Werner Heisenberg - Session VI

[Before the recorder was turned on, Kuhn showed Heisenberg a long letter from Pauli, in Copenhagen, to Sommerfeld, dated 6 June 1923.]

Heisenberg:

Yes, that's most interesting. ... Well, he reminded me actually by this letter of many discussions which we had. I think that is a very correct statement. Also that one found more and more reasons not to believe classical mechanics. I mean in some way, of course, one had always known that classical mechanics can't work, but now one finds better reasons for it.

Kuhn:

What about this remark in the letter that sounds so much like the Bohr-Kramers-Slater paper. Do you remember any talks with Pauli about that?

Heisenberg:

This comparison of the electronic orbits with oscillators —?

Kuhn:

Well, really it's not just the orbits but I think it is the Fourier components which are to be compared with oscillators.

Heisenberg:

Well, I could not say that I do remember definite discussions about this, but again it belongs to those ideas which come up in discussions and then one forgets about it again. And after all, the Correspondence Principle is already an expression of this idea.

Kuhn:

Well, it hadn't been always an expression of that.

Heisenberg:

Well, I mean that one said that there are the actual frequencies of the lines, and these frequencies of the lines correspond to Fourier components. Now a Fourier component is not something in itself. It is actually just a part of a motion. So the motion is not one Fourier component; the motion is a total of all Fourier components. And then also a Fourier component is not only a frequency, it is also an amplitude. So this amplitude must have some meaning. How could it happen that the frequency has a meaning if the amplitude has no meaning? And actually the amplitude does have a meaning as one sees from these intensity calculations of Bohr. So in this way it was always in the background, but it was not in the full light of consciousness of the people. It just was in the background, and occasionally one took it up again and talked about it. It is quite possible that we had many discussions about these points. I don't remember many discussions on these things, but certainly it was in our minds and gradually developed as a topic.

Kuhn:

When I talked with Professor Gerlach yesterday, he said something which clearly referred back to certain of the problems that you and I had discussed before about the differences between Bohr and Sommerfeld's attitude toward the Zeeman effect. On the other hand, what he said went almost the reverse of what I would have expected. Furthermore, the documentation for it is very good because he had the letter that he wrote to Edgar Meyer, part of which was written the day they finished the equipment and part of which was written the next day when they got their first result. And therefore what he said to me subsequently, he also says in the letter, and it's probably right. And I was somewhat surprised by it. I wonder whether you could illuminate the issue. Apparently, they felt they knew, that Bohr believed they would get a separation of the beams, and that Sommerfeld felt they would not. Sommerfeld thought they would simply get a continuous spreading out, and this letter, which begins on one day and then is continued the next day, draws a picture of their first result, which is not a separation of the beam, but is a spreading of the beam, and says, therefore, Sommerfeld is right. And when Gerlach succeeded in improving the apparatus while Stern was at Rostock, he got a splitting. He just sent the following wire: "Bohr is right."

Heisenberg:

Ja, ja. That's interesting.

Kuhn:

Now it's hard —. It's not hard for me to see that Bohr —. I mean, after all, there is to be a real magnetic field. There can be space quantization with a real magnetic field. It's not like your problem. But that Sommerfeld should not expect —.

Heisenberg:

Yes, that is very strange. That I just can't understand. It's entirely new to me, and I can't understand it because Sommerfeld wrote in his book long chapters about space quantization. He loved space quantization. Well, as a general rule of quantization, you can say a set axis is nothing real, but in this case one had a set axis by means of the magnetic field, so that could not possibly be the problem. That's very strange.

Kuhn:

Well, we will let it go, but as I say, it gave considerable surprise to me that actually with the magnetic field.

Heisenberg:

And he mentioned in the letter that Sommerfeld is right?

Kuhn:

Sommerfeld is right, and when they got the other result they wired Stern, "Bohr is right."

Heisenberg:

Very interesting. Yes, but this statement, "Sommerfeld is right," is almost in flat contradiction to what he writes in his books, because in his books he writes about space quantization and he explains the normal Zeeman effect, of course, just in that way. Normal or anomalous Zeeman effect — whatever — in both cases he uses this interpretation. Why should he say that it is washed out? Well, perhaps he thought simply of trivial perturbations — perturbations by collisions or something. He might have thought it was too difficult to separate just for experimental reasons. I don't know. That could be the problem.

Kuhn:

Probably not.

Heisenberg:

No, because from the letter and from these telegrams it sounds as if it was an issue of principle or something like that.

Kuhn:

Now Gerlach does quote Debye as having said, "Oh, stop worrying about this problem. This whole thing is just a calculation device. There's no real reality in it, you're just wasting your time." But that's not necessarily speaking for Sommerfeld.

Heisenberg:

No, and also I wouldn't believe that even Debye would take it that way because Debye very soon found an explanation of the Compton effect which certainly makes use of the light quanta. Well, the idea of having just a calculation device is an idea which had been discussed. That's quite true, because the contradictions were too heavy. And so one said, "Well, we don't mean it too seriously, but still one does mean it so seriously that one does calculate the Zeeman effect, and so the levels are there as tools of calculation and why should they be different from the Franck-Hertz level?" That's very funny. Well, that's a complete surprise to me, I don't recall that. Does Gerlach remember having talked to Sommerfeld about it?

Kuhn:

He's not clear where this idea came from, but he's perfectly clear that they had it. In their own minds, the issue of what would come out was whether they would get Bohr's result or whether they would get Sommerfeld's result.

