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In footnotes or endnotes please cite AIP interviews like this:
Interview of Max Born by Thomas S. Kuhn and Friedrich Hund on 1962 October 17,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
Part of the Archives for the History of Quantum Physics oral history collection, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Niels Henrik David Bohr, E. Bormann, Louis de Broglie, Cauchy, Peter Josef William Debye, Paul Adrien Maurice Dirac, Albert Einstein, James Franck, Josiah Willard Gibbs, Werner Heisenberg, David Hilbert, Huang, Ernst Pascual Jordan, Felix Klein, Alfred Landé, Max von Laue, Erwin Madelung, Albert Abraham Michelson, Hermann Minkowski, Wolfgang Pauli, Max Planck, Venkata Chandrasekhar Raman, Erwin Schrödinger, Arnold Sommerfeld, Otto Stern, Toeplitz, Woldemar Voigt, Theodore von Kaman, Norbert Wiener; Como Conference, Universität Göttingen, and University of Cambridge.
There is a place in your writing, or a couple of places, where you mention the fact that in the early years of the century you remember that little or nothing was being said about Planck's work. Is there more that you can say about that? Can you remember times that you heard about it or did not hear about it, when you would now expect to?
Well, you see, I think it was in Germany, and very different in different places. In Berlin, where Planck was, people were very much interested right from the beginning — you see Nernst's experiments were started from the formula and such things. But where I was, in Göttingen, there was hardly any mention of it. First in Breslau, my home city, I never heard of it. Then I came to Heidelberg, Zürich, for short periods — I never heard of it. And, then I came to Göttingen; it wasn't much better; but then it suddenly appeared — I don't know when. I went back to Breslau after my doctor's thesis — that was, I think, 1905 — '04 or '05.
I think it must have been when you went back to Breslau; I think that would have been 1907 or '08.
So, was it? I was' first in England for about half a year — not quite, a few months — and then I was in military service. Then I went to Lummer and Pringsheim in Breslau. There were Ladenburg, whom you will know from Princeton, and a man called Waetzmann, Land old Clemens Schaefer who is still alive in Cologne. He's about 90, I think. And there I heard of it. And I think I thought it was crazy.. And then there was a meeting — this is a dark memory of mine — of the Physical Society in Berlin where somebody spoke about the photoelectric effect, and such things. This must have been after 1905, after Einstein's paper, and everything seems to be serious. As soon as one saw that there the density of energy was not proportioned to the energy of the particle emitted, but quite a different law, it looked serious. And then I had the crazy idea to make a mechanical model which I remember because Planck mentions it. This is also only a memory, I haven't looked it up, but I think Planck mentions it in his little autobiography. Planck himself was so doubtful about all these things of Einstein. He believed in his own things, but not Einstein's photons. He thought any model which would help out of this complication would be very welcome, and my model was the following: Imagine a tree with apples, and the apples on the low levels had a long stem, and higher up shorter and shorter, i.e., the periods of motion of the lower ones were long and, the periods of motion of the high apples were short. Then if you shake the tree, the apples fall down. Those of the low pendulum energy fall in a short interval and come out with small energy and the higher ones which have a higher frequency come down with higher energy. This simple model gives you all the properties of the photoelectric effect. And this I had the impudence to mention in a discussion in Berlin about Einstein's explanation of the photoelectric effect. And this made the impression on Planck; you see, it was not so absolutely crazy as one might think it to be.
Do you have any recollection now of other things that go with that which would help to figure out when that may have occurred?
I can't say. No. It must have been perhaps during the time when I was a soldier, and had to do service in the army.
During the war now you think?
No, it was earlier. It must have been, let's see you can see in my Recollections. It was after my doctor's thesis.
And after Cambridge?
Yes. Before and after. Before Cambridge I was in another Berlin regiment. Then I got ill. Then I got into another regiment after Cambridge — in Breslau — and it was very disagreeable. So I was twice in the army. It must have been about 1905 or '06. And it was at this time, though it was certainly after the Einstein paper of 1905. The change of mind came, I think, through Kármán. Kármán and I lived at the same house; we had just a house in Göttingen; just an ordinary boarding house. We had rooms, one above the other, and we were very often together. At first he was very much interested in physics, then later he went over to hydrodynamics, and specialized in that. But at that time he suggested to me to study Nernst's experimental research and his specific heat of solids — that must have been after Einstein's paper — I don't know when Einstein's paper was. He directed my attention to this Nernst, and he thought it rust be quite a general rule. Nernst's few examples are quite sufficient to show that it would hold everywhere. And then we discussed this thing and came at once to the idea if that is so then all attempts like Planck's to assume that the quantum is an effect of absorption or emission is nonsense. It showed clearly that the effect was not connected with the oscillators or something, but was a quite absolute law because it's connected with the normal modes of the vibration. Who came to it first? I think it might have been Kármán because he worked an normal modes, but when he explained it to me, I certainly grasped at once that it was an absolute proof that if it's an effect of the normal modes it's nothing elementary, but a fundamental property of mechanics. The mechanics must be quite wrong.
Let me ask you further about that. My colleague Dr. Heilbron has talked a bit with Dr. Von Kármán in Pasadena. His recollections are that at the time that you and he undertook the early work on specific heat you had some notion that perhaps if you really did succeed in doing the vibration problem properly, you would discover important non-linearities, and that at that point one would preserve the old mechanics and find another source.
I can't remember this at all. I don't know. But you know, Kármán was a li e older and much more experienced than I at that time; I was not the leading partner in this thing; it was certainly Kármán — that is my feeling. Later, a very short time later, he gave it up, and then it was entirely on my side.
It's interesting, you know. It's his general feeling now that really this whole thing originated with you. And it's your feeling that it originated with We need not know the answer, but I think it's very interesting.
We lived in the same house, and every morning everybody came to breakfast said, "Oh, I have a new idea." And you see how it is, one can't really decide who has done it. But I have the feeling he was more the leading person at that time than I was. In the first months of this investigation certainly.
At the end of that first paper you have a paragraph which clearly still shows some scepticism. At least it may indicate that you were not yet fully persuaded that one is yet thinking properly about this as fundamental.
... One couldn't imagine something for the normal modes, and this is just what I said before. We saw at once that Planck's idea is a much more fundamental one. and could not possibly be reconciled with any mechanical model. ... We were sceptical, of course, because we had no idea of how one could transform this into a decent theory. I don't know. I can't remember what went on in my mind then. ...
You think then that it may really have been not until you got back Breslau, after your army service and after Cambridge, that you really began to know seriously of Planck's work?
In Breslau I heard of it and was interested and thought it crazy, but not more. And then I came back to Göttingen, and of course I wrote a paper on the (electromagnetic mass of the electron — relativistic contraction.) I considered this as a kind of rigidity in its relativistic sense for special movement: I don't know whether you know this paper.
I know of it, but that's not one of the papers I have read.
Of course, I didn't know that quantum mechanics would change the whole situation at this point. And then I sent this to Minkowski, and he asked me to come to Göttingen to work with him. And I was awfully happy for I had made an awful mess in Breslau. There was a tube coming from the mains with water as a cooling liquid for some radiating body. I left the water running the whole night, and in the morning it had slipped off from the connection and the whole room was full of water two feet high. Lummer was awfully angry, and said, "You'll never become a physicist," and wanted to throw me out. And at this moment came a letter from Minkowski inviting me to come to Göttingen, and I was very happy.
You speak in the autobiographical bit that is reprinted in Physics in my Generation of having been at Cambridge and there having taken the resolve to become a physicist.
I wouldn't say that. No. At Cambridge I was mainly interested in two things. First I wanted to learn from Thomson about electronics. His lectures were very good, but I couldn't understand most of it because my English was so bad. But then I tried to listen to Larmor, and his English was quite un-understandable for me because he had an awful Irish accent. And also his way of thinking wasn't in my line. I was spoiled by Minkowski, and to me it wasn't so clear. But what I was really interested in was Gibbs statistical mechanics and I worked through all the two big volumes of Gibbs Statistical Mechanics at that time, and I didn't care about what was going on in the world — I think it was wasted money and time.
But when you went back and worked with Lummer at Breslau this was with an eye to making yourself an experimentalist?
I wanted to learn a little experimenting. And he gave me a Black Body — what was called then a Black Body — and a tube of porcelain material with a heating arrangement and a table with a gas fire and a cooling mantle of water around. And I got no results at all. I never reached the temperatures which I ought to and I couldn't keep them steady. I was not very gifted for this type of work. I failed it entirely and I was very pleased when Minkowski wrote to me to come to Göttingen. In Göttingen I arrived and it was a very pleasant beginning with him. He gave me all kinds of ideas, and I also gave him some knowledge in physics — of course he had much — and then he died.. He was operated on, and when I came back from the Christmas holiday, he was dead.
Well now, when you say that in Gottingen you learned to take the quantum more, seriously this would not have been from Minkowski.
