Oral History Transcript — Dr. Oskar Klein
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Oskar Klein; February 25, 1963
ABSTRACT: This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Svante August Arrhenius, Pierre Victor Auger, Carl Benedicks, Christian (Nielsís father) Bohr, Harald Bohr, Niels Henrik David Bohr, Max Born, Louis de Broglie, Walter Colby, Arthur Compton, Charles Galton Darwin, Peter Josef William Debye, Paul Adrien Maurice Dirac, Paul Ehrenfest, Albert Einstein, Hilding Faxen, Richard Feynman, James Franck, Erik Ivar Fredholm, Walther Gerlach, Werner Heisenberg, Harald Hoffding, H. H. Hupfeld, Frederic Joliot-Curie, Ernst Pascual Jordan, Kaluza, Hendrik Anthony Kramers, Ralph de Laer Kronig, Rudolf Walther Ladenburg, Hendrik Antoon Lorentz, Mrs. Lorentz-Haas, Lise Meitner, Yoshio Nishina, L. S. Ornstein, Wolfgang Pauli, Harrison McAllister Randall, Leon Rosenfeld, Svein Rosseland, Erwin Schrodinger, Manne Siegbahn, John Clarke Slater, Arnold Sommerfeld, Otto Stern, Llewellyn Hilleth Thomas, Pierre Weiss, Eugene Paul Wigner; Kobenhavns Universitet, Stockholm Tekniske Hogskola, and University of Michigan.
Heilbron:I have again written out a few questions. We might proceed that way. I think we left off last time just when you were finishing your thesis. That was 1922. In looking through the letters I was interested to see that you were surprised that disputation had been so pleasant.
Klein:I never liked such official things, but mine was very easy. First of ail, Kramers was an old friend of mine, so we had quite a lively discussion. Professor Fredholm, the great mathematician, was very kind and nice, so there was not much opposition. Kramers told me afterwards—we were sitting together on a hill outside Stockholm where I lived with my mother—that he had found something wrong with my thesis. But he didnít mention that in the disputation. He asked me several years later, when I was in Ann Arbor, what my argument was, and that is in one of these letters. But he thought that was a very serious objection which he didnít mention.
Heilbron:Do you remember what it was? I didnít read the Kramers correspondence.
I had built my thesis on some work by, of course, Lorentz. His daughter, Mrs. de Haas, had continued this and had written a little book in which she treated not only the Brownian movements of the coordinates as Einstein has done but also that of the velocity of the momentum. My idea was not only to take the average, but to find, such a Gaussian distribution formula, and then use that for different derivations — differential equations and things like that. But in that connection I introduced an argument similar to that of Lorentz to get the average values of the squares of the components of the velocity. Then Kramers said that I had neglected the possibility that those components could again depend upon the velocity when they had different directions. Ö Then one could, with a very simple argument, show that my way was correct. If you think of a ball, with a hole through it, free to move along a horizontal thread, you could consider the thread to move sideways but still one could use the Lorentz argument. Ö I donít remember it exactly in detail now, but itís mentioned shortly in the letter. It was very curious that neither Kramers nor I — not so much I because it was published in Dutch — knew that Ornstein had published something similar. Several years after that was when Diracís theory was new — I lived at Ornsteinís house a few days when Bohr and I went together to Holland; then I went on to England.
Then Ornstein and I had very nice talks, and we came to mention these things. He gave me his paper and I sent him my paper. They were very greatly alike in that we both started from these ideas of Lorentz. I donít remember quite what he did, but I think it was very nearly the same. Yes, the doctorate was very nice. Often, at those times, one had a very official doctor dinner. I donít remember if my mother persuaded me, or if I persuaded her to have that at home. We were living a little outside of Stockholm in a villa, and that was very nice. I remember that Professor Fredholm came also; he was very kind. Afterwards he was not so very well, so that he left early. He didnít live so very far from us, so that a friend of mine and I accompanied him, and then we went back to the others who were there. A few of the older people were also there; among them was Arrhenius. He had an academy meeting afterwards, so they also left early. But then several of my younger friends and Kramers were present, and they stayed.
Heilbron:Was Fredholm interested at all in modern physics?
Klein:He had the professorship, which I had then afterwards, called, at that time, Mechanics and Mathematical Physics. He treated the physical problems electro-magnetic problems and mechanical problems — by means of the Fredholm equation and those things. He tried to follow new theoretical physics so that he gave lectures even on quantum theory, and even on relativity theory. I went to some of them in my student days, but partly they were above my head mathematically and partly I hadnít the feeling that he had a very close touch with the physics in it. But he was very deep in the mathematics. I think the manuscripts of those lectures exist.
Heilbron:Were the other Swedish professors much interested in the quantum theory at that time, like Oseen, say?
Klein:Yes, the professor of physics from whom I took my examination was Benedicks. His main line was metallic conductivity, where he did important work. But he had some curious ideas against quantum theory and against relativity theory. We had a peculiar discussion about that which started in my student days and went on almost until his death not very many years ago. He thought first, of course, that it went against the ordinary ideas of physics. But then he had some curious ideas of how to remedy that and how to derive Planckís formula from some more classical concepts. That was impossible. I remember one discussion we had in the Natural Science Studentís Association where he gave a lecture called ďThe Physicistís View of Space and Time.Ē He tried to define simultaneously by a very (big ________) — going out in the universe and then turning around. We had a discussion and I objected that the notion would not (give) the velocity of light but of the elastic waves. I think he was a little bit convinced every time, but he always came back to it. Then many years after — after the last war — the philosophers who used to object to these things asked me to give a lecture on such things. Then there was no opposition from the philosophers any more, but Professor Benedicks was still there and objected, He was a very nice man otherwise, so that we had very nice personal relations. When I got the fellowship for Copenhagen then he was the inspector of it. And he treated that very nicely, but he didnít like very much that I —. He liked Bohrís philosophy better than Einsteinís. He didnít like Einsteinís because it was also so mathematical, and he didnít like the more mathematical papers on quantization. He liked Bohrís ideas better with the models with the electron orbits and so on, but he didnít like the whole quantum philosophy.
Heilbron:What was Bohrís reputation in general at that time, 1921 or Ď22, in Scandinavia?
In Sweden we had rather few physicists. We had, of course, Siegbahn whom I hardly knew during these years. But he very soon got some good connection with Bohr, so that he quite believed it you know. He began rather early with his X-ray work which then contributed very much to the knowledge of the inner groups of atoms. He was in Lund; he was usually a little far away from me, but I met him during my Copenhagen years. There was some intercourse between Lund and Copenhagen. I think I told you last time that there was a very nice meeting in Lund—it must have been in the autumn, 1919. Sommerfeld was invited to Lund. Siegbahn had studied some with Sommerfeld and had a good connection with him. Then Bohr was invited, and then we who were with Bohr were also welcome so that we went there. There both Sommerfeld and Bohr gave very interesting lectures. Ö Sommerfeld gave a lecture where he had begun with the anomalous Zeeman effect. Ö Bohr, even in these later years, still had difficulties with Sommerfeld, but he impressed Sommerfeld more and more, and he had very friendly relations with him. Bohr gave a very lucid lecture.
I remember that I was full of admiration for the way he presented it. Sommerfeld was talking about the anomalous Zeeman effect which was a rather difficult and acute problem at that time. Of course, Sommerfeld had contributed very much to the hydrogen fine structure and also the fine structure in the X-rays at that time. Then he continued the study of spectra and made, of course, very important contributions. But all this Bohr would say (???). During Sommerfeldís lecture, I was sitting at the side of Bohr. Sommerfeld had a few numbers for these anomalous levels. The first was so and the second was so — they were something like 1, 3, and so. And then Sommerfeld said the next must be 5, or something like that. Then Bohr smiled and said to me, ďI donít believe that.Ē And Bohr was right. Then afterwards Lande got the correct basis, and, of course, there the good work of Heisenberg and Pauli — especially Pauli — began. But that was a very interesting meeting. I remember a Norwegian physicist, Vegard, was there. He made something with X-rays. I have forgotten just what he did but only remember the comical aspect. All were speaking German for Sommerfeldís sake. Vegard read first a paper which was written in German. When that was finished he had a further manuscript but it took a little time before he could find it. After a while he found it, and then he said in Norwegian, ďJavel!Ē Then he translated it immediately into German, ďJa wohl,Ē and went on. But we had some nice days in Lund. (Then Sommerfeld also) came to Copenhagen. I have forgotten if that was a little before or a little after. I was talking with Jacobsen about that; he remembers very well both these things. I must have known at that time that Bohr knew Sommerfeld already, but I had quite forgotten that they had already met in Munich in 1914.