Heisenberg:

Very strange. I certainly never found in any letters —. There are my letters to Pauli — they exist, you know. And I don't think that I ever mentioned this possibility in these letters. I looked through the letters when I got them from Franca Pauli. I don't think that I ever found any remark in that direction. Well, I mean when this Stern-Gerlach experiment came out, everybody was very happy to see that now quantum theory is so well-established. There had always been doubts as to how well established it is, since it was in contradiction to classical theory, wave theory and so on. One always doubted, "Well, will it actually come out that way, or will it not." And in so far, such a fixation of an experimental result was always a very agreeable statement; but still, I don't see why Sommerfeld should or would have expected a continuous distribution. I just don't know.

Kuhn:

How many people — you refer to this in that paper with Born — were deeply upset. I mean the Einstein-Ehrenfest arguments that somehow this effect just can't exist. Would that have been a problem for you people at Gottingen? Or at Munich or at Copenhagen? Did you worry about the Stern-Gerlach experiment much? Or did you just take it as telling you the answer?

Heisenberg:

Well, there was the following trouble: Assuming that we have this space quantization, then we can understand that an atom in a magnetic field has a certain number of positions. But then still we can make preparations, and by means of these preparations, it must be possible to turn the atom continuously from one position. That means we have more than just one position. Now this was, of course, a clear contradiction, because either there are only three possibilities or there are continual possibilities. And, of course, everybody worried about it: what does it actually mean? What does one say when one says there are only three directions, and why just the three directions in a magnetic field? Let's have the one magnetic field vanishing, then we have no magnetic field. And then we have a new magnetic field oblique to the first one — what happens then? Does the atom turn around suddenly, and why does it turn around suddenly, and all that kind of thing. So this was disagreeable, and I would say at this time one started the kind of argument which later on — I think it came out most nicely in the introduction to Dirac's book of quantum mechanics — took the form of one saying, "Let's assume we have polarized light and we put this polarized light on a Nicol prism in an oblique direction. What happens to the light quanta? Then, of course, the light has to decide whether it is this polarization or that polarization. This atom has to decide whether it will become parallel or perpendicular to the magnetic field." This idea of a decision by the atom occurred already in these discussions on the Stern-Gerlach effect because one had always a contradiction between the continuous space distribution and the discontinuous states.

Kuhn:

Where would you say this sort of conversation was going on? Everywhere, or Gottingen?

Heisenberg:

Certainly at Gottingen, Munich and Copenhagen, I should say. It did play a great role in these discussions which Bohr and I had on the resonance fluorescence of sodium. I think Bohr even shortly before I published this paper on the resonance fluorescence wrote a short note to Nature or to Naturwissenschaften. I don't recall the contents of the paper. I think that this paper must contain some of our worries concerning the continuous change of direction in space.

Kuhn:

It relates in particular, I think, to degeneracy.

Heisenberg:

Yes, it's always a problem of the degeneracy. Yes, that was the way it was stated in Bohr's language. The degeneracy with respect to direction — what does this degeneracy actually mean when I change from one magnetic field to another magnetic field or from one polarization to another polarization? So it was a kind of surprise to Bohr and Kramers that one could use this space quantization in such a strict way as I had tried in the resonance fluorescence, because I said that I will just assume a magnetic field in a direction which I think is convenient, which pleases me. And apparently this did work and that showed that one could play with these magnetic fields in a reasonable way, and could use the concept of space quantization even in a situation where there was really no magnetic field.

Kuhn:

In that same paper with the resonance fluorescence problem, you also talk about a variety of other things with which one might be able to do the same sort of stunt. Particularly you talk about the Ornstein-Burger-Dorgelo work. You say on the one hand that we've got to take this seriously, and we ought to rebuild the Correspondence Principle to make it give these results. Then you point out, quite properly, that that's a terribly naive way to keep quantum mechanics, and that although there is really no contradiction between the principle of spectroscopic stability and space quantization, it isn't really coming out, the way you'd expect it to come out.

Heisenberg:

You mean not expect it to come out from what?

Kuhn:

Well, Sommerfeld often, always with appropriate provisos, had suggested that all the magnetic states are of equal weight. Now, if you do that, you don't get spectroscopic stability.

Heisenberg:

Oh, ja, ja, ja.

Kuhn:

You certainly don't have to make that assumption. But on the other hand, it's a terribly, terribly natural assumption to make. What you have in these various papers coming from Utrecht is something that really you're quite right in pointing out is pretty naive stuff, yet you take it terribly seriously. I wondered how did others feel about it? Do you remember those papers?

Heisenberg:

Yes, I remember those papers. I don't know why other people shouldn't take it equally seriously because, first of all, the experiments were quite good, and, one saw what happens there. And then also, at that time one was already accustomed to always finding contradictions and nobody believed anymore that these things could be made consistent. In such a state where contradictions are something quite normal. Then you must have other criteria to judge whether a thing is good or not. These other criteria must be based on the question, "Does it look reasonable," or something like that. And these measurements of Ornstein and others did look reasonable; in some way they made sense. Now one couldn't rationalize this sense yet, one couldn't exactly say what kind of sense it made, but it did make sense and that was perhaps the best criteria which one had at that time. I think that is perhaps a very general characteristic feature of the physics of that time. People were accustomed to things having contradictions. All right, if you have physics full of contradiction what criteria have you to believe something is correct or not? So the only criteria was — does it make sense? Does it look reasonable or so? So that was then the strength of these experiments of the whole Dutch group of Ornstein. It did make sense.