No, not at all. Nor from Hilbert or anybody, nor from Voigt — this had not to do with it. I think in the whole institute of physics there was hardly a mention of the quantum. I can't remember that there was a report of Einstein's papers of 1905 in the colloquium — it was only in our private circle that we did this. And all these things I learned very late. I had no idea of nuclear physics and radioactivity. There was Johannes Stark — he was a great Nazi later — and he was a Privatdozent there and gave a lecture on radioactivity. And I found it so horrible. It was all so dogmatic, and no proofs which I con- sidered to be necessary. And I left it after a few weeks. And this is the reason why I've never done nuclear physics at all. One has to learn it young, otherwise one cannot do it. I think it was all very old-fashioned physics.
A paper you published in Naturwissenschaften in 1913 is really the first time that you talk about the black body problem. At the end of the. paper, again you speak of Einstein's efforts to avoid the quantum and speak of the possibility that this might still, be successful. I was very curious to know whether this came out of conversations that you had had with Einstein this early?
No, at '13 I had no conversations with Einstein. This came only when I cane to Berlin in 1915 during the war. And then my military office where I had to do work on sound range was only a few streets from Einstein's home, so I saw him almost every day. You said that I mentioned Einstein's attempts to rid physics of. . the quantum, but that I don't remember. Do you know what I meant?
I don't know. ... But your remark in 1913 interested me in view of Einstein's later attitude toward quantum theory because it must point to something in his biography that we do not know about.
Well, I talked with him, but I don't know — The complete conviction that the quantum was fundamental — I think you have that already from the specific heat work. But the next step was after the war. During the war I was in Berlin in the military, and then I was quite good friends with Rubens who was an experimentalist — I think a brilliant one — with his work on infra-red and all that. And he had, conducted a colloquium every fortnight for a year. But after the war when we had this awful hunger period he was so down that he couldn't continue, and he asked me to take it over. So I took it quite harmlessly; I thought it would be a group of young students. But instead of that, all the people who had served in the army — people of great fame and name — Franck and Hertz and Westfall and (Bier) — came along in their uniforms, for of course we bad been demobilized in Berlin. Where they were stationed they were all taken to Berlin. There they were demobilized and they used their time to come to the colloquium. So I think it was the most brilliant collection of people I have ever directed. And there were arranged, of course, talks about the most modern discoveries. And one of the first things was to ask my friend Franck to speak about his work. What he had done on the excitation of atoms had made a great impression on me. But I had never heard it from himself. So he (or Hertz) gave a talk about it. And there it seemed so evident that all this was to be taken directly and not only as a round-about thing. And it convinced me very 270 much. And then at the same time — I'm not sure about this, you must ask Franck himself — I remember darkly that Franck had mentioned in a talk that all this is now already brought into a coherent theory by Bohr — Bohr's paper of '13. And I had seen that, but couldn't make anything out of it. But the few remarks Franck made gave me the correct indication of what it meant. But I may be quite Bohr before. If I had seen it, I had no time to study it properly to be convinced confused about this. ... It's very possible that I hadn't seen the paper of —
You don't remember any colloquia dealing with it at Göttingen?
In Göttingen? No. Oh, it might have been —
I'm quite sure there was a colloquium at Göttingen at which there was a report on the paper. And I take it it was not very well received.
No? I can't remember that.
Professor Herzfeld in particular had word-of-mouth reports on it. He rose bit more seriously than this, and to Professor Rubens (Runge, in fact) in just arrived from Vienna and had some to say that it really should be taken a point out a couple of more things about it. particular, was quite negative on the subject,
Oh yes, he was quite conservative.
But you have no recollections yourself of talks at Göttingen and may well be — It may be or not, I can't remember. There were so many exciting things going on, politics at this time, so that I can't remember. I even can't remember whether when Franck talked in his colloquium in Berlin' — and that must have been in '18 or '19 — if I knew all these things already from before the war. But there were four years between, when I never thought about it.
Well, I don't know whether this will help at all, but of course those wonderful experiments of Franck and Hertz are now thought of always as the first great demonstration of the validity of the Bohr atom. But they were not undertaken with that in mind, and indeed until 1919 Franck and Hertz themselves in discussing them make no reference to the Bohr atom. Didn't they? Well, then I'm sure I also didn't connect it with Bohr's paper.
In the 1919 paper, which may very well be a product of the colloquium talk you speak of, there the connection is very firm. ...
So it's quite possible that in this colloquium somebody mentioned it and we discussed it. Maybe even myself, but I don't know.
They're still apeaking of ionization energy instead of excitation energy as late as 1916.
Oh, yes, I remember that e well — that they always thought it was an ionizatic not an excitation.
And I take it, in terms of what you've already told us, that letters from this period, notes, and so on, are now all gone.
I have none. My letters were all in the department, and I had to leave Germany . suddenly; I left them there because I thought they were quite safe. And, the few letters I had at home, the few files, were in the attic somewhere. My wife, later, was going back to Germany and returned our furniture to England, and she left all the things in which she wasn't interested there as rubbish, and, they were destroyed. There were also personal (letters) of mine, and these were all lost.
Do you think there might still be some of these, at the University?
I have several times made inquiries with Pohl first and, later with (Hilsch) and they said there are heaps of old books and rapers on top of the building somewhere, but they couldn't say.
But they might be there?
I don't know, you must ask them; I don't know.
Well, it would perhaps be worth a real look because those would be very precious if they could still be found... Let's switch a bit forward in time. By 1923, perhaps already in, 1922, Gottingen, under your leadership, had now become one of the very very few places to do atom mechanics. ... I wondered, in your case, what brings you into this sort of study? Well, I can't quite remember. I was always interested in the atom. For the lec ture I had to give on the occasion of my Habilitation as Privatdozent, when every one has to give a public lecture, I chose Thomson's atomic model. There is a sphere in which negative electrons are swimming and in the sphere they are partly attracted to the center. The electrons form regular shells and this has a kind of periodicity and gives something like the periodic system. So I gave an extensive description of this model. I think it is in my collected papers. It will not be in the collection now made, but I have it. And, of course, it was an amusing thing, and from this time I was always interested. But then came what we called then the "term zoology" that means the ordering of the spectra lines according to rules — Balmer and Rydberg, and then the multiplets and, so on. And. I found this rather distasteful; I didn't like it. I thought it was purely uncritical — they found rules, but one didn't see any reason why they should be so. The Balmer series wasn't explained. And so I thought always about it, but I didn't write anything about it until I found a point where I believed it could be taken rationally.
Well, in this paper which, again, I have parts of here, there is a place at which you indicate quite clearly that you were taking the Bohr model very seriously and were still very optimistic.
This is Bohr's model? Eucken has made another model.
You see this is 1923, and Bohr's model is now fairly old. It has had various troubles. Eucken is here suggesting a model that really will not work at all well, quantum mechanically. And you suggest here that one cannot get this far away from the principles of the Bohr atom.
Yes, as a basic principle. You see the thing which began to attract me more and more in this direction was the appearance of some general principles. The first was this Ehrenfest principle, the adiabatic principle, which made it clear that in all multiple- periodic systems there would be such invariants which could change either not at all or by jumps. And this was the first indication that this wasn't all nonsense, arbitrary. And I think this is mentioned here also. . Then there are other such things coming up. My reluctance to go into it was simply that the enormous, amount of empirical material that was accumulating was for me not attractive. It was the opposite — disgusting. I couldn't believe that a fundamental thing could depend on an accumulation of guesses. But you need one important principle, and I waited until this came. And, then I made investigations where one could see.by simple models that it didn't work — like the helium problem.
When you speak of the important fact coming, do you think of a particular event?
Well, the important fact was simply Heisenberg's idea to give up mechanical, visualized models and to describe it by the transition. The main change in my opinion was the discovery that the fundamental quantities are not the positions of particles and momenta, but the transition amplitudes. This is already old of course; when was Ladenburg's paper? I think it was the first.
Ladenburg's paper I think, 1920 — '22 perhaps.
That's about the time when I started. Then after Ladenburg came Kramers-Heisenberg on dispersion.
But by the time that the dispersion paper comes, you have already been, for two years, doing your work on the problems in atom mechanics.
Yes, but I used the old method, the Bohr method, to calculate the things as far as possible just mechanically and then apply these quantum rules of Sommerfeld and Bohr. And my idea was certainly that I wanted to show that it's (in error), that they were only roughly true, and I wanted to find out where they were untrue.
Initially you're not trying to any great extent to use these rules at all. Then there comes a point early in the Twenties when you do apply to atom mechanics the Bohr-Sommerfeld conditions.
It must have been much to do with Bohr's lectures in Göttingen.
Professor Rudolph Minkowski, who was assigned to do the Ausarbeitung us copy his own set of those lectures.
I did the same for the Lorentz festival, which was two years earlier. [Talk about perturbation theory and the lectures on atom mechanics as "volume one" here omitted.]
Heisenberg and I were collaborating all the time; we were always together and he was, of course, much younger and much quicker in thinking than I. I was much steadier, but he was quicker. It was this idea of the importance of the transition amplitudes. It wasn't so easy to go over from the intensities of a transition — probabilities as Einstein called, it — to the idea that there are transition amplitudes which are the square roots of these intensities. And. I think this is indicated by Ladenburg in his paper and then by Kramers and by Kramers and Heisenberg in their joint paper. And then Jordan and I took it up in a paper on Planck's radiation theory where we saw that there was a break in it. We calculated, classically, the connection between the mean energy of an oscillator in the field and, the field energy. Then we applied to the oscillator quantum rules. Then we transferred it by this connection to the field. We thought this was a break and we wanted to make it unique. And, therefore, we did, not change the quantum part into classical — we thought this impossible — but the other way around; we transferred the classical part into a quantum language introducing these transition amplitudes. This paper appeared to me important then. I don't know whether anybody knows it now.