Heilbron:Did you go on to Berlin to study after your disputation? I noticed there was a letter shortly after your disputation that was dated from Berlin.
Klein:Oh, no. I went there with my mother in the summer to visit sortie relatives. That was Ď21. I was there both in Ď21 and Ď22. In Ď22 it was after I had been with Bohr in Gottingen. But at both times I visited Riesenfeld; you remember him from my first paper. He was then with Nernst in Berlin, and he took me to a colloquium. I think, it must have been in Ď21. There I saw Einstein for the first time, and that was even the first and [last] time before I saw him in Ď49. Planck gave the lecture, I think. At least it was something about a statistical thermodynamic question. But I have forgotten who started that lecture; I have forgotten whether it was Planck, or if Planck only took part in the discussion. Einstein said something, and I tried to say something about it, but (I have forgotten how it was.) (I tried to see him afterwards, but then he vanished so fast that I couldnít). I think that was in Ď21. In Ď22, I remember I went also to a colloquium. Then there was a lady, [Hertha Sponer], who gave a review of Rosselandís paper; it happened to be just at that time when I came there.
Heilbron:Then when you went to teach in Stockholm, there are a number of letters you exchange with Bohr over something you call ďyour little workĒ together. What was that about?
That was a sad story. I came to Copenhagen in, I think, September, 1921 to stay there for the whole year. Just before I came there had been a lecture by, I think, the physical-chemist Christiansen on some attempt of Debye to explain van der Waals forces. There were some difficulties in it which I donít remember. That led Bohr to the idea that one should perhaps get something better if instead of spherical molecules one took ellipsoidal molecules. Then he asked me to calculate the van der Waals ďbĒ correction in that way; I think I mentioned something of this before. That was a very difficult mathematical problem. I tried to find something like a more rigorous solution, but I didnít get on at all. Bohr was rather eager, and then finally he showed me that I could take this ellipsoidal surface as a perturbation using spherical harmonics — just as he had done in the surface tension problems.
That made it better to calculate, but still the calculations were very long. I had many other interests there, so that went on very, very slowly. Then Bohr was eager that we should do something. There was a physical meeting that summer after Gottingen; Gottingen was in June, and this was in August in Uppsala. He wanted that we Copenhageners should have something to present. Bohr asked me to think a little bit about this again; I had made some calculations, and I thought I got a positive result. Later on I found that that was wrong; the result was zero in the first approximation. Then I gave a very short talk on that, and Bohr, I think, gave a lecture on (collisions) in a more general way. I think the idea was that he wanted us to write a little paper together on collisions, but my contribution, I think, would only be this thing. Then he was eager to (have) that. In this term — autumn Ď22 — I was extremely busy; I gave two lecture series on difficult questions, so I didnít get on until rather late. He was rather impatient, and through Kramers I was reminded of it; I had a rather bad conscience. Then finally toward the end of that term I sat down and made those rather long calculations. Then I got definitely the result 0 in that approximation; there must have been some contribution in the higher approximation. But I think then we all lost interest.
Heilbron:What did you teach at Stockholm?
Klein:I gave one series of two lectures a week on atomic theory where I tried to give a review of Bohrís theory, and one series on statistical thermodynamics. So it was rather hard work; I had to do, practically, the reading and the writing at the same time. I hoped that I should get a position as lecturer, dozent, in Stockholm, but they had no money. Then I got this in Lund; I think then I gave a similar series on atomic theory in Lund in the spring term.
Heilbron:I think in one of the letters you mention that you had been made dozent, or you had the duties, but no one was paying you. That was in Stockholm?
Klein:Yes. I did that because I thought it might be a good thing to do and that perhaps they would find something for me. And, of course, I was rather interested in those subjects.
Heilbron:Oh yes. There was a very interesting thing in one of the letters that you wrote from Lund. You suggest a ďghostĒ mechanical model, you say, for the stationary states. What did Bohr think of that?
Klein:It wasnít so very serious; it was a curiosity. I didnít take it seriously at that time. I suppose I came to think of an electron moving in a viscous liquid because I was probably lecturing a bit on Brownian movement also there. Another thing which I did that term was to write a paper which I have never published on a continuation of my doctorís thesis where I gave a rather general treatment of that kind of thing. That paper I still have; I might show it sometime. You could read these letters in Danish? Iíve noticed that my Danish got better after I had been married.
Heilbron:But in 1920 youíre writing to Kramers in Swedish.
Klein:To Kramers I wrote in Swedish because, you know, he learned languages immediately. So when he came to Sweden the second time he spoke Swedish already. Our last visit by Kramers was the first Christmas after the war. He came up to Stockholm and then he spent Christmas with us, and he hadnít been in Sweden for a long time. At Christmas we always make rhymes for the children, and he made long rhymes in Swedish. [Reads from the letter in question] ďA little magnetic pole is moving,Ē I had forgotten that I made it magnetic, ďin a plane around an electric current which is perpendicular to the plane and is acted on by a central force which is directed against the point where the current cuts the plane and by a frictional force proportional to the velocity of the particle. Such an orbit, where the angular momentum has a given value, is stationary, since the pole, on account of the current, gains a constant amount of energy in every revolution, and the loss of energy thru friction during a revolution is proportional to the quantity ĎIí which is again proportional to the angular momentum.Ē ďAnd one can also change this stationary state adiabatically and see how the new state has adapted itself after a non-adiabatical change of the field.Ē But I meant it only as a curious illustration of the case, not seriously. (I donít think Bohr mentioned it).
Heilbron:There was one thing though that I donít quite understand about the proposed joint paper with Bohr. That is that in one of the letters you say that you got a negative result, and you recommend that you just drop that portion of the paper. Ö There must have been more to it since the second part of it was to be dropped.
Klein:The paper was about the van der Waals correction, and there was no correction in the, first approximation.
Heilbron:So one should discontinue that? Then you must have been involved in making arrangements to go to Michigan shortly thereafter.
Yes. You see, in Lund I had no real position; I was promised five thousand kroner a year, but also for a rather uncertain period. Then at that time one had something which was called dozent fellowships, but there were none free. They were a little bigger, but not much, I think they were 6,000 a year, and that was not easy for a married man to live on. At that time my wife and I were engaged to be married; we wanted to marry as soon as we could. I knew that Bohr himself went to England in his early years, and I asked him if he thought there might be a possibility for some position at an English university. He said that he didnít believe that there would be because now they had many people in England. But he said that he had just been asked by an American theoretical physicist if he could think of someone willing to have a position in Ann Arbor. He hadnít thought of me because he thought that I had my things arranged and wanted to stay in Sweden. He didnít know that conditions were very uncertain. Then he said that he would propose me. That American physicist was Professor Walter Colby. You know he had a very high position in the Washington Academy in later years; he is now over eighty, but he has been very active until recently. We always get letters from him at New Year. Then he was in Copenhagen, so I came over from Lund to talk with him, and he engaged me. At that time Professor H. N. Randall was head of the department; heís still living also, and is active. I think heís 91 now.
