Oskar Klein – Session II

Heilbron:

I had jotted down a few things as I looked through the transcript of the first interview. Perhaps I can just begin by asking a question or two and then you can proceed as you did before so well.

Klein:

I’ll try to do what I can.

Heilbron:

Well, to get back to the quite early days, I was wondering whether when you were, so to speak, a protege of Arrhenius he had other students as well and if that were a common arrangement?...

Klein:

Oh, I came on a rather personal basis. My father knew him. There were at that time advanced people working in the laboratory, but I was the very youngest of them because I hadn’t been at school yet. Then a little later his son, who is one year younger than I, also began to work there some. But that was mainly after (???) after he was a student. But he came, and I met him.

Heilbron:

You said that Arrhenius surprised you considerably when he introduced you one day as a theoretical physicist.

Klein:

Yes, yes. He liked to define things which I hadn’t thought of defining myself. My first examination I had taken already, and that was the regular three subjects: chemistry, and physics and mathematics. But the next should be only one subject, and then I thought of taking chemistry because I thought it was chemistry that I had done. I knew it was physical chemistry, of course. But then he asked me why I thought of taking this examination in chemistry since I was working with physics. Then I think I had bought a big chemistry book, and then one of the fellow students bought that from me, or I think we changed it for a physics book. Then I read this big book of _______________; I had almost forgotten what the beginning of one part was about when I had come to the end of the next. Then I had the examination in physics; I mean it was the same work, just the definition was different. Then he introduced me, when Bjerknes came there, as a mathematical physicist. I didn’t know that I was that. Of course I wasn’t it very much because I had so little regular study; mostly by myself. Afterwards I had good occasion to miss the more regular studies in these things. Then I got against mathematical difficulties which were quite unnecessary, quite elementary.

Heilbron:

Can you remember any in particular?

Klein:

Oh, the main thing was of course with wave mechanics. I was trying on a rather similar line to de Brogue, and I started it rather early. I think it was in the spring of ‘21 when it first occurred to me that one had different ways to have whole numbers in physics. Interference, might, I thought, in some way give the quantum conditions. I studied earlier some of Fresnel’s work in that connection. Then very gradually that became a little clearer. Then I got it mixed up with this five dimensional thing from the point of view that —. I knew too little of the mathematics of the things to know—and this was de Brogue’s discovery that one could have a wave equation with a mass and that could then give different velocities. So I thought it would be very strange if you had some waves that they shouldn’t have a definite velocity. Then I thought that they might be waves in a space of one dimension higher, so that what we had was the projection in four dimensions. In that way I got these two things combined. Then it took quite a time before there came anything real out of it. I remember that in the summer of ‘23 I was working with light because I was writing a book on light.

I had been asked to do it—it was rather postponed. In that connection it occurred to me that the quantum conditions could be compared with the eigen vibrations. For instance, if you had a drop, the [surface] waves would interfere with themselves. I had earlier thought of this interference with itself on the periodic orbit, but then it occurred to me that that would be something like eigen vibrations. Still I knew hardly a thing of the mathematics of these things, so the progress was very, very slow. I had this connection with the Hamilton-Jacobi equation; I got that through Whittaker’s book. That was at a rather early stage, but then I was troubled partly by my lack of mathematical knowledge and partly because at that time one wanted in some way to combine the particle view with the quantum view. It was not clear to me that one should have this super position principle as a rigid principle. I studied a little (Hadamard’s) work on waves.

Therefore I knew that one could have such a wave front equation like the Hamilton-Jacobi equation also for wave equations which contain non-linear terms. It was difficult then to decide to drop these non-linear terms because I thought that it might help in other respects. Then later in Ann Arbor I gave a lecture-series on quantum theory, and then I got a little deeper into the formulation of the relativistic particle motion in electro-magnetic fields. Then it occurred to me that one could formally compare the Hamilton-Jacobi equation for this relativistic particle motion with the Hamilton-Jacobi equation for ordinary particle motion in a space of a dimension higher. I had already thought of this in a vague sense, but then I saw it could be done in mathematics. And that really led me to difficulties because I concentrated then very much in the five dimensional theory. Really I learned relativity mostly in that connection; I had learned only a little of it before. And that took very much time. It was clear to me how the quantum conditions should be connected, so to say, in this semi-classical way.

Heilbron:

That was already in 1921?

Klein:

No, 1920, but I had only the vague idea that there should be some connection. I don’t remember exactly when I thought of these quantum integrals as interference. It must have been about that time, but then I got it more closely connected with the Hamilton-Jacobi equation. So, therefore, it was very near to me when it was clear then that the wave equation worked, but I couldn’t prove that. I had been in Ann Arbor until the end of the term and I think I left about the beginning of June or the end of May, 1925. During the summer I worked on five-dimension theory. Then in the autumn I got very long jaundice and didn’t come back to Copenhagen until the beginning of March, 1926. That was very near the time of Schrodinger’s [work]. But then I had begun to concentrate and see if I could solve the wave problem for the harmonic oscillator. I didn’t know anything of the [Hermite] polynomials and things of that kind, so I didn’t get through it. But then Schrodinger’s [paper] came — that was the background… In this period I was very near, I thought, but I hadn’t [gotten] through it.

That was partly a lack of mathematics and partly lack of a clear view on the superposition principle, because I was not decided that there should be a linear-wave equation. I thought it might be that those terms with second derivatives should be linear, but then there might be some first derivatives which were non-linear, and that was, unfortunately, in that connection, wrong. Then I had mixed in — I remember that was also in the question — a rather vague remark by Bohr. He stressed that one could not hope to have a theory in the usual way connected in four dimensions, but perhaps one could have it in high dimensions. He mentioned that. Then I thought that that might go together with the other things. I put in a note in my first paper… But I think his view was more the negative one that one could not have a theory in four dimensions. Should I go on and tell how I came back to the line of real quantum theory from this attempt to make something more like the classical theory in five dimensions? Finally I regarded this attempt as decidedly wrong. But that came rather slowly. It was very clear to me very soon after I learned about Heisenberg’s work and Schrodinger’s work that there was a way to continue quantum theory by a similar quantization of the field, but I tried to think that it may not be necessary and that one might still have something more in the ordinary way in five dimensions.

I never believed, like Schrodinger, that one could do it in four dimensions, but perhaps in five. Then I tried to work in a more provisional way to see what one could do on such a correspondence basis. Bohr got very interested in that work, so that he took a very vivid part in the paper I wrote there and criticized and helped. So that took a very long time. But then I was still not decided against the five dimensional theory. That paper was finished, I think, a little before Christmas, ‘26. The first version of it I had written in the summer, but then I started it anew in the fall, and Bohr took a very great part in it… In the early fall of ‘26 Schrodinger came to Copenhagen and Heisenberg was there. Then there were very intense discussions between these two and Bohr. Bohr and Heisenberg tried to persuade Schrodinger that he could not get on in his way. There were very clear arguments; for instance, that the probability for a spontaneous emission of light would, according to Schrodinger’s theory, come out so that it would be proportional to the number of atoms in the upper state and the lower state. It was, of course, nonsensical. Pauli’s Principle was not so very clear at that time, but at any rate it was quite nonsensical.