The first of your papers with Jordan — the one on quantum theory of aperiodic processes.
Was it called aperiodic processes? I thought it was called Planck's quantum formula. Yes, I think that's all right. And then this other paper, "Quantenmechanik," where I derived the second order perturbation term of energy by such correspondence considerations. It was a (great formula.) It came later also, but I didn't know there were two such papers with this title... Looking at this makes me wonder about myself — why haven't I seen at once it is a matrix; if one had a little sense, one would have seen. I knew what matrices were. But it took another month or two until Heisenberg's paper and then I found it. And then this happened to me again, and there I didn't do it in time. I worked with Wiener. We introduced the operator calculus but in a very clumsy way. But for time we did the right thing. We expressed the energy as d/dt and "we rote le commutation law for energy and time as an identity by applying (t(d/dt) - (d/dt)t) to a function of t; it was absolutely the same as for q and p. But we didn't see that. And I never will forgive myself, for if we had done this, we would have had the whole wave mechanics derived from quantum mechanics at once, a few months before Schrödinger. That is absolutely unexplainable, that one didn't see that. It always makes me a little doubtful about the Intelligence of Wiener. I was then very tired. I had to give two sets of lectures at MIT and a lot of discussions with other people and so on, while he spent all his. work on this paper. He showed it to me, and on it I made my remarks and suggestions, and why then did he not see this. He also had been working all the time on the functions. So I'm not so great an admirer of Wiener's.
Is it partly that he was a mathematician and not a physicist? And for him it really didn't make any difference if it was an integral representation or a differential representation.
Yes, but in one case he saw it was a simple differential representation and in the other case he insisted on this very complicated integral representation, which I didn't like and didn't quite understand. And we could understand only after having the wave theory. Then we knew why the exponential factors came into these integrals.
Sir, in the "Quantenmechaniks," in the Atommechanik book, also in that first joint paper on aperiodic processes with Jordan, you do insist several tines on the idea that then becomes generally known in Professor Heisenberg's paper — the idea that the new quantum mechanics when we know it will deal only with observable quantities, and that one index of what is wrong with existing quantum mechanics is that we are constantly hypothesizing quantities like orbit.
I always thought that was mainly Heisenberg.
Maybe it was, but in print this is certainly something that appears earliest — [Enter Professor Hund]
I had attributed the demand to use only properties or quantities which can be observed to Heisenberg, but he has showed to me that it is here in this paper of mine, clearly expressed.
The part I just showed you was actually out of the Atommechanik.
But you see the book appeared much later. Therefore, I never quoted it. never quoted anything which I wrote, even if I knew it before if somebody else has said it. And, therefore, I always quote Heisenberg about this idea. So it perhaps is not with Heisenberg.
Yes, but this is written after the Kramers dispersion formula was known to you. And Kramers dispersion formula follows this same point. I think also then in Göttingen in these years you often discussed with us the problem of the old perturbation theory We used frequencies, classical frequencies, but in reality these classical frequencies don't exist. There exist only quantum theoretical frequencies, and it was clear to you I remember that at that point quantum mechanics must be revised. And Kramers' dispersion formula was a step in that direction. And that is written after Kramers' dispersion formula, and you cite this dispersion formula in the forward of the book.
Yes, there is no question that that is after. And yet, I think, it was possible for many people to look at the dispersion formula and see it as an important step forward and yet not verbalize what was important about it in this way. And it is not really a question now of who first said what, but how did the idea develop. Now it is clear in Kramers! dispersion theory paper, and also in the earlier paper from which that in part comes — the Bohr-Kramers-Slater paper this notion of restriction to observable quantities, if there at all, is very deeply hidden. In the book, also in this paper with Jordan, toward the end there is again a quite clear statement that a difficulty of the older quantum mechanics — one of the evidences that it is wrong — is that it calls upon nonobservable quantities. And this is, of course, exactly the place where Professor Heisenberg's paper opens. It is not, so far as I can tell, a widely held idea that this is an important criterion, and I wonder how it had developed.
In these days there had been discussions between Copenhagen and Goettingen — '23, '24 —
I was never in Copenhagen at this time.
I don't know whether Heisenberg was in Copenhagen the first time. I think I remember that you and Heisenberg had been aware that Kramers' dispersion formula was an important step. Of course I cannot remember at what time that was; it was before you cite it, and that was in 1924
And then, of course, Heisenberg very rapidly did the paper with Kramers which both supplies the missing steps in the Kramers paper and goes on to elaborate the formula further. And there it leans also on your own quantenmechanik paper. But one need not read the Kramers paper as saying we must use observables only. One can use it as an example of having done it. But it isn't clear to me that that idea is an idea from Copenhagen.
You have also written before this book, a paper with a similar idea. [Hund quotes from an unidentified paper in German referring favorably to Bohr-Kramers-Slater and the Kramers dispersion formula.] That refers to a paper of '24 on quantum mechanics, yes, but here you have noticed the dispersion formula of Kramers. And here also you replace a differential quotient by a difference quotient.
Yes, I think this was done by Kramers too.
Yours is clearer, more systematic. Yes, the published source of these ideas is Kramers' dispersion formula, I would think. But what has been written or spoken between Copenhagen and Goettingen I cannot remember.
I think that Heisenberg had more connection with Copenhagen than I. I was there once for a few days only, and never was really belonging to Copenhagen. But Heisenberg was. And there was even a period when I was angry, because when I discussed and experimented with Franck about these collisions of the second kind and so on, and I said you should try this and that. And a fortnight later: I asked him, "Have you tried this?" And he said,"Oh, no, I have had no reply from Niels yet." And this made me always very angry. But this was very stupid of me because my experimental knowledge was very little.
Have you discussed the question when it appeared that Kramers' dispersion formula is quite independent of the Bohr -Kramers-Slater theory?
No, we have not, and it's a very good and important question, I think.
Can you explain to me what the Bohr-Kramers-Slater theory was? It was a thing I never grasped properly in my whole life. It seemed to me so involved.
Yes, it was wrong, or rather not quite right. Bohr-Kramers-Slater wrote that the energy theorem, and perhaps also the momentum theorems only hold statistically. The experiment of Bothe and Geiger proved that there was not a statistical connection between these elementary processes.
I have a dark recollection that why I was never interested in this Bohr-Kramers Slater theory is that I believed that these integrals of the motions shouldn' t be statistical. It was of course an accident, but I had this conviction. And to make energy statistical seemed to me a rather wild contradiction against this principle of mine. At that time I was rather confident in my own convictions, as I later wasn't so much.
I had asked Professor Born before — there is in looking at his papers an undateable, but still a rather clear transition from a period of considerable optimism in the early twenties that better perturbation techniques will resolve these problems to quite clear recognition that now we have to find a very different way of doing it. And I was wondering what the main sources of that transition were. I would say it's pretty clearly marked by '23, perhaps not quite yet in '22.
Were you there already with me in my department?
I came to you in '22. There had been Bohr' a lectures at Gottingen in June of '22. And to us younger men, his lectures had a great influence.
On me too.
And Bohr had, I remember, a more pessimistic attitude, contrary to Sommerfeld. And we young men believed to hear some differences in the attitude of Somnerfeld and Bohr toward quantum theory. Sommerfeld was more convinced of integral p dq, phase integrals and such methods, while Bohr was reserved toward this. He formulates his sentences always more with correspondence principles. I thought that was the impression — we were young men — it had only been some weeks before that I came to you and then heard Bohr's lectures. Before I didn't understand anything of quantum theory, and, therefore, I cannot say much, but that was the impression of us younger men.
What are now, sir, your own impressions as to the relative influence on Goettingen of what went on at Munich, what went on at Copenhagen; and how close was the communication?
I think my connection with Sommerfeld was little. No, it wasn't very close at all. I heard from him occasionally or at meetings talked to him a little, but he was a little sarcastic always. You know he made fun about everything, and he took his own papers very seriously. He jumped from scepticism to enthusiasm. I have learned a lot from his book but I think I hadn' t much inspiration from him. But Bohr's lectures, that was quite a different thing. The connection of the quantum of action and the angle variables with these integrals, that was new to me.
There was a paper of Bohr' s in the Danish Academy of 1918, and it may be that this was not known at Goettingen before the lectures. But afterwards we studied it.
These big papers I remember now — I have nothing now, but I had such big papers of Bohr's.
Do you think you, yourself, might not have known of those until 1922?
I think so, yes; certainly not very carefully.
Sommerfeld was at least two times at Gottingen. At the Bohr lectures he was at Gottingen, and then there were discussions between Sommerfeld and Bohr. And I think late in '22 or early in '23 he came from America and was in Gottingen and told us of the Compton effect. That was the first knowledge of the Compton effect we got. It must be late in '22 or early in '23. I remember we had been in Franck's room near the little lecture room. There was you and Sommerfeld and Franck. But there had been some connection, not only by letters and books.
What was the origin of the Bohr Festspiele?
