Oskar Klein – Session IV

Heilbron:

Well, I had thought that we might begin with your return to Copenhagen in ‘26 after you had recovered from your illness. I thought first of all we might talk about the matrix mechanics. I noticed in one of the letters that you wrote to Bohr before you came here that you were quite enthusiastic. While you were still ill you must have read those papers.

Klein:

Yes, yes. I was half-way well then; I think I was at home. You know, as I mentioned last time, I hoped that there would be another way, but still I thought that this was a very great progress on the line of the Correspondence Principle. I definitely converted to this ordinary quantum theoretical view two years after, but during that first year I believed that Heisenberg and Born and Jordan and Dirac, and so on, had made also very important progress but that perhaps these things might be derived from something lying behind it. At that time already it was clear that this view could be extended to the field also — to the electro magnetism — and very soon Pauli and Jordan wrote a paper about that. But I think that was clear to everybody already. … It was already quite clear from Rayleigh’s researches on the classical theory that there could be a possible extension of that kind. After the spring ‘27, I doubted no more that that was the right way to do it.

Heilbron:

When the Schrodinger papers first came out, you were then in Copenhagen. Was there a sigh of relief? Were people pleased with their appearance, as you no doubt were?

Klein:

I think that usually one was a little mystified, and I was also a bit mystified, by the way he presented it. Then I tried immediately to write it up in the way I had thought of it myself, so the paper I wrote first then was, of course, inspired by Schrodinger bit was also very much what I had thought before.

Heilbron:

Did you make an effort yourself to try to find the relationship between the matrix and the wave mechanics?

Klein:

The time was very short. I hoped there would be, but I don’t think I saw any way out to establish it. I think the first I heard about it was from Pauli. Pauli had found it independently a little before Schrodinger’s paper appeared. Then Pauli came to Copenhagen. He told me that on the ferry to Gedser he had been walking on the deck, back and forth, and made that up in his head. It was quite clear, so that he told us about it then. Then very soon after Schrodinger’s paper came.

Heilbron:

Also at the time spin was new here.

Klein:

Spin? Yes. There was, of course, a long history, but I think you have that better in—.

Heilbron:

We still lack a few pieces for the Copenhagen end of that story. For instance, it’s said that Kronig had lectured on the subject in ‘25 and had gotten no response.

Klein:

I never heard that. Now, you see, I only saw a glimpse of Kronig in the summer ‘25, when I came back from the United States. I don’t remember that he told me about that. We had a little talk, but I don’t remember that he told me about that. So I think I heard about it first after —. My wife and I went up to Dalarna, and on the way we made a visit at Siegbahn’s in Upsala. Siegbahn told me, “For a time they talked all about matrices, but now they seem to talk about ‘spin’ in Copenhagen.” I think that was the first I heard. Kronig came back later, and then we had long talks about it, and Kronig told me the whole story from his side. But I don’t remember that he said that he had lectured. He said that he had been talking with Bohr and Heisenberg and Pauli and that he had been a little disappointed because I think it was uncertain if Bohr saw what he meant. Very often when one tried to talk with Bohr, he was thinking of something else.

Then usually one stopped because one didn’t get anywhere. So I think it is very doubtful if Bohr ever knew anything about it, but I think Pauli and Heisenberg did. You know that Goudsmit and Uhlenbeck had some correspondence with Heisenberg where Heisenberg mentioned that he had heard somebody, but he didn’t remember whom, say that spin could explain the multiplet structure, and they quoted Heisenberg for that. Of course, Kronig was rather upset about it, but the whole came in a very innocent way. Pauli, I think, was against it; and Pauli had, of course, good reasons. Later on he himself made a very important paper, you remember, on this subject which was a preparation to Dirac’s paper. Then it was clear that you couldn’t take this rotation as a real classical model. It was a kind of picturing of things which could not in a strict sense serve for a picture. Still, of course, Pauli was not right that it was not a fruitful beginning.

Heilbron:

Were there attempts made at Copenhagen to try to include spin in the new formalism at all?

Klein:

Yes. You remember that I mentioned last time that I thought that, when a particle moved in a magnetic field, that it was a little like light rays in a doubly refracting medium. And in that connection I tried with this five dimensional theory in the background to see if one could find a kind of vector or tensor equation. So I tried to compare spin with polarization, so that the differently polarized rays would go different ways. Of course, I never succeeded in finding a correct equation because one should have half integral spin. What I tried were such equations which would lead to integral spin, tensor or vector equations. I tried to put up an equation and simplify it, and so, but it never led to anything, so that when Dirac’s work came, I was immediately quite convinced that that was the way.

Heilbron:

Were there other attempts made here?

Klein:

No, I don’t know that there were other ways than such general discussions. I remember there was a bet between Heisenberg and Dirac. I think Dirac said that in three months he would have it. So in that way it was a very lively subject. Then of course Dirac got it very fast; it was about a year later.

Heilbron:

I remember in Gottingen, Wigner and Jordan were working on the problem. They were very near to Dirac’s views, very near. They started from Pauli’s matrices, and tried to get further.

Klein:

But that Kramers and Kronig did also. I heard about that just when Dirac’s work was new — that must have been rather early in ‘28 because it was on my way to England. I think Dirac sent a summary in ‘27, just around Christmas. But then Bohr invited me to go to England to hear more about it, and I was there about the beginning of March.

Heilbron:

It must have been in the winter, yes. I remember when the news came. Wigner took it elegantly. I mean, he said, “Weil, Dirac has won, you see.” But Jordan was quite depressed. Then it was a joke because then he started taking lessons in jujitsu — not to fight Dirac, but to recover his health. You see, he got a nervous depression.

Klein:

I see; I see. Do you remember what they had done? I think I remember what Kramers and Kronig told me then what they had done before Dirac’s paper came. Do you remember what Jordan and Wigner had done?

Heilbron:

No, no, I don’t know any details about it. I only know that Wigner had gotten news of Dirac’s paper before it appeared. He told me what Dirac had done, and then he added, “We were very near to it, and I cannot forgive myself that I didn’t see that the point was this linearization.”

