there was a commission for relief in Belgium which was founded in the United States under the chairmanship of Hoover, the later President. I remember that they sent flour to Belgium and I remember the sacks in which it came; they had the various stamps of American flour mills on them. They were distributed — one could buy them, I suppose — and then the ladies embroidered those designs and made cushions of them. That was really the fashion of the time. Anyhow, when the war ended, this commission was left with unused money, so Hoover had the idea of giving this money to the Belgian universities as ‘patrimoine’, a sort of capital which was independent, not under state control, and the property of the universities. It is still there and I suppose it has been replenished; I hope so. Anyhow, this money was used for various purposes and one of the purposes was to give stipends or fellowships to people to go abroad.

Kuhn:

Then you really held these for four years, didn’t you? A year in Paris and then a year and a half in —

Rosenfeld:

Well, in Paris I was under a state stipend. Then in Gottingen the first semester, I think, I went on this Belgian stipend, then I got an assistantship in Gottingen. Then in Zurich I was again under the Be1gian stipend.

Kuhn:

Throughout your stay there?

Rosenfeld:

Yes, they were extremely generous, and when I came back from Zurich, I had a chair, or readership you would call it, which was especially created for me at Liege.

Kuhn:

With these same funds?

Rosenfeld:

No, then it was a state readership…

Kuhn:

Before we get to Zurich, you say you first came up here to Copenhagen.

Rosenfeld:

Well, that was for the conference only, because I intended to come here to stay, but that was not possible at the time. Bohr started with an introductory talk on the impossibility of measuring the spin of the electron by classical methods. Then there were disconnected topics which arose from the publications immediately preceding: Heitler spoke about chemical bonding; Mott, I think, spoke about this scattering and the influence of the statistics on the distribution; and there were, of course, more subjects, but I don’t remember exactly more details.

Kuhn:

Were there any particularly vital discussions or any issues that seemed particularly alive and pressing at that point?

Rosenfeld:

Yes. For instance, I still remember that this paper by Mott, which we would say now, was a straightforward application of Bose statistics and a very clear analysis was received with great surprise and as a great novelty, even by Bohr. Of course, when one saw it, it was clear that it was a consequence of quantum theory, but it was a consequence which had not been thought of; and so it was with most of the things at that time. I cannot mention special points, but the general impression one had at that time was that one opened up a world of surprises. [The same was true] of Gamow’s theory of radioactivity which he did in Gottingen, and I still remember the colloquium which he gave and the surprise that arose. Born jumped up and said, “That is a very fundamental thing.” It has many applications, and as one of the applications he mentioned the phenomenon which is now called the “cold emission” from metals by pointing out that you have a barrier also due to the Coloumb field at a surface of a metal and therefore electrons must leak out.

Kuhn:

Born did not try to do that one by matrix mechanics immediately, did he?

Rosenfeld:

No! Born was quite alive to the advantages of wave mechanics. Surely.

Kuhn:

Did the problem of the electron in the nucleus come up in Copenhagen in ‘29?

Rosenfeld:

No, not that I remember. Then Heitler’s theory of molecular binding was very controversial, in fact, with good reason, because it was very a doubtful approximation.

Kuhn:

Was Hund there for the meeting?

Rosenfeld:

I don’t think so, but that can be ascertained.

Kuhn:

When you speak of his coming I gather that other people have spoken about arguments over it; do you remember how the parties lined up about the Heitler binding theory?

Rosenfeld:

No, I have no very distinct recollection. I think Pauli was, of course, the most critical. There was this famous Pauli effect, you see. After the lecture by Heitler, Pauli went to the podium and started criticizing and pacing to and fro; he said, “at large distances we know that it’s not varied because there we have the van der Waals forces; at short distances we know it’s not varied because there we have the constant forces; why should there be a region in which it has any sense?” At that time Pauli was going towards Heitler who was sitting in a chair on one extremity of the podium, and, as Pauli went towards him with that question, the back of the chair collapsed and Heitler fell over backwards.

Kuhn:

How did Bohr feel about the Heitler theory?

Rosenfeld:

Bohr was as always very optimistic. He said, “It may be that the mathematics has to be refined, but it is surely essentially correct.”

Heilbron:

What did he feel about the great quantity of group theory that Heitler employed in that analysis?

Rosenfeld:

Bohr did not attach much weight to that.

Heilbron:

As a matter of fact, I have asked Heitler and he doesn’t like it; he says he would have done it in a much simpler way.