This is a very funny thing. There was a man named Wolfskehl who lived somewhere in Mannheim or Karlsruhe, and he gave a great amount of money as a prize for the solution of the Fermat problem. And he gave, I think, a prize of 100,000 marks a very great capital — for somebody who could prove the theory. And from this point on, this was already ten years earlier or more, the Gottingen Academy got thousands of letters every year from people who wanted to get the 100,000 marks. And sometimes only postcards with the whole solution written on them. And it took them such a time even only to answer these letters, that they at last decided, when the man Wolfskehl had died, that they felt no obligation anymore to keep to this rule and would apply this money to better purposes. And the first purpose to which it was applied were these lectures. There were three as far as I remember. The first was Poincare then Lorentz and then Bohr.
Now how was the decision to invite Bohr reached? You say you think you may not have known his l9l8 papers until after those 1922 meetings. And that it was really that these had a great role in turning your own —
Oh, I knew them. Of course I had looked through them and so on, but I had not studied them in a careful way. We all knew that Bohr was ahead of us, and we tried to understand him; we had the feeling that we were all kind of pupils of Bohr. Before the festival it was like this: Bohr had a brother, Harold Bohr who was a mathematician — a brilliant one — and he was a good friend of Courant, my colleague. He came often to Gottingen, and he told us about this brother — that he was a most clever man — and we became curious about what he was doing. And I think that was the reason why we invited him. The Academy — of course that meant only the physicists in the Academy — there was Planck, Franck and Pauli and myself and perhaps a few chemists — made this decision. What else do you remember from this period?
I remember that I came to you, and that I had no idea of modern physics at that time, and so that was the first impression. I had heard a lecture on quantum theory, but that was quite another thing — specific heats and so on. But then I studied classical physics and mathematics, and that was my first (introduction to) quantum theory — these Bohr lectures in June '22.
I would like to talk a bit more about this period leading into 1925. I would like this afternoon, however, to talk about what happens immediately after 1925. You had spoken of your reluctance in connection with the Bohr-Kramers-Slater paper at the idea that energy might be only statistically conserved and clearly most people must have felt this way and been delighted when immediately afterwards it turned out. But this is an idea — this idea of statistical energy conservation — which you must also have had.
Yes, we discussed all these possibilities.
In your paper on phase relations with Heisenberg in 1923 at the very end of that paper you turn suddenly, and somewhat unaccountably, to the Stern-Gerlach experiment and to the adiabatic objections to it. And you suggest at the very end that you have, perhaps, a way out of this. This last paragraph has rather little connection with the rest of the article but it does indicate that already in 1923 in Gottingen this possibility of statistical energy conservation as a way out of some of the difficulties is being discussed.
That was in January 1923.... I don' t know that paper well . I think we have two rotators with interaction and then they show the quantum conditions if the phase is completely undetermined.
On the contrary, you show that they must be in phase. That paper has an argument in it which I now found very difficult to understand. But basically the argument is with the two rotators. There is an argument that if they begin to get out of phase on the application of the interaction, then it will not be possible in taking off the interaction to bring them back to the positions from which they started. So that by adiabatic variance they may not start to get apart in the first place for a physically permissable motion. And then this is used to show later phase relationships between various orbits in an atom. It's a very interesting paper. It was particularly for this last point that I wanted to ask you about it. The question of whether the people were talking first in Goettingen or Copenhagen about statistical energy conservation is unimportant. The question how people felt about the state of physics in ttingen at this point is surely very important, arid it is in hopes that this may bring back whole conversations, some uncertainties, that I point to a passage of this sort.
This kind of thinking seems to me all so strange and so foreign that it's difficult for me to understand.
I cannot remember that in Göttingen at that time this was discussed. I cannot remember any discussions on the statistical conservation of energy before the Bohr-Kramers-Slater paper, but I was very young at the time.
There must have been at least a little. What about the feeling about the Stern Gerlach experiment at Gottingen?
Stern-Gerlach? Well, this was made in my department in Frankfurt, so I was in it from the beginning. And it took me quite a time before I took this seriously; I thought always that this direction quantization was a kind of symbolic expression of something which you don't understand. But to take this literally like Stern did, this was (his own idea) — I had nothing to do with it except the arranging of the experiment. That seemed to me awfully strange, and I was first very much shocked. I tried to persuade Stern that there was no sense, but then he told me that it was worth a try. First he had to learn to take atomic rays, molecular rays, and he did this experiment about the Maxwellian distribution of free velocities. This led me to try to measure the free path with Frl. Bormann and this is something that has never been continued anywhere. It was a beautiful measure of tiny numbers of atoms, so it would be easy to calculate the interaction between two molecules by just observing how they were scattered.
How did you happen to go back at that point to experimental work?
I had only two rooms in Frankfurt. And in one room there were some students. There was Lande working in the same department. Stern's operation was made up in my little room, so I saw it from the beginning and watched. And I was quite envious of how he managed — he didn't touch it at all, for he's also, just like me, not very good with his hands. But we had a very good mechanics man, and he did it for him. He told him what to do, and it came out. So I decided I should try it also. So I suggested to Stern to try the free path experiments and he said, "Well, that's a good idea, but I'm busy now and I want to go on from here to the quantum theory." And so I told my assistant, Miss Bormann, to work it out And then I went deep into it, particularly in the method to discover silver atoms in a very small number, optically. Other methods were not known at that time. And there was a little interferometer which we invented for use under the microscope. This was then produced by the Zeiss works and was in their catalogue and was sold for medical purposes. But we did much more than is in the published paper; we had later a very complicated and nice apparatus, but then I was called to Gottingen and gave it up.
Did Professor Stern himself expect to get the two beams out of that experiment do you think?
I think he did, yes. He was convinced that this was not only a formula, but it simply is so. And I think nobody among us would have believed him. But I encouraged him because I thought the idea was worth trying.
Well, now going on from the actual performance of those papers, clearly finding the effect did not solve the problem as to how there could be such an effect. Did one continue at Gottingen to worry about the Stern-Gerlach experiment? I think we did yes. How to reconcile these whole number appearances with the continuous character of mechanics, that was the main problem. It came also out in the multiplets.
Which were the places which were most on peoples' minds? Was the Stern-Gerlach experiment still an important source of the crisis?
As far as I remember the main indications of the crisis were the multiplets and the Zeeman effect, and these things. That we called the zoology of terms.
There was the Zeeman effect on the one side, and on the other side the perturbation theory which didn't hold — didn't give the right results.
Landé came to my department — I don't know the period exactly — and was my student in Gottingen. Then he disappeared and got his degree somewhere else, in Munich or (Stuttgart), I don't know. Then he came to Frankfurt again, and his head was completely occupied with the paper which I didn't grasp at first. It was these whole number relations between the intensities of multiplet lines and Zeeman-effect lines. And he did it in a way which seemed to me horrible, namely, simply by guessing about numerical values. He wrote long lists of numerical values and said they must be contained in one formula — how can one 'construct it? And he tried the most impossible things. And at last it came out. At last came a formula which gave all the results he wanted. I couldn't check it — I can never do numerical calculation problems. So I didn' t take much notice of him, and he also did not take much notice of our work, though we were sitting all the time in the same room. But two years later, or three, when we derived the suare root of integers formula from quantum mechanics, we saw at once that it was very important. Some of these formulae were known before for multiplets from the Dutchman Ornstein. But for the multiplets, I think, and the expression of this "g" we were first given by Landé. And how is it now? The effect is not quite correct. In quantum electrodynamics, there is a small correction.
Yes, but these are small corrections.
They come from the self energy terms.
There is another source of discomfort which involves you, Professor. What about the Ramsauer effect?
Oh, yes, that played a' great role, and, of course, Pranck was interested in it. It was more in Franck's line, and he had a lot of discussion in seminar, also in our colloquium, but I can't remember any detail.
In May '22 a student gave a lecture on the Ramsauer effect. in the pro-seminar — Wednesday morning — you remember. That seminar you hold with Franck. And Franck thought perhaps that an electron would turn about 2π and then go in the old direction, perhaps due to a special field of force. And I thought I could be that keen theoretician, and I thought some days on it and calculated some fields. And for a special field you got a turning by 2π, but only for special field. At that time, only the Ramsauer effect for argon had been measured. And at the same time Minkowski and Sponer made an experiment in Goettingen, I think with Krypton and Zenon. And it seems that we have found preliminary results at that time that the Ramsauer effect will be a more common feature of rare gases. And then my doctor thesis contained parts. First part to calculate special fields which gave 2π, but that was only possible for special fields.
For what reason did you have 2π for the Ramsauer effect?
For low velocity electrons only. At low velocities most of the electrons went straight through. But it seems, and I told that in my thesis, that it is very important that for more than one gas that would be right. Therefore, in the second part, I followed an idea of Franck to use the correspondence principle in the following sense: for small velocities and classical mechanics electrons can (not) come out. And, therefore, there must be a larger change in the quantum mechanics and [the thesis was to give] some estimation of the limit where that deviation must be. It gave some results — not very good. Of course the theory was not true, but I got a doctor degree.
That's the main point.
That was in summer '22. Perhaps Franck more than you were interested. And I was interested because I had the impression that is an aperiodic system and one must learn how to use quantum theory in aperiodic systems. Of course it was no solution . If I had given, the right, solution, I must have detected the de Broglie waves, and I did not.