Kuhn:

Was Bohr also a good deal impressed by this?

Heisenberg:

Well, yes, he was certainly interested in these intensity ratios and I think just this paper on the fluorescence was also, of course, by this interest. Actually, he had started thinking about the resonance fluorescence, and he had written this short note. He had written the note I think mainly to avoid the worst inconsistencies and contradictions. He was so worried about what came out that he wanted to give some kind of interpretation and at least to see how one could possibly avoid the worst disagreements. I came to it with an entirely different intention; I just wanted to see if one could not, by using reason, calculate intensities just by having some sense in the whole thing. And since the Ornstein experiment did make sense in some way, I felt that one would be able to use this kind of consistency to predict something about intensities, polarization.

Kuhn:

Before getting into the papers, if it's agreeable with you, what I'd like to ask you to do is to tell me now about Copenhagen in a general way. I'm afraid if we start on the papers, we'll never get back. I want terribly to hear about how you got there. Here I have a letter from the summer of '23 which speaks about the possibility of your coming to Copenhagen, presumably in the fall, and it's the next year, actually, that you go.

Heisenberg:

Well, I think I had been to Copenhagen already in the spring of '23, but only for a few weeks. I was invited by Bohr just for a short visit, so far as I can recall. But then I was invited to come for a longer period from Gottingen to Copenhagen. First, I think it was a kind, of Rockefeller fellowship and on that money I could come to Copenhagen for half a year. That was then the winter term of '24 and '25. That was the time I wrote this dispersion paper together with Kramers. Then I went back to Gottingen. I came then in a permanent position to Copenhagen in the spring of '26 when Kramers had left for Holland.

Kuhn:

You were then there on that fellowship for only one semester?

Heisenberg:

I think only for one term. Because in the summer term of '25 I definitely had been back in Gottingen to give lectures there. I already was privatdozent, so I had to give lectures — I was expected to, and so on.

Kuhn:

When were you habilitiert?

Heisenberg:

That was in the summer '24.

Kuhn:

Before you went to Copenhagen.

Heisenberg:

Before I went to Copenhagen. So actually things happened like this. I was in Gottingen until the end of the summer term of '24, and I think I became privatdozent there in July '24. And then after the holiday, the summer holidays, I went to Copenhagen for one term on a Rockefeller money. I came back from Copenhagen around Easter, and then gave my lectures in Gottingen. It may even be that I had been back from Copenhagen somewhat earlier, perhaps in March, or so. Because I remember one thing. It's very difficult to find. I remember that I spoke with Born about the paper of Kramers and myself on the dispersion. We had a long conversation, not only about this dispersion, but the connection with Ornstein-Burger-Dorgelo intensities, and with this paper of Sommerfeld and myself on the angles. I told Born, "Well, one has such an impression that one could almost guess now all the intensities if one only did it well enough. So I will now try to work on the hydrogen atom and find out the intensities just by guessing." Namely, the idea was that I would make very careful calculations on the classical intensities, on the Fourier components of a Kepler ellipse. And then I tried to change these classical formulas into quantum theoretical formulas by, say, replacing L² everywhere by L times L + 1, and, of course, using all kinds of connections between amplitudes which I could guess. And so that was it. Born said, "That is a good idea, you try that. Then you probably want to know something about the classical Fourier components; there you need Bessel functions." And so he handed me a book in which I could learn the Bessel functions. Now, I would have said that this conversation with Born must have taken part already rather early in '25, perhaps in March, or so. But it may be that I just came back from Copenhagen in March. I don't know.

Kuhn:

That paper never came out.

Heisenberg:

No. Well, the point was that from this moment I actually did work on quantum mechanics straight away, because when I had studied the classical intensities of the Kepler ellipse, I very soon found out that it was too complicated to guess the intensities. And then I found — that was the point — that if I knew the Fourier series of, say, a coordinate x, I wanted also to know the Fourier series of x². And so I studied more generally the question of the connection between the Fourier series of x and that of x², or that of x and y and that of x times y. And that was, of course, already practically matrix mechanics. Then I went from the hydrogen back to a problem where I could do the thing by just multiplying in a simple way so that besides x, I only needed x² and x³ and not more. The simplest example was the an harmonic oscillator and thereby I came to the an harmonic oscillator in quantum mechanics. You will find in the first paper on the an harmonic oscillator in quantum mechanics also a statement that it was (at fault) if one knew x also to know x² or x times y and that kind of thing. So that was really the point. But this point came out from my attempts to work straight on the hydrogen atom and since these attempts had failed, I went to the more general question of what I could do about multiplication of these Fourier series. But that was all much later. You asked me about Copenhagen, so we should go back to Copenhagen. Of course, when one comes into a new place, the first thing one realizes is that the style of work is somewhat different from the style in other places. I would say that the style with Bohr was clearly this: Bohr was more worried than anybody else about the inconsistencies of quantum theory. So he always tried really to understand what is behind all these difficulties. I should say that neither Sommerfeld nor Born had been so much worried about these things. Sommerfeld was quite happy when he could apply nice complex integrals as good mathematics and he didn't worry too much whether that was consistent or not. And Born, in a different way, was interested also in mathematical problems, mostly mathematical problems. Inconsistencies were realized, but, after all, I would say that neither Born nor Sommerfeld really suffered from the inconsistencies. But Bohr really suffered from it, and Bohr couldn't talk anything else. Whenever one went for a walk out with Bohr — sometimes I was invited to his country house and went for long walks with him — he would always discuss these difficulties and what one could do about it, and how it actually was, and all these things. He in some way directly suffered from this impossibility to penetrate into this very "unanschaulich", unreasonable behavior of nature. So my strongest impression of these first months in Copenhagen were the discussions with Bohr, where I really came to see how terrible the situation was. I realized how unavoidable these contradictions seemed to be. I realized how difficult it was to reconcile the one experiment with the other ones. I think already at that time it started that one spoke in terms of "Gedanken-experiment." One had a certain contradiction; then one tried to avoid the contradiction; then one saw that this was "ausladen", was not really a solution. Then one said, "All right, perhaps in this experiment it actually works such. But now lets think of the following experiment." Then one would find the experiment to force nature to decide the most disagreeable question, and so from this time on, one always talked in terms of "Gedanken-experiments." Sometimes these"Gedanken-experiments" could be translated into real experiments, but the first point was to put nature into a situation where it has a very disagreeable decision to make. Therefore, to get into the spirit of quantum theory, was, I would say, only possible in Copenhagen at that time. Of course, in other places one did speak about these things, but one was not so much worried about these inconsistencies. But that was Bohr's whole philosophical attitude — he was a man who really wanted always to go to the last degree of clarity. He would never stop before the end. Most other physicists are inclined to stop somewhere and say, "All right, we have it." For instance, Schrodinger. Pauli called it "osterreichische Schlamperei." Schrodinger would say, "Well, after all, don't worry." But Bohr would never do it that way. Bohr would follow the thing out to the very end, just to the point where he was just at the wall. You know, when you hit the wall. You can't do anything, you couldn't solve it at that time. But I had very soon the impression that there was nobody who had thought so deeply about the problems of quantum theory as Niels Bohr. That, of course, made a strong impression. Also personally, I liked Bohr very much. We became very good friends and we did many things together out in the country. It was an entirely new life. I should say that Bohr did not talk so much to the students as Sommerfeld did. It was only more occasionally that he would come into the library to ask about something or be quite excited about a new situation. But when discussions took place they were mostly, I would say, very critical discussions on a special point which had to be solved; one should try his best to solve. And I told you already about this discussion about the resonance fluorescence. It was quite typical for this kind of thing. Bohr and Kramers would have probably talked already several hours about the thing to come into it. Then one would take the thing up again and again. The style was one of extreme "Sorgfalt", extreme care. For instance, when Bohr wrote a paper, usually he used to dictate the paper to me.

Kuhn:

Did he do that in your first term or did he then work with Kramers only?

Heisenberg:

I wonder. That's quite interesting. That is difficult to know because I know that I had to write very many letters for Bohr, and papers for Bohr. He would walk around in the room and dictate, and I would try to put it down on paper. I think it was already in that time; I would say yes. When writing a paper, Bohr would always change the sentence again and again. He could have filled half a page with a few sentences and then everything was crossed out and changed again. And even when the whole paper was almost finished — say, ten pages or so — the next day everything would be changed over again. So it was a continuous process of improvement, change and discussions with others. So this extreme care in formulating a paper was quite new to me. Certainly, it was quite different from how Born or Sommerfeld would write. Sommerfeld would first discuss all the essential parts of the paper and then he would just write it down. Of course, I would be allowed to make remarks and perhaps to suggest improvements but it was written once and that was all. With Bohr it was written, I should say, ten times and always changed again and again.

Kuhn:

Were those changes generally useful changes? That sort of thing can be useful up to a point, and then with some people it gets to be, I suppose one wants to say, neurotic. There no longer continues to be a real point in making further changes. Now, I've got no notion how that worked out with Bohr.

Heisenberg:

I would say that there you must distinguish whether you mean useful for the others or useful for Bohr. If you ask useful for the others, namely for the readers of the paper, there I have some doubts. The final text of Bohr's paper was so subtle and he would think about half an hour whether in a certain case he would use the Indikativ or the konjunktiv and so on. The reader would just read over it and would not realize how much work was put into it. But for Bohr himself, that was quite different, because writing a paper was a process in which he could clarify his own mind. I think for himself it was extremely important to make these changes and thereby to get deeper and deeper into the problem. So in that sense I think it was useful but probably not for the reader. I have found that many people have said, "Well, the papers of Bohr are very difficult to read. They are so heavy; one doesn't know what he really means." I remember once Dirac made a remark which surprised me and I couldn't understand it. He said, "Well, Bohr could have become a poet." "Why a poet?" "Well, he just takes so much trouble with the language and he always improves the language. He really is born as a poet. He should have written poetry." And that was a somewhat surprising remark because Bohr has certainly never attempted to write poetry, I'm sure. He has not.

Kuhn:

He read poetry.

Heisenberg:

Oh yes, he liked poetry. He had a very strong connection to language. That is quite true. Quite contrary to Schrodinger, who actually has written poetry, Bohr has never written any poetry.

Kuhn:

I have never known anywhere anyone who has had to write, as I gathered Bohr did, with somebody, dictating, giving everything to somebody else, not writing himself. That apparently goes way, way back to the college. His thesis was done by his mother and the prize essay was done by the family. ... I gather he always needed to work with people.