We heard from him when he was 90. His daughter and son-in-law are old friends of my wife and me, and so we learned that he would be 90. We wrote a little letter to him, and he answered personally. He has done much work on the application of the infra-red spectroscopy to biological problems after he was eighty. Heís still rather active. Then after our wedding, we went to Michigan in early September. Colby was nice to meet us in New York even, and took care of me very nicely in Ann Arbor. I think I told you that he sat at the lectures also and corrected my English. At first I made my private errors, but also I used such expressions of Bohr as ďto look apart fromĒ. That means ďto neglectĒ in the mathematical sense. Bohr has that in his papers you know.
Klein:But I was very much teased about these things. They arranged it very nicely for me, so that the first two terms I had no elementary teaching but only lectures on such subjects as atomic theory.
Heilbron:Did you find the students reasonably prepared?
Klein:There were very few theoretical students, but the experimental physicists went to those lectures as they had done in Lund also, the term before. That year there was one advanced student, and that was David Dennison who is now head of the department in Ann Arbor. He made his doctorís work at that time. Colby was the main theoretical professor, and he had given already much time to Dennison. He went on that year, and he had his doctorís degree in May, l924 — the first spring I was there. Randall was also very, very kind, so it was really very agreeable. I had already in Lund tried to learn a little bit about molecular spectra because Hulthen was there during the term in Lund, and he was very interested in that. Then I went on with that also, and that was the way I came to this work on the crossed fields, because I wanted to think of a very simple analogy to a rotating molecule. I thought that if you take the hydrogen atom, then if you have an electric field, that would be a little like the action of the other [atom] on the electron in the first [atom], and the magnetic field would be a little like the rotation. So, therefore, I got interested in seeing that problem more closely. Then it came after that that it could be solved by the same perturbation method which Bohr had used for Stark effect. But Bohr thought at that time that it couldnít, so I was rather astonished that it could.
Heilbron:But Epstein had already shown at least that the problem was a periodic one.
Klein:It would be nice for me to know when Epsteinís papers came, because I think one had no real solution. There was Halpern who had done something, but I have the impression that Halpernís paper was also rather far from the solution of the problem. I havenít checked that since those years; I may be quite wrong. I donít think Epstein had the solution. Later Lenz got the solution about the same time as I, so we published it about simultaneously, but I donít think I knew anything on that before it came out.
Heilbron:Well, there is a footnote in your paper about Epstein, but—.
Klein:Yes; I remember that Bohr also wrote in one of those letters that he had made some change as to the quotation there, so there must have been some recent work. But there might have been some criticism of it. I havenít seen my paper for so long, so I have forgotten what it was. You donít remember what was in that?
Heilbron:I have it. [Goes to find the paper.]
Klein:Bohr used to put criticisms in footnotes.
Rosenfeld:Yes, yes, yes.
Klein:The final shape of the paper and such things was determined by Bohr and Kramers. [Now has the paper before him.] Let me see what is said in the text. Ö [Epsteinís] work was published in the Physical Review of 1923. Ö But does that agree with my results? I canít see it so fast because I havenít read it sufficiently. I have a vague memory that that was not the right result, but it might be good to check that.
Heilbron:But you donít point out that you get different results.
No, but I wonder how much I knew because there is one letter in which Bohr says that he and Kramers have made some changes in my quotations. What that meant I donít know. I may possibly find an early manuscript of my paper when I look through my papers. I know in comparatively late years I have had the manuscript of the second paper which was never published because I sent that in when I applied for my professorship. Probably I should have some manuscripts somewhere of the paper. I have very little memory of this, but the vague memory I have is that neither Halpern nor Epstein had any more definite contributions to the problem. One may look up Pauliís Handbuch article and see what he says because he quotes these things rather at length. He became impatient that my second part never came so that he finally found it himself and published it in the Hundbuch. The second part was very much delayed, as you may have found in those letters. The main reason was that is also described in the letters that I had the result that one could, by an adiabatic transformation, go from a good state to another, which one thought one must exclude, where the electron goes through the nucleus. I had difficulty in believing that.
That was then one of the examples of the failing of the mechanical description. I was very eager to know if there really was no error in these things. Then, also, I had many other things to do and was rather distracted by many things. According to one of those letters, I must have had the result already in December, Ď23. (By the time I had made a treatment such that) I believed in the results, I think it was about Easter Ď25. So that was a very long time; of course, I left it alone for a long time, but then I took it up again. I was rather definite at that time, but I had strong doubts that there could be something wrong because the whole was a perturbation calculation a secular perturbation. One might think that it was wrong but I think that was not justified. It was really correct. Then Pauli had already written that, I think, when I came back, or at least when I saw him. I remember we had a talk on it in June, 1926 when I was on the way to Leiden. When I made my paper in a rather definite form in Ď25, Lenz had also given the quantization, but that was not correct; I found that and Pauli had also found it. But I had also found where the error was. Then Pauli and I discussed whether there was any reason to publish it. (I thought that now that Pauli has published the correct result thereís no need for me to do it.) (But it was a very hard job admitting somebody —.)
Heilbron:What did Bohr think about the result?
Klein:He was very interested. When he came, I hadnít that result ready; he came, I think, in early December of Ď23 to Ann Arbor. Then I had the first part, so I told him about it, and he got very interested. He was eager to see the papers, so I sent the first part as soon as I could. Then I wrote about the second part, but I never sent it. I think I must have shown it to him in the summer Ď25. I have forgotten if I did that because we had so many things to talk about then, but I remember I mentioned it to him.
Heilbron:Was it an important problem before you got involved in it the cross-field problem? Since there is this spate of literature about 1922 and Ď23 I was wondering whether it was an important problem.
Klein:ÖAs I mentioned, my interest in it first was to have a little better understanding of the molecules and to have some simple basic model which one could treat rigorously. Then, of course, when I saw that it could be treated that way, I got rather interested also in the problem itself because I knew that Bohr believed that it couldnít be. I donít remember that I knew this work of Epstein at that time.
Heilbron:But even after Bohr had reached this conclusion that it was not a soluble problem, that the results were aperiodic, it was not a great problem to—.
Klein:No. It was a part of his general idea that the stationary states could not be better defined than the periods. Therefore, he thought that since the periods are not defined, then the states will not be defined either. So that was the way it came in. Then he got interested in it in another way, as one example of the failing mechanics. But then there were many other things at the same time there, and we were very near to the period when Heisenbergís work appeared. Still, one was not so certain which I think is shown by my hesitation to deliver the result.
Heilbron:Did Bohr lecture when he came to Ann Arbor?
Klein:Yes. I heard him both in Ann Arbor and Chicago; I went to the Physical meeting in Chicago also. He had spent quite some time in Amherst College and the American theoretical physicist, (Hoyt), was there. He was then a young man; he was in Copenhagen for a year I think and then he was going with Bohr and acting as his assistant. At that time I think it was the theory of series spectra and the Periodic System which was his main subject. That paper with Kramers and Slater was later after he had come home to Copenhagen.
Heilbron:You say, in your letters, that you found that paper very interesting. What about the others there? Colby, for instance?
Klein:Well, I think they were all interested in it, and I think I was the first to read it, and then I told about it. And I was even invited to Schenectady by Langmuir to lecture about it; that was then in the autumn Ď24.
Heilbron:What was Langmuirís opinion?
Klein:Oh, he was interested in it. You know Langmuir was interested in all sorts of things. I think we had a general belief in it, partly because it impressed, and partly because of Bohrís authority. But Pauli objected to it, and constantly too. I must say that afterwards I regarded this as one of Pauliís very great points that he saw so clearly that one could not give up the energy principle. Now, Bohr saw it rather soon himself, so that when I came to him in the summer Ď25, then he had already given that up. He had written a paper, which I remember very vaguely, about the passage of alpha particles through atoms. I remember it very vaguely, and I have looked at it later without, I think, finding any clear connection with this theory. But in my memory there was some connection, in that just thinking about the energy exchange from the alpha particle to the atom had contributed to his giving up this statistical way of looking at the energy principle. He mentioned to me that he had given that up before the experiments of Geiger and Bothe.
Heilbron:Do you remember in detail what Pauli had said about the theory?