Rosenfeld:

Yes, it was a general attitude at that time. People were so impressed by Wigner’s success with that, that everybody wanted to do group theory. I remember another episode which took place in Zurich, I think, when Bloch, Peierls and I were present. Peierls explained the property of the wave functions in metals, a very simple one that you could see immediately from the equations, and Bloch was very pensive; then he said, “Ja, das kann ich auch mit Gruppen machen,” and he filled the blackboard Then came the reaction and people began to speak of the “Gruppen-pest”; they were very happy when Slater came with the Slater determinants which were obtained without any explicit consideration of groups and were just fine for embodying the exclusion principle, which people had tried to do with symmetric groups, and so on.

Kuhn:

Dirac does a little paper which is sort of group theory without group theory; is that an influential paper?

Rosenfeld:

Yes, that was part of this general reaction. In fact, Dirac took up the ideas which underlay Heitler and London’s theory, and he showed how to do it by very simple considerations without any explicit appeal to groups.

Kuhn:

But was this paper widely greeted by people and much used?

Rosenfeld:

Oh, yes. People didn’t like Heitler’s characters and that kind of thing at all. I have a feeling that Heitler did not like them either.

Kuhn:

Then what happens when you get to Pauli?

Rosenfeld:

There I got to know Peierls very intimately; we were always together.

Kuhn:

Who else was there? Peierls was there as an assistant.

Rosenfeld:

Yes. Another one who was there was [J .H.] Bartlett who worked on the nebular lines; he calculated the transition probabilities of those forbidden transitions. Bartlett was very fond of walking and still is. He was in Copenhagen last year and visited us, and I noticed that he was still as fond of walking as he had been in Switzerland when we had long walks together in the mountains. Peierls came [to Zurich], too, as well as Gamow, and of course Landau came like a meteor. Landau asked the various people, “What are you doing?” So Peierls, Bloch, and I started explaining the problems that we were struggling with, which at that time were mostly problems of metals, apart from the quantum electrodynamics. Landau went away then, I don’t know exactly where, and a week later he came up with the solutions to all those problems. He had a special technique, I don’t remember exactly what it was, but he had a trick, and one could find it by looking at his treatment of the diamagnetism of metals because he succeeded there by pointing out a special feature of very general validity. I remember a conversation in which he explained that to the others, and Peierls said, “Oh, but I can use that that’s fine, because that’s just what I need,” in order to treat some problem in thermo conductivity, probably. And Bloch said, “Yes, but this is exactly the method to apply to my problem.” Then Landau said, “Yes, but please remember that that is my idea.” He began to be a bit disquieted! Then Peierls remarked that “Wir leben alle von Brocken aus Landaus Tisch.”

Kuhn:

How does it happen that quite this much of the work on theory of metals was being done around Pauli, who had announced that he didn’t like this?

Rosenfeld:

At that time Pauli liked it very much. That was probably a later reaction, but at that time he even gave a lecture, though not a very good one, on magnetism in metals. On the contrary, he was very lively and very much interested in those things. Peierls had just defended his thesis at that time, and Debye came on that occasion.

Kuhn:

You yourself were not so much involved with the theory of metals?

Rosenfeld:

I started various things, but I had also started studying diamagnetism, but then Landau came and that was the end of it. Then I started other problems on the optical properties of metals, but I didn’t finish them in Zurich, and when I came to Copenhagen, I got involved in those other things. The reason why I did not finish them in Zurich was that I got provoked by Pauli to tackle this problem of the quantization of gravitation and the gravitation effects of light quanta, which at that time were more interesting. When I explained to Pauli what I intended to work out, I think it was the Kerr effect or some optical effect, he said, “Well, you may do that, and I am glad beforehand for any result that you can find.” That was a way of saying that this was a problem which was not instructive, that any result might come out, whereas at that time, the calculation of the self energy of the light quantum arising from its gravitation field was done with a very definite purpose. One knew that there was an infinite self energy for particles like electrons which had finite mass, and it was unclear whether this self energy was not due to the idealization of a mass point. Of course, one knew that the quantum self energy was different from the classical one, it was not just the e²/r for r=0, but we knew that there were other contributions from quantum theory. One did not know that it was reduced to a logarithmic expression, but anyhow, one knew that there were other quantum effects. But one did not know whether those divergences were not due to, this original divergence which was there in the model itself, in the Hamiltonian, actually. So it was thought interesting to study the self energy of things like the light quantum whose Hamiltonian did not contain anything, with the zero rest mass and no singular field; but then the only field that one thought of at that time, because electron pairs were not imagined, was the gravitation field.

Heilbron:

That was Heisenberg’s suggestion?

Rosenfeld:

No, that was Pauli’s. Pauli raises the problem.

Heilbron:

I thought that you had pointed to Heisenberg in the article itself, and that Pauli perhaps had had it from Heisenberg.