Heisenberg:

Yes, he wanted the conversation with the other one, the criticism of the other one. He would always in between ask, "Well, does one understand? Well, how do you understand?" And then, when I said something, he would say, "No, but that was not exactly what I meant. Could you suggest a better word at this point? This word doesn't express exactly what I mean. You understand I mean that and that." Yes, he would walk forth and back. No, he could never sit alone in his room and write a paper. That was not the way he could do physics.

Kuhn:

Have you known anybody else who was like that?

Heisenberg:

Oh, no, no. Oh, he was quite unusual in that way. Probably his enormous influence on all the younger generation of physicists comes also from this property, from this habit of doing things with others.

Kuhn:

I wasn't sure whether I read this remark of Pauli correctly, but I gathered that by implication there was some feeling in here that working with Bohr took such a lot of time away from one's own work that it created a special problem.

Heisenberg:

Well, maybe he meant that. It is certainly true that one had to spend very much time with Bohr working with him. Well, I must say that I never felt that I should mind this. On the contrary, I felt it was extremely agreeable to have this conversation and thereby to clarify my own mind. After having written a paper or letter for Bohr I had always the impression that this time was by no means wasted. It was just the contrary: I felt that now I had learned something which I could use for my own work. And in some way I never felt that I had too little time for my own work. I always found the time.

Kuhn:

When you were there for the longer period, in '25, '26, how much time per day do you suppose you spent with Bohr?

Heisenberg:

Well, I should say, usually he would come in the morning to my room and say, "Couldn't we write a few letters?" And he would dictate letters, and then he would perhaps also be involved in a paper and he would say, "Could we not try to get a bit further in the paper?" And so we would sit together perhaps two or three hours. But then in the afternoon I would mostly be free. I used to either eat my meals with Mrs. Maar or just make a few eggs myself in my own room upstairs. And, I would say, after eight or nine o'clock in the evening, Bohr, all of a sudden, would come up to my room and say, "Heisenberg, what do you think about this problem?" And then he would start talking and talking and quite frequently we went on till, twelve or one o'clock at night. Or, sometimes, he would call me to his flat near the institute — at that time he stayed at this flat there — and finally at one o'clock at night we would feel that we were tired and would take a glass of port wine and then would go to bed. So it was very irregular. There was no rule about it. I mean Bohr never was a man who had definite habits. To the contrary, everything was irregular — it depended on whether there were visitors to the institute, whether lectures had to be given and so on. But still, it was a considerable time we spent together every day.

Kuhn:

And that really is more time than you had spent with him in the previous time.

Heisenberg:

Yes, I should say yes. Then, also, I had to give lectures. That did make quite considerable work for me because I had to give them in Danish. So I had to brush up my Danish at that time. It was some work to give lectures in a language which you really didn't know too well.

Kuhn:

This was the second time you were there?

Heisenberg:

This was the second.

Kuhn:

Perhaps even the third time since you think you were there for a week or so in 1923.

Heisenberg:

Oh yes, in that sense, the third time, yes.

Kuhn:

Is there anything that is likely to be helpful to pin down some of these dates? We're getting now into exactly that area when the whole question of when you could have talked to whom in Gottingen or in Copenhagen or in Munich becomes really quite important. And I wondered whether there is anything that might —

Heisenberg:

Well, I would say, if you look through the letters in Bohr's institute there might be a good chance that one might find something. ... But I would believe that I had been in Copenhagen, I would say March or April in '23, perhaps for one or two or three weeks.

Kuhn:

This is funny, because in this letter of Pauli, it says that Bohr has the fondest recollections of his talk with you at Gottingen in '22. It doesn't sound as if you've talked with him in the interim.

Heisenberg:

Yes, I was also surprised to see that. Again, it may be that I'm mistaken there, but still I feel that I have been in Copenhagen. The other date is quite clear. That is, I became privatdozent in Gottingen in the summer of '24. There's no doubt about that. That must have been July, '24. And then I came to Copenhagen after the summer vacation. So that is fixed. I would believe that I was there in '23. I'm thinking it might have been autumn '23. Bohr used to invite people in September. In some ways, September is a good month to go to Copenhagen. It's not quite impossible that this was September '23. Could you not, in Copenhagen, look through the old letters? There must be letters. It seems all these letters are kept in the —.

Kuhn:

Yes, I think it's very likely that we can find out the answers to this there. But it sometimes happens if you ask a question like this, it turns out that someone has saved all the little pocket notebooks in which you find all the appointments that he ever had, and if you can get that —.

Heisenberg:

No, unfortunately, I have never had any pocket notebook. I should have had one.

Kuhn:

What can you tell me about Hans Kramers? This is the great big problem — that whole period from the time Kramers joins Bohr. Also Kramers himself. This is really terribly important.

Heisenberg:

Well, I must say that Kramers was, besides Bohr, the man who made the strongest impression on me in Copenhagen from the very beginning, and in an entirely different way from Niels Bohr. I must say, in some way, it was a mixture of extreme admiration and some criticism because Kramers was clearly much less serious than Bohr. I mean Bohr was terribly worried and he was always in a state of despair about quantum theory and so on. It was quite different with Kramers. He was always very gay and a very nice fellow. What I admired is that he knew, in general, things in life so very much more than I could ever hope to know. First of all, he spoke Dutch, Danish, German, he spoke French, he spoke English. All these languages came out from him just as if they had been his mother tongue. Then he played piano, he played cello; both he did very well. Since I was interested in music, I did play music with Kramers.