Then in that connection I tried myself to give a little contribution to this. I took a look at how you would get the temperature radiation law if you took Schrodinger’s radiation theory literally. Then one got something which was, of course, Rayleigh’s formula. That was so curious. There was a constant also possibly appearing, but the main result was Rayleigh’s formula. One couldn’t possibly get Planck’s. That wasn’t astonishing at all. Then after that time I began to think a little more about how to formulate the many particle problems. Initially, it had only been a one particle problem, so to say, with a field of force. [But now I was concerned with how] to formulate the many particle problem. Then I saw that also the five dimensional theory got in the same kind of trouble as Schrodinger’s; it looked quite impossible. Then at that time there appeared that very beautiful paper by Dirac on the Photon theory. Then I tried to formulate this interaction problem in that way, and then it came out very nicely. Apart from that I got the equivalence with this Schrodinger configuration space equation; apart from such terms that really had to do with self energy. But I was very annoyed by that and left this work. I hadn’t very much [to do with it] until the next autumn when Jordan came. Then we talked of it, and Jordan said that he had also thought of this way. We talked of it together, and then Jordan immediately saw that these were self energy terms which one had to subtract. And we saw that by changing the order one could get rid of them. I think I knew — no, I don’t know if I knew that one could do that; at least I hadn’t thought of this that it had to do with self energy.

Then we wrote a joint paper on that. But it turned out that from that time when I had the main ideas of that paper clear — I think it must have been something like March, ‘27 — I was quite decided that the (wave) quantum mechanics was correct, and that all the others were incorrect, and I have never fallen back from that. You know finally Schrodinger was convinced, but he came back, and I think de Broglie also. But then I thought that that was quite decisive. I may tell in this connection a funny thing that in ‘49, like all other people who visited Princeton, Einstein began to ask me what I thought about his way of looking at quantum theory, and he told me about it. Then we had some talk about it, and then I asked Einstein — we were talking German — if he had ever looked more closely on this question of second quantization. And then Einstein smiled and said, “Zweite Quantelung, das ist (Sunde im Quadrat).” But the background was this that played a very great role in my conversion to quantum theory. I saw that that gave the many-body problem quite smoothly, while the other way was impossible. One could always with the other way think that one could hope that one should do anything because everything was so difficult, but then I saw how smoothly it came this way. That seemed quite convincing.

Rosenfeld:

By the way, what do you think about the name “second quantization”?

Klein:

Not so good.

Rosenfeld:

It’s very misleading.

Klein:

Yes, yes. I don’t think Einstein ever had looked at it.

Rosenfeld:

You didn’t look at it in that way, I suppose, as a second quantization?

Klein:

No, no. It came formally in that way because Dirac had expressed it so. But I had still that left over from the five dimension approach that I wanted to regard, so to say, the wave equation as a space-time thing. Then at that same time when Jordan came, he told me his main idea about this Fermi-quantization, and that impressed me very much because I had been trying — and never been able to find it — to look at the thing qualitatively. You had in the Schrodinger problem a number of eigen-vibrations, then it was very strange that the Pauli Principle demanded that you should just have one, and only one, particle in such a state, and I tried to dream about that, but it never occurred to me that one could have such a simple mathematical formulation. Then Jordan told me, and it was clear like that. And that satisfied me very much more than the Schrodinger approach with the configuration space. And I say that that was the reason that I —. Then he had not gotten the mathematical apparatus in order at that time, so I think that Wigner contributed there such a great deal. Those were interesting years. But now I feel that I have talked too long about this question.

Heilbron:

You have mentioned that in 1917 you were ready to go abroad. You made various arrangements and had thought of going to visit Einstein. Was there a particular subject in which you were interested?

Klein:

May I think a little bit? First it occurred to me, or rather one was told, that it would be very good to go abroad and see a little and learn a little from those who really knew something of physics. It was the son of Arrhenius who said that. He was my friend; he was a little younger than I. He said that very eagerly, and I suppose his father was a little bit behind it, but he didn’t tell me. There was something about this in the paper, but I think there was a little misprint there. Arrhenius’ son helped me with the application for a fellowship; I hardly knew that I could apply for it. I remember that he arranged even to type it out, so I had only to sign my name. Then I forgot to sign my name. I heard later from one of the professors that they were amused on the faculty that they had gotten this paper with the name printed but with nothing of a signature.

While I was applying for this fellowship I began to think of what I would do. I was very interested to know more about Bohr’s work, first because the results were very impressive, but I understood the arguments very vaguely. I thought at that time that other work which I also tried to read, such as that of Sommerfeld and Schwarzschild, was in some way different because it was more difficult mathematics. That means that I really didn’t understand it. But Kramers made a short visit in Stockholm in the autumn of ‘17, and then he told me, of course, of Bohr also. That was too short to give me any real idea, but it did contribute, I think, very much to my wish to go to Copenhagen. Before that, I think, I was working on questions which were closely connected with the work of Debye. Then I had a very general admiration of course, of Einstein, and I had read some of his quantum theoretical work. I have forgotten if I had read his derivation of the Planck formula. I read rather carefully at that time, but I don’t remember quite when it appeared. I see that it was published in 1916 in the Berlin Academy, but I don’t think I saw it there. It appeared in Phys. Zs., and that I think was in 1917, so I believe I must have read it. And I had read some of the work of Ehrenfest I remember, and I had read some in the book of Gibbs.

I was a little prepared for statistical theory, but I had seen more of the formal side than the real content of it. In any case, I think that this contributed to my wish to go to Einstein. In my application I think I wrote that I would first try to go to Bohr and then to Debye and then to Einstein. Then I wrote the letter which you have here in this folder from Bohr’s correspondence. Bohr answered me very kindly, but I couldn’t get away from Stockholm immediately. Arrhenius had put me on an experiment on (adsorption) and that took a long time. I was very little skilled in these things and. broke many glass tubes and things. That was a very slow thing. But then I got it rather finished so that I could leave in the beginning of May. Then, of course, very soon I saw that I had not allowed myself a long enough stay with Bohr in order to learn all the things which he was about. So I never went on to Germany to Debye and Einstein. And I came very soon into other lines of work, also. I first met Bohr at his little room in the Polyteknisk Laereanstalt. I went there, and he was very kind and began to talk of the things I had said in a paper. He said a little about that and had some critical remarks which were very just. Then, I think, he began to talk about the work there, and then he invited me also to his home in Hellerup. A little later he took me on a rather long walk, and there he talked very much about his general ideas, both in physics and also in philosophy. He continued this also when he came up later with a number of friends for a skiing trip in Sweden. That was, I think, over a year later. But I suppose he must have told you about this. At that time it was something which had already some touch of complementarity, but he had a very curious formulation of it… He was thinking, of course, of the possibility of getting into logical difficulties due to the fact that thinking about oneself was a singular point. Has he told you that? I don’t think he ever wrote it.

Rosenfeld:

He never wrote it down, but in his last interview he got back to that. He gave sonic indications.

Klein:

So then you have it —.

Heilbron:

But unfortunately it’s quite vague in that interview.

Klein:

Did he also tell you about similarities with many-valued functions on a Riemann surface? I think that was his main interest. But then the problem on which he wanted to use it was the problem of the will.

Heilbron:

Do you remember how that worked the details of the application?