Rosenfeld:

Well, if I pointed it out then, that must have been so, but I’ve forgotten now. It may be that it arose from conversations or from letters from Heisenberg; that may have been the case. I don’t remember exactly, but anyhow it came up in conversations. I only remember the fact that Pauli had the impression that I had not enough initiative at that time, and therefore, he did not give me problems. He refused to do that, saying, “You ought to find your problems.” So I knew that afterwards, but in conversations in which Peierls was also present, since Peierls was more or less in Pauli’s confidence at that time, they raised this problem and, discussed it and that provoked me to do this thing. I heard afterwards that Pauli had been very pleased that I had taken up the challenge indirectly, since it was a more or less indirect provocation.

Heilbron:

You had earlier published some papers on quantum electrodynamics, before the gravitational —

Rosenfeld:

Yes, it was immediately after I came to Zurich that I got the proof of this paper by Heisenberg and Pauli to study. Then Pauli told me that he was not at all pleased with those longitudinal waves, so he wanted to have them treated another way, which I did, but that was not more enlightening, far from it.

Kuhn:

Apart from the reality within this treatment of certain of the difficulties that already seemed to be there, how did Pauli himself at this point feel about this whole theory? Did that seem likely to be the answer?

Rosenfeld:

I can answer that by an anecdote. There was this point in their proof in which the invariance of the Hamiltonian seemed to depend on a special structure of the Hamiltonian, and that looked very suspicious. In fact, I said that directly to Pauli when I had read the proofs, and he said, “Yes, I understand that, but we have not been able to find any mistake in our calculation and we do not understand what this means; we suspect that it must be wrong, but we don’t know.” Then the thing came to a crisis through the fact that I then tried to make a more general formulation of this field quantization, starting from Lagrangian, defining the momenta through the variational derivatives, and then I saw that I could do that without specializing the Hamiltonian. It was a purely abstract scheme which worked in a completely general way with only this complication of the accessory conditions, but that was, at any rate, not due to any special structure but only to the existence of invariance with respect to group. So at that stage I was convinced that there must be a mistake in the original paper; it was quite clear, and then I set myself to finding this mistake. By going very carefully through every step several times I spotted it; it was an extremely subtle point about two points which had been exchanged in the delta function which was not legitimate. But then it came out all right, so I wrote up a little note about it and I started the note with the sentence, “In ihrer grundlegenden Abhandlung uber Quantenelektrodynamik,” and so on. When Pauli saw that, he said, “Ja, das ist ein ziemlich morscher Grund, den wir da gelegt haben.” [so that was struck out] Then I suggested “In ihrer ersten Abhandlung,” and Pauli agreed, Ja, das ist sinnvoll.” Then he told me that obviously, the general method must be right, that is, we have to quantize the fields; since there is a classical Hamiltonian, the Hamiltonian method must be good enough, but since it leads to those consequences, it must be wrong somewhere. Probably we have not yet got the right variables, he said at that time. That was the first reaction to it; very early in ‘29.

Kuhn:

“Probably we have not yet got the right variables”; that’s very interesting. Which of the consequences of that paper do you suppose most troubled him: the zero point energy, the self energy —?

Rosenfeld:

Yes, all those things which were in it. One did not know how to separate those infinities. We knew that the classical model contained by itself an infinity, and if it had been possible to trace the other infinities to that one then that would have been fine. But then this paper on the gravitation energy showed that this was not the case, that one got an infinity in that case also, so one had the impression that there was something deeply wrong with the whole theory. Then it was not clear whether the difficulty was a methodical one, or was in the mathematical procedure or whether it was in the physics; and this uncertainty prevailed until one had this manifestly co-variant formulation which showed that the difficulties were not in the mathematics, but in the physics. Probably many people guessed at that time that it was in the physics and not just a matter of the formalisms.

Kuhn:

When you speak of the manifest covariant formulation -–

Rosenfeld:

Schwinger and Tomonaga.

Kuhn:

But you think it waits that late before it’s really clear to people?

Rosenfeld:

Before one was absolutely convinced. But surely many people were of the opinion that it was a deep-lying physical difficulty and that there must be something like a smallest length. That was a very early speculation, but one did not know how to tackle it. The one who went furthest in that direction was Heisenberg, who even before the war in his papers on cosmic rays tried to play with non-linear wave equations and various ways of introducing the lengths. He was the one to point out the essential difference between electrodynamics, in which the coupling constant is dimensionless, and, for instance, various forms of present theory, in which it is not. Then the argument went that if we get to higher energies, corresponding to momenta h/l where l is this characteristic length, then obviously perturbation theory must fail completely because a production of n mesons, for instance, must be just as likely as a production of one meson. So that was the first intimation that there were two types of theories: one type with the small coupling constant, dimensionless, in which one might hope perturbation theory might converge, or at least, give good results; and meson theory, which was of a quite different character, and in which there was no hope of convergence of the usual methods. So that was already clear at that time, if I may say so, about 1937, when those papers of Heisenberg appeared. The fact that one did not [sic] know that everything was done in a non-covariant way was also very disturbing, because those papers of Heisenberg showed a connection between the failure of the perturbation theory and a physical feature of the theory. Nevertheless, the two things were not clearly separated; it was not clear whether a modification of the attack might not save perturbation theory, provided that one had another parameter to expand. In fact, that is what has been done with this covariant formulation, because one sees now that the parameter is not at all the coupling constant but a more complicated combination involving lengths.