Kuhn:

What was your instrument?

Heisenberg:

Well, when we played together, it was usually that he played cello and I played the piano. I simply said, "Well, how can a man know so much?" I had great difficulty in learning my poor English and my poor Danish and before that time I just knew German. I would play just one instrument fairly well — that was the piano — nothing else. And I said, "Well, how can a man learn all these things?" And then at the same time he was always very gay, always very amusing. He could entertain the whole party when we were invited to Mrs. Bohr's. So in some way I thought, "Well, that is far beyond anything I could ever try to reach." And at the same time, I was always a bit angry about his way of taking things not so seriously as Bohr and making jokes when I didn't want to have any jokes made, and so on.

Kuhn:

Do you remember what sort of jokes?

Heisenberg:

Oh, just very nice jokes about physics. Certainly never any indecent jokes; that was quite far out of the question. He was always a perfect gentleman in every way; he was too much of a gentleman. That was the point, you know. In some way he was the type of a man which was far above my own reach and at the same time a type which was a bit strange to me. And it took some time until I really became friends with Kramers. I must say that later on I liked Kramers very, very much. Then everything was quite simple. But in the very beginning —. Well, perhaps also I felt too much that I knew so much less than he did. I don't know what it was. So it was certainly entirely my fault, because later on I liked him very much, and thought he was a very nice fellow, and everything went on excellently between us. But to begin with I had some difficulty, but I would say mostly from my enormous admiration of Kramers. He was a very unusual figure. He was also a good sportsman and he could walk for many hours. He could talk in any language about problems. But with respect to physics, I found it still easier to talk with Bohr because, with Bohr, one got into the real desperate problems, into those dreadful difficulties. I mean Kramers wouldn't take these difficulties so seriously as Bohr did. But I would say that Kramers did contribute enormously to the scientific life in Copenhagen. In some way, probably Kramers was the most important figure in this institute besides Bohr. Bohr hadn't too much time for the people, but Kramers had time to talk to the people. Everybody talked first to Kramers before they talked to Bohr. Kramers would listen to the ideas of these younger people and would criticize. So certainly Kramers had an enormous influence on the development of this institute.

Kuhn:

When you say that Bohr didn't have time to talk to the students, what was he doing? Physics?

Heisenberg:

Well, I would say administration. He had quite a lot of administration. He had many visitors and then writing letters. I would say the main point was that since it took him so much time to write even a single quite trivial letter, it's obvious that he couldn't find time for many other things. So he was always very much worried. He had difficulties in the institute. I remember once he had difficulties with the workshop just because two of the mechanics couldn't agree with each other — a very normal affair in an institute. It worried him terribly and it took him hours and days to smooth the thing out. That kind of problem. So I think he was taken up by rather much administration work, also for, building new parts of the institute. As I said, writing letters took him more time than most other people and in this way it was difficult for him to do physics. But he actually did physics also in writing the letters. Yes, he would ask me to help him in writing a letter, say, to Fowler in Cambridge. And then, of course, in writing the letter the whole problem would be clarified and he would discuss the problem with me. So it was this mixture of physics and administration.

Kuhn:

What do you suppose Kramers' role in the development of complementarity and in the quantum theory of line spectra was?

Heisenberg:

Well, I would say that Kramers did offer an enormous help to the whole development just because of his physical strength. He was a man with an absolutely inexhaustible energy. He could work three days without sleep or anything. One has the impression there was simply an inexhaustible amount of energy available with Kramers. If Bohr would have Kramers try to calculate this and that, he would do it and he certainly would do it well. Just by the strength which came from Kramers he did play a very great role. I also feel that he really had very good ideas with the whole thing. His dispersion theory started from a physical idea, and he had hit on a very important point. This paper on the continuous X-ray spectrum also was a very essential paper. So I always regretted that Kramers never had, gotten the Nobel Prize because I would feel he certainly has deserved it if anybody has deserved it. The actual amount of contribution was very large and perhaps only it had not been seen so clearly because he always had been together with Bohr and, so far, was a bit dependent on Bohr. I don't know —. The ideas did come partly from Bohr. But still, Kramers had, an amount of force which was absolutely unique. I have never seen a man with this amount. Well, perhaps (Bethe) still, but (Bethe) was more of a quiet fellow. Kramers had so many other possibilities besides physics.

Kuhn:

When you say the dispersion formula started from a physical idea, do you have a particular thing in mind?

Heisenberg:

Well, I would say that his idea was that there was the Einstein paper and there was the Ladenburg paper connected with Einstein's. On the other hand, there was Bohr's Correspondence Principle and the idea that finally this has to do somehow with Fourier components as oscillators. Kramers had the force to combine these two possibilities in one simple formula — the dispersion formula. And this I think was a very important idea that one should combine the Einstein paper, which was very far from the Bohr model with the Bohr models. It was a very important idea. Behind this idea was already the idea of connecting the oscillators with the Fourier components, which, as I have said many times, was in the air somehow in these years.

Kuhn:

Were there still discussions of the Bohr-Kramers-Slater paper when you got to Copenhagen?