I donít think I saw Pauli until quite long after, but then he repeated it. I think originally I knew of it from Bohr, probably, because after my Ann Arbor years, I didnít see Pauli until the spring, Ď26. Then, of course, the Bothe-Geiger and everything were out, so then no one doubted it any longer. Ö I think Pauli had a general feeling that that could not go. There is one letter — perhaps you saw it in the Kramers correspondence — where Kramers had written something to me about it which I couldnít quite understand and where I made some comments and questions, but I donít remember that discussion. I have the feeling Kramers had tried to see what the temperature equilibrium between radiation matter would be on that theory. There I wrote to him: [Reads from letter of 24 August, 1924] ďWhat you wrote about the fluctuations of the energy in your letter interested me also much, but I donít think I quite understand you.
I understand that the average of (Delta E/t) cannot be equal to zero although possibly very, very small. But it seems not to be this quantity which is of interest but rather quantities like the time derivative of the average of E and the time derivative of the average square of E.Ē That must be something about the way an equilibrium is established, I suppose. Then I said that, ďI suppose these quantities must be zero in any statistical equilibrium and you wouldnít deny the possibility of a statistical equilibrium between radiation and matter. But I understand that it is thinkable that the energy principle is not even valid on the average in systems which are not in temperature equilibrium. It may be also that the statistical equilibrium in a given ensemble of systems is not determined by the temperature only, but also by a number of other parameters, so that what we call temperature equilibrium is no real equilibrium. But then I admit that this may be stupid talk, and I would be glad if you would let me have a clear understanding of your view of it.Ē I donít remember this discussion at all, but maybe I can find that letter by Kramers.
Rosenfeld:I think that would be very valuable because that is just a point which is now completely forgotten of course, and therefore it is so difficult to figure out what the feeling must have been at that time.
Klein:Of course, the whole paradox about (this quantum ???) was so very strong, Bohr, of course, was completely right, when he pointed out the necessity of the wave properties, that you could not do without superposition. But the way to reconcile that with the quantum seemed so impossible. Also when you read that paper by Bohr, Kramers and Slater — I read that recently then you see that there also one thinks of two views. One according to which the energy is concentrated, namely, Einsteinís view; and the other in which the waves are, so to say, virtual, and only determined in statistical processes. Then, many years after, when Bohr came to complementarity, I remember there came a paper by Slater, which I think he sent to Bohr, where Slater had come to the same view. Ö It must have been in Ď27Ö It was about the time when Bohrís work on complementarity was rather new. It might be nice to see at what time this paper of Slater was. I think itís a very lucid paper and a very short paper where he had, for himself, worked out the general relations between quanta and waves. It was very similar to the Como paper. Of course, I think that those who were responsible for this paper were all a bit depressed by it; I think Bohr least of all because he was always prepared that one may (learn something) and perhaps do something better afterwards. But I remember that Kramers was rather depressed, although Kramers at that time had made a very important contribution to this dispersion theory. I saw him then when I came back in the summer Ď25, and he was rather depressed. Then he had also given it up. I donít remember if the Bothe-Geiger had come already, but I believe that had. Ö Could it have been known in July, Ď25, in Copenhagen? It may have been. I remember that Bohr told me that he had already changed his view before he knew it, but it could very well have been at that time because I saw Bohr in July, and then he may have known itÖ
Heilbron:So in spite of this great contribution Kramers had just made, he was quite depressed over this paper.
Klein:Yes. You can see from my letter that we, regarded this idea of statistical energy conservation, for a time, as a progress comparable to that made by the Correspondence Principle. Ö There is one letter where I mention that to Bohr.
Heilbron:I thought that you had written this in connection with Kramersí paper on dispersion.
Klein:No. I think that may have come a little bit in the background. He published it shortly after, and I donít think at that time that I knew the way he had calculated it. I think I only knew the results. [Locates the letter of 6 May, l924 and reads] ďIím very eager to know the new work about the radiation which Kramers mentioned in his letter and which seems to contain a similar progress as did the Correspondence Principle in its time.Ē Ö Then I also got very enthusiastic about it; but Pauli didnít. And it was the same, you know, many years later when Bohr talked about the failure of energy conservation in beta decay. At that time Pauli was again very definite in his opposition. But also at that time I rather believed Bohr. I donít know what your view was, [Rosenfeld]. Were you in Copenhagen in 1930 when he wrote a letter to Nature about it?
Rosenfeld:Oh, I had no strong views about that. Ö Sometime later there was a scare when a young American published actually wrong experiments which seemed to be contrary to—.
Klein:Shankland! We didnít believe it.
Rosenfeld:Then nobody believed it; it was found out very soon. Still I always remember there was here in Carlsberg a reception, and there were many people. Amaldi and (Rasetti) were there I know; I remember the conversation. Amaldi asked Bohr what his views were now with regard to this energy conservation. Then Bohr explained the situation, and he ended: ďSo we have come to the conclusion that there is no reason to abandon energy conservation — at the moment.Ē
Klein:That was a very early thing with Bohr. I mentioned in one of our earlier talks that Bohr mentioned this possibility very early.
Heilbron:That was already with Einsteinís work on the transition probabilities.
Klein:Yes. I remember it first, I think, in connection with what he mentioned in the summer Ď18; I think he mentioned it then already.
Heilbron:He hadnít entertained those views before Einsteinís paper?
Klein:Einsteinís papers they had appeared already in Ď16 and Ď17. We knew them already then. But I think Einsteinís papers had to do with it because the whole statistical nature of the radiation processes, which was in principle known, of course, in the earlier papers, was so directly formulated. Then there was a time when Ehrenfest, I think, came to Copenhagen, and he had been talking much with Einstein, and then they used the word ďGespensterfeldĒ; that was before this Bohr-Kramers-Slater paper. That had a little bit to do with his work, but I think the main thing in that work of his was virtual oscillators.
Heilbron:In what connection did the ďGespensterfeldĒ come in? Was that also with radiation?
Klein:I think that was an attempt again to make the electromagnetic theory sufficiently mysterious to reconcile it with the quanta. Ö Einstein wrote in those years I have forgotten where that one should look for deviations from the superposition principle in optics.
Heilbron:Were Kramersí notes in Nature about the dispersion theory well received at Michigan?
Klein:I think so. I think so very soon. Then he wrote a more extensive paper on it not so long after. Then — as we mentioned last time — Born also wrote something in that connection. Then Kramers came to discuss the thing with Heisenberg, so that they came to write a joint paper on it. That was, of course, very strongly suggested by Kramersí earlier work. But there were new applications which could then explain the Raman effect.
Heilbron:What did people at Michigan find immediately so attractive about it? I can see what a ďCopenhagenerĒ would find it it, but what did the people there find so —?
Klein:I donít think I ever knew the real dispersion theory — I mean the way Kramers calculated it — until I came back to Copenhagen. I donít think the calculations were published. So I donít think that I could have known more than that it was probably a correct and interesting result; but we hadnít much discussion about that. There was more discussion on the principle ďIs energy conserved,Ē or ďIs the whole statistical,Ē and so. My personal interest in dispersion came later and was really due to a remark Heisenberg made when I had given the wave equation with time dependence. You know Schrodingerís first paper was only a static equation; he had no time dependence; he had the energy in it. Then I wrote my paper just after that had appeared, and I had the time dependence. It was also relativistic, but the time dependence was more important. When Heisenberg saw that, he said, ďThen you ought to be able to calculate the dispersion in analogy to the radiation from one stationary state to another.Ē And he said that this had been the trouble also for matrix mechanics — his theory up to that time. That was rather interesting. I mentioned that in a footnote, and then I took it up later on. It was published then rather much later in my paper on the correspondence way to calculate radiation processes. But it came from this hint from Heisenberg because I hadnít thought of the problem before. Then I came to think of the Compton effect in this same line. Ö We saw a paper by Dirac which was very hard to understand.