Heilbron:

What would you say then was the effect of your paper on the gravitational energy?

Rosenfeld:

At that time it had the effect of showing that the divergences were not the result of this classical singularity.

Heilbron:

Was it compelling to anybody? Was it considered —?

Rosenfeld:

Yes.

Kuhn:

Can you remember discussions of it both in and outside of the group in Zurich?

Rosenfeld:

Heisenberg was interested, he told me. I can’t say that he was glad about it, because it was a very sad conclusion, but anyhow, it was something which was settled in the sense that one no longer had to hope that it could be reduced to this classical singularity. It may have encouraged Pauli and Weisskopf to take up again the problem of the self energy of the electron, since one was sure that there were essential divergences which were of quantum origin and were different from what was thought. But I think it is characteristic of the pessimistic attitude of the time that the first result of Weisskopf was a conclusion that the quantum divergence was worse than the classical one; the reverse conclusion, the better one, was only arrived at more or less as an afterthought by revising the calculations. Bohr was, of course, very pleased by this.

Kuhn:

By the revision?

Rosenfeld:

Yes, because with his characteristic optimism, Bohr jumped to the conclusion that it showed that the quantum theory helps, and that by a bit of refinement, one ought to get completely rid of the divergence. Of course, ail this time Bohr insisted very much that the only guidance we had in quantum electrodynamics was the correspondence, and that everything that went outside, beyond the correspondence, was doubtful.

Heilbron:

That’s clear in the next papers you write.

Rosenfeld:

Yes, that was an attempt to put in formulae what Bohr was thinking at that time.

Kuhn:

I think there are a number of papers intervening before one comes to this direct attempt again to build up the correspondence treatment. How did that paper, the critique of the Dirac theory, originate?

Rosenfeld:

That was at the conference that year, ‘32, I think it was –-

Heilbron:

‘32 one was when you showed that the new Dirac quantum electrodynamics was equivalent to the Heisenberg-Pauli. This was 1931. I think it was the first paper you wrote in Copenhagen, “Zur Kritik der Diracschen Strahlungstheorie.” [Zs. f. Phys. 70 (1931) pp. 454-62]

Rosenfeld:

Oh, yes, but that was trying to show that there was nothing more than correspondence, or have I forgotten that paper completely?

Heilbron:

No, it’s the one in which you show that if you consistently apply the Dirac theory —.

Rosenfeld:

Oh, yes. That arose at the conference in ‘31 and was directly inspired by Pauli. The question put by Pauli was ‘how general is this divergence business, how far do the —’

Heilbron:

— tentacles spread.

Rosenfeld:

Yes. So I took up that problem. One knew the divergences in the energy eigenvalues. Then there was a suspicion that if those energy eigenvalues were, strictly speaking, infinite, how could one discuss transition probabilities at all? The whole formalism is ridden with infinities, and it was very unclear whether one could get away with it and could nevertheless get finite transition probabilities.

Heilbron:

Had Pauli expected difficulties in that particular place when he posed the more general question of seeing how rotten the structure was?

Rosenfeld:

I think he was prepared for the worst, but it was really a bit uncertain; it was something which one could not judge without really going through the calculations, one argument, I suppose, being that those transition probabilities, as they were calculated, i.e. neglecting those infinities, in fact made good sense. They were in accordance with correspondence and so on, so they were significant quantities and perhaps could be separated. Again, the general preoccupation was whether a prescription could be found allowing one to separate the reasonable conclusions of the theory, which one knew ought to be contained in it, from the spurious ones. The result of this calculation, which was then followed by others and finally by a more general argument by Pauli which is in his Handbuch article, gives the impression that such a separation was not possible.

Heilbron:

Was Dirac present at that meeting in ‘31?

Rosenfeld:

I think so.

Heilbron:

Do you recall whether he had any statements to make about the difficulty?