When was it connected with the de Broglie waves?
When he was in Gottingen?
I think it must have been '25 or '26. I think Elsasser saw very early that it was connected with the Ramsauer effect.
Your thesis was actually in '22. Did. you feel at the time that this probably was the solution?
That is difficult to say. I think at that point it was not quite wrong that according to the correspondence principle and such considerations there must be a large deviation from classical mechanics especially with slow electrons. But that was, quite unclear of course.
How big a problem did that one seen to be. We're talking again about that range of things that aren't working right. The helium atom is one, and the anomalous Zeeman effect. Is the Ramsauer effect ever really in that group of bad anomalies.
Was it Franck who regarded this as a very bad anomaly?
Yes. This was one of the first indications for electron waves. Franck has taken it seriously.
But certainly not connected it with the waves. The first indication of the waves came from a letter I got from Einstein. And it was quite a short letter. I haven't got it any more, but I remember he wrote, "I am quite excited about a paper by a young fellow in Paris, de Broglie, and about waves which correspond to particles in the same way as photons correspond to the waves in optics. And you must read it." And now it wasn't so easy to get it from Paris, so at last I wrote to de Broglie. I got the thesis with his own dedication — but I have given it with my library to America. And then I tried to read it, and it was very impressive. But I didn't think about how to verify it experimentally at all. I thought that it was only abstract theory - an abstract idea. But this consideration that to the hv of Planck belonged also an "h" times momentum was so convincing. And then came a letter from Davisson. He sent me a letter with some photographs of deflection experiments of electrons by Nickel, I think, as far as I remember. And there were diagrams which showed anomalous maxima in different directions. And I looked at it, and I thought, well, that's not very remarkable such a crystalline lattice, and in different directions there are different forces so why shouldn't there be such anomalies. I showed it then a week later to Franck, and I told Franck about this letter from Einstein. And Franck became very worried and said, "Now I don't believe these are just responses from different forces. Don't you remember what you have told me about de Broglie's paper which you learned of from Einstein?" And then he sat 'down and combined these things, and he said, "Well I should like to try." And we had hours of discussion on how one could find a simple criterion, and then at last quite simply we hit on the idea of the connection between momentum and reciprocal wave length. And I made quite a rough estimate in my mind and said to Franck, "It seems to be in the right order of magnitude."Then give it one of your boys,"he said. I said, "I have none now; we are all busy." And then Franck came to me the next day and said, "Oh, I have one I want to get rid of, and he's the right man for it." That was Elsasser He was an experimentalist, but Franck was always exasperated about his inability to tackle simple experimental things. And so he wanted to shift him to me. I didn't know him, but when he came to me, I found him a very nice and attractive fellow and very clever. So I suggested to him this problem. And I said I had quite a crude estimate and thought it might be right and that he would have great success if this was right. And in a very short time, he got this result. It was, I think, the first experimental verification of de Broglie.
How had you known Davisson previously?
He had visited us sometimes in Goettingen.
I would like now to pick up with the time in 1925 presumably in July, when you first read the Heisenberg paper, and then ask you whether you would tell us as much from that point on as you could. The first of my questions would be about the mathematics in those papers and how much of it you then did for yourself?
I certainly did no mathematics particularly for this work. I knew matrix mechanic because I had attended a very excellent lecture on linear algebra by Rosanes in Breslau. He was a pupil of Frobenius who was much better known. Of course, he did these group theoretical things about algebra. And there I knew what matrices were, and I had tried them before in physics several times. i.e. I remember — it was when Mie developed his non-linear electrodynamics. He had said somewhere (about the) conservation laws of his very general field equations, but it was a very complicated way when he did it. And then I gave a quite short derivation by several matrices. I took the electromagnetic field in the Minkowskian way but transferring to Mie's generalization. And I had several other occasions to use it but I never looked up any book at this time. And if I quoted books and literature it was certainly only a kind of politeness, but I had not necessarily looked it up. I read of course in Courant's book later, but I never studied it carefully.
But you had discussions with Courant?
About these things? No, certainly not.
The mathematicians then at Gottingen never entered actively in this development?
No, only indirectly. I was always in touch with them and learned a lot when I was younger from Hilbert and Minkowski, but at that time I was not a pupil and I couldn't see them very often.
So that they really knew of tins work only after it appeared.
Yes. And then I think even at that time Courant didn't care very much.
Hilbert was always interested in mathematics and theoretics. And, you had a seminar with Hilbert.
— Yes, but not at that time. It was earlier. And Bocher I must have mentioned only by accident, for I can't remember anything of Bocher.
Was it a book that you owned do you know?
When I left England and came here I wanted to build a house. I needed money, so I sold my whole very large library which was sitting in my department in Edinburgh to the University of MaryIand — which was said to be a very modern one, and a progressive one. They paid me a very decent sum for it, much more than it would have brought in England. And there it must be. I also decided not to do any physics any more, and I sold all of my very nice collection of separate prints. And I sold a lot of manuscripts and all kinds of things.
Those are kept together at the University of Maryland?
Yes. It was quite a good collection — in quantum mechanics it must have been pretty complete. I have still one box which is very complete. This was much later when I made this theory of electrodynamics and non-linear electrodynamics with Infeld. The first two years I collected all papers written about it. And I have them still. I haven't given them away because I thought there might come out of it something new, but it didn't.
The notion that figures so very large in the first paper is that of taking the derivative with respect to a matrix and of the matrix as an independent variable, not as something in whose elements time may figure.
Perhaps the suggestion to do it came from me, but the way of doing it with the help of these commutators that was Jordan, I am quite sure. Jordan was very good in this formalism. The first thing was we derived the matrices with respect to (number), time, which we did in two ways. In the first paper we did it in a very complicated way because we thought (there was some danger). Then when Heisenberg joined us we saw that it could be done much easier. And the paper with Heisenberg it's done in a very simple way.
This was taking the time derivative as a commutator that you mean now?
No, it was simply to take the usual definition — take a matrix, whose elements are functions of time, at "t" and at "t" plus tau. Divide by tau and go to the limit. That was the whole definition — the second one. In the first one we had fine definitions; it was quite unnecessary.
I would have said that the change was not in the derivative with respect to time, which you do quite simply in the first paper, but is in the definition of the derivative of a matrix with respect to a matrix. You permute the product cyclically and either drop the whole term or drop out of it only the thing with respect to which you are taking a derivative. And you then prove a quite elaborate and unfamiliar theorem. But this whole way of dealing with this problem is new, I think.
No, this was certainly mainly an invention of Jordan's. Perhaps I helped, but I have the feeling that doing such things was not in my line. But what I think was the connection in the end of seeing that the derivative of a function of p and q with respect to p was the commutator of f with q — I think this was my idea, but I'm not sure; you must ask Jordan about that.
Of course I shall ask him, but partly because I think one cannot hope to learn it, and partly because from the long run point of view that sort of attribution is not the stuff of which history is made, the question for me doesn't even need to include which of you did it. Rather I would be more interested in hearing how did the need to do it at all come about. How did you feel about this rather strange sort of calculation which one then calls the derivative of a matrix with respect to a matrix?
It was quite straight forward. We knew Heisenberg's paper, and he treated his symbols just like numbers and wrote down for the (specification of oscillator) the equations of motions. Now if you write the equations of motions, you are led to the idea that you have also Hamilton's equations. And there it appears — the Hamiltonian derived with respect to q and p. That was the idea we had — to imitate these matrices.
In Heisenberg's formulation the Hamiltonian never appears, and he takes the equation in a Newtonian form. It would not necessarily be a precondition on quantum mechanics that it would have to go into the Hamiltonian form. One might have handled it in a Newtonian form.
I was convinced it must be Hamiltonian because you see I had written this book on mechanics completely from the Hamiltonian standpoint and I was convinced that the best way to present all the central mechanical laws was the Hamiltonian form.
So you think that from a very early point you tried to put this to practice?
I would say also that the phase integral — integral pdq — gave a strong weight to the Hamiltonian formulation. Its canonical invariance — you especially in the book—
Yes, I had based the whole mechanics on the Hamiltonian and on the canonical transformation, and I thought that came so close to quantum mechanics seen from Bohr's theory. I thought that the real quantum mechanics must keep this formalism. But in my book on these American lectures I had given up all this already, and there is the simple definition which can be proved in a few lines by showing that it is correct for the sum of the product. And the commutator is defined, and there is nothing difficult.
Already in the next paper — that you and Heisenberg and Jordan do together much of that transition has already occurred. At the very beginning of this paper you offer two alternate definitions of the derivative of a matrix with respect to a matrix and then you use neither of them. You go on from that point to do the thing in terms of commutator brackets. And that whole thing drops out again.
In my book I have never seen that it drops out — I have never used it at all. Perhaps we did it because we write it here, formally, in the newer way of doing it as a differential coefficient. And we want to use this as a theorem and not as a definition. And in the book I use it already as a definition, that's the difference.
Do you have any sense now of how those transitions came about?