Rosenfeld:Yes, but itís a very important paper. He shows that the time can be treated as the other variables and quantized in the same way. But he gets difficulties because then he has four components, and he doesnít quite succeed in understanding how they can be compatible. Now, we could very easily, because it is what we call auxiliary conditions; but that, of course, was not known then. But nevertheless, he managed to circumvent this difficulty and to get the Compton effect.
Klein:I never understood how he did it, but Iíve always admired the fact that he did it because he got the right result. Then it was very easy to see that one should —. That hadnít occurred to me earlier, but it occurred to me then immediately, and they were discussing it very much. I made some provisional calculations in Leiden at that time and discussed it with Ehrenfest. I never finished those calculations. Then Gordon got to the same thing, and he carried them through and got the result. He got, on the whole, a very nice statement. That is the origin, you know, of what was called by Dirac the Gordon-Klein or Klein-Gordon equation. Before Gordonís paper had appeared I had given a lecture in Copenhagen where I had given the expressions for current density and density on the relativistic equation. I donít remember whether it was quite at that time that I mentioned the possibility of calculating the Compton effect. At least I mentioned it to Bohr — that was also in Ď27. Dirac heard about this and he objected somewhat against this already at that time. Then he worked out his theory with the spin. He didnít know what to call this old relativistic equation, so he called it the Klein-Gordon equation. This was not so unjust. I remember that Schrodinger made a point of it that he had found that equation earlier. I had it before he began the thing at all, but I hadnít published it. Iíve never checked it, but I believe that even my first publication of the equation was earlier than Schrodingerís, but Iíve never taken the trouble to look it up. It might be nice to see how that was. You know, I published the relativistic form of the scattering equation in this paper on quantum theory and five dimensional relativity. At that time Schrodingerís work had certainly not appeared, but it may be that it appeared earlier than mine; I donít know. But Schrodinger made a point of it. I never mixed in that; I called it the scalar equation.
Heilbron:You were telling me before Professor Rosenfeld came some interesting things about the de Brogue thesis that you had not seen when you were at Michigan and only found out about when you returned to Copenhagen.
Klein:At first it didnít, interest me very much because I believed that my view at that time was better. So I didnít look much at it. Bohr showed it to me, but I didnít look at it much then but continued with this five dimension view. It was only after Schrodingerís work — I think it was about the time when Bohr started complementarity — that Bohr and then I also began to look at it more closely and found that it was a very nice way to treat the things. Oh, I think I must have known it a little earlier because I remember I had some little correspondence with de Brogue. I also made a thing for which I (have repented every minute of my life — rather earlier than before.) I had so very many things in these days that I began to lose patience a little because I got so very much behind in publishing things which I had. When I published my paper on five dimension theory I had found a result there about the way to treat gauge invariance in five dimensional theory. Then Kramers pointed out that that was analogous to something which he had done in a very early paper with statical gravitational fields, where then the time played the role of the fifth dimension in my paper. It was rather analogous, but Kramers had given me that paper at a time when I hardly knew anything of general relativity so this I hadnít got into my mind at all. So I found this when I was working out the five dimension theory. Then I think Kramers mentioned it to Bohr, and Bohr pointed it out to me, so then I quoted Kramers. But de Broglie got the idea that I had quoted Kramers for the whole thing, and he quoted it that way. I corrected that in a paper, which I thought was to make fuss about a small thing, but after those many things (which I had thought were a little unfair —.)
Heilbron:Yes, I understand that. You had said that before you read the thesis, you had seen a couple of his earlier articles.
Klein:Yes, I remember, I had seen such small papers, but they didnít impress me much. There was something, I think, about an electron in a coulomb field, and I think I noticed that he had a similar idea to mine about the [origin] of the quantum rules. So I think that was really his origin also. I donít think he knew — which I knew at that time — that this corresponded to eigen vibrations. I remember I knew that in the summer of Ď23. I never published it, and therefore I couldnít claim it. I donít think he had that. I think he had the formal relation that one could look at this as an interference with itself, and that was the way I started the things also. He used the fact that the waves have different velocities of propagation, and I thought that that was very (ugly). It didnít occur to me that one could have that by a wave equation which contained a constant — just a mass. De Broglie found that, but I donít think that was in, the earlier papers; I think that was only in the thesis. Before that time I had only the impression that de Broglie had some ideas which were similar to mine, but I knew that mine were not finished, and I thought his were (still less finished.)
Heilbron:When you first got the idea of this way of generating whole numbers for the quantum theory, what did Bohr and Kramers think of that?
(I mentioned very little about it.) You see I had that in the back of my head when I was doing much earlier work, but I feared that it was too fantastic to be anything, so I mentioned very little about it. You know, Bohr was also very busy, so I was always afraid of disturbing him. I was thinking very much about it in 1922 in Gottingen, and when I came back from Gottingen, I came out to Tibirke to him. I remember that we were on bicycle together — I think he met me at the station. Then I mentioned this to him, but I saw from his reply that he didnít get what I meant. Then I thought I had better not disturb him any further. I remember I mentioned it then the next summer to Rosseland. I asked him about it afterwards, but he had forgotten what I had said. I never mentioned it explicitly to Kramers, but I mentioned a little bit what I was thinking of these Hamilton-Jacobi equations. I think I made some very vague mention of it. I repented later that I hadnít really mentioned it because then I would have gotten help to carry it out, because Kramers was so good on the mathematical side. But we didnít meet so very much during that time.
You see, before Ď22 my ideas were completely vague. I have forgotten when I got them in a little more shape; I should believe that it would have been when I was home in the autumn Ď22. I began to get them in this connection with the Hamilton-Jacobi equation when I bought a then rather new edition of Whittakerís Mechanics. There Whittaker treated very nicely the canonical transformations in the way Hamilton had first found them in optics. That helped me to get on with it. But I remember I was thinking of the fifth dimension already in the summer in Gottingen. Ö I think I wrote my name and probably the year in my copy of Whittaker, but it must have been around these years. From Ď22 I saw very little of Kramers, because I was then first in Stockholm and then in Lund. Occasionally I saw him, of course, but he was also busy, and I had been working on other things so that I never came to mention it in any better way. I must say that I never thought that it was any other personís fault than my own that I didnít get these things in shape and publish them. I wouldnít have mentioned them at all, but since I started to tell how de Broglie mentioned them I thought I would continue as I remember them. I mean, sometimes people claim things which they have done and not published, but I think one shouldnít do that.
Heilbron:It is of great interest to know, not only that you were thinking along these lines, but how others might have responded when—.
Klein:Yes, but unfortunately I talked very little about it, and it began to take a little more definite shape when I was in Ann Arbor. There I had very little occasion to talk also, because I met very few theoretical physicists.
Heilbron:Can you tell us how you got the idea of going to five dimensions?
Oh, yes. I think the main thing was that I wanted to have waves with a definite velocity. Then it occurred to me that if you have a particle moving in 3 dimensional space with constant velocity, the projection of that particle on a plane will have different velocities, although the velocity of propagation is given. So that was the first. I got further in the late autumn Ď24. Then, as far as I remember, I gave a lecture course then on electro-magnetic theory, and also on the motion of particles in electric fields. Then I saw that one could write — I suppose that was known, but I donít think I knew it — the Hamilton-Jacobi equation also for the relativistic motion of an electron in an electro-magnetic field in quite a nice way. You had a quadratic form first, and, then you had a linear form with the vector potentials in the momenta, or the momenta would be then the derivatives of the Hamilton-Jacobi function with respect to the xís. I knew a little of general relativity theory, although not very much. Then I saw that if you wrote the corresponding equation for the motion of a particle according to general relativity, then you would have a square form: ds/dxi times ds/dxk and multiplied by this gik. Then it occurred to me that these electro-magnetic terms could be written in the same way if you assumed that you had a momentum component in the fifth dimension which was constant. That would appear as constant and then you would have the potentials which would then correspond to the gio. Then it was clear that the momentum in that direction would be simply connected with the charge of the particles. I knew, of course, that there had been much discussion about the relation between gravitation and electro-magnetism. Although I had followed it very vaguely, I knew a little about Weylís work.