Rosenfeld:

No, Dirac in fact kept a bit aloof from this whole development. I remember that when he started his new attempt he obviously started with the ‘many times’ theory because he knew that the other was in a mess — he wrote this quite fresh approach, which, in his mind, was quite unconnected with the other so that he might just do it better. When it was shown that the two were equivalent, only then, I can guess, he started studying the others. He had not been much concerned with the whole Heisenberg-Pauli business. I guess that because he wrote to me asking me elementary questions about the Heisenberg-Pauli theory which he certainly would not have done if he had followed the preceding development.

Kuhn:

Who was impressed with that Dirac ‘32 “new theory?” I gather from your account that Pauli was supremely unimpressed with it. [“Nogle minder om Niels Bohr,” in K.G. Hansen, ed., Niels Bohr, et Mindeskrift. Fysisk Tidsskrift (1963) p. 71.]

Rosenfeld:

Yes. But, you see, Pauli must be taken with a grain of salt because he affected to be unimpressed, but I think everybody was impressed. Perhaps Pauli less than others. But I am not so sure whether this gibe of Pauli is genuine!

Heilbron:

Was it felt, after this work of yours in ‘31, that the new correspondence principle approach, in the nature of Heisenberg’s, would be a way that one could proceed?

Rosenfeld:

No, it was rather the extreme position of defeat, if you like; it was an attempt to save whatever could be saved in the spirit of Bohr. I gave a paper on that at the congress in Rome, but it fell completely flat. People started saying, “Yes, but this is no theory,” or asking questions, “You have the Hami1tonian; why do you forbid us to handle the Hamiltonian according to the recipes?”

Kuhn:

Who said this sort of thing?

Rosenfeld:

That was general, from the audience; I don’t remember exactly who I said then finally, “Yes, but what I intended to show is that by a simple correspondence prescription one can get all safe results, or all results that are saved, and the suggestion is that the only way one can work with this formalism is by not considering it a closed formal scheme.” Then Fermi, who was in the chair, just to close the discussion, said, “Yes, we have understood that, but that is not the usual conception one has of physical theories.” That was the general feeling.

Kuhn:

Who else was involved with you in this approach?

Rosenfeld:

I think that Pauli was mildly interested; in fact, I think that he was rightly critical of some things which I had made on the line widths because I had been a bit sloppy there. I had not considered all — done it properly. At that time Casimir was his assistant, so he put him on the problem and Casimir did it more cleanly and better, but this shows that Pauli was really interested. However, the line width was the most that one could get from it; I suppose one could have worked out in the same way (fourth order) effects, but I have the feeling that such things as the Lamb shift, for instance, could have been found at that time if anyone had had the sufficient faith in it, because, when the effect was there, Bethe could do it with very simple arguments, without any manifest covariant thing or formalism of any kind. It was an elementary thing, and it could have been done at the time, but people were discouraged. One felt that one was groping in the dark and that whatever result one could get was doubtful; and since those effects were very small in any case, and outside the experimental technique of the time, it was also not worthwhile to tackle them. I remember one had some spectroscopic evidence by (Pasternak) on the Lamb shift, I think, but it was at the limit of accuracy and so it was considered very doubtful and not worth investigating.

Heilbron:

We still have to clear up a few biographical details: how you came to Copenhagen, and how you seemed also to have a simultaneous position at Liege, and the oscillation you must have performed.

Rosenfeld:

Yes, indeed, we performed oscillations. That was just a trick, you see; without any enthusiastic cooperation from the authorities in Liege, I managed, simply by brute force I think, by putting before people a fait accompli, to give my lectures in Liege within a semester, and then I simply went away for the other semester.

Kuhn:

You returned to Liege when?

Rosenfeld:

It was the winter, according to my notes, of ‘30-‘3l. In the summer I came to Copenhagen, so I started this job, this jumping about, in the winter of ‘30. I took up my duties in Liege — at that time this readership was only for a semester, so it was quite regular. But then I got a chair, so the regular [procedure] would have been to extend the course over a year, but I just condensed it into a semester by giving more lectures during the week. It didn’t make the least difference to the students; they did not understand a word of it. They were not prepared for that kind of lecture. So I could manage this double life. I went to Liege again in the winter of ‘31-‘32, but I’ve lost count here. I oscillated also according to Bohr’s convenience, and so it went on until the outbreak of the war in 1940.

Heilbron:

You began to assist Bohr then whenever you were here?

Rosenfeld:

Yes, in ‘30 I was mostly in Zurich and I came to the conference which was a bit later in that year, in September, and I stayed for two months, September and October of ‘30, in Copenhagen.

Kuhn:

Then you went back to Liege?

Rosenfeld:

Yes. It must have been at that time that Bohr proposed to me to come back the next year, because he had promised to write up this Faraday lecture and he asked whether I would help in writing it up, so I accepted.

Kuhn:

That was really then the summer of ‘31?