Klein:

Oh, it was this old difficulty about the will. What do you call it in English? The freedom of the will and the other side of it. Then he thought of this applying to oneself — to one’s own thinking — as similar to a branching point in a many-valued function. One used the name “will” and then one continued to use it in this way, and suddenly one came up to another meaning of the word. It was very beautiful. That he told already on that walk in the summer of 1918, so I think he must have thought about that a long time. Then he spoke — but that was very vague, at least to me about an analogy between that and the quantization. But I don’t think anything came of it; it was more the feeling that quantization was so impossible from the classical point of view that there must be something. Therefore, I think also this thinking of spaces of higher dimensions had to do with the same analogy that one could get a many-valuedness in some way which could be continuous in the space of higher dimension.

Heilbron:

In your walk with Bohr, how did it come about that he began speaking of this?

Klein:

Oh, he talked of so many things. One of the physical things he mentioned was some work of Debye which I think I had looked at a little but didn’t really know. Debye tried to use Bohr’s first rather primitive model of the hydrogen molecule to discuss the dispersion of light from a hydrogen molecule. Debye found the perturbations of those circular orbits from classical mechanics and electrodynamics, and then he got an expression for the scattering of light which happened to agree rather well with the experiments for a region of frequencies far away from the spectral lines. I don’t know if there’s anybody who has cleared up why it agreed rather well. But Bohr’s criticism was very decisive, and I saw later when I was preparing my lectures that he had really written that in some of the very early papers. It was perhaps not at first, but it was before 1916, I think. Bohr especially points to these beautiful experiments of R. W. Wood which show that absorption and emission and dispersion all belong together. And in the dispersion formula that Sellmeier, I think, first gave the denominators contain these characteristic frequencies of the spectrum — the real spectral lines.

But in Debye’s theory it would be the mechanical frequencies. Now at that stage of quantum theory they were very different because then one applied mechanics on the stationary states. Bohr did it very cautiously and was very clear that this was really to go a little further than one was permitted to do from the Correspondence Principle. But one got so good an agreement to a certain extent that Bohr thought that in these stationary states, which were periodic, it may be that the deviations from mechanics, in this application, were averaged out. He also regarded this mechanical transformability of the stationary states in a similar way to Ehrenfest. I think he got to it independently of Ehrenfest. I don’t remember if he mentioned all this on that walk, but I think at that time he mentioned all these things. But then it was very clear for him that this dispersion theory of Debye could not be correct, but that one had to connect it formally to the transition processes and that the frequencies had to come out as the differences of energy between different stationary states. I believe that already then I’m not absolutely certain he talked of the possibility that the energy principle was only true statistically. I believe he said that… I don’t think he published anything about it.

The Bohr-Kramers-Slater was much later. But I believe that he mentioned this and I remember that he mentioned dispersion theory. I think what Kramers did was very important because I don’t think Bohr had any idea of how to formulate this mathematically, but, so to say, the physical ideas I think he had then. Then, of course, Kramers found this very nice way to do that. The Kramers dispersion theory came out in connection with this idea of virtual oscillators and statistical conservation of energy and momentum. But then really this dispersion theory was independent of this particular view of the connection between quantum processes and (dispersion in the radiation field.) I can’t be certain that he mentioned all these things on that walk, but I believe he did. I remember also that he mentioned early physicists, like Maxwell arid Rayleigh, whom he talked of with great admiration. And then he spoke about philosophers. I happened to have read a little popular book by Bergson, which had not impressed me very much, but I thought it was perhaps nice. But Bohr was very, very critical of Bergson. I must say that after I had seen more of it I quite agreed.

Rosenfeld:

But Bohr had not read Bergson himself?

Klein:

Oh, yes; I think he must have because I had no deep impression at all; I only thought it looked nice, and so I read a little bit. But Bohr was very critical.

Heilbron:

What was his main criticism; do you recall?

Klein:

It was this Elan Vital. That could, in some way, be considered to be like Bohr’s later ideas on life, but, of course, Bohr always pointed out that they were very different from this kind of view. I wonder. I believe at that time already he said that his father had some ideas about biology and that one might think of quite different kinds of laws in biology than in physics, that in biology one might have finalistic laws. I believe that he mentioned that already at that time.

Rosenfeld:

Well, he was always anxious to come back to those ideas of his father. They were expressed only in a very short introduction to one of his father’s papers. Obviously what was there written down was only a condensation of what the father had expressed many times, probably, in conversation and which had impressed him very much.

Heilbron:

How would you characterize those ideas of his father?

Klein:

I think the main idea is that in practical biology you … must consider a living being as acting in order to conserve its living conditions. Therefore, in practical biology, you must use teleology. I think his father said something of that kind. That impressed him very much. It therefore seemed that in biology one may have laws which, from a teleological point of view, have a certain meaning, but which, at least practically, one cannot trace back to physical and chemical things. This is true, for instance, of almost everything in behavior. Now in later years one has discovered such wonderful chemical mechanisms so that again it might appear tempting to try to get as far as life. Bohr was very impressed with these developments in later years even more than I. I had the feeling that he gave up a little too much of his earlier ideas.

Heilbron:

This was part of his earlier thinking? This was all part of his thinking in those days?

Klein:

Yes; he had, so to say, the general ideas of it, but they were very much more carried out and, to the point in later years. For instance, one idea which he gave up recently but which played a very important role was that you could never make a physical-chemical analysis of a living being to the point where you could apply, let us say, quantum statistics, without killing the being. That played a very great role, but he didn’t have that in 1918. That, of course, came sometime in the late 20’s. But the general background, so to say, he had. Also, I think he had the general background of philosophy, although the way of formulating it — the complementarity — came almost ten years later.

Heilbron:

Was he reading much formal philosophy at that time?

Klein:

He had read very little — very little. Bohr has written about this in that paper which he wrote after Hoffding’s death. Hoffding was a very close friend of Bohr’s father, and his father and Hoffding and the physicist Christiansen used to meet in their respective homes. When they were at the Bohr home, then Niels Bohr and his brother took part in those discussions, or listened to them. But in that connection Hoffding asked, I think, for Bohr’s help or criticism. He had written a little textbook on logic, which was not his main object, but as a teacher in philosophy he had also to teach about that. Bohr read that very carefully and I think criticized it quite a lot. He read, I think, some of Hoffding’s books, but I think he read very little more.

Rosenfeld:

That was about all, I think.

Heilbron:

When you came here you didn’t know much of the quantum theory. How was it suggested that you go about learning it?

Klein:

Oh, I had tried at that time to read what I could about quantum theory because that was a fascinating problem. I tried at that time to combine it with my older problems, namely, to understand first the electrolytes and then also other chemical processes more clearly. It was quite clear at that time that if you wanted to go into these things then you would need quantum theory. But by and by these problems were all solved before I began, and I got more and more interested in the problems behind them.

Heilbron:

I meant to ask what was thought here of Sommerfeld’s methods of quantization, about the idea of space quantization, and whether it was recommended that you spend much time trying to master those papers.