Yes, we discussed it every morning. Jordan came to me and we talked a few hours, but how the progress was, I don' t know. I remember only that I insisted on a certain simplicity, and Jordan had an inclination to make things algebraically involved, as he always does. I didn' t want that; we had some little fighting about that. And Heisenberg was even more in my line. He wanted to have everything very very simple, but he wasn't there, and we had to correspond. But the point that interested me very much was the one which van der Waerden found out. I had always believed that the development of the perturbation theory went in the following way. All of us put the problem, and Heisenberg wrote us letter with the formalism. And meanwhile, before this letter came, we had already found this transformation of a matrix into another coordinate system S' = U-1SU. And then I looked at Heisenberg' s paper and thought that' s pure nonsense — it's so complicated when he has only to develop S into a power series in regard to a given function. And we did this and it came out beautifully. And so I was in the belief all the time that Heisenberg's suggestion was wrong. Now Van der Waerden has gone into it very carefully and has used letters which were found in Pauli's papers after his death. He has used letters from Heisenberg and also a few from me I think. It turned out that Heisenberg's thing was completely correct. He had only attacked it from a different angle. His formulae were completely right — they look very complicated if you write them out directly instead of saying you develop this simple transformation formula in a power series. You write it down, and his second order approximation looks already rather complicated. And this Heisenberg had written down in a round-about way. So there I was in error; I had believed that Heisenberg had been wrong, but he wasn't wrong, he had only made it very complicated.
In working with Jordan, and also later, you say you came together every morning?
Yes, with Jordan certainly for weeks and weeks every morning. Heisenberg was away, but when he came back we did the same. And then I went in the middle of August to Switzerland and came back at the end of September, and then we collaborated again. First Jordan and I and then perhaps two or three weeks later Heisenberg appeared. And then it appeared that it was almost finished.
How did you work that closely then? Did you in the afternoons go about other things, or did you work further alone on these problems and come back and prepare results?
I don't know how it was. I certainly did a lot of other things. When Heisenberg came it was a little hectic, for I had to leave on the 2nd of November for America, and I wanted to have it finished when I left. And Heisenberg was also very keen on it, and so we worked very hard. But in this paper we divided our competences. I took the chapter on perturbation theory and the Hilbert space. Heisenberg and Jordan did the angular momentum things; I hardly took any part in that. I checked it, but I didn' t work on it. And the writing down of it we did also in parts, and then we put it together like a puzzle. And I think the style is essentially mine, for they were very young, and they weren' t accustomed to writing papers. [A discussion of the fact that the step — on p. 571 — from time independent to time dependent perturbations, which is achieved by adding the term h/zπi ds/dt , is not an "einfache Ueberlegung" but really an extrapolation is here omitted. Professor Born cannot recall the situation and suggests that Heisenberg be consulted.]
You say that the treatment in terms of quadratic forms in the three man paper was in the section that you worked on yourself. Had the notion of using quadratic forms been there from the start? This is in a way a deeper mode of treatment of the problem that you had previously treated by the more straight forward matrix treatment.
Well, I think I had a faint recollection that to consider a matrix as operating on a vertical column was not familiar to Heisenberg and not quite familiar to Jordan, but I think it must have been familiar to Jordan, but it didn't occur to him. But it occurred to me at once, and I wanted to know what this function S means. Therefore, I wrote it down and tried it out and found that it gives the same perturbation theory as the other one. It gives exactly the same only with another (way). What interested me at once was what does this function — what did, I call it, it was — what does it mean. This occupied my mind all the time. I saw that if one could find out the meaning of this, one could come to a real understanding of the whole thing. And this was one of the steps which led me to the statistical interpretation. But much later. I couldn't do anything with this discrete method, but then when Schroedinger came, I saw that the same thing goes continuously. Heisenberg insisted all the time that he knew what it meant physically because he said that the square the matrix element is the transition probability. And I still think, and there are other papers about it, that this can be taken as the starting point. Lande has now something like that. He says one can build all of quantum mechanics on this. Well I wasn't satisfied then with that because why just take the q? The q' s themselves were not the transition probability. You had to multiply them by the charge to get the polarization. Why not take the p or any combination of them. There must be behind it some general principle, and I was looking for that all the time.
Were you looking for it already in the period when these matrix mechanics were developed?
That is difficult to answer. I think I had it in mind. If you compare this formula here [in a paper he is showing to Prof. Kuhn] with the formula in my paper about the adiabatican variance, then I knew already then that the X2 were transition probabilities. It came out there problematically, and therefore I must have had it in mind here already, but I can't promise you that that is true.
Was there much discussion about these problems? The formula you have just pointed to is the transformation theory formula in the Hermitian form.
I remember darkly that Heisenberg and Jordan both were not interested very much in this chapter and left it to me. Heisenberg checked everfthing, but he had not a deep interest in it. And this was the point then where we diverged. I had a much quicker way of assimilating Schrodinger than he, I think. And I remember darkly that he wrote me a letter after my first paper on collisions saying, "You have deserted our camp; you have gone over to the enemy Schrodinger." He was very unhappy, and only when I sent him a letter mentioning the paper of Dirac where he did the same as I and practically at the same time, then he came over.
From what point have you discussed the following: In Heisenberg's paper there were ("Gesamtheiten") which were multiplied and added. In your paper with Jordan there were matrices, and you give calculation rules for matrices. And then a matrix is something which stands before a column. And there must have been a problem. If I have understood you correctly only you have thought of the question "what does the column mean." This column was afterward the Schrodinger function, but not at that time. Have you discussed this with Heisenberg?
At times I remember that he was, rather negative. He didnt like to discuss this — it was not in his line. He stuck to the argument that qmn2 means probability of the transition. And to take one column (without an) index he disliked. He said probability as such has no meaning and, you must give one state and then give a probability of going to another — therefore, you have two indices and the matrix elements are the only things that have a meaning. I said, "No you may leave this initial (state) completely indistinct and consider this vector —
Which afterwards is called the (state) vector.
Yes, but I'm sure I didn't speak about this in any clear way. I couldn't make myself understood at all. I only had the feeling that from this moment on in the question of interpretation we went in different ways. And I saw quicker that with the help of the wave function of Schrödinger one could make the demonstration that it is so. This was also a deception, for in this case what I did with the collisions was only asymptotic behavior; and this is not the same.
At the time that you put in that section on the relation to Hermitian quadratic forms you seem to find this the deeper treatment. At that time, no, I didn't think it was the deeper.
Well, what is it that leads you to put this in? Is this simply to show another way of doing it?
The proper calculations with the matrices seemed to me rather artificial and complicated, while this went straight forward with only algebra.
That leads me to wonder how early you can have seen the possibility of doing it this way. If you had seen that at the very start, you and Jordan might yourselves have gone ahead and done it, this was the first time.
You see with such things one is first clinging to the things which the other one has done. We were entirely in Heisenberg's footpath. Yes, that opened the thing, there's no doubt. He had the idea that one should take matrices — though we didn't know they were matrices. Symbols which behaved non-commuting and imitate the formalism of ordinary mechanics and would bring the laws of the transition probabilities — that was about his program. And when one has such a program it takes some effort to get rid of it. Though it seemed quite natural to me to represent the thing in this way, I didn't express it as a particularly new way — it was just another way of representing the thing.
Had you known for a long time of the mathematics of quadratic forms?
Yes. I had had other experience with quadratic forms of an infinite number of variables and even tried here in this case to see whether these matrices fit in what we called — [Prof. Born goes to look for a book — train of thought is broken The book is (???) papers on integral equations. Born points out a paper in which (???) starts with integral equations goes to differential equations and ends up with quadratic forms of infinitely many variables. Born points out that this is one of the few books he still has and says that it is one he had really known very well.]
We have learned this from Courant.
Here the history of this thing is this: Hilbert tried to apply the ideas of algebra directly to integral equations instead of (???) integral. And he got into trouble with mathematic things — when it converged and so on. And then came (Erhard Schmidt). He has published only a very, few papers, but his thesis was considered the most brilliant paper for ten years in mathematics at Goettingen. He succeeded by adding a little sharper conversion condition to transfer the whole algebra to this infinite number of dimensions - and not going, out of the integral equations. He wrote everything in integral equations. And then Hubert transformed in back in discrete coordinates; this is here in the next paper. And this I know, and therefore I took it over into this here.
In reading over those papers of this group one of the things that is immensely striking is the particular examples that you give as illustrations of the method. It is, of course, obvious that you must have tried other examples, some of which did not respond.
We tried, of course, the hydrogen atom and couldn't, but Pauli could.
The particular illustrations seem more arbitrary than they can really have been. You must have tried some other things. It was stupid that we couldn't do the hydrogen atom — it was straight forward. In my book I have it already. The lecture was given in November or December — just after this. At that time I knew Pauli's work already — from letters, I think. I don't think I knew the paper — it wasn't published yet, but he had that in it. I remember that Heisenberg was also quite angry with himself that he hadn't done it. There is a very nice letter of Heisenberg to Pauli congratulating him.
What other sorts of problems were there. Did you try aperiodic problems?
Yes, we tried very much, but we couldn't. As long as we were together we were too busy with writing this, and then I went to America. And in America the first thing I did was to find someone with whom to collaborate. And there came Norbert Wiener. I said to him that we must do the same thing for aperiodic motions. And he told me we should try this operator calculus of his. And we did it, but we never succeeding in doing more than the straight line motion, and that wasn't much. It was so clumsy. We had not the differential calculus. That was awfully silly of us.