Rosenfeld:

Yes. Then very soon we got involved in this controversy with Landau and Peierls which went on and on, through ‘31 and ‘32 to the beginning of ‘33, in fact, with various interruptions. And the Faraday lecture was a disturbance, or the other was a disturbance of the Faraday lecture, I don’t know, but the two interfered with each other rather badly.

Kuhn:

Your first extended stay here, then, was the two months in ‘30?

Rosenfeld:

Yes.

Kuhn:

How did you happen to stay then? What were you working on?

Rosenfeld:

I took the chance, since there was this conference. I had left Zurich and I knew that I had to take up those duties in Liege, but there was this interval before I started in Liege.

Kuhn:

Did you work closely with Bohr at that time also?

Rosenfeld:

Yes. Well, not as closely as later. At that time I just took part in the general discussions which were more in the nature of conversations where nothing was planned.

Kuhn:

Was Bohr yet, at that point, showing any real interest in the problems of electrodynamics?

Rosenfeld:

Well, he knew what was going on, but he was very —. You know, Bohr’s interest cannot be aroused by a formal theory; there must be some concrete point in it. At that time there was very little that was concrete because, after all, no new consequences had turned up except those very annoying self energy things, so his attitude was rather that this was a very complicated way of making life difficult for one. He did not think that there were serious physical problems involved at that time; he thought that it was just a miscarriage of the formulism and nothing more.

Heilbron:

It was the Landau-Peier1s paper really that created the —

Rosenfeld:

Yes, that created the crisis that was the starting point. That was a very crucial issue. Then Landau and Peierls encroached, so to speak, on Bohr’s domain, and he was immediately able to say, at least in the negative sense, that all this rough handling of measurements was certainly not allowed, that you could not pull any conclusions, either pro or contra, from such sloppy considerations. That he said right away.

Kuhn:

Were you actually here when that paper appeared, or when he first knew of it?

Rosenfeld:

No, I was in Liege at the time, and I heard of the controversy when I came in February ‘31.

Heilbron:

You’ve written about the colorful meeting, but what you didn’t say in those interesting few paragraphs is just what Bohr was trying to say to Landau.

Rosenfeld:

I don’t know. They were arguing back and forth and Bohr at that time had not yet understood the problem; when Bohr has not yet understood a problem, he suggests all kinds of things tentatively, so I don’t know what he may have said. He may have asked are you sure that it is a unique consequence, that this is not the result of an unallowed extrapolation of the formalism; I say that because that was the first question that he put to me when I came.

Kuhn:

Did you go to work on it with him immediately on your arrival in February? Or was there some attempt first to do the Faraday lectures?

Rosenfeld:

Yes, I think the two things interfered right from the beginning. He often repeated the famous sentence, “I am feeling like a murderer [criminal]” because he had a guilty conscience that he was not writing up the lectures and fulfilling his obligation because he was more attracted by the other problem, which was really -–

Heilbron:

But anyway, at the point which you had arrived, you think Bohr had not focused his criticism on any particular -–

Rosenfeld:

He was provoked, but he did not know what the situation was.

Kuhn:

Was he sure they were wrong?

Rosenfeld:

No. In fact we were not sure they were wrong until the very last. He always kept an open mind, all the time. At some points it was very soon clear that Landau and Peierls were wrong, and that was in their argument of the big radiation because then one saw that with an extended test body one could cut it down, so that was a point in which it was clearly –-

Heilbron:

But the general philosophy –-

Rosenfeld:

Yes, that was uncertain to the last and the real nature of those fluctuations was only understood at the last moment, so to speak.

Heilbron:

I notice that the first paragraph of your lecture in Italy [Uber die quantenmechanische Behandlung der Strahlungsprobleme.” Atti del convengo di Fisica Nucleare, (Rome, 1931).] reads a good deal like the first paragraph of Peierls and Landau.

Rosenfeld:

Yes, sure.

Heilbron:

This business at the end of Peierls and Landau where they throw all the existing difficulties on the bandwagon, was that seen immediately as sort of attaching irrelevant things to the whole argument? I’m thinking particularly of the beta decay question which they also throw onto the general list of grievances.

Rosenfeld:

Yes. Well, I suppose, at that time, the general feeling was that the whole thing was a complete mess, that the electron theory was seriously wrong and the protons still more so. In fact, Bohr had an argument that the proton was worse than the electron because of the smallness of the Compton wave lengths of the proton. One was already in the unallowed region where h over mc is of the order of e² over mc², which is a classical limit for electrodynamics, for separating the Coulomb field from the radiation forces, and therefore, that even the classical model of a point charge for the proton was doubtful. And therefore there was no justification for applying Dirac’s equation to the proton, and there was some support for that in the fact that the magnetic moment of the proton was anomalous. This is still a valid argument, as a matter of fact.