Klein:

Yes, because Kramers and Kronig made Pauli’s relativistic by adding such a relativistic Pauli term to it, but of the second order. .. Do you remember some years ago Feynmann took this second order equation up again because he thought that his way of (functional integration) fitted better than Dirac’s. That must have been five years ago. I didn’t believe myself that there was much point in it, but for him it led to this inversion theory of weak interactions. I think it was Kramers who told me about his and Kronig’s work. He took it very mildly. Kronig was, of course, upset. Kronig had been upset when that letter of Goudsmit and Uhlenbeck with the addendum by Bohr appeared. He wrote a letter to Bohr which I think Bohr didn’t like, but —. Kronig felt it was tragic. But such things are not so tragic. I had the same thing with the wave mechanics. Of course, one feels disappointed, but I decided then that I shouldn’t take such things tragically —. Of course, a little bit. But Kronig took it seriously. I had a long talk with him; we went for a walk. I like Kronig very much. I tried to tell him that one should not think of such things in that way, and that if one hasn’t published a thing then it’s one’s own fault. Often one does it the other way, and publishes it too fast. So that one shouldn’t take this so seriously, and one should try to go on. No, of course, Kronig did very nice work after that.

Heilbron:

How was Pauli’s spin theory accepted? Did people like that?

Klein:

Pauli made a non-relativistic theory where he added a spin term with two row matrices, which one calls Pauli matrices now. That was a very nice paper, of course, Darwin made about the same thing at about the same time; Pauli’s was more elegant and more connected with the whole of quantum theory. Darwin wanted to have it as wave-like as possible. So I think Darwin carried it out, but his general ideas were not so different from what I had vaguely had before when I thought of the waves. I think Pauli’s was better connected with the whole systematic quantum theory, and was, therefore, more important for the continuation.

Heilbron:

The objection to it being its non-relativistic nature?

Klein:

You remember that the inclusion of spin couldn’t be entirely non-relativistic because there was this factor 1/2 which Thomas showed in a very nice way by using the Lorentz transformation. Thus, one could get a mechanical argument before one had a wave equation for this factor 1/2. In that way he corrected the relation between the anomalous Zeeman effect and the multiplet structure. So that, I think, was a very important intermediate step, and Kronig didn’t have that. That came after. Thomas was in Copenhagen when he made that. I met Thomas when I came back in ‘26, and then he had done it already, so he must have made that early in ‘26, I think. At that time he was working on some very, very intricate kinetic problem. Thomas was very good; he liked such very intricate problems. I met him later in Cambridge where I remember he said he was trying a problem because Fowler had said that it was easy, and he wanted to prove that it wasn’t. Of course, Kronig had more than Goudsmit and Uhlenbeck because he knew that one could get the anomalous Zeeman effect and the multiplet structure, apart from the factor 1/2. … Then, you know, that Bohr, when he came to Leiden, didn’t believe it. He didn’t believe that one could get the multiplet structure because he thought there was no magnetic field. Then Einstein burst into it…

Heilbron:

To change the subject slightly, I just wanted to ask a question about one of the letters. I noticed in one of them from Leiden that you wrote back and said that you had had long conversations with Heisenberg and Bohr, but you don’t say about what.

Klein:

Oh, that was before I came to Leiden. I might look it up perhaps, but I read it also. I went to Leiden to lecture about this five dimension theory, and then before I left they were kind, enough to listen to this, so that I went through what I intended to say in Leiden. Then, as I mentioned last time, I tried to do what Ehrenfest called my non-linear philosophy — the whole field theory, of course, is non-linear. I tried to divide the quantities between such which are independent of this fifth coordinate and those which contain it. For these latter one had a kind of Fourier expansion then with a period, so that one obtained terms which correspond to singly charged, doubly charged, and so on, fields. One also got then this difference between the energies coming in and corresponding to the combination principle in the spectral lines. That came out nicely.

Heilbron:

You went to Leiden specifically to lecture on that?

Klein:

I was invited for that. You see, Thomas was the intermediary. I had written that short paper on the wave mechanics and five dimensional relativity, and Thomas was interested in it and got a copy. And he showed that paper to Ehrenfest in Leiden. He went through Leiden on his way home to England. I think he even gave a talk on it in Leiden. Then Ehrenfest got interested and spoke to Lorentz about inviting me. Then I got a very nice letter from Lorentz inviting me to Leiden. So I spent most of the month there and had very many discussions with Ehrenfest and Goudsmit and Uhlenbeck who were all in Leiden at that time. Lorentz came also to the lectures and made very lucid remarks. Once he invited me to his home, and we had then a very nice conversation.

Heilbron:

He kept up in all aspects of modern physics?

Klein:

Yes, yes. He was then over seventy and he still had this presence of mind for which he was so known in the Solvay Conferences. He always summarized in a very lucid way what was said before, and then he put in some points. He had at that time read Schrodinger’s paper. I don’t know if Schrodinger already had published the harmonic oscillator or if Lorentz really had done that before. I think Lorentz had done it before, but he had never published it. He had regarded the harmonic oscillator wave function, and then he wanted to see how near one could come to the particle on this model. As far as I remember, he had studied just the wave package in the harmonic oscillator, so I think Schrodinger’s work was later. But Lorentz never published his, and Schrodinger never knew it. Then he showed that that was making oscillations in this way, and that the wave packet didn’t spread on account of only a single frequency appearing there. Schrodinger made a point of that, but I think Lorentz knew that this would be an exception and that ordinarily such a wave package could spread. I think his viewpoint was then that you had about the same difficulties that you had before with the light quanta also here. That was very hard to see how you could have a theory where the particle properties and the wave properties came out. He was very interested.

Heilbron:

What had he thought of the matrix theory? He might not have been so happy about that.

Klein:

I really don’t remember if he had looked much at that. I would almost think that he hadn’t looked very much at that, that that was a little far away from what lay near to him. But I remember that he had looked closely at the wave question.

Heilbron:

It was there in Leiden that you began to write the paper on the Correspondence Principle and the wave mechanics?

Klein:

Yes. I wrote two small papers after I came home from Leiden in the summer, but they were never published. I have the manuscripts still. The one was about the interaction of electrons with electromagnetic fields which was, so to say, the beginning of this work on the correspondence. The other was on the energy momentum principle which I had done with the five dimension theory. There also I showed that one got — I knew that before then, of course, — the Hamilton-Jacobi equation as a limiting case. I thought that that would include such a consideration as Lorentz’ about the motion of wave packets, because there you showed that a classical motion would come out in the limit. It contained the energy momentum principle of wave mechanics, which Schrodinger published then before I had published it, and then I never published it. I had done so very much on this work which never came out. I have those manuscripts still, I think I started this with the energy momentum principle in a new version after I had finished this correspondence paper, but then Schrodinger’s came before I had finished that. Then there was no point in publishing. I could show you those manuscripts.