So, having seen this, I thought it would be a very nice thing to see if you could not write Maxwellís equation and the gravitation equations together just as the fields appeared here. I tried to see how that would work if you showed that the deviations from the ordinary Lorentz metric are small, just in the first approximation there. I saw that that came out very nicely. Then when I came home in the summer, I worked very hard with the generalization, and I succeeded in making the general proof through very heavy calculations. Later I got a simple proof, but then I calculated. I really got better acquainted with the relativity theory in that way because I calculated all these metric quantities, λik, and so on. I knew already then — I found that in the spring — that you could make a transformation which kept the gik independent of xį , and that would correspond to the gauge transformation. That was something which was similar to Kramersí static gravitational field. Then I found that they were rigorously valid, and of course that made me believe very strongly that I was on the right path because it was not so (ordinary for one to find rigorous results here.) So that rather deviated me from the wave mechanics, and I spent so very much time on that. I had, at that time, the main ideas of wave mechanics. I had written a little bit on the connection between the Hamilton-Jacobi function and the quantization already in Ann Arbor. It was only a sketch on a few sheets of paper, but I couldnít find that later on when I wanted to find it. It may have been left in Ann Arbor; I never came back there. That meant also then that I spent the summer with these things, and I mentioned both things to Bohr in Tibirke, so he knew about it. (I wrote it also in that paper from that time.) Then in the autumn I got first the flu, and then I got the jaundice which was rather lengthy, so that I spent a long time in the hospital. Then I didnít come back to Copenhagen before the beginning of March. But before that I had started to rewrite the five dimension paper. So that I had written an earlier copy of the five dimension part, and that I took with me to Copenhagen. When Pauli came later, I showed that to him. Then, after Schrodingerís paper came, I wrote that paper about the quantum theory and five dimensional relativity theory. Then I tried to get on as I could.
Heilbron:This will be very difficult, but I wonder if you could tell us the way you regarded this five-dimensional wave.
Klein:Iíll try to. Of course, it is very vague. There were many errors in that, and very little was clear.
Rosenfeld:[Returns to the room after having found a note]. Here is a note which was written by Bohr which has turned up among the reprints here at the Sekretariat. It is just about the point that we discussed about the Compton effect. This is a calculation of the Compton effect. This is obviously the plan of a lecture starting with Warmestrahlung, then there is the photo-effect; spectral lines; and the the Einstein [derivation of] the Planck formula; then Compton effect; then paradox; then Geiger; and then Lewis. What Lewis may do in thin connection Iím not quite sure.
Klein:I donít see that either. Bohr usually quoted him for his atomic models.
Heilbron:I see here that the Geiger-Bothe experiments were already published in l924.
Klein:In 1924 already? I see. I had thought that that was very new when I returned to Copenhagen in the summer Ď25. I donít think I knew anything on them before I came back to Copenhagen. But Bohr must have known about the Bothe-Geiger experiments very soon after; I think that [Geiger] must have written to him. He knew Geiger well from the early times.
Rosenfeld:Yes. Well, he writes to Geiger here, which may mean that he had a letter from Geiger.
Heilbron:Theyíre not very extensive lecture notes, are they? [General amusement.]
Klein:No. I think he worked very much on them, but I donít think he had—. Then in later years he often wrote quite a lot on the blackboards.
Heilbron:Professor Klein was going to try to give us an idea of how he pictured those waves, and how they grew out, probably, of the Jacobi-Hami1ton analogy.
Klein:Of course, there was very much error in it. I think my general view of it appeared rather well in one of these letters to Bohr which I have just read. I sent this letter very soon after I had read the continuation of Heisenbergís work by Born and Jordan. [Locates the letter and reads] I said, ďI have read with very great interest your lecture in Nature.Ē What can that have been? It was in 1926.
Rosenfeld:That may be ďAtomtheorie und Mechanik.Ē It was also published in Nature.
Oh, that came in Nature. Oh, yes, then it must have been that. [Reads again], ďthen also the new work of Heisenberg, Born and Jordan which I think contains a very beautiful and important progress. At the same time I have thought a little more about the five dimension speculations which I hope soon will be ready for a paper. In spite of the beautiful and, in a certain sense, satisfactory way of a description of nature in the work of Heisenberg, Born and Jordan, I find it difficult to acquaint myself with the thought of giving up that kind of connection between the physical phenomena which the description by means of differential equations means.Ē Of course, everybody had that difficulty, and we all had to give it up. That was in the winter Ď26. Then that goes together very well with my memory that when I came to Copenhagen there was much discussion, of course, and Bohr and the other people there were already very convinced at that time that even in the fifth dimension one should not have a kind of classical description, but rather a description like that of Heisenberg. But I thought, nevertheless, that there was something a little bit hopeful in the progress which I made that spring and then the summer. Namely, using five dimension theory you could develop all the quantities according to the fifth dimension which then should be periodic. As I thought of it geometrically at that time, it was closed in the fifth dimension. And that was to account for this elementary quantum of electricity because it came out that the momentum of a particle in the direction of the fifth dimension was proportional to the electric charge.
That would then mean that if you had the electric charge a whole number of something, then all wave equations should be periodic with that period. And that period was a curious number which was determined by the gravitational constant and by Planckís constant, and that came out something 10-30 or 10-31 centimeters. Then I tried to continue this and to say that the field quantities themselves should be periodic functions, so that one should be able to expand them in a Fourier series. Then one should be able to divide the quantities into those that are independent of xį — they are our ordinary quantities — and those which contain it. These latter appear then only in averages, but they appear then so that you would always have a combination of one term (with + iPoXį and Ė iPoXį). Then one could see also that one could regard a Schrodinger wave equation, in the fifth dimension, as a real quantity. That was still what we call now the scalar wave equation. Then one could also formulate those rules for giving the density and current density which gave rise to the radiation processes and so on. One could regard them as averages of real quantities of the fifth dimension. Then this difference law, the combination law of spectral lines, came out automatically; and that impressed me a bit. I remember I told that to Lorentz in Leiden. Lorentz said that he would be a little suspicious; he would say that only a non-linear theory would contain difference frequencies and sum frequencies (that would become) combination frequencies. But really the theory was so built that it would only give different frequencies in that way. In some way, of course that impressed me, so that I kept this view also in that paper, which Bohr had me publish, on the correspondence approach. Bohr didnít like that paragraph, but I kept it. So, I mentioned it explicitly in that paper. I had written some other manuscripts before but I never published them. But then, as I mentioned last time, after those discussions with Schrodinger about the attempt to have the four dimensional theory on the ordinary differential equation lines, I began to look at the many-body problem from the five dimensional point of view. Then I saw that it was no better there. Then I saw that one could, by means of this so-called second quantization which I (looked up in Diracís paper again) — made it go well together. So then I (came back Ö then Jordan was taking the other view.) In the meantime, Pauli had been very critical of that correspondence paper. He didnít know quite the history of it, so that afterwards he treated it very much more nicely in his book than he had treated it privately in letters.
I think he thought that it was dishonest that I believed in the five dimension theory and still wrote a great part of the paper just to show how the experimental quantities could, come out in a four dimensional way. But I didnít think there was anything dishonest in it. One could say that when one knew, and saw through the thing, that it was not connected because one couldnít carry through the five-dimension view. But at that time I still hoped that one could and that the four-dimensional treatment was a more provisional thing. I wanted, of course, to describe the experimental things so then I felt this would be a beginning of it and that that might come out. At the same time I thought about Pauliís principle — that, so to say, one had one particle for every eigen vibration — but I couldnít see how to formulate it. That came out very nicely then in Jordanís formulation; Jordan got at that independently, of course. Then I wrote a paper where I tried just to take the quantum field point of view, but together with the five dimension theory. And Pauli rather liked that paper. He and Heisenberg, when they wrote their papers — their big paper about the quantum-field theory — , started to use this, but then they gave it up in the meantime because they thought it unnecessary then. Then I gave it up when Diracís theory came. Before that I had tried to explain the spin with some kind of (tensor-vector) equation, but then, when Diracís very nice solution came, I gave up these things for quite a number of years. I remember that Pauli and I drank some wine on the death of the fifth dimension in Ď28. We tried then a little bit to do something where we used gauge invariance, but that didnít go far enough. So—.