Klein:

At that time I was very confused by the whole business, because quantum theory was very confusing. But I tried to learn the formal side of it as well as I could. I read almost all the papers that appeared at that time. When I came to Copenhagen, Bohr had, with Kramers’ help, finished the Part I of these big papers. I don’t remember whether he sent me a reprint or gave me one just when I came. In any case, that had appeared already. There his reaction to Sommerfeld’s and the other quantization was, so to say, settled. That had taken quite a long time. … He started to summarize his own theory for purely periodic motions, and that paper was later published, on Sommerfeld’s advice, together with his collected early papers. But he had withdrawn [the original English version from the Phil. Mag.] because Sommerfeld’s work appeared. Bohr tried to work that into his paper, but he didn’t get time to do it. But then he took that up, I think, very strongly as soon as he came to Copenhagen as a professor. Then Kramers became his assistant, and he also took it up. By the way, would such personal things as how Kramers came to be his assistant be interesting in this connection? I don’t think that’s very known. Kramers told me once. Should I tell it?

Heilbron:

Yes. Please do.

Klein:

Kramers told me that he had studied with Ehrenfest, and he had read Bohr’s papers and wanted, of course, to go on. But he hadn’t thought of going to Copenhagen to study with Bohr at that time, if I understood him right. There was a student meeting in Copenhagen, and I don’t know how he got to know about it—from some Dutch friends of his, I suppose. But then there was an aunt of his who invited him to go to that meeting, and he went there. I think be told Ehrenfest about it, and Ehrenfest just said that he ought to visit Bohr. Kramers very much liked to see people, so he went up to Bohr right at the beginning. I think they had a very nice talk, and I think Bohr got a very good impression of him immediately. Kramers was very clever, of course.

Rosenfeld:

As Bohr told it to me, he was a bit embarrassed by Kramers’ sudden appearance. He called Harald and told him, “Now, this young man has come;” and Kramers had some paper with very complicated mathematics that Bohr hardly could understand. So he asked Harald, “What shall we do with this learned mathematician who is proposing to work with me?” Then Harald told him, “Well, if he wants to work, take him, and don’t bother about his mathematics. He will settle down to physics very soon.”

Klein:

But if I remember Kramers right, I would, suppose that this came in the second talk. According to Kramers, he went to the students’ meeting after the talk he had with Bohr, and then he spent all his money. He had no money to go back to Holland. So he went back to Bohr and asked if he could borrow some money from him. Then they got into further conversation and Bohr asked him — there might, of course, have been some days in between — to be his assistant. So I think Kramers stayed on; I don’t think he ever went back to Holland at that time. I know, of course, that he went back later for visits, but he stayed for ten years, almost.

Heilbron:

That’s very interesting.

Klein:

But I suppose that must have actually taken a little longer than Kramers told me, so that at some point Bohr discussed it with Harald.

Heilbron:

What about your own work with Kramers? You said in our last talk that you and Kramers had tried to work out something on the Hamilton-Jacobi problem.

Klein:

Oh, yes. I was working on the statistical theory of electrolytes and Kramers took a very strong part in that. We had many discussions on it. Then Kramers even came back later and wrote a paper on that topic, even after I had left it. After the Debye-Huckel theory came I left it. Kramers’ problem was the coordinates in which the Hamilton-Jacobi equation could be separated. The first Christmas vacation, after my first stay with Bohr, Kramers came to Stockholm; we were going up to Dalarne to go skiing. There wasn’t very much skiing because it was above freezing the whole time we were there, but then we talked very much. Kramers talked very much about this separation problem; then part of it occurred to me; then I got very interested in it and continued. (And we proved) that if you had orthogonal coordinates, then they could only be elliptical. I learned a good deal of the background of relativity theory at that time. There was a big book by a French mathematician who wrote about such conditions which corresponded to the vanishing of the Riemann-Christoffel tensor. I didn’t know that through relativity theory yet, but I read it in that connection. I didn’t read the whole book but only this part. He was one of these well-known French mathematicians who was just writing on these analytical geometry questions. I think I don’t remember the name.

Rosenfeld:

Could it be Darboux?

Klein:

Darboux, yes, yes. So then by looking at those conditions and assuming that the kinetic energy was the sum of quadratic terms, then one could prove that it could only be elliptical coordinates. But we never published it because Kramers never got time to look more closely at it. We thought that we must generalize it to skew coordinates also. Later then I think I saw some paper of someone who had done that. I think I must have some manuscripts somewhere. Later that became quite uninteresting from a physical point of view, but at that time one thought that that was important for the quantization.

Heilbron:

Did Bohr think so too at that time?

Klein:

I think Bohr was not interested in it at all. I don’t think that Bohr (???).

Heilbron:

Do you remember other conversations during this period when you worked together with Kramers?

Klein:

Then, of course, he taught me as much as I could digest of what he had learned from Bohr, so that at first he was my main interpreter. I didn’t know the Hamilton-Jacobi equation at that time, and he told me about it, and then I read it in Jacobi’s book. We had many conversations; we met almost daily in that time because we took dinner together at this kind of students’ cafeteria which was for the University. One had dinner for 50 ore at that time, and then he used to write on the table napkins. He told me about his work. He was already very advanced in this work on the Fourier components and the estimation of the transition probabilities, and the hydrogen lines with the electric and magnetic fields.

That was rather advanced at that time and it was finished during that year. That was then his thesis. Bohr went with him then to Leiden in the spring of ‘19, one year after I came there. That was a very interesting problem. Kramers had learned the correspondence view from Bohr, as far as I remember. Bohr had, of course, the beginning of it in his first paper already, but it hadn’t occurred to him, I think, that one should be able to approximate that way the probabilities for transitions and especially also the absence of certain transitions. That puzzled him very much. You know that very early, in a very curious theory for the Zeeman effect, Bohr had given up the condition hv equals the energy difference. He tried to simply add the Larmor frequency on as a special assumption in a magnetic field. That is in one of the early papers. I didn’t remember this, but, I saw it when I prepared my lecture about it. It was rather curious… Then Bohr saw that that was immediately clear from, what he called at that time, the analogy principle. There he used this idea of the asymptotic equality between the resulting spectrum — although the processes were different — on quantum theory and classical theory. And in that evolution, the work of Einstein — the derivation of Planck’s formula — was very important.

There Einstein, you know, had explicitly formulated such probability laws. I think Kramers told me that it had occurred to Bohr while on a trip he had made walking in Jutland. When he came back from that he told Kramers about these things, and then Kramers immediately tried to calculate Fourier coefficients. Then he went on with that work. There were very puzzling problems, of course, because one wanted to know the probabilities for transitions between states with finite quantum numbers, and not just the limit. One didn’t know how to find them because one didn’t know whether one should calculate the Fourier coefficients in the upper or in the lower state, or in the middle of the states. But Kramers tried some kind of average; of course, this was very, very bad, but at the same time, he got very good estimates which agreed very nicely with Stark’s measurements of the Stark effect. Kramers started very soon — I think it had begun already at that time — on a deeper study. You know Sommerfeld had studied the fine structure by means of this relativistic precession of the electron orbit. Then Kramers took the case where you have an electric field plus the relativistic motion. He treated that and had then the transition from this pure relativistic effect to the pure Stark effect. I think on the whole that agreed also, but I think already at that time there appeared certain difficulties in the probability of transitions which were only solved after Dirac’s theory. I think it was already in that work of Kramers.

Heilbron:

What did Bohr think of that Einstein derivation?