Heilbron:

Oh, we certainly want to see them, as well as the other papers that you say you have. We would be overjoyed if you would let us photograph them.

Klein:

Oh, if you’d like to. I would be glad perhaps to have copies back. It would take a little time because I will be very busy in the first time now. Some of them perhaps I can find easily enough…

Heilbron:

While we were talking about Leiden, there were a few other questions I thought I might ask.

Klein:

Of course, this Compton effect I think I mentioned to you because that happened during the Leiden time. Dirac’s paper came, and then it occurred to me immediately that that could be done on the wave mechanical way in analogy with the ordinary scattering of light. So I began to calculate, and we did that also partly together on the blackboard, but we never finished a quantitative calculation. I never finished that before Gordon’s paper had come. Qualitatively, one could see immediately that one got the right energy momentum relations.

Heilbron:

By ‘we’, you mean —?

Klein:

I really did it, but Ehrenfest and Uhlenbeck and I discussed it so much; we discussed those papers, and they were so kind. So therefore I tried to publish together with them. They perhaps did right to refuse it. But, on the other hand, that very much delayed the publication of the whole thing. I would have been happier if they had really taken part in it and also in the calculation.

Heilbron:

What did people think about the matricization of time?

Klein:

Ehrenfest didn’t like these matrices very much. I think he thought they were so hard and sticky in some way. He thought the waves were smoother and nicer.

Rosenfeld:

Another story about the waves was with Born and Ehrenfest. Ehrenfest came to Gottingen, and there was a colloquium done by a student. He discussed a problem that had been solved just by wave mechanics. Then Born said, “Oh, but that’s easy; it can also be done with matrices.” Then he started to write up the solution. Then Ehrenfest said, “Yes, but I like it better with waves.” Then Born said, “Oh, well, what’s the difference. Es ist nur eine Frage der Gewohnheit.” Then Ehrenfest said, “Ia, aber es gibt auch schlechte Gewohnheiten.”

Klein:

That’s like Ehrenfest.

Rosenfeld:

Born was rather piqued.

Klein:

I remember when Darwin came to Copenhagen, he used to say, “I was brought up in the waves.” And he said also about Dirac, “What Dirac calls a special example I call a general theory.”

Heilbron:

I was interested that in one of the letters you said that you all became aware of Dirac’s theory through Lorentz. He had gotten the paper beforehand or something of that nature.

Klein:

Oh, I think I know what you mean; I had forgotten it again. That was the paper on the Compton effect — Dirac’s earlier papers were known. I had forgotten it, but I think that was in the letter. It was Lorentz who pointed out to us, or to Ehrenfest, that there had appeared a paper by Dirac, but I don’t think there was a reprint. I think the paper had just appeared.

Heilbron:

That makes it even more remarkable that it should be Lorentz who would point this out.

Klein:

Yes. Did I say that in the letter? Would you look that up?

Heilbron:

Yes. [Finds the letter.]

Klein:

I remember the letter very well, but I don’t remember that it was with Lorentz. I think we saw Dirac’s paper there, but from this letter it looks as if we heard it first and saw the paper then. I have forgotten that it was Lorentz who told that, but it was so early, so I think he could hardly have been sent a reprint at that time. I think Lorentz must have seen it, because it must just have appeared. I think it was in the Cambridge Philosophical Society, because I have a picture of this small gray paper cover.

Rosenfeld:

It was the Proceedings of the Royal Society…

Klein:

You looked it up? Yes, yes. … I have the vague memory that we saw the paper in Leiden, but I’m not certain. I remember that immediately — and it seems according to this letter — that we started it when we knew only that indeed he had made it. It lay very near then first to make the perturbation by the electro-magnetic field on the wave equation. Then one combined these perturbed wave functions in the same way as one combined wave functions of undisturbed states in order to calculate the ordinary transitions, the spontaneous transitions. That would give then the scattering in the non-relativistic case — the ordinary scattering and the dispersion formula. In this case it ought to give the Compton effect, and I think that this was so immediately evident that I think I was astonished that I hadn’t thought of it before. I remember that a little before Thomas went, we had had a little talk, and he used to say that he wouldn’t believe in the newer quantum theory before one had explained the Compton effect. But at that time it didn’t occur to me, so there I regarded it still as very mysterious. Then at that moment it became immediately clear that one ought to be able to get it in this way, and then we began to do it. We never carried it out quantitatively, but I remember we had it at the blackboard there. One saw then that the energy and momentum equations came out immediately. Then there came another paper in the same line, I think by Schrodinger, where he compared it, I think, to a, theory of the reflection of light waves by sound waves. That was a nice comparison. Then there was Gordon’s paper; I think Gordon was together with Schrodinger at that time, so I think their papers were connected in some way. I think Gordon started it, and Schrodinger wrote this remark to it.

Heilbron:

I wanted to ask you a question in connection with your paper on the correspondence treatment. There you consider, of course, a rho to be a correspondence analogy to the charge density. I wondered whether the Born school was discontent with that approach leaving out the probability.

Klein:

Oh, you see, Born’s interpretation had appeared before my paper was finished, but it hadn’t appeared before the main content in my work was already there. I think Born’s paper appeared sometime in the late summer, and also a similar paper by Dirac. I don’t think I at all read that carefully at that time. And you see, my aim was still to avoid probabilities. I would have probabilities, of course, as a result, but I wanted to avoid them as a postulate. Bohr was very much for the postulate. I think one reason that I didn’t study Born’s paper carefully was that it had very much to do with this interaction of particles on the basis of a configuration space wave equation. I hoped always that one should be able to get rid of that. Then, finally, it was clear that you couldn’t get rid of it in field quantization. But that made it so that I had a tendency to avoid such problems at first. Then I tried to get into them, and that led to the fact that I abandoned my older view just by looking, at them (and getting accustomed to them.) So I think at that time I didn’t think much about Born’s paper. On the whole I followed Dirac’s work much more closely than I followed Born’s work, so I think I came a little bit to underestimate Born’s work. In connection with his Nobel prize I learned that I had done that. Then, of course, we were looking at it in this connection again. Then afterwards when he got his prize he gave a very nice historic lecture…

Rosenfeld:

Yes, yes. He always emphasized that that was his idea — this was not influenced by the others. But when I came to Gottingen, he was more concerned with reducing everything to matrices. The product was this book, Born and Jordan Elementare Quantenmechanik, in which the Schrodinger equation is introduced in the form of a matrix equation to determine the canonical transformation diagonalizing the energy. … I remember at that time he gave me as a first exercise the translation of his probability interpretation in collision problems into the language of matrix mechanics. That was 1927.