Heisenberg:

Well, I certainly have had many discussions about this paper. I think mostly with Kramers; perhaps even more than with Bohr. The general feeling at the time when I discussed it was that it seemed to be the only way out of avoiding the inconsistencies between waves and particles and therefore the non-conservation of energy seems to be unavoidable. At the same time, one doubted whether this was actually true. One had the impression, "Well, after all, these things are perhaps still deeper than we imagined and perhaps even nature can manage to conserve energy in spite of all that we have understood." So the paper was taken as something which was very natural and fitted into the general development and at the same time, the conclusion of the paper, that energy was conserved only statistically, was doubted. People thought, "Well, yes, it may be true. But that's dangerous. There you touch a thing which perhaps one shouldn't touch." So Pauli never liked this idea of statistical conservation. He said, "Well, that's too dangerous. There you try something which one shouldn't try." Much later, of course, the physicists recognized that the conservation laws and the group theoretical properties were the same. And therefore, if you touch the energy conservation, then it means that you touch the translation in time. And that, of course, nobody would have dared to touch. But at that time, this connection was not so clear. Well, it was apparently clear to Noether, but not for the average physicist. Also in Gottingen it was not clear. The Noether paper has been written in Gottingen, I understand. But it was not popular among the physicists, so I certainly wouldn't learn that from Born in Gottingen. By the way, do you recall when the Noether paper had been written? I think it must have been also around '23 or so.

Kuhn:

I've heard of that paper, but never looked at it.

Heisenberg:

One really ought to look up the paper. I'm sure that the paper itself did not play a large role for the development of quantum theory. It did play a role for the development of general relativity. It was actually formulated in connection with general relativity, which was an interest with (Hilbert's) group and therefore also Noether. But it did not penetrate into the circles of quantum theory, so I didn't realize the importance of that paper.

Kuhn:

When did you first begin to become conscious of the greater recognition of group theoretical properties within the field?

Heisenberg:

Well, actually after quantum mechanics. There was first the helium problem where one saw the two term systems. And then I tried to do a similar thing for molecules with three equal nuclei. There I realized that I had to do with a new group property. But I couldn't do it well, and then the paper of Wigner appeared, who really did the things well. I at once realized that Wigner had done a much better job than I had, and then I realized that the group theory was a very important part. So for some time then everybody learned group theory and representations — the papers of Schur, the books of Schur. But then there came the paper of Slater, who succeeded, more or less, to reduce everything to the Pauli principle. So one didn't need too much this detailed work of Schur. But still, I think from that time on everybody had realized how important group theory was, and that never has been lost since that time.

Kuhn:

Who else was in Copenhagen when you were there?

Heisenberg:

To begin with, I remember the following people: There was Oskar Klein, there was Urey, and Rosseland; I think also Dieke from Holland; then Kronig was there for some time; Pauli was there occasionally, but not regularly; Slater was there.

Kuhn:

Was Slater actually there while you were there or was he there before you were there?

Heisenberg:

No, I'm pretty sure that I have been there together with Slater. Whether he came when I was there or the other way around — that I don't know. But I certainly had conversations with Slater in the time I was in Copenhagen.

Kuhn:

Hevesy was there.

Heisenberg:

Of course, Hevesy, yes.

Kuhn:

And Moller.

Heisenberg:

Moller. Cristian Moller was there from the very beginning.

Kuhn:

Hoyt must have been there just before you were there.

Heisenberg:

Oh, I still have known Hoyt, yes, yes.

Kuhn:

Did you know Dennison?

Heisenberg:

Oh, yes, yes. I knew Dennison quite well. I remember many discussions with Dennison. That was in the period when we spoke about molecules. I think he did some work on the specific heat of the hydrogen molecule and he found out that there are two components of the hydrogen. Was it actually his work that showed one could have hydrogen in two forms, ortho and para? At least I remember many discussions with. Dennison on the specific heat question. Well, that was the time when I worked also on this group theory of molecules. I found it very interesting that one had non-combining term systems with no transitions from the one to the other. So I had many discussions with Dennison, yes, yes. He was a very good physicist. I haven't met him since that time, practically. Where does he live now?

Kuhn:

Michigan? Ann Arbor, I kind of think, but I'm not perfectly sure.

Heisenberg:

Do you meet him occasionally?

Kuhn:

I haven't met him, no. I trust that I will see him next year. I would like to talk with him also more briefly.

Heisenberg:

But that was a bit later, I. mean that was already the time —. Well, in this time when quantum mechanics developed, there I had many conversations with Foster from McGill. Foster lived also with Mrs. Maar, so I met him many times. We were together on the Stark effect on helium, I think. That was a very interesting period also. He had done excellent experiments on the Stark effect of helium, and then one could do the calculations by means of quantum mechanics and compare with the experiment. That was very exciting.

Kuhn:

I am somewhat surprised at what you told me about the fact that the students often did not see very much of Bohr.

Heisenberg:

Ja. Well, he would go around in the house, but in some way Bohr was always in a hurry. He was always in a state where somebody wanted to talk with him and couldn't talk to him or somebody was waiting at the door for seeing Niels Bohr. One had always the impression that Bohr was under some stress to fill all the duties he had in connection with the institute. I think he would talk to many students, to many of the young people, but no so regularly as Sommerfeld. You know, Sommerfeld was that type of man who had his special hours. His lecture was from nine to ten and between ten and one he would talk to the students. This was a fixed time, and he would not be disturbed by administration. If he had to do any work with administration, he had a fixed time for that — in the afternoon between five and six. One could be quite certain that he would dictate his letters between five and six and not at any other time. He had this kind of systematic use of the time. But that was not with Bohr. With him everything always went irregularly. So Bohr was always under some stress.