Heilbron:

Was that a tremendous surprise in Copenhagen, the magnetic moment to the proton? This series of arguments preceded that?

Rosenfeld:

I don’t quite remember that.

Heilbron:

Pauli is supposed to have been completely amazed at the result.

Rosenfeld:

I was not present when the news came, so I don’t know what Bohr’s reaction was when he heard of it for the first time. But from his general philosophy I would imagine that he was not surprised — or he may have been surprised — but I don’t think that he had any clear expectations about that. He took that as information which pointed to a limitation which was quite in line with his general principles of consistency, limitation of applicability of theories.

Heilbron:

I think, in this article in the Bohr Festschrift [w. Pauli, ed., Niels Bohr and the Development of Physics, (London, l955).] you mention the semi-infinite number of proofs that the paper went through, and when you say that it was only at the last moment, so to speak, that this business of the fluctuations was seen to conform. This did, however, precede the first writing of the paper, didn’t it? Or was this a correction in proof?

Rosenfeld:

I cannot say quite definitely when it came. There was certainly recasting of that particular paragraph very far in the successive proofs. I hope that one can perhaps get hold of the proofs yet; that would be interesting to see. But all I remember now is that this point was troublesome to the last and there were oscillations. It was not troublesome in the sense that one did not understand the formal relationships. For instance, the fact that those fluctuations coincided with or were the result of fluctuations in the number of light quanta in the test bodies and that they must coincide, that became clear not immediately but certainly before the proof reading. How this had to be formulated, the definite formulation, was very hard to get, however.

Kuhn:

I’d be really very much interested in anything you can remember about the successive stages in the development, the very long development, of this paper. It goes on over two years, doesn’t it? You said that perhaps the first stage was teaching Bohr quantum electrodynamics.

Rosenfeld:

Yes, that was very quick because he was very quick at grasping the essentials. Then a rather decisive point, decisive in the sense that it really helped a great deal in securing a firm foundation, was the calculation of the field due to the motion of the test bodies, and the realization that this field had just the general expression which also entered in the commutators. Now, of course, we know from Peierls’ paper that this is what had to be expected, that there is this relation between the Green’s function and the commutator, quite generally. But still that is, if you like, the physical meaning of this connection, the physical content of it. But this calculation could only be done when one had fixed the mode of measurement of the field, letting the test bodies loose but not letting them run away, just quenching their acceleration so as to keep them in the same element; then it was possible to idealize the motion with those delta functions and then the expression followed very clearly. Once one had that, many things became clear; namely, those cases became immediately clear in which there was no mutual disturbance of the test bodies, and also the single field measurements and all that were done without great difficulty.

Kuhn:

How early, do you suppose, in this development you got that far?

Rosenfeld:

That was rather early. As soon as Bohr had realized that one had to work with extended test bodies, he very promptly devised how one had to manipulate those test bodies. Then the calculation of the fields followed — that was not difficult. At that stage Bohr got confident that the theory must be consistent, that one ought to find the thing.

Kuhn:

You say it was at this point in a sense, then, that he knew that –-

Rosenfeld:

He knew that the formalism had a harmony in it which could not be fortuitous. He also saw that there was a very essential flaw in Landau and Peierls’ argument, that there was nothing in it; now the thing was put on a new basis, so to speak, and had to be decided on its own merits. But there was no prejudice against the field concept of the kind that Landau and Peierls had put forth. Then followed the analysis of the perturbation of the measurement by the other field and the possible compensation, at least for the simple case in which there was only a one-way perturbation, so that there was only one term in the commutator which was different from zero; then it was realized that the mutual uncertainty resulted from the fluctuation in the number of photons, from the fact that you could only compensate the average field but not the actual field. It must have been realized at that time that this had to do with the fluctuations, with the zero point fluctuations. Then it was realized that this field, due to the fluctuation of photon numbers, was just exactly the zero point fluctuation of quantum electrodynamics. I don’t think that people knew that at that time; that was discovered, so to speak. But then the result was a regaining of popularity for Landau and Peierls because we thought that, although their argument was wrong, their conclusion was nevertheless right; that is, that there was this fluctuating field which could not be gotten rid of and which perturbed the definition of the field.