Klein:

I see. I didn’t know you were so early in Gottingen already. So you were there together with Dirac.

Rosenfeld:

Yes, Dirac was there, yes, of course.

Klein:

He was in Copenhagen in the autumn ‘26, and then he went to Gottingen. Oh, that reminds me of a thing perhaps I might mention now about Dirac. We were talking about my paper on the Correspondence Principle. There I derived the Kramers-Heisenberg dispersion formula. When Dirac was in Gottingen — I think rather shortly after — he had worked out these papers about the radiation theory very important papers. He had just been working on the second part which was not ready yet. He wrote a very curious letter to me. Namely, he said that Heisenberg had gotten the correct dispersion formula in the wrong way because he had used a scalar potential for the electric field and this matrix mechanical method of calculating. But he thought that I had gotten the wrong result because although I had used the right potential, the vector potential, he thought that the theory was wrong. Then he gave me his formula. I had never looked at Heisenberg’s formulas very closely. But I read that and then I saw that it was just a transformation using the minus QP. Did you learn that from Dirac at that time?

Rosenfeld:

No, no. I just learned it by myself because I was worried. When I studied your paper, you see, I saw that you had the vector potential, whereas I had learned it Heisenberg’s way. And I had trouble in convincing myself that it was the same.

Klein:

Was that in Gottingen?

Rosenfeld:

It must have been in Gottingen, yes.

Klein:

First I was a little puzzled, but then I saw that that was so. So I answered Dirac. But I felt a little proud because it was very rare that one found an error in Dirac’s work. You did that later with his new formal electro-dynamics.

Rosenfeld:

Oh, yes. Well, yes, it was not an error, but he thought that it was a new thing, and it was actually equivalent.

Klein:

Should I tell such a story in advance? This came some years later, in 1931, but we might easily forget it when we get to that period. You may know that other part of it also — I think I told you at that time. I came one day too late to that meeting, and then Bohr said that Dirac had presented such a very interesting paper, and he asked Dirac to show it to me. Then Dirac gave me the manuscript, and he sat at my side. And when I turned the first page, Dirac said, “You ought to read the paper more slowly; Heisenberg read it too fast.” And then I heard that Heisenberg had objected that this was just the old theory in a new form. You showed very shortly afterwards that that was really true; Heisenberg said it as a guess. [General amusement].

Heilbron:

I wonder if we could try to discuss the growth of Complementarity and the Uncertainty Relations, and so on, in ‘26-27. Just to begin with, can you tell how the discussions of these measurement problems developed from the earlier considerations about the stationary states and the energy-time relationship? You see, Bohr had been talking the whole winter about something which had, in some way, to do with complementarity. I don’t think it was clear to him and certainly not to anybody else. But I think it contained, in some way, just the beginning of these things. I think he talked much with Heisenberg also about these things. Also Bohr and I had many discussions; we were talking quite much also about the wave theory. Bohr didn’t know —. He knew very much about basic classical wave theory, but he didn’t know this quantum wave theory. I think he learned that at the same time as he was trying to help me with formulating my paper on the correspondence standpoint.

So we met then very, very often. I think he had found some difficulty already at that time in his discussions with Heisenberg. Heisenberg, of course, always made a point in stating his view rather sharply. But Bohr’s views were then working towards clarity and trying to keep the truth, you know, according to his usual way. So I think there was some difficulty and some friction at that time. Later on — I think it must have been in March — Bohr was very tired and went to Norway for recreation. Then he came back, Heisenberg had written the manuscript of his paper on the uncertainty principle and showed it to Bohr. First Bohr was very enthusiastic and thought that was a very great progress and on the line of what he had been thinking himself. However, Heisenberg had some discussions of observations there, and Bohr then began to look more closely into that. Then he saw that they were not, the point, and then he got very upset. So there were some very hard discussions between him and Heisenberg there. Then Bohr started to see what was behind the whole thing. You remember Heisenberg had done something similar to what you told me about Born; he made a point of doing it not with waves — which were more obvious in this case — but with matrices. He started from Jordan’s formal transformation theory, and he derived his principle in that way. Bohr began to think about it, and then pretty soon he saw that this could be looked at from this point of view which Rayleigh had used in deriving the formula for group velocity and which Bohr had used himself in the indeterminacy of the stationary states. So he began to think about wave packages.

First he asked me to do some calculations. But before I had started Darwin was there, and he liked these things very much, so it was agreed that he should make such calculations. Of course, he did that very nicely and published a paper on it then. Bohr tried to look in closer detail at this observation business. Heisenberg had defined something which he called the gamma ray microscope to observe the position of an electron. Heisenberg had stated correctly that the change of the state was very important. However, he had missed the point that it was not the change of the state in itself, but the indeterminacy in the change, which was important. Bohr saw that, but the whole was very hard, so that he took it up and took it up. Then he had new examples which he treated; I remember the question of the deviation of particles when one measured their charges and their masses. He took one example after the other. I think already in the comparatively early spring — April or May — the main content of the later paper was there, but it was still in such a form that it was hard to connect it. He worked the whole summer. We were living not very far from his summer place there, so that almost every day I came on bicycle to him, and he dictated. That was quite like in (???), so that the next day everything was (???). Have you ever been with Bohr at such times? I (had) been so full of admiration. How much exactly was, ready at the time you [Rosenfeld], helped him? Because during that summer nothing came of it, although an enormous number of pages were written. Nothing came of it. Only, at the last moment, he was going to give a lecture at Como, you see, as he had promised. Then he and everybody around him were very upset. Then his brother Harald, who always helped him and often took a very strong hand when they found he was having too many scruples, stepped in. I remember they were in the auditorium in the Institute, and I was there also, and they were having a very, very heavy talk. … If I hadn’t known them, it would have sounded as if they quarreled. … But the result was that he wrote a small paper. Did you ever see the proofs of that?

Rosenfeld:

No.