Heilbron:You were telling me before Professor Rosenfeld came that you hadnít known of Kaluzaís work on the five dimensions until after you had worked it out yourself.
Klein:Yes, yes. I had seen a notice but I never knew what it meant — in Einsteinís Princeton lectures which had appeared about Ď22, or Ď21, or something like that. He said that there were such attempts by Weyl and Kaluza to make a unified theory. Weylís I knew, but he never mentioned Kaluzaís (source). I donít think there was a quotation. I wondered later on that I never saw Kaluzaís work, because I read rather much at Ann Arbor and (browsed in the library.) But I would imagine that those volumes of the Berlin Academy which were rather near to the war were missing, that they hadnít gotten them yet. I never heard anything more than this notice in Einsteinís lectures about Kaluza before the spring Ď26 when I showed Pauli my manuscript on the five dimension theory. I had thought of publishing this manuscript but then I changed it very much after Schrodingerís paper came. Pauli told me that he had seen something of that kind by Kaluza, and then I looked up that paper of Kaluza. Now, Kaluza had made a first approximation calculation, and he came to it in a different way than I. I think he got it from the analogy of these three-index gamma quantities with the quantities appearing in Maxwellís equation. I think that was the way. He only derived the field equations in the first approximation. I had already worked them out, in the summer before, rigorously. So I was not very impressed by Kaluzaís paper, but thought that since he was much before me I should quote it. Nobody could see that I had it independently.
Rosenfeld:These quotations which are only courtesy quotations much confuse the historical record.
Klein:Yes. I thought that since I hadnít published it I should rather quote it. (I was a little sick of the whole of that), especially also that Kramers let me know through Bohr that I should have quoted his paper. I mentioned that to you, I think. That was his paper about the static gravitational field which he had written very much earlier. I never understood that and had no knowledge or memory of it when I found (my five dimensional theory.) So then I quoted it, and then de Broglie quoted Kramers for the whole thing, and then I got a little bit impatient. So I wrote a little — I sent (Piauget) whom I knew, a little paper, and then I got a nice letter from de Broglie where he said he was (actually a little disgusted by the whole thing, and I think he was right.)
Heilbron:Before you hit on the five dimensional approach, had you any picture of what the waves were when you began working in the four dimensions?
Klein:Oh, rather vaguely still, but I knew that they should be connected to the Hamilton-Jacobi equation. At that time I had very little learnedness in mathematics, but, unfortunately, just at that point I had a little too much. Namely, I had read some in Hadamardís book Propagation des Ondes. And I knew that a wave front equation, although a non-linear equation, was only determined by the linear second derivatives in the wave equation. Therefore, the Hamilton-Jacobi equation could not be uniquely made into a wave equation. I thought that the non-linearity might be an advantage in getting quantum waves at the same time, but, of course, it made the whole a little too ambiguous. I knew that there was one simplest way to have the linear equation, but I was rather uncertain as to whether that was the correct way. But I knew the connection to the Hamilton equation, and I also knew that the quantization of the stationary states meant eigen solutions. And I thought of that in analogy with vibrations on a drum. Also I thought of the water waves which returned in themselves. First I had thought of things on a string and a wave train coming and being reflected upon itself. Then in the summer Ď23 I was writing a little book on optics, so I thought quite much on this, and I made simple experiments on water waves and also on optical things. I was thinking of these things a little more, and then it occurred to me that stationary states are analogous to such eigen vibrations. But I knew so little of the mathematics that I didnít come further.
Heilbron:Did you try a number of equations? Did you actually reach wave equations in which you had non-linear terms and try a number of them?
Klein:Oh, yes. Just in the spring, when I came back to Copenhagen, then I had written that paper on five dimension theory, but wanted to leave that for a time. Then I took up the other part — which would be the other part of the work. Then I began to think more seriously of taking the simplest possible wave equation, the linear one, and see if I could calculate it. I remember talking with Wailer about that, so he remembered it afterwards. That was before Schrodingerís work came. Then I was trying to find the stationary states of the harmonic oscillator. But I knew too little about the mathematics there, so I hadnít found it when Schrodingerís work came about the hydrogen atom.
Heilbron:But you had had the equation, so it was just not knowing the Hermite polynomials.
Klein:I had the equation. Unfortunately I had missed the Hermite polynomials; I should have been able to learn it very well from Fredholm. But you see I came on quite a different way to physics, so I had no regular studies in mathematical-physical work, but came to it gradually from the other side, so to say. Ö I mean, such things are not important, but there may be curious examples of the way scientists develop. Ö Schrodinger was rather versed in mathematical physics. He has told himself, I think, in his collected papers that he gave a colloquium in Zurich on de Broglieís thesis, and then he thought that if you had that connection, you should write a wave equation. But I thought afterwards — to remember very vaguely — that I had seen that also de Broglie had written somewhere a wave equation, but I never found that again, and I may have been mistaken. That should have been rather late because I fancy that I have seen it in Sweden, so it may have been later than Schrodingerís. I have some vague idea that he also somewhere had published a wave equation after his thesis. It could have been in the winter Ď26. Ö I saw something of that kind before Schrodingerís paper came. I see myself in the library of the Swedish Academy of Science, and I may have been there before I came to Copenhagen in March Ď26, but my memory is very vague, and I donít remember where I should have seen it. It might be worthwhile to look up and see if there is anything of that kind.
Heilbron:It certainly would be.
Klein:It had no influence with me because I had these things in my head at that time, but I have some vague memory of it. When I published I donít think I thought of it. I quoted his thesis, and I quoted Schrodingerís work which was later, so there was no particular reason to quote it. But it would be nice also because there was astonishing competition about who gave the relativistic scalar wave equation first, which I thought was a very uninteresting problem because, particularly, I thought very soon that it was wrong. Then I thought it was quite self-evident as soon as one thought of such a wave equation in relativistic mechanics, which was a known thing. I started the whole thing in relativistic mechanics because I had this five dimensional approach. I never thought that that was any important thing, just to have the relativistic scalar equation after Schrodingerís equation. But I thought there were some other things which were important, for instance, that it was time dependent, which, as Heisenberg pointed out to me, could give important applications which one couldnít have from Schrodingerís first work. Of course, Schrodinger very soon got to that himself, so I think he had published that before my paper came out, but not before I had written it.
Heilbron:Did Schrodinger ever say once he had decided that if there is a wave there must be a wave equation how he went about looking for it?
Klein:Yes, I think he mentioned it in the introduction to his collected papers that he gave a colloquium in Zurich on de Broglieís thesis. Then he thought that since de Broglie has thought of these waves there ought to be a wave equation, and it would be interesting to see how that looked. Then when he published it first, he gave it in a little bit mysterious way because I think be gave a static one and he gave a solution to the hydrogen atom starting with the transformation of the—.
Heilbron:Taking the variation of the integral.
Yes, yes, yes, yes. Of course, later on that was quite a good variation principle, but at that time it looked very mysterious. But for me it, [Schrodingerís paper), had that importance that I never thought I would collect together what I knew about it, [the five dimensional theory], and what I learned about it. I learned something from Schrodingerís paper, but that may not have been his first paper; that was this way of defining density and current density. I hadnít thought of that before. So that came in then very naturally in my way of looking at it, so that I started that also in a five dimension way, then. That I think I learned from Schrodingerís paper. That must have been in one of his later papers. I wrote a paper after I had been in Leiden; I wrote two manuscripts. Let me see. One was about just the way to get to the classical equations from the wave equation treated in a five dimension way. I had discussed it so much with the people in Leiden, so I tried to write, I think, the names of Ehrenfest and Uhlenbeck on it. I have forgotten if I wrote them on both. The other was, so to say, the first version of what later became that paper on the correspondence approach. It wasnít carried through, but I had the formulae for the density and the current density, relativistically.