Kuhn:

Was it, nevertheless, a really exciting place to be for the students?

Heisenberg:

Yes, I would say that it was a very exciting place. For me, I would say it was more exciting than Munich or Gottingen.

Kuhn:

Even in your first trip, when you didn't see so much of Bohr?

Heisenberg:

Well, I did see enough of Bohr. I would have a conversation with Bohr and then I would have time to think about it and to talk to other people about it. I had discussions with Oskar Klein or with Rosseland or with Kramers. It was not so that the conversations were only rare occasions. No, that I couldn't say. But they were not so regular, not something you could count on. They just happened. In the later time when I was there as successor to Kramers, I think I have spoken to Bohr every day quite a number of times. He would also ask my advice in matters even of administration. Well, then there came all these kinds of letters you get from people who have invented something like the perpetuum mobile, and then one had to do something about it. I usually tried to induce Bohr to a more careless handling of many things of administration, because it's a pity if a man like Bohr wastes much time on these things. But even if one had to answer to a man who had invented a perpetuum mobile, Bohr would not be willing simply to write a short formal letter and say, "Well, I'm sorry that I have no time." Bohr would try to go into the problem and explain to the man what he thought. Of course, that shows a very nice side of his character. He wanted to be kind to the people, but in this way it was a bit difficult for him. Well, there was a story, I think I have only been in the story myself for a short time. There was a man who had invented a perpetuum mobile which worked by avoiding the second law of thermodynamics, somehow. And then, of course, there came the paper, and Bohr was obliged to write an answer. And then Bohr explained to him why it was wrong. This was simple, but I think either Klein or I, myself, suggested to Bohr that he not explain too much, because he would be sure to write a new paper, and a new letter, and Bohr would have the same trouble again. So the man actually did write a new letter and a new paper on a new machine which he had constructed, which was already more complicated than the first one. So it took considerably more time to find the mistake. Our advice was that one should simply not answer the letter, but Bohr didn't follow the advice. So out went the second letter explaining why it was wrong. And then, of course, there came a third letter from the man saying that he was extremely sorry to waste so much of Bohr's time, and he had completely understood what was wrong with the paper and was so grateful, but now he really had avoided the mistakes of the first two papers, and now he had found a scheme which certainly would work, and could Professor Bohr look into this, and so on. And. I think the story actually goes, but I cannot say that it's true, up to the seventh paper of this man. Only then did Bohr stop answering. I don't know whether that is true, but anyway there's no doubt that Bohr tried again and again to be kind to people of this kind.

Kuhn:

Did he ever say why he did it? Most people obviously would not do this. What was his sense of his role?

Heisenberg:

He could express pretty harsh criticism of people. But at the same time, he felt this man had tried seriously to do something, and one should take this effort seriously and that one should be kind to people of that kind. I think it was a deep human feeling that, well, the other fellow has insight into this world.

Kuhn:

He was wonderful.

Heisenberg:

Yes, he was wonderful. Yes; that's just one of his very, very great qualities.

Kuhn:

Let me then at least open up a topic which we will undoubtedly not get finished with this morning. While you were at Gottingen, before you go to Copenhagen [in the autumn of 1924], you were involved with Lande on the paper on the doubling of states. [Termstruktur des Multipletts hoherer Stufe" Zs. f. Phys. 25 (1924) pp 279-86, (Eing. 18 May 1924)]. Soon after that there is the paper on the alteration of the rules of quantum mechanics in the anomalous Zeeman effect in which you define an invariant which is an integral from j - ½ to j + ½, and then you substitute the difference equation for the differential. ("Abanderung der formalen Regeln, etc," Zs. f. Phys. 26 (1924) pp 291 -307, (Eing. 13 June 1924)]. Now at virtually the same time you're doing that paper, Born comes out with a paper called "Zur Quantenmechanik", ["Uber Quantenmechanik, Zs. f. Phys. 26 (1924) pp 379-95, (Eing. 13 June 1924)], which is submitted just about the same time and which refers to your paper. There're important similarities between them and there're certain similarities to the Kramers' formula also, to which you both refer. At least I know Born refers to it and I expect you do too. He's particularly concerned with using the Kramers' formula as a model. These papers get terribly elaborate; there's one a little later which I decided I could not read because I would have to read too many other papers before I could read it. On the other hand, it's also the paper that gets in deeper than almost anything else that I have run into. This is "Quantentheorie der Multiplettstruktur und der anomalen Zeemaneffekte" [Zs. f. Phys. 32 (1925) pp 841-60 (Copenhagen, 10 April 1925)]. This is the one where you try to show that there are all sorts of different ways of using non-mechanical "Zwang." There are several different models around, and some people double up the Rumpf, and some people double up the valence electron and some of these worked better some places than in others. You say one ought to be able to find a common denominator. And I don't think you do, particularly.

Heisenberg:

No, no. Certainly I don't. I would say that I do very well remember the general trend of these papers. Actually two things at that time are still mixed together which later on only became separated. One is this famous factor 2 — the doubling of the levels — which later on was known to be due to spin. Somehow we never really quite understood what happens. This factor 2 was there. And the other and entirely different thing, and which was for the future I think still more important, was this trend to change classical mechanics in such a way that you have to replace differential quotients by