But from the start you were looking for a way to handle the aperiodic motions?
Yes. You see in this three-man paper there is a section about it. Now really a new term came when Schrödinger's paper appeared. It first bewildered me. I saw that integral equations and algebra are parallel, but that differential equations of this type should also be the same was quite surprising, and I couldn't quite understand. So I wrote Pauli. And Pauli in about two little pages explained to me how and what the connection was, the definition of the matrix by integral f.
Well, that was Pauli's approach.
Well, of course, I knew it too, but Pauli wrote it to me — only just this one formula or two, and, then I saw how it was and could reconstruct it.
But you thought at the very beginning that there must be some such connection?
No, I was quite bewildered. I didn't understand that there are two different ways of treating the hydrogen atom that are both getting the same result and seem to have no connection. I was quite happy when Pauli explained it to me, and then about a week or two later, Schrödinger's paper appeared about the same connection.
When did you hear of Schrodinger's work — before publication?
No. There was also Dirac. Dirac also exists. Our paper was sent in I think in November, and then I went to America and left Boston at the end of January to go on a lecture trip over the continent. And the day before I left there appeared a parcel of papers by Dirac, whose name I had never heard. And this contained exactly the same as was to be in our paper. In turning it in we were about four weeks earlier than him, but not in publication. And I was absolutely astonished. Never have I been so astonished in my life; that a completely unknown and apparently young man could write such a perfect paper. But I didn't know who he was. Only a half a year later, when I came to England, I met him. And then I came home to Göttingen, and a short time later I got the first paper of Schrödinger.
How were other people struck by the Schrodinger paper?
Well, I must admit that it made much more of an impression than ours, much more. It was as though ours didn't exist at all. All the people said now we have the real quantum mechanics! Even after Schrodinger showed that his method and ours were equivalent they neglected ours completely. Only Dirac saw and insisted on the equivalence of both, and through him slowly the opinion changed. But all together we were rather disappointed that Schroedinger had gotten ahead of us so much. It was clear that it was a very new method that he had used, and it was quite forgotten that his analytical methods were only a translation into infinite variables from the algebra. So, I think, even now Schrödinger' s method is the one which is preferred by most people.
It's your own feeling that the Schrodinger papers from the very beginning met a very warm reception.
Yes, at once.
Was this true also at Gottingen?
No, Heisenberg was already away — Heisenberg disliked Schrodinger's paper at first. He wrote me this abusing letter saying that I use in my coilision theory functions instead of using only transition probabilities. And this I remember quite clearly. But Dirac's papers were always parallel to ours, and it was very difficult to see what I should do next, because I didn't know what the others were doing.
What people were even aware of the matrix mechanics? What sorts of reactions did you have?
I have also a very faint recollection - I remember one case — that was the Russian (Frenkel), who was a very clever fellow, wrote me a letter and called it crazy. He thought it was an insane thing, and he was completely against it. But Fock came to work with me the next term because he was quite attracted by it. So there were quite different reactions. There came a lot of people from America and from Russia and from Italy and it was a terrible strain for me at that time. It was very quickly going like that — that the younger people took it over and made it so complicated that I couldn't follow it any more.
But there was a very short time between your first notice of the Schrödinger equation and your first paper where you used it. You sent in June '26, your paper on collision processes. You use the Schroedinger equation in that. You were aware that the Schroedinger equation was fit for Solving such collision problems, and you give the probability explanation of Ψ. That must have been only two months.
Yes, because I knew the integral papers. I knew the connections already. As soon as I grasped Pauli's letter on the connection between a matrix ana a function, I could work with it because I knew the whole apparatus. I worked on these collision problems at first quite alone. But on this other adiabatic method, which I think was just as convincing, I took a system which was explicitly depending on time — that means an external force acting on it — and calculated then with this perturbation method the probability of transitions. I was mainly interested in what happened if the rate of change in time was very very slow. How could the probabilities go to zero as they ought to — what would happen? For the system doesn't remain unchanged — it changes (then continuously) in quite a different way. And I was going into that perhaps more than it deserved. I lost a lot of time. And I think I (???).
They come out very close together.
Yes. And this was very hard work. There were these many Americans there and there was Oppenheimer to whom I gave a paper as a thesis for his doctor's degree. It was a complicated paper and he did it very well.
So quickly after the Schrödinger paper comes out you have a program for something to do with it. And in particular there are these two problems you immediately put it to and the other underlying problem of interpretation. That draws you to the collision problem in particular?
It was right from the beginning, even when I started with Wiener in MIT. I wanted to use quantum mechanics to calculate collisions because that would give the only way of experimenting with these things. The spectroscopic methods give only terms, energies, nothing more. If you want to show the series right you must get the transition probabilities from one state to another. And the direct way of measuring is by collisions. Even excitation of light in an atom means collision. So this was very early in my program. I couldn't until Schroedinger's paper came out and I saw that was the right thing.
This problem is closely tied to your interpretation of the Schroedinger equation. How did those two get tied together? One would like to know about the collisions quite independent from the interpretation.
I knew quite early Rutherford's collision formula where he calculated the probability of finding an alpha particle deflected on an atom by averaging. And it was quite clear that one could now try this with waves. The collision must be a scattering of waves. And then this would give the proof of the Ψ2 assumption. I first went quite wrong, because I thought one had to calculate the Ψ2 as the density of particles in a volume, but one had to calculate the flow of particles through a cross section. Then one has to calculate first the continuity equations for energy momentum. And I think I first made a mistake, and I have always believed that in vfv paper which I published this mistake is contained — until somebody a few weeks age showed to me that it is quite correct in my paper. I must have recollected it in the last moment. You see when you get the density of something and you know it must satisfy the continuity equation you have at once also the current. And what you need for scattering is the current. If you can prove the current is correct then it means also that the density is correct.
From the very beginning of that paper you express the concern with what is the Ψ function. Was that in your mind from the beginning as you worked on the paper, or did you try to solve the collision problem and then begin to get the interpretation?
No, first the interpretation. I had that in my mind at once. There must be somewhere the correspondence between Schrödinger and myself. We were in a rather acrimonious debate about this. He believed Ψ2 meant some continuous matter. And I was very opposed to it — simply because every day I saw Franck and these people counting particles and not measuring continuous distributions. And I couldn't believe something like that was right. But he was very offensive — as he always was when somebody objected to him. It never disturbed our friendship, but there was a violent discussion between us.
That started even before the appearance of your own paper?
Oh, yes. I suggested that it must be presented in this way, and he objected at once. And then I told him I would show him by calculating thern probability of a collision. Then I wrote my first paper. Then after that I gave it to Elsasser who worked, it out numerically, but only approximately. And then I thought one could perhaps work it out for the hydrogen atom in a closed form. And this I did in two papers. And a very funny thing happened. I did them quite alone — long calculations — and I gave it to Oppenheimer to cheek it, and he came back and said to me, "It's completely right; have you done this alone?" They all knew that I never made calculations which were correct And so he was very surprised, but he was the only one who was Frank enough to express it. And about the same paper I had later another experience which was not funny. I was already I think in Cambridge, and there appeared a paper by Bethe where he saw that there was a connection between the scattering of electrons by fixed force fields of nuclei and about the scattering of X-rays by the same field. It was the form factor. He published this paper, and I wrote him a nice letter, and said that it was beautiful and that he got my results oh so much simpler and so much clearer. And he wrote to me an offensive letter saying, "Oh, that's so simple you ought to be ashamed not to have found it yourself." And I thought this must be a rude fellow. Later I met him, and he wasn't a rude fellow at all, he was only just letting himself go. I met him about three years ago the last time I visited my college in Cambridge; he was half a year a guest of the college.
Having looked through a lot of your papers in the last few weeks, the interpretive element which shows up so clearly from the first collision paper on seems quite new. Did you yourself have this feeling that in dealing with the problems of interpretation you were doing things which were in a new range of interest?
Yes, I think I was very much worried because it was so new to me. I always liked to do optics, and I knew there were complicated papers about the scattering of optic waves with the help of spherical functions — Sommerfeld and these people — and the developments with respect to Bessel functions, and so on. And this was too mathematical for me; I never followed this properly. The different behavior of the Bessel function at infinity — I always mixed it up and couldn't do it. And there I certainly saw that if I was to do it properly, I had to do it with this method; but I felt that I couldn't. And therefore I invented this approximation method, which they all call after me, and this I was very angry about. There appeared then many years later the book of Mott and Massey on collisions. And in this book they don't mention that the whole problem of treating collisions by the Ψ functions was done by myself. They just give the theory, and then they introduce "the Born approximation." And that made me very angry, for they missed the main point and took one which for me was only a flight from the difficulties of the regular treatment which they did.
This helps me a great deal, but it does not quite answer the question that I meant to raise, which was about the problem of the physical significance of the Ψ function. That is a more philosophical concern than you have previously allowed yourself to express in writing, is it not?
No. There were a few remarks in Einstein's papers that one ought to consider the electromagnetic wave as a probability wave for photons. They are not very explicit, but they are there in several papers of his.
Had you taken those seriously?