Klein:

It was a very short paper for Nature in the form of a letter to the editor. That was one night before he and Mrs. Bohr were going away to Como. Mrs. Schultz was there and Harald Bohr was there and I was there, and Bohr was trying to finish. Then suddenly he said, “Now, everything is ready except the letter to the editor.” We were a little astonished, but he meant a special letter accompanying the “letter to the editor.” Finally he signed the letter, and he wrote “Niels Bohr.” The he got very much upset because he should have written “N. Bohr.” So his brother said, “But your name is ‘Niels’.” They were going to take a taxi to the station; their train was going a little after 12:00. I left for home I think a little before that. The next morning, when I came, I heard immediately that they had just left in the morning, and that was because in the last minute they couldn’t find their passports. They were trying to find them, and they were looking everywhere. Then finally, I think they were found on his table at the Institute. I heard also that the paper was not sent away, but that he had taken that with him. Now, in that case it was really lacking, and he made a very much extended paper; this was so short that nobody could have understood it really. Then after Como, Pauli went with him to a place at the Como Lake…

Rosenfeld:

I was later with Bohr at Como; it was an isolated villa near the lake; it’s called (Mount Pensada).

Klein:

It’s very likely the same place. I think they stayed there for a week or a fortnight even. Then Pauli got him to write it down in a very much extended way, and that was the main manuscript for this. That, I think, was written in German; the first was written in English. But then, you know, there came proofs and proofs and proofs, and finally after very many proofs he wrote a new manuscript because there were so many corrections during the winter. And everybody who was working at the Institute was reading proofs during that whole winter. But there came more into it the whole time, so that the subject developed.

Heilbron:

Do you remember any of the stages through which it went?

Klein:

That is hard. That’s very hard. When I see the paper again I might remember it a little better. There are many points; of course, in it he treated these different thought experiments. They were very thoroughly treated behind the paper, but they were, of course, very softly expressed in the paper. But that came very much nicer in his paper on the discussion with Einstein. Were you helping him with that paper?

Rosenfeld:

No, that was written when I was not here, but Pais was here. I think Pais helped him for that paper. … There was something which has always puzzled me in Heisenberg’s paper; that is the note added in the proof at the end in which he says that in discussion with Bohr he has realized that he had overlooked essential points in his paper, and that Bohr hoped to come back to them. Does it mean that he had nevertheless sent this paper to print before these discussions with Bohr?

Klein:

I think he had probably sent it away before Bohr came home. I’m not quite certain, but I believe he had. I think it took quite a time before Heisenberg saw this, so that there was quite a bit of talking before that came in there. Pauli was also involved in it at a later stage. But that was a subject which lay very strongly at the heart of both of them; that one could see. I mean, both Bohr and Heisenberg were, on such occasions, very hard. During that I had a little bit to do with these things in trying to help Bohr — which I didn’t do very successfully. But then Kramers came, and he had such a curious expression where he just mentioned this. He rather meant that one shouldn’t take a very definite standpoint in such a thing. I mean, Bohr had certainly a deeper view of the whole subject and a more correct view of the whole subject. And Heisenberg was very hard in not giving way, but you understand when you know both of them that that’s how it was. Later on Heisenberg wrote very nicely in his book on the “Copenhagener Geist” and so, but still Bohr had quite a number of objections against the book, also.

Rosenfeld:

Oh, yes. Oh, there were surprises, you see. The only example of a field measurement which is treated in Heisenberg’s book is completely wrong. It is one of the few cases in which, in fact, there is complete commutation. It’s only when you make a measurement with only an electron instead of a big test body that you get a measuring error. But this is spurious; it should be zero in that case. But the curious thing is that Heisenberg never corrected that error. There was a later edition of the book, and nothing was changed.

Klein:

He may never have seen that it was wrong.

Rosenfeld:

Oh, yes, of course he had, because he came to Copenhagen, and that was explained to him.

Klein:

Yes, of course, but you know to explain and to see is not the same. These experiences there made me feel that really to discuss correctly these observation questions was so difficult. I remember that it happened that some of my advanced students said that they wanted to do something of that kind, and then I advised them very strongly not to do that. Of course, you did it together with Bohr in a very fortunate way, but otherwise I don’t think anybody has done such things correctly. You remember Landau and Peierls tried something which was rather — Then in late years Wigner and (???) attempted it for gravitation. So that, in itself, is not so astonishing that Heisenberg made errors there. But you see there was one thing. Bohr had a veneration for Heisenberg. Heisenberg is, of course, very, very good, but for Bohr he was a kind of Messiah when he came with this new theory. I think that was really exaggerated, and I think that was the background then for the fact that Bohr was so upset that he had made those errors. Heisenberg is certainly human like everybody is. Bohr was also human, but just at those points he was almost perfect.

Heilbron:

“Those points” — you mean the measurement questions?

Rosenfeld:

Yes. That was absolutely —. Oh, just the experience I had in working with him on those points —. It was absolutely fantastic, the ingenuity that he had. And also the perseverance that he had —. He would never leave a problem before he had seen it through to the last detail.

Heilbron:

Did those discussions between Heisenberg and Bohr polarize the Institute? Did people follow them avidly?

Klein:

They were not generally followed, so I think I was at that tine the only one who was following them very closely. Then at the later stage, Pauli also came. Pauli was very helpful because he was a very old friend of Heisenberg. He was, of course, also a very good friend to Bohr. So he found the right way to them, so that he came to harmonize them.

Heilbron:

Do you recall the reception of those ideas at Como?

Klein:

I wasn’t at Como, so I only know that Pauli got very enthusiastic immediately.

Heilbron:

Do you know how that went at Como?

Rosenfeld:

No. I was not at Como, but when the paper appeared in Nature, it was commended in Gottingen. Well, personally, surely, I understood very little of it.

Klein:

It must have been extremely difficult when you hadn’t all those —.

Rosenfeld:

Yes, yes, very difficult. Surely I was not the only one. I remember Wigner’s comment because that struck me. He shook his head, and he said, “Well, this paper will not induce any one of us to change his views of quantum mechanics.”

Klein:

One, who was ultimately impressed but who didn’t quite agree with Bohr at first, was Dirac. I remember one way of his showing it. I came to Cambridge in March, ‘28, as I mentioned before. Then once Dirac took me to dinner in his college. After dinner we met Larmor. He introduced me to Larmor, and when Larmor heard that I was with Bohr he said, “Lately Bohr has gotten so metaphysical.” I think he had read that paper in Nature. Then Dirac said, “Shall we say philosophical?”