Klein:

Oh, he admired it very much. When, in the following years, a few other people came to Copenhagen — Rosseland, and so, — then Bohr used to have small discussion seminars where we had to do some reading and give a review of papers. Then this paper of Einstein was something which played a very great role, so that I wonder if it wasn’t reviewed more than once. Bohr considered it very important.

Heilbron:

Is that part of the background of your paper with Rosseland?

Klein:

That was about the same time because that was when Rosseland had only been there a short while. For my part, it was rather a chance, because I hadn’t been thinking of such problems. I knew, of course, of Franck and Hertz, but I hadn’t been thinking of the problem at all. But Rosseland began one morning when we were sitting in the library, of the Polyteknisk Laereanstalt to talk about it. He wondered, “How could it be if there is a temperature equilibrium there?” He had apparently thought of it before. Then, when I went away to my pension for lunch, I began to think about it. Then it occurred to me how one could formulate it … as a kind of statistics in analogy with Einstein’s paper. Then in the evening Bohr had taken me to the theater. (I think Bohr was very literary at that time), and he told me that it was such a funny play, a (comical) play of (Jensen); it was (an old comedy) play. I told him about this, and he got very interested in it. I accompanied him home, and he took me up and we talked on about it, and he said that I must publish it. Then I said that I had the problem from Rosseland and that be might have thought more about it than I knew. Bohr said that he would talk with Rosseland. Rosseland had actually thought more about it, so Bohr advised us to publish together. Rosseland was really more interested in the problem. I was very interested that one could treat a case of temperature equilibrium that way, but Rosseland was very interested in a practical way in the problem of the application of it. I never did anything of that kind, but he continued it.

Rosenfeld:

Was Rosseland already thinking of applications to stars?

Klein:

That came a little later, but I believe that he had that in mind already. I think that in a paper very soon after he got the idea of what is called the Auger effect. (I just told Auger that he ought to have mentioned it.) Rosseland had that quite clear, but I don’t think he had applied it to electrons in atoms. I think he had been attempting application to something with beta rays. And I think that is the reason that it wasn’t quoted as his effect. But then came Franck. Franck got hold of that paper and got very interested in it and began to apply it to fluorescent radiation and other things. I think Rosseland had already been interested in that. I think he wrote some more on it, but Franck was the one who made people take interest in this paper because he had many experimental things to which he applied it. For me, it was just application of a statistical principle.

Heilbron:

Were the Franck-Hertz experiments in 1918 or so considered to be a great demonstration of the quantum principles, because Franck and Hertz themselves don’t know it even so late as that apparently…

Klein:

Bohr met them later. That was in 1920, I think; he went to Berlin and gave this famous lecture there, and there he met them. Lise Meitner often tells about when Bohr came to Berlin and how enthusiastic they all were when they came to know Bohr and his ideas. I don’t know how it was with Franck and Hertz; they must have read Bohr’s earlier work. He perhaps had a correspondence with them earlier because I think they accepted it as soon as they knew it. Was there ever a controversy over it?

Heilbron:

Well, they did refer to Bohr in 1916 when they did, a long paper in the Physikalische Zeitschrift. But they still thought that they’re measuring the ionization. …

Klein:

And they still believed it? I see. I don’t remember that Bohr told me how they were convinced. Then Franck got very enthusiastic about all Bohr’s ideas, and Bohr got very enthusiastic about Franck. I remember he said, after he had been in Gottingen, that one could really envy Born that he had such an experimental physicist at his side as Franck was in Gottingen.

Heilbron:

At the time when the Institute was beginning to take shape and he was deep in the quantum theory of line spectra and so on, Bohr still had much time available for the work in which you were engaged, the theory of electrolytes, which was apparently so far from his own immediate concerns.

Klein:

Yes. Of course, he was interested in any part of physics which he happened to think about. Really, he was interested in any part of physics. I remember that I often felt very badly that he spent much time on my things. It was very difficult, you know, when he got eager and I was also. He discovered mistakes in my work which I was very ashamed of. I think that one reason which might have contributed to his willingness to work on my problems in 1919 was that Kramers was away. After his doctor’s degree in the spring Kramers got very ill — I think it was typhus. He was ill, and he was confined several months. He only came back to Copenhagen a little before Christmas — about December. At this time he was absent, and Bohr had gotten stuck in the problems he had been working on. I think he had wanted to go on with the many electron atoms and the molecules, but there he had gotten stuck, so that he didn’t at that time, have any real idea of how to go on. That came a little bit later through the analysis of spectra, but at that time he had gotten a little stuck. That might have contributed a little bit then to the fact that he got interested in these things. Partly, it was, of course, his general kindness, but I think that might have contributed somehow.

Heilbron:

Bohr had no compartmentalized idea that “This is basic physics, and that isn’t,” and so forth?

Klein:

Of course he had in some way, but he was interested in all applications from which one could learn something. As soon as one knew how to calculate things, then he was not interested in repeating the calculations. But while the real problem was unsettled, he always got interested without regard to the subject. His fundamental work, I think, almost always grew up in connection with more special problems. For instance, take Bohr’s efforts to understand how atoms are built up. You could, of course, call this application a fundamental problem, but he was, at that time, certainly as much interested in knowing how atoms are built as in knowing the general laws governing the atoms. Then the general laws were discovered, and he was no longer so very much interested in how the atoms were built. So these things were not such that one could separate them.

Heilbron:

A remark that Bohr made about his early work on surface tension was quite interesting: “Nowadays people aren’t interested in such subjects, but they should be.”

Klein:

I’ve forgotten exactly how it was, but it was made the theme, I think, for this Gold Medal. … I seem to remember jets of mercury, but at the same time I had the vague idea it was water, but probably it was liquids in general. … Do you know how he came on these surface waves? I think Rayleigh had developed a theory for surface waves, capillary waves. Bohr had studied that very carefully, so that he remembered it still a little when it came to the work on fission with Wheeler.

Rosenfeld:

Yes. And even before that there was the droplet model of the nucleus and the work with Kalckar. … I remember very well that we were all impressed and a bit ashamed that he came with this Rayleigh formula which we should have known.

Klein:

Oh, I had thought it was in the work with Wheeler first, but they had it already? To what did he apply it at that time?

Rosenfeld:

Well, to understand the general shape of the nuclear spectrum. You see, he interpreted the spectrum as essentially a vibration spectrum with various modes. Then he also applied at that time the famous formula of Hardy and (???). … And in order to get the order of magnitude of the excitation energies he applied Rayleigh’s formula.

Klein:

I see. So then the work of Lise Meitner and Frisch lay, in some way, still nearer to Bohr’s work than I remember. … Bohr once showed me the apparatus which he had used to measure the surface tension—the glass tubes and so on. I think it was in Gersonsvej in Hellerup where he had them in some cupboard. But also the mathematical work there, I think, was very impressive. I remember another application of that. Once when I came back to Copenhagen in the fall, 1921, Bohr had heard a lecture by Christiansen — the younger Christiansen — about some attempt of Debye to calculate van der Waals’ forces between molecules. That didn’t fit very well and Bohr thought perhaps if one had the ellipsoidal form that would be better. He asked me to calculate this van der Waals “b” coefficient with ellipsoids, and I tried to find some kind of solution, but I didn’t get on. Then he said, “You can take the first approximation and develop the surface then in spherical harmonics.” I don’t think I knew, at that time, what spherical harmonics were. But then, very slowly, I carried that calculation through, but in the first approximation there was nothing to see, so nothing came out of it.