I had discussed this with him very often. He said that as long as there was nothing better one can do it. You know he didn't believe in these probabilities; he wanted everything deterministic. So we considered this only as an expression of our lack of knowledge, and nothing in principle. Therefore, he wrote about it very little. But it stuck in my mind, for I couldn't reconcile photons with electromagnetic theory in any other way. So I was accustomed to this although I never spoke about it. Perhaps I mentioned it in my optics lecture once or twice. As soon as I had the v function at once I saw that it was not the solution — that something connected with the Ψ2 must be the probability. Just as in the photon case. Now the question was only to find out the proof of it, and this took me some time and some thinking.
It came together nicely with your previous concern with scattering.
No, the (scattering) came afterwards. This I had in mind already — as soon as it appeared in Schrodinger's paper. I had it at once in mind, I think. And I wrote about it to Schrodinger, and it made him furious, for he didn't want that. Then I wrote to him, "I want to show it to you." I considered the possibilities for showing it, and I think the first thing was this adiabatic external force consideration.
In practice they come out in the other order, though very close together. That really makes very good sense and helps me a great deal if actually the first one on which you began —
But it made much more difficulty for me, because I didn't know the methods to treat the integral equations like they appear there. Perhaps I did the collisions first because collisions were the main problem in the Franck Institute in Göttingen. And everywhere we heard nothing but collisions of the first and second kind, and I thought that perhaps I could help there a little. That may be the reason. You might ask Fock, perhaps he would remember.
The paper with Fock is actually two years later than your own first paper on that problem. from that first paper in the summer of 1926 on collision processes and the interpretation one of your functions in physics is to document and argue this question of the statistical interpretation; you are being one of the few philosophers of the new movement. You had not been so philosophical before.
I haven't expressed it, but I was always interested in the philosophy.
What sort of discussions or unpublished attempts lie behind this beautiful work that begins in 1926 to '28 to '30 on the interpretation?
Well, I think I have told you all about it. I didn't consider it very philosophical. I thought giving up the description in space and time and, replacing it by the symbolic description was much deeper and much more philosophical. And to find a way of expressing it in simple terms — the probability — seemed to me not so very important.
Perhaps the expression "philosophical" is not quite correct in this matter because numbers of particles is a physical quantity and not a philosophical one.
We were so accustomed to making statistical considerations and to shift it one layer deeper seemed to us not so very important. And I was very much opposed to philosophizing. And I can tell you one story. There appeared at this time Fritz London, who was an excellent physicist in Goettingen. And he wanted to work on philosophy for his thesis — the philosophy of the new quantum mechanics. And I said, "No, my fellow. You must do real work — calculations — Work out a special problem. Before that I wouldn' t give you any such question, even if I knew one." And he was quite intolerable and insisted on having such a fundamental problem — the other didn't interest him. I tried to persuade him and Franck tried and although he seemed like a nice kind of fellow, we couldn't do anything with him. And since I knew no way, I wrote to Sommerfeld to see whether he would like to take him, for I knew that Sommerfeld had much more interest in young people than I had. And so I sent him to Sommerfeld, and Sommerfeld put him right. He persuaded him by the force of his personality to do a very simple and straight forward calculation. I don't know what it was, but he got his thesis and he never became a philosopher again. We were not very philosophical, and we disliked many letters from philosophers and theologians which we got.
Has there been in your recollection of that day a connection between the older attempts to solve aperiodic motions as a test for quantum theory and the collision problem? Before '25 I thought you almost were convinced that solving aperiodic motions would be a (???) for any quantum theory.
Well, yes, we were aware that to understand quantum theory one had first to solve aperiodic motions. But I think that we weren't aware earlier.
Yes, there is the paper with Jordan, but that is more general and not specified.
Wasn't there also a paper with Franck on molecules?
Yes. But that also may be some reason for the quick development of that application of the Schroedinger equation.
And in the summer I was terribly tired and I was invited to go to Cambridge to give a lecture there. And there I said in the lecture that a really urgent problem in calculating collision problems was the scattering of alpha particles — the Rutherford formula. And I sketched the method how it could be done. I mean the formulae were all there; I had only to put in the Coulomb law, but this was divergent, so I suggested to take an exponential factor to cut it off and to put a limit. And I remember that I said it there. And then I came home and I got a paper by Wentzel who had done it. So this was also on my program, but he was quicker. Then there came later a paper which did it without the approximation, correctly. And this I have never understood; it's so complicated with mathematics. [He cannot remember who wrote it]
Schrodinger, I take it, was never happy to the end of his life with the statistical interpretation. Did you continue yourself during the war in England when you saw him —
Oh, we had terrible discussions. I was his guest several times, and we had terrible discussions, but he never believed it. And I have had awful letters from him. He was always opposed to these things. But this is the problem which you should better answer. There were Einstein and Planck and Laue and Schrodinger and Pauli all the founders of the new theory who didn't believe in the modern aspect — why? What is the difference between their kind of mind and Bohr and myself? We are the only old fellows who took up the new line.
It is remarkable to me how very quickly this point of view was taken by the profession as a whole. But I don't really know in any detail how that happened. Was it already clear by the time of the Como conference in 1927? What sort of argument and discussion was there at Como?
No. There was no discussion. I gave my lecture — it was an awfully stupid meeting. I gave a lecture and then there was a formal discussion. Somebody said how beautiful the lecture was, and then it was finished. And it was so dull that one day in the morning at 10 o'clock I left the meeting and met Rutherford and (Aston) going out. We three decided it was unbearable and we wanted to go on a trip on Lake Como. We took a taxi and drove around the lake. We had a lovely day together, and this was for me a very important trip, for it was the way I came to England when I had to leave Germany. Rutherford and I became great friends at this (time.) No, there was no discussion of these things.
There must have been corridor discussion though.
Well, I found that this was assumed by the whole body of physicists and practically never mentioned that it came from Goettingen, but it was taken as an absolute given. And only a few outsiders didn't believe it. Only in the latest four or five years, since I got my Nobel Prize, one has remembered that it came from our department.
But you cannot really think then of an intermediate period before it was taken for granted in which people who were not lonely hold-outs argued about this matter
No. Can you?
There was a discussion at the Solvay Conference. Heisenberg was there and I think also (Gerlach) but not Schrodinger — he was invited, but he didn't come.
I was only once at the Solvay Conference and that was in '28. And Heisenberg was there and I think Schroedinger and also Bohr and Einstein. And I gave a lecture on these transition probabilities. There was a cool reception — there was no excitment about it. Yes, Heisenberg gave his uncertainty rule at that time in '28. It was already a year old. And there was a violent discussion about that, but not on the interpretation of the v function.
How about the uncertainty principle itself which is so closely related?
That is also a rather funny story. Heisenberg you know worked with me in Gottingen, but he was at the same time doing a thesis in Munich on hydrodynamics. Then he had to go in the Spring of 1926 to Munich to have his orals. He said he would come back for the summer term in April, but he appeared four months earlier and was suddenly standing in my study. And I said, "what are you doing here; I'm glad to see you." And he said, "Oh, I am so depressed." And then be told me that he almost had failed on his oral examinations because Prof. Wien had a notice that Heisenberg didn't do his experiments properly, and he had asked him all kinds of experimental questions. He came also with the question of the resolving power of an optical instrument, and Heisenberg couldn't answer it. So Wien decided he should not let him pass at all, though he had a most brilliant thesis. But Sommerfeld fought with all his power against it, so he got his degree, but with a very low grade. And someone was giving a little party in his house and had invited people, and Heisenberg appeared there a moment and excused himself, went to the phone, packed his trunk, and took the night train to Goettingen to find consolation in my arms. And there he was, and he asked me whether I would still like to work with him after the debacle. And I said I would, and I asked him what it had been that he hadn't known. And he gave me several points, but the main point was this power of resolution of a grating, or something like that. Now the funny thing is that that is exactly his uncertainty rule for the resolving power of an optical instrument, is wave length times momentum. Then I told him to learn it properly, and this was just in the right moment. And he learned it and he applied it. There was another case, and that was Delbruck. He was also a very brilliant fellow, and he wrote a very good thesis — this was later, it must be '28. or '29. But when he came to the orals Pohl objected to his answers on experimental questions and insisted on his having failed. I wasn't powerful enough like Sommerfeld to bring him through, and so he did fail. And this fellow was so depressed that I feared he would commit suicide. So I took him home because I didn't want to leave him alone in town. And my wife then told him how silly it was, and she set him right. And we told him that it doesn't depend on such official things — he should be quite content that his Professor was content with him. And a half year later he got his degree. And now he is one of the leading men in America in genetics — he left physics. He was fed up with it, rightly.
You mention, Sir, in your autobiography that people did not take very seriously the final section of the Born-Jordan paper — the electrodynamics section. Was it about that in particular that Frenkel wrote you?
Yes, it was this in particular that Frenkel disliked so much. The general quantum mechanics he accepted.
That itself disappears also in the next paper — the Born-Heisenberg-Jordan paper. There is here no attempt at field quantization. Had you tried something in between?
I hadn't no. I can' t remember how it was. I didn't work in that line at all. But I think it was like this — there came Dirac' s paper — he did it much better — he derived also the spontaneous emission.
But not that quickly. Not between the first and second papers. That is actual February, 1927. The real radiation scattering paper is Proc. of the Royal Soc. received February 2nd, 1927.