Then Bohr started prodding me to find out how general this feature was because it was very uncertain, for instance, whether this fluctuating field should depend on the average field, or whether it should be the same for any photon composition. That was quite unclear, and it was a great surprise when I tackled that problem to find that it was general, because I went, as always of course, the complicated way. I just worked it out for a given photon composition and I found that it was just a zero point fluctuation, whatever the composition was. I remember at that time that Heisenberg came and he was extremely skeptical. In fact, he treated me so roughly at that time that he himself felt the need to apologize. He thought that that could not be true and that I must have made some error or handled the problem in the wrong way. When I offered to repeat the calculation of the blackboard before him, he said, “so, give me your calculation and —. No, I prefer not to hear about your calculation; I prefer to work it out myself.” He did so, and then he came the next day, very mild and apologizing, saying, “Yes, I hope that you will not be sorry that I was such an unbeliever of those things.” For him it was a complete surprise, especially as it comes as an exact result, without any approximation. Bohr witnessed this skirmish as an amused spectator - - the two ogres throwing bricks at each other — but then, when he saw that the ogres were in agreement, he became interested in this result, in this fact. And then it was Bohr who found the simple interpretation of this agreement by pointing out that we had the classical solution plus the radiation contribution separated: a very simple thing, but which neither Heisenberg nor I had seen.

Heisenberg then got interested in this fluctuation business and he worked out the fluctuations for the fermion field also. What he had done before I’m not quite sure, but he discovered an error in the published paper on field fluctuations by Born, Heisenberg, and Jordan, in which they had thought that they had derived the Einstein formula for the fluctuations of thermal radiation, but that was actually wrong. If you do it with a sharp domain you find that the fluctuation is infinite. You only find a finite fluctuation for an unsharp domain, and he found the same situation for the charge fluctuations. So that was the next problem for us to tackle. Our first reaction was to say, ‘Well, this zero point fluctuation is just a feature of the theory which imposes a limitation on the field concept,’ so we swung over to the standpoint of Landau and Peierls. Then we got into trouble with this minus sign; that was a terrible business. There was a stage in which we had a complicated discussion of all the cases: one could draw the world lines of the two test bodies, or the two time intervals, and according to the situation of the two time intervals and the lengths, one could see whether it was possible to get light signals from the one to the other. We distinguished I don’t know how many cases, some of which agreed with the predictions and others, in which there was a double inference, did not. We got a plus sign instead of the minus sign predicted by the commutator. At that stage Teller was shown the discussion; he read it through with great concentration, and he immediately produced another case which we had overlooked. Incredible sharpness. I was absolutely impressed; I got the impression of this powerful mind put before this complicated problem for the first time; he just read it through once, and immediately –-

Kuhn:

How long did this take from the time he first looked at it?

Rosenfeld:

Half an hour. That was very complicated; it was at that stage that the paper was presented at the Academy, as I remember.

Kuhn:

Was this still in ‘31, or by now is it ‘32!

Rosenfeld:

It was the same date as the date given in the published paper [December, 1932] but it was only published a year afterwards.

Kuhn:

Was Landau himself also involved in these continuing discussions?

Rosenfeld:

No. Neither was Peierls. Only Pauli was very interested at that time arid Heisenberg also, but Heisenberg did not follow it closely. It was just this business in which he first got acquainted with the problem, and then he pursued his own investigation of the fluctuations which was very fundamental.

Heilbron:

Did Pauli or Heisenberg have any notion of how it was going to come out either?

Rosenfeld:

No.

Heilbron:

So the paper went to the Academy before you had found the sign problem?

Rosenfeld:

No, we had found how to account for the sign; that was only done by signaling. Then we found that this presentation with the world lines, where you saw the two signals and so on, was very suitable just for discussing points and showing the difference between the two cases. So that was adopted by Bohr in his exposition at the Academy. But I don’t remember what his conclusion was, whether it was in favor of or against Landau and Peierls with those fluctuations. Perhaps it was noncommittal; that I don’t remember, unfortunately. Perhaps one could find it in the manuscript.

Heilbron:

Did he care about which answer he got? At any point had he convinced himself that —

Rosenfeld:

No, not particularly. He had no emotional preference for the one or the other; it was just to learn.

Heilbron:

The preference needn’t be emotional; I just wondered –-

Rosenfeld:

What could they be? Before you have the solution what could it be? The great trouble with those fluctuations was to decide whether they were a boon or a curse for the theory, and it became a question of trying to formulate the case one way or the other to see which way it looked better, or more logical or consistent. That was obscure for a time. Of course, afterwards, it is hard to realize the hesitations that go before, but it was such a subtle point.

Heilbron:

Was it widely read with care, do you know?

Rosenfeld:

In general?

Heilbron:

In general. It was certainly widely cited with care.

Rosenfeld:

Yes, I think it goes with that paper the way it went with Klopstock’s Messias there is this famous epigram of Lessing which I can’t quote, but it’s about Klopstock’s Messias: everybody agrees that it’s a masterpiece, but do many read it? And Lessing concludes, “Wir wollen minder gepriesen und fleissiger gelesen sein.”