I typed them myself in the summer; I had a typewriter in Leiden. Then I sent them to Ehrenfest and hoped that they would join me in publishing them because I had discussed them so much with them that I wouldnít separate my contribution from theirs. I remember that Ehrenfest had made a special remark on the solution of the Zeeman effect which I then took up in my later paper and mentioned that I had it from him. But they refused flatly to join me in publishing and said I ought to do it myself; then I never got them ready. I didnít know quite how to do it. Then I think after Schrodinger had been in Copenhagen I told Bohr a little more about it. The he began to get interested in it so that we had very many talks about the things; the view he took there much influenced the form. There was one point there was a factor two which I hadnít thought of, but which already came in in Heisenbergís theory. Bohr knew this and this was behind this, a little strange, way of formulating it by regarding it as an ensemble. That was really Bohrís formulation. I was not so very happy about it because I had this five dimensional view in the background, so I had very little connection with that. But I think it was quite good, and I think the paper got more readers than I would have had without these things. It got a certain concentration on the applicable things in that way. I had made those calculations about the different fields, the static and the radiation and such things, using Maxwellís equations, and I think they impressed Bohr a little at that time.
Heilbron:What became of the early work on the rotating molecule?
Klein:Oh, nothing came of that. I think later on such things were carried out, but I think I tried to apply it to experimental things which didnít belong to it. There was the question if you had a linear molecule and then you have an angular momentum which forms an angle with the axis and precesses around the axis, what would be the quantization of that? Then I took the quantization from the Correspondence Principle by calculating the frequency and so, but then the application of it —. There were some measurements by, I think, (Barker) and (Duffendike)(on the ultraviolet spectrum), and I donít think it fit it. I never followed it later, so I believe such things come in, of course, but I donít think they came in just there. This had been in the spring Ď24, I think. I donít remember that we took it up later. I came very soon on this other work which I mentioned. In the summer I had rather hard work in summer school. Then we went to Colorado. When we came back I had some elementary teaching, undergraduate teaching, and then I had some other lectures also and students, so I had quite a lot to do. Gradually then I came into this five dimension work which I described. So I never followed this up — and I believe the reason was that it didnít check with the experiments. And I believe the reason for that was that we tried to check the experiments with a theory which didnít belong to them.
Heilbron:When you came back to Copenhagen in '26, Heisenberg was here, was he?
Klein:Heisenberg was absent then, but he came back later in the spring.
Heilbron:You mention long discussions with Bohr and Heisenberg, and sometimes also with Schrodinger I think in one of the letters.
Klein:That was in the autumn; that was in September, I think. Then Heisenberg was there, and Schrodinger was invited to Copenhagen, and then there were joint discussions just on the principles of quantum theory.
Heilbron:Do you remember any of those discussions in detail?
Klein:Yes; I remember some of it; I remember that they pointed out very strongly to Schrodinger that his radiation theory would lead to a transition probability which would be proportional to the number in the upper state times the number in the lower state, which, of course, would be quite wrong. And I think that impressed him. Then there was a curious talk which Bohr reminded me of in later years — I think he put (most) of it in the Heisenberg paper. Heisenberg tried to prove that Schrodinger could not describe the Stern-Gerlach experiment because a wave packet could not go both ways. Bohr reminded me that I had said and this has to do with the fact that I had been interested in optics — that this would probably be similar to double refraction. In a magnetic field those with different spin would behave a little like waves in a double refracting medium and they would go different ways. In that connection I was also thinking of spin in this way, but tried it then mathematically with tensor and vector equations, which was wrong. But the general idea had some meaning. You see, I never took it up because I was not interested in this configuration-space wave equation. I was interested in a type of special wave equation, not in this. Therefore, I never carried this out, and that could not be carried out at that stage without this configuration-space wave equation. Later on Darwin did that, and I think Bohr proposed it to Darwin. He really carried out the calculation on Schrodingerís lines on the Stern-Gerlach experiment. That gave just this result.
Heilbron:Schrodinger was not at all convinced by this business?
Klein:Schrodinger was, I think, converted to the usual quantum theoretical view at that time. But he wrote a very strange paper some time after—.
Heilbron:Thereís that very peculiar paper in the Solvay Congress in 1927.
Klein:Was he still opposing there? Then my memory failed me there because I thought that he was converted there. But he was converted some time because I know that he repented very strongly in later years. I had some correspondence with him in later years. It was twice; I think the first time I only answered a little in a general way; well, also it was that way the second time. But one time I wrote by myself because Lise Meitner was eager that I write to him. I told here a little about him. Then I found a manuscript which I had written at the time of the first discussions, which I think I mentioned. There I proved that one finds Rayleighís laws through his, and then I rewrote it in a more short, clear and concise way.
Heilbron:You were beginning to tell us of Lise Meitner.
Klein:Yes. Lise Meitner asked me, I think, the first time to write to him. I think it was in that connection that I sent him a summary of that derivation of the Rayleigh law by means of his radiation process. He answered me something like that that was beside the point. I didnít understand it, so then I never answered him. But then there was another time when either he or I wrote first — I have forgotten. But it went in the same way. He gave some view, and I tried to say something against it, and he thought that that had very little to do with his view. Then I didnít know what to write, so I think it ended with that. I never understood it; he made a point of not calling energy ďenergyĒ, but calling it frequency. But I couldnít see —. Youíve never read anything of these later papers, have you?
Rosenfeld:No, no; I tried sometimes, but one has the impression that he was not very serious. In l952 an organization of philosophers, which meets every year in Geneva, had thought of inviting three physicists. There was Schrodinger, who had to make the main speech representing the point of view of the scientist, and then there was Born, and myself. In order to be very kind to the physicists they had put them up in the same boarding house, so that we were all three together all the time. Schrodinger gave a talk which was terrible because it was before a large audience of people who did not understand anything of the topic, and he started saying, ďnow the physicists donít know whether there are atoms.Ē All the rest of the discussion was poisoned by that, you see, because the philosophers said, ďNow, you see, science is in a terrible crisis; the physicists donít know what they are talking about. They donít know anything about matter, and they donít even know whether there are atoms.Ē So Born was absolutely furious, and he tried to intervene in the discussion, but, I mean, it was hopeless. Well, the funniest thing was that Born tried to argue with Schrodinger at the table in the boarding house. I did not take part in the discussion, and Schrodinger said to me, ďWell, I believe that we have agreed to differ.Ē So that was settled. But Born wouldnít agree at all. Then I had the impression that Schrodinger was just pulling his leg; he was not arguing seriously. He went so far as to say, ďOh, yes, but think of waves — they are so much more beautiful than particles. You see, if you think of a lady whom you love, then you telephone to her, and it goes by waves,Ē and so on. Born did not at all like this kind of joke. Then Born, when he met me somewhere on the stairs, you see, he took me into the corridor, and he said, ďNow, I have thought of an argument which he wonít be able to answer.Ē And he told me some argument; of course, there are many arguments. And then I told him, ďWell, you are wasting your time.Ē Born came with this argument, you see, and Schrodinger answered him as a joke.
Klein:1952 was about the time when I think I corresponded with him first. The second time, I think, must have been somewhat later. But I couldnít make anything of his answers; I gave up then.
Heilbron:I presume he had not always taken that attitude. Was it typical of him in later life to have such an attitude?
So far as I can see, yes. Although, I mean, it depends. You see, I saw him in Dublin in Ď46, and there he was very concerned with the unification problem in general relativity. I was so uncautious as to tell him once, ďWell, this unification problem reminds me of the aether problem in the nineteenth century,Ē but I immediately saw that I had made a great mistake. He was very upset about it.