Heilbron:

I wanted also to ask you about the calculation you did on the scattered X-ray intensities in the Phil. Mag. How did you happen to do that?

Klein:

There was an old friend of mine who was working in Arrhenius’ laboratory — he was about twice my age at that time — and he was a teacher in a seminary for school teachers. He was a very nice man. He made measurements on the absorption edges of X-rays, and then he wanted to know the scattering under certain conditions, and asked me about it. Then I just tried to derive the formula for it. I think later on it was discovered that there was an error of calculation in it, but I’ve forgotten how it was. It was to calculate an integral. That was rather early; I thought it rather amusing to try to calculate integrals. But that was just to help him. Then he insisted on my publishing it.

Heilbron:

Oh, I see. It was originally just an exercise on the integrals.

Klein:

Yes. There was no point in publishing it, but when he insisted on it, I wrote it up.

Heilbron:

Well, that more or less exhausts my questions about those earlier days, and depending on your plans we could continue or — break off and have tea.

Klein:

Would it not perhaps now be wise to concentrate a little bit on these things which had to do with Bohr? Then we might always in time come back to the other things, but they are not so urgent…

Heilbron:

Perhaps we can continue with your relations with Bohr after your thesis was completed? You continued to visit Copenhagen with the same regularity and followed things here?

Klein:

Yes. I was very interested to read my correspondence with Bohr that you have here. I didn’t remember that my plans about coming to Copenhagen were changed so many times by very special reasons. Then I remember that when I had made my thesis, Bohr wrote me very kindly — I haven’t had time to read it through yet, but I’ve looked at it. But I believe that in that letter he also said that he had found a fellowship for me to come back to Copenhagen in the autumn, ‘21. I did so and stayed the whole year then. In that year I got a little bit stuck in my work for a number of reasons. The first was that Bohr asked me to do this calculation about those molecules, and I couldn’t get on with them, and it didn’t interest me very much, so that made it especially slow.

Then I think I was still thinking, for a part of the year, a bit on the electrolytes. Then came the Debye-Huckel work, and I left that. That was also a very difficult mathematical problem, but then Debye had a very good idea. Kramers and I were trying, but we never got any good approximate view on this. Then I had been asked by Oseen, who was professor of theoretical physics in Uppsala, to write a review of Bohr’s theory for a newly started physics periodical in Sweden, Cosmos. That took me a very long time, and the result was that I didn’t get anywhere during that year in my own work. That was the time when the Institute was very new. Kramers was there. He was still working with Bohr, and so I had not any direct work with Bohr. Contact with Bohr was always the occasion when one got to know more closely his ideas. I followed them; I talked with several people there; Rosseland was there still. We had, of course, many talks always together, but I had the impression that I didn’t know so much of how progress went on during that year as during the earlier years and some of the later years. That was ‘21 to ‘22.

Heilbron:

You didn’t assist by any chance in the preparation of those Gottingen lectures that Bohr gave in 1922?

Klein:

Then comes the summer, and Bohr asked me to follow him to Gottingen. That was a very interesting time. I have forgotten if he had begun to prepare his big papers. You know in these years there was again a strong development of his general ideas. He and Kramers together were working out this theory of multiply periodic systems more closely than earlier. I was with him in the summer of ‘19, and then he was writing very eagerly on a paper which was the preparation for his later Berlin lecture. I have forgotten when it was meant to be published; that must be found in some letters because we had much correspondence. He had come back to Copenhagen after Kramers’ dissertation, and then I came in the early summer. Then I went to Tisvilde and stayed there during the whole summer. Bohr dictated every day; that was the first time he worked with me in this way. I think that what he began there became gradually this Berlin paper on spectral lines. I’ve forgotten if it was then or in the next summer that he first got hold of this idea which was so important about these penetrating orbits whose apparent quantum number was different from the real quantum number. I can’t remember if that was already in 1919.

Rosenfeld:

About the first publication I could not say now, but I have just seen a note which dates from December, ‘13… He pointed out that the derivation that he had in his first paper, which was of the same year, remains the same if you put n + alpha instead of n. And then he says that that might be an indication of how to derive Rydberg’s law for series spectra.

Klein:

That’s very interesting; it means that he had that in his head the whole time. But then I think Schrodinger’s paper might have been in the autumn ‘19. Schrodinger began to talk about these Tauchbahnen, and that helped Bohr in this. But I think he was on the path to it already, and that was then, of course, very important. Then gradually I think he had, in all, three versions for sodium. First he thought the quantum number would be just the same as in hydrogen, and then he thought it would be one more, and then it came out that it was two units more. So that in lithium it was one unit, and in sodium it was two units. I think that was the starting point of this development which led to the interpretation of the periodic system. But I’ve forgotten how much he had begun on that in the summer [of 1922] so that some of the things I have been talking of I might have learned first in the summer, ‘19, because then I met him practically every day.

Heilbron:

Did you take the dictation?

Klein:

Yes, yes, so that I learned much of the English language that summer. I had had some English in school, but I hadn’t practiced it. Then I came to the United States some years after, and I used such expressions as “We must look apart from,” to the amusement of the auditors.

Rosenfeld:

That was the same with me. [General laughter]

Klein:

I learned it then in ‘23 in the United States. Do you know (Walter Colby)? He’s now over 80, but he was a middle-aged man then. He was a professor of theoretical physics at Ann Arbor, and he took special care of me when I was there. He used to sit at my lectures the first year, and then he always corrected my English. But the other auditors thought that he spoiled their fun. But that summer [of 1919] I remember Bohr had rented a room in a little house which belonged to a farm a little bit away from the house in which they stayed. Did you ever see this house in Tibirke that belonged to (Borgmester Karper), the mayor of Copenhagen? It was a little light red house (???) which they rented. That was very nice. Then he had rented a room. When the cat ran around on the roof it made a noise like a thunderstorm, but otherwise it was a very good place to work. I feel that it is rather confusing because I jump from one time to another. This was about ‘19 because that was really the first time when Bohr was working with me in this way. I’m sorry that my memories of the problems he was working with are so vague. I have the idea that he was working with these spectral problems, but on the other hand, it seems that he couldn’t have done that so early. So I’m a bit confused about what he really did. There must be some papers from that time because he worked the whole summer. If I didn’t know that the lecture in Berlin was in ‘20, I would have thought that he had already given the lecture and was trying to write it up during this summer. But it might have been that he gave a lecture in Leiden in connection with Kramers’ dissertation and that he was trying to write that up.

Rosenfeld:

That may be, yes. Downstairs I found some papers about a lecture in Leiden in ‘19.

Klein:

Well, then it might be that. It would be nice to know what it was. I wonder if he could possibly have had these ideas about these penetrating orbits. When I think of them I think of his room in Hellerup and speaking of Schrodinger there, so then it might have been in the following autumn.

Heilbron:

We can try to find out about that.