Heilbron:

Do you know what Dirac had said at first when he wasn’t impressed?

Klein:

Oh, I remember he had — but I’ve forgotten what time that was made some kind of observation philosophy which had to do with permanent marks. Bohr objected a bit to that because although it is true that you get that in some way, butt that is not the essential thing in the observation. But Dirac made that, so to say, as the essential thing. Do you remember when that was — if it was before or after Bohr’s paper? I have forgotten.

Rosenfeld:

I don’t know about that.

Klein:

There was a time when he was speaking about this, that the main thing in observation is that you have got, on a photographic plate, for instance, a black spot.

Rosenfeld:

Bohr took very much that view.

Klein:

Of course; he used it also, but he thought that Dirac in some way exaggerated it. Because one part of Bohr’s view was that you had to, and you can, use the whole classical theory in describing observation. And I think that was not near to Dirac’s mind at that time, but I have forgotten exactly when that can have been. It is, of course, an important thing that you can keep the observations so that you can use them afterwards. But without a description of the way you have gotten them, with the whole apparatus and so, you cannot make much of such a permanent mark.

Heilbron:

Did Einstein get much of a following at first?

Klein:

Oh, this I think is the proper place. You may know much of this, so I shall only tell my personal memories from that time, later on in the same autumn as the Como meeting there was a Solvay Conference. I think on the way to that Bohr passed through Berlin and met Planck, or he met Planck at Solvay; I’ve forgotten. Then he met Einstein at the Solvay Conference. Bohr thought that this would almost be evident to Einstein, and he had mentioned beforehand that he looked forward to seeing Einstein and hearing what he said about it. And then Einstein began to object, immediately. He came with (???) after the others. Bohr, or else Ehrenfest, said that every morning Einstein came, and was very fresh, and had a paradox. Then towards the evening Bohr had solved it. Then they continued that at Ehrenfest’s home in Leiden; they both went there. Ehrenfest had made some photos which they didn’t know that he had taken. He gave them to me; unfortunately I have lent them to someone and never got them back. But they were so nice. They were such that first one showed Einstein giving the paradox to Bohr. In this picture Bohr looked very serious and thoughtful, and Einstein looked happy. Then I think there was an intermediate photo where they didn’t look so very different, and in the end Bohr’s looks very, very happy, and Einstein doesn’t look so happy.

Rosenfeld:

Yes. Well, we might get hold of then from Mrs. Ehrenfest; she may still have them.

Klein:

Yes, she may have them; oh, I shall ask her then when we see her in Leiden. They were so very nice. He sent them to me then. You know, Bohr’s greatest triumph over Einstein — I believe that came already then, or could it have been a little later — was the Einstein box.

Rosenfeld:

Yes, that was three years later. It was at a conference on magnetism in 1930. They had nothing to do but confront each other. … I was there by chance. I was not at the conference, but I was in Liege, and I came to Brussels to talk to Bohr. I witnessed their coming out of the meeting for dinner, the meeting at which Einstein, as I gathered, had proposed the paradox. So he was in the triumphant stage, and he was royalized. Everybody clustered around Einstein, and Bohr was terribly upset, terribly upset. The first thing he said when he saw me was, “Have you heard what Einstein says? It is complete nonsense!.” He could hardly explain it, so upset he was. Then during the whole dinner he tried to persuade all the people sitting at the same table that it could not possibly be right. But he had no argument of course; he had not yet found the things. Then after dinner he disappeared. I still see them, you see, Bohr hopping around Einstein and trying to explain that it could not be true, that there must be something wrong, and Einstein of course —. But then the next morning it was a little different. I saw Bohr the next morning and then immediately he said, “I have it.” …

Klein:

It was fantastic that Bohr, who had in no way followed the general relativity more closely, had got hold of that.

Heilbron:

Did Einstein succeed, you say, in converting everybody with his objection at that point?

Rosenfeld:

Oh well, you see, the other people really —. First of all they were experts in magnetism, but they were not especially expert in those questions. They looked at it as they would have looked at a boxing match between two champions.

Klein:

That was the magnetism conference. I think it must have been after that conference that Bohr came home and said that now he knew that Picard was really a brave man, a courageous man. You know, Picard went up in his balloon very high, but that wasn’t it; it was because he stood up against Weiss’ magneton at the meeting.

Heilbron:

When did Weiss give up his magneton, or did he?

Rosenfeld:

He didn’t give that up. I don’t think he ever did.

Heilbron:

Well, we’re at about the tine of the Dirac equation, I think. Could you tell us how things were; what Bohr thought of it when it came out, and how much of a difficulty the negative energy states were.

Klein:

I think we were very impressed. Bohr got a short summary manuscript which he lent me at that time, so I began to study it. I had a little preparation to the mathematics which I got in quite a different context, namely, in studying Jordan’s procedure for anti-symmetric quantization. I’d been looking a little at the mathematics of such what are they called, after an English mathematician — Clifford. I had been reading about that in this mathematical encyclopedia, but in a different context. I thought they were, of course, very important for the understanding of particles and charges, and such. So I was a little bit prepared for the algebra of it, but I hadn’t thought of it in connection with the spin at all. That was, of course, very impressive because with so little he got so much. Then Bohr was, of course, very, very impressed, although I don’t think he ever studied it in detail. But we were talking of it, and in that connection he invited me to go to England a little later to see Dirac. Then afterward Dirac came also to Copenhagen in the spring and lectured about it.

Heilbron:

But the negative energy states?

Klein:

Oh, yes. Oh, yes. I remember Dirac had thought of them very early. When discussing the scalar wave equation, which I had been working with, as one of his objections against it Dirac had mentioned the negative energies. That was when he was in Copenhagen in ‘26, so he had thought of them then, but the solution came later. Then, of course, everybody was very upset with the negative energies.

Heilbron:

You have quite a paper about the negative energy.

Klein:

I got into that by chance. I think I mentioned to you that when I came back from Dirac, I had thought a little bit about attacking the Compton effect. I had been interested in Compton effect earlier but had never carried it out with the scalar wave equation because Gordon’s paper came before I had really begun the real calculation. Then Nishina came to Copenhagen, and he wanted to study theory more closely; he hadn’t so very much time before going back to Japan. He had always been interested in theory. He had visited us in the country together with Kronig the summer before, and we had had long talks. He always wanted to have the view on things and followed, it in a general way. But then he wanted to do some work also. I think that there was also a curious coincidence here. He was in Hamburg, where he had met Gordon. Gordon had said that perhaps the Compton effect would be something for him. Then he came to Copenhagen, and I had been thinking about the Compton effect. So Nishina and I decided that he should try it and I should try to guide him. But then the whole became so difficult that I got quite involved in the thing also.

The summer came, and we hadn’t got very far in it. We were very uncertain if we should expect just a new proof of the old formula or if there would be a new formula. Nishina came with us to the country; you saw there was one letter to Bohr in that connection. Then we were trying very hard on that. I was trying, first, to use the method that I had outlined in that correspondence paper I had intended to use it here. That was to have the electron waves in a box, to make the states discrete, and then to calculate the transitions between such discrete states. I tried to have the Dirac waves in a box, but one couldn’t do that because there were four components there, and one couldn’t make them all zero without making the whole zero. Then I tried to have a potential to include them, to have it more physical, and I couldn’t do that either because (???) … Nishina had to go away, so finally I looked at Gordon’s paper and used the way he had done it. Many years after one of my students discovered that that was really only correct for an electron at rest; it wasn’t correct generally. But he worked out the other way then also. It should have been easy if only I had thought that instead of having such standing waves one could have had running waves with a periodicity condition. But it didn’t occur to me.

So that was really the way to solve the thing if I had thought of it. Then there was a lot of such Dirac algebra. I was rather interested because I had looked rather much at these equations, so that came gradually clearer after we had got the principal thing of it. Then there was a lot of algebra to get a definite formula, so we began to fear very much that we would make errors of calculation. We decided to separate while we were doing them, and each of us did them independently. He sat in his room at the pension, I sat at home, and we calculated and compared. Of course, first our things differed. I really got the correct result first, but it was first by only a very little bit — he got it very immediately afterwards. But we checked all those; we did every detail, both of us, on all those calculations. They could be made shorter than we made them, but that was quite a heavy calculation. I think Nishina had found some paper which gave experimental curves, and then we made a theoretical curve. We had not much to draw with, so we did that just a little primitively. But then I think he went to Copenhagen and had it nicely drawn out. So we sent a letter to Nature about it, and then we sent the paper. He went back to Copenhagen then, and there he attacked the question of the polarization, and that he did quite alone. I was very busy there, so I never read that paper in detail, but Moller helped me to correct it, so he read everything in that.

Then I think I told Bohr about this curious paradox. [The transitions to negative kinetic energy states caused by a potential jump.] Pauli came also, so we were talking of it. I remember I got a reprint of a paper by Pauli after he had gone, where he wrote, [on the reprint] (“Publiziere uber das Paradox”). I did that. Bohr made a nice remark on it. I have forgotten if I mentioned in the paper. That was that one could, if one hadn’t a very steep potential, get a smaller and smaller effect. Still we were very puzzled by the whole effect, and I tried some very impossible way to get rid of it. I remember we were discussing at one of the meetings— were you there at that time?

Rosenfeld:

Yes.

Klein:

…I remember that Jordan had a strong argument. I tried to have some theory where the potential should be absolute, but that was impossible. But I was very sorry afterwards that Bohr was impressed for a little while. I always thought it very unlucky when he happened to believe in wrong things. If he disbelieved in right things it wasn’t so bad because then one might (yet triumph), but if he had believed in wrong things that was very (disappointing). That happened a few times with me. It happened a few times with me that I had done something wrong. Already with the electrolytes, before I wrote my thesis, I had done something where he found the error. And that was a very essential point which was wrong, so I felt very badly. Here I think it was more Jordan who gave the convincing argument against it.

Rosenfeld:

I don’t remember the argument.

Klein:

I remember that I gave it up definitely at that conference.

Heilbron:

Yes, yes. Oh, yes. It was the most short-lived theory that I recall.

Klein:

Yes, it was. I think I only had it a few weeks before the conference, and then I gave it up. Was it at that conference where Heisenberg presented this grating — this space grating — or was that later? I wonder if it wasn’t there.

Rosenfeld:

No. I’m not sure; I’m not sure. It may be, but I don’t remember.

Klein:

Then came Dirac’s holes; that was not so long after this. Could it have been a year after when Dirac began with these holes? Then I think we were rather skeptical. You know, there was this infinite sea of an infinite electric charge which was without action, and the whole thing looked very queer. Did you believe in it?

Rosenfeld:

No; I was in Zurich at that time. Certainly not; but for special reasons. Dirac had presented it as a theory of protons, but then Pauli found a proof of the complete symmetry. So that those positive particles should have the same mass as the electron; they could not be protons. So for us, at that time, that was an argument for disbelieving the thing.

Klein:

Yes, yes. You know, Oppenheimer about the same time came to the same argument. That may have been an argument for Dirac also; I don’t know. Heisenberg told me that when Dirac got the Nobel Prize some years later — in 1933 — he asked Dirac if he had believed in his own theory. Dirac answered, in his very precise way, that a year before the positive electron was discovered he had ceased to believe in the theory.

Rosenfeld:

There was a very strong resistance in Copenhagen, from Bohr, when the announcement of the positive electron came. Bohr would not believe it; he would not believe it. He did not make, and nobody here made, the connection with Dirac’s theory. I think somebody may have mentioned Dirac theory, and then Bohr dismissed it by saying, “Oh, but that is no theory. That is not a theory that one can believe in.” So he wanted to examine the evidence on its own face value, purely experimentally. He found that there were so many possibilities of electrons going in wrong directions.

Heilbron:

There were Anderson’s.

Rosenfeld:

Anderson’s, yes. But even a bit earlier he got from Joliot a letter with a cloud chamber picture with a pair. But then he wrote back suggesting that it was just an unfortunate coincidence, you see. Joliot answered that indeed he could not dismiss this possibility. … That was shortly before Anderson.

Klein:

…I think that Blackett was influenced by Dirac’s theory. I think he believed it.

Rosenfeld:

Yes, I remember when Blackett announced his result. It must have created a sensation, at least in Cambridge, because there was an article in the newspaper with a title something like: “The Dirac Theory Confirmed Experimentally.” May I come back on this point. Do you remember the argument of Jordan against the absolute potential?

Klein:

I think it was on the same line as what you had said about a bird flying very high in a thunder-storm being affected if the [absolute value of the potential had physical significance.] I think he made some estimate of how such a high potential would have to be. Or perhaps he made, rather, an estimate that the limit for the potential would not be sufficiently high, that one would have to have much higher potentials than this; I’ve forgotten. I’ve forgotten if I had got a definite limit for the potential, or if there was (an earlier thing). It was so short-lived that I (remember) that I thought it was stupid to remember it. It couldn’t help the difficulty, after all.

Rosenfeld:

Anyhow the question came you see, whether such high potentials could occur in thunder-storms. Then Bohr said, “Well, if a bird flew in such a thunder-storm, then he might be killed. Has one any evidence for such a phenomena?” And then, when the discussion went up and down, Ehrenfest commented, “Well, is the bird still alive?”

Heilbron:

You propose at the end of the paper with Nishina that if your results are correct, then the current ideas of the hardness of the cosmic rays are incorrect.

Klein:

Yes, now I don’t remember very much. We had some evidence, I think, of deviations from the older formula of Dirac and Gordon. We had some evidence, but it was very uncertain. I think the first certain evidence came out in the research by Lise Meitner and (Hopfeld). Lise Meitner wrote to me about it, and we had a little bit of correspondence. At the same time she did then really find deviations due to pair creation at the heavier nuclei, but I think with the light nuclei they confirmed the formula very well. I don’t remember — I don’t think there was sufficient knowledge about cosmic rays to enable one to test anything.

Heilbron:

I was just interested in the suggestion that if your results were right, then the frequencies had to be higher than had been expected.

Rosenfeld:

At that time one thought that the whole of cosmic radiation was gamma rays.

Klein:

That is true; that is true. And that one might have made a wrong estimate on the frequency by using the other formula, oh, yes. I had forgotten that.

Heilbron:

I was wondering in reading over that very long calculation whether or not as a result of that there was some little bit of despair at what physics was coming to, that such an effort was needed to attack a problem which really —.

Klein:

Oh, I see, but we did the best we could in the short time we had, you see. Nishina was leaving, so therefore we were both very eager to have a result, and I would have felt very much ashamed if he would have had to leave before we had got any result. So therefore we also used the short-cuts, as I mentioned before, and we carried, out the calculations as far as we could. We checked very carefully, so that the formula then really came out correctly, and of course we were very happy that it came to such a simple formula. … One might have done it perhaps a little shorter by choosing a special coordinate system, but apart from having an electron at rest, I think we didn’t specialize the coordinate system with respect to the rays of light.

Heilbron:

Since the calculation, of necessity, is so long and involved, I was wondering if there was any feeling that physics has now got to the point that there is —.

Klein:

Oh, I think that if I had been alone, I never would have done it. But then I felt, in some way, that since I had put Nishina on this — or at least contributed to putting him on this — then I was very strongly bound to help to have it carried through. That is, of course, a very great advantage with joint papers; the one drives the other and the other drives the one. Nishina was very energetic, so that if he had known the principles, he might have done it alone; but he didn’t know the principle. He was rather a beginner there. He had read Dirac’s paper very carefully, but, I mean, still he was quite a beginner. But I wouldn’t have done it alone.

Rosenfeld:

But Mr. Heilbron’s question was a bit different. He wanted to know whether one had the impression that physics was becoming too complicated.

Klein:

Oh, I see. Oh, I thought you were asking if we thought it would be worthwhile. We were very doubtful if any different result would come out. Now, there came different results, so it could be tested. But we were prepared that perhaps we would get the old formula again. Therefore, we didn’t know if there would come any new physics — perhaps only a new (motivation). But that physics, on the whole, got very complicated — of course, one felt in that problem. I think then later Casimir attacked the problem on the photo-effect, and that was immensely complicated. I never read Casimir’s paper in detail. So that it was, of course, as you say, and it has gotten worse still. Feymann has been a very great help there.

Rosenfeld:

What was considered as the top achievement, before the war, was Euler and Kockel’s calculation of the scattering of light by light. That was a terrible business. They had to enumerate all the matrix elements, you see, along with the graphs. Then they had to enumerate all of them and to calculate them — well, each side at least — by a separate calculation. It came to Copenhagen and it was considered almost unbelievable. We knew that the effect should exist, but nobody thought that anyone would have the courage to do that.

Heilbron:

For instance, did you read through Professor Klein’s calculation on that Compton effect and check the left-out algebra?

Rosenfeld:

Yes, yes. Oh, yes. I think in that time one reproduced calculations. There were not so many papers to read at that time.

Klein:

Did you read it in any detail?

Rosenfeld:

Oh, yes.

Klein:

It was, of course deficient with respect to method at the point I mentioned. Did you notice that?

Rosenfeld:

No, not particularly, no.

Klein:

I didn’t notice it either; only I was a little unsatisfied because I liked the other way in which I wanted to attack it, and I was angry that I couldn’t use it. Many years later one of my good students, (Berno), wanted to write a paper for his examination, or a theme for his examination. I proposed to him to calculate the Compton effect for particles of higher spin. Then, I think before he had quite started, he saw a little note in Nature of some people — I think they were Russians who had done something of that kind. I believe that they already had used this method of a periodicity condition for a traveling wave in calculating that. I don’t quite remember that, but I know that he showed me definitely that that could be done without any difficulty, and that that would be relativistically correct, and that our procedure was correct only for an electron at rest that was a little astonishing. That was much later, I think; it must have been in the beginning of the 40’s.

Heilbron:

Well, the other questions I had were with respect to the paper about the potential jump — whether or not that was taken as any sort of “in principle” objection to the entire Dirac theory?

Klein:

Yes, it was. I think it contributed rather much also to such a view as that of Bohr that he didn’t believe in the positive electron. Now, of course, that is no objection against the newer form. I never tried really to treat this problem in detail with the new view, but I think it has been done. Do you know?

Rosenfeld:

I think so, yes. It is just pair production by a transition.

Klein:

It could be real pair production, but that depends upon the potential.

Heilbron:

There was no question of anyone being interested in doing an experiment?

Klein:

I think we took it as objection; we took it as insane. I think Gamow called those electrons donkey electrons because they went against the field.

Heilbron:

Well, that rather exhausts what I have today.

Klein:

I’m very glad to be reminded of all those things, and it was very nice to hear what you said.