Klein:

I have the general impression that he was; a little bit stuck in those problems on the constitution of the atoms at that time, but that he worked with them and tried to formulate them. So that in my memory it reminds me a little about the summer of ‘27 when be tried to write the paper about complementarity. He didn’t finish it, but he was still turning these things in his head. Then it came more definitely after that. That was ‘19. Then in ‘20 I had made a very short visit in the spring, but then I was there again in the autumn. Then I think Bohr was working very eagerly again, however he was working on these spectral problems, mainly. I remember one summer in Tisvilde when he was talking with me about this problem of the electronic groups, and he was trying at one time there to compare them with regular bodies—a little bit like Kepler. But then be abandoned that. That was out in the country; that might have been in the summer ‘21. May I think if I came there in the summer ‘21? I was with my mother in Germany, but then I think at the end of the summer I came out again. Yes; I came for a visit at Tisvilde and stayed for some days there. I think it must have been at that time when he told me about this. That was before the Pauli Principle, but he was always trying to get some shape into those electronic groups in the atom. He called them groups; I think this “shell” was Sommerfeld’s word.

Heilbron:

Do you remember any details of the regular body approach?

Klein:

At one time — it might have been then — he compared the way the electrons moved inside one another’s groups with the Franck-Hertz collision, so that the electrons would, so to speak, interchange energy with each other. So I think that was very related to what one called later the exchange interaction. In some paper I think he has mentioned that. I don’t remember.

Heilbron:

Lande had a model something like that where the electrons would interchange their velocities. They were each restricted to a part of the sphere, and their motions were synchronized so that they would collide with one another at the boundaries of their separate sections and interchange their velocities. I think Born was doing some work on cubical atoms as well. That was 1919, 1920.

Klein:

That might have played some role for Bohr; I don’t remember that. But Bohr’s idea was more quantum theoretical because he knew that the Franck-Hertz collisions were non-mechanical. So I think that there he had begun already to see quite clearly that also in the stationary states there would be a limit to the use of mechanics. For the one-electron problem it looked as if mechanics was correct for the stationary states, but that these exchanges would be outside of mechanics was quite clear. But I’m a bit confused about the time. After the summer [‘21] I came back in September to Copenhagen. That was not a very active year for me, and I did not work with Bohr because he worked then with Kramers. I think he continued [with this work on electron groups.] I remember various occasions when he came and told us of some new idea he had had, but I cannot quite time it. Once it was about helium; he came very enthusiastically one morning and talked of it in (???). Could that have been a problem of pare-helium and ortho-helium? I think before Gottingen already he had gotten the main lines — that there were two different kinds of spectra.

One had also those curious experiments with collisions in helium. … Perhaps it was Franck. But it came; this separation between two spectra was, I think, one of the things which interested him very much during that time. It must have been either a little before the Gottingen time or a little after. Then there was in those years, as I mentioned before, the formal development of this theory of multiply periodic systems, and the perturbation theory. And all that he had done already in the Copenhagen Academy papers pointed very strongly to this, that a quantum condition is not directly connected with the number of degrees of freedom but is connected with the number of independent periods in the motion. That was, of course, his main criticism of Sommerfeld, and it was a very important part of the Correspondence Principle. In these times he also came to the question of the limit of the definition of stationary states. He found that they could not be better defined than the period was defined. I think he had already studied Rayleigh’s work very closely, so that he got the idea that if you wanted to define a period then strictly you ought to have infinite time. If you have a limited time it means that the period is not quite defined; but you can then have the corresponding Fourier integral, which contains other frequencies. That, I think, one could say was very close to the indeterminacy principle for energy and time… Do you remember the paper, “Grundpostulata der Quantentheorie” which came in Zs. f. Phys.? I think it came at the same time in Cambridge. I think there he had discussed these things. But I think he mentioned the ideas earlier also. I think that paper was a little after the Gottingen lectures; it must have been written in ‘22. I think he went to England in the autumn ‘22. I remember Pauli was in Copenhagen then. Pauli was very angry because Bohr persuaded Kramers to go with him because he wanted to work with Kramers on the boat. Pauli wanted to have Kramers in Copenhagen, and he thought it was quite an impossible idea of Bohr to think of working on the boat. He said Bohr would certainly be seasick. Kramers went, and Pauli was really angry.

Heilbron:

What did Pauli have in mind to work with Kramers on?

Klein:

I don’t know what he wanted to work on with Kramers, but Pauli was at that time mainly interested in the anomalous Zeeman effect. It was from that time when he wrote that (???). Harald Bohr said to him, “Why do you look so unhappy?” And Pauli said, “How could one be anything but unhappy when one cannot understand the anomalous Zeeman effect!”

Rosenfeld:

Pauli told me also of that time that he was out walking and dejected and thinking of the anomalous Zeeman effect, and suddenly he heard a deep, earnest voice behind him say, “Think of the Lord!” [General laughter] It was one of those street-corner preachers.

Klein:

I’m sorry that these years — ‘21 to ‘23 — are a bit confused, so that I cannot quite remember which came when. I had many private things which were going on at the same time which may have contributed to this confusion. Then Bohr published a very nice paper, also in England, which I think may have been that lecture he gave at that time, where he gave a very beautiful derivation of the Rydberg-Ritz formula. In ‘22 I was in Stockholm in the autumn, and then I came to Lund in ‘23. After that I came quite often to Copenhagen, so that I heard much about the things going on and saw Bohr several times. I didn’t work directly with him during those years; but I heard, of course, very much from him of those days in Gottingen.

Heilbron:

Would you tell us about those?

Klein:

That was in Gottingen in the summer ‘22. There he gave a whole series of lectures where he summed up what he knew. Many problems came up there and many people were there. Ladenburg came there; he had at that time made his contribution to the dispersion theory where he pointed out that one could have those virtual electrons, so to speak, coming in. I think this was most important for the further work, and I think Bohr was very interested in that. Then he met Heisenberg and Pauli for the first time; they were quite young at that time. Bohr was particularly impressed by Heisenberg. I was more impressed by Pauli. Bohr saw Heisenberg when I was not present; then when we met afterwards Bohr was quite enthusiastic and said, “He understands everything.” (Heisenberg was so very like himself.) There were so many people there listening very eagerly to Bohr’s lectures. Minkowski and Hecke were young theoretical physicists, and they took notes on Bohr’s lectures. After the lectures were finished, [Bohr] went with me to a place called (???). We rented a pension, and there he tried to work out more closely the things in those notes, but he was too tired. But we went for some nice walks out there. One evening Franck, and Courant and perhaps Born came out there, and then Bohr talked the whole evening about his general ideas about quantum theory. Then we had some coffee. That was not so long after the war, when coffee had been very scarce. The next morning the Germans complained very much that they hadn’t been able to sleep on account of the coffee. I remember I had not been able to sleep on account of the ideas, and I think that must have been the reason with them also.

Heilbron:

Do you remember any of that discussion?

Klein:

I remember the general trend of his ideas at that time, but I have some difficulty in separating it. It was easier for me the first years because then I heard these things for the first time, but then afterwards there were continuous developments so that he retold things many times with always some new point to it. I think that is the main reason that it is so much easier to remember the first things than the later. I was also in these years reading with more understanding than before, and therefore I couldn’t separate so much what I read and what I heard from him. What he was speaking of there was really similar to what he wrote in the papers from those years. It was not so new to me as it was to the others because I had been much with him.

Heilbron:

Do you remember then any objections that his audience might have had?

Klein:

I think the physicists who had spent some time with these things had not so much objection any longer. Sommerfeld had even before that time met Bohr, and in the beginning I think he was very skeptical against the whole correspondence point of view. Then gradually he got interested in it, and in the later edition of his book, which was from about ‘20 or ‘21, or perhaps a little later, Sommerfeld had a chapter or a paragraph on the Correspondence Principle. Still, of course, his presentation and Bohr’s were rather different. I mean we “Copenhageners” had the feeling that Bohr understood the problems in a considerably deeper way than the others. We felt that the others had a more literal way. I remember from that year that Born and Pauli, who was his assistant, had worked out a big paper where they had used mechanical perturbation theory to any order. Bohr was very critical of that because he thought that one must treat mechanics very carefully. Pauli has written himself that at that time Bohr asked him if he could come to Copenhagen, and he said to Bohr and me: “The physics won’t be difficult; what I fear most is the language.” Pauli wrote that both Bohr and I smiled at this but that he didn’t quite know why. Then, in the autumn of ‘22, he came to Copenhagen, and he saw that the physics was not so easy as he had thought. He had written this book, you know, on relativity theory. He was very advanced in that and had also written some paper about the hydrogen ion. But he was not so deep in quantum theory at that time, and he saw that very soon after he had been with Bohr.

Heilbron:

Was Born, do you think, as a result of these lectures, put on the track that eventually became this Gottingen approach to quantum theory?

Klein:

I think Born was very open minded, and he has very much imagination himself. Especially he gets mathematical ideas, and I don’t think that his mathematical ideas at that time could have been very close to those of a couple of years later. About the time of the Kramers’ dispersion theory, however, he had some similar ideas to Kramers’. I have forgotten the relation between them. Kramers first made these calculations with the angle and action variables, and then he generalized that quantum theoretically. I think Born had a similar idea, but I’ve forgotten how it was related. But that was later than ‘22.

Heilbron:

That was in ‘24. In fact Born almost justifies his final expression by appealing to the similarity with Kramers’ dispersion formula.

Klein:

Oh yes. That must have been it. But at this time his ideas were more to try to do the mechanical treatment in a more rigid way. Bohr objected very strongly to that because there’s no use in making a more rigid mathematical theory when the basis of it is not rigid. I don’t know if Born came to agree. They had many discussions, and I think Born was very open minded.

Rosenfeld:

About l950 I was asked to provide an article on Born on the occasion of some anniversary of his. I more or less identified two schools, that of Copenhagen and that of Gottingen. I spoke of the joint work of the two. And Born wrote to me; he was generally pleased, but he wanted to stress that he had always been quite independent of Bohr.

Klein:

That means that he himself didn’t consider that these 1922 lectures were essential for him… I have no memory of how it really was, but later on, of course, he came into the main line, then, after Heisenberg’s paper. I thought of this thing which had to do with the dispersion theory but it was not so far from it… There was one question which was on your list of questions which perhaps we might talk a little about. This has to do with this general discussion, which would be too long for today, of the problem of waves versus particles. This was the Compton effect. Now, I think we in Copenhagen were really unprepared for the Compton effect because we were rather far, the whole time, from taking Einstein’s light quantum seriously. That had to do with the fact that Bohr so very strongly pointed to the necessity of maintaining the wave theory of light. Still, of course, he was quite clear—more than anyone else—that there was this unclassical feature of atomic transitions, so that radiation processes were quantized. But to think of light itself as something quantized did not lie near, I think, to us “Copenhageners”. Now and then one thought that one might apply quantum theory there to scattering problems such as those Rayleigh treated, but nothing was done along those lines.

I felt that very strongly in the winter of ‘23. I had read, or reread, a paper by Poincare, which was very nice, where he pointed to the fact that the scattering of light by electrons did not fit into quantum theory and could not explain Planck’s radiation law. I spent quite a lot of time in speculating over how one could alter this so that one did not come into conflict with the Planck law. I kept trying to find the solution and I didn’t know Compton’s work which was already published at that time. Then some months later, in the summer of ‘23, Pauli showed me a very nice paper where he had solved the whole problem and based it on Compton’s work. I may have known Compton’s work then in the meantime, but I hadn’t had any time to spend on it until the later part of the term. But that I think shows a little bit that we in Copenhagen and also Bohr himself had a little aversion for these light quanta. Now, of course, Einstein had exaggerated it in his way. … Bohr not willing to take light quanta seriously, and Einstein thinking of not taking the super-position principle for light too seriously, and Bohr thinking of not taking the energy principle too seriously — shows just how big the problem was.

Heilbron:

Do you remember if there was any suggestion that the experiments were just wrong? Duane was unable to duplicate Compton’s results and challenged them.

Klein:

I don’t remember. Now, I was absent from Copenhagen during most of this time. I was in Lund in ‘23, and I came now and then to Copenhagen, but I hadn’t heard anything of Pauli’s work until later. I think that he did it in the summer, and that it had not been published yet. I knew a little bit of Compton’s work through Siegbahn, so that I knew some of it, but I knew it only superficially at that time. I remember the name of Duane, but I don’t remember what it was about.

Rosenfeld:

Probably you remember his attempt to account for Bragg reflection of X-rays without the wave concept, just by quantized exchange of momenta.

Klein:

Oh, yes, oh yes I remember; but that was a little later, wasn’t it? ... I remember Ehrenfest told me about it. He came to Ann Arbor when I was there—that must have been in '24—in the spring sometime. Then he told me about that. That puzzled me very much because I was then thinking about electron waves and so on, and I didn’t see how it could be done. That which then became Complementarity was, of course, prepared through those difficulties, so that the only astonishing thing — but that belongs to the next chapter — for Bohr was that Einstein didn’t accept it immediately. He was very, very astonished.

Heilbron:

Well, there is one other question I think that belongs to this period, and that’s the Stern-Gerlach experiments and their interpretation. How they were regarded in Copenhagen.

Klein:

That belongs, of course, to the whole chapter of the action of magnetic fields, but then Bohr was very interested in it. I have forgotten how early that was.

Heilbron:

Well, they were in '22.

Klein:

'22. Bohr was very interested in it, but then he became still more interested in it later when he discussed complementarity because that would be a means to define stationary states. At that time I think there were problems already about the definition of the states because of a limited time. I think that he discussed such problems, but I don’t remember it clearly. Then there was the whole chapter of the anomalous Zeeman effect, which was a very troubling chapter, and to that Pauli contributed so much. Lande did, of course, very important work there.

Heilbron:

Was Bohr much interested in the anomalous Zeeman effect to begin with?

Klein:

Oh, he was very interested in this, and he tried to acquaint himself rather early with the idea that the bound electrons behave differently in the magnetic field than the others. But that was very difficult because the Larmor theorem was a rigid theorem in classical physics and one couldn’t quite see why it shouldn’t be rigid in quantum theory also. It was so very simple that it could be interpreted immediately by the Correspondence Principle. So it was very, very puzzling. Then there was this, that the atomic core should behave in a different way, and why should that be? I remember that when I was in Lund in '23, Siegbahn gave me a paper by Compton to review. Compton had some such idea that the electron was spinning, but I don’t think that Compton applied it to these questions at all. I read it and had the idea that that was a speculative paper without any interest. And I haven’t seen it since then, so I don’t know if there was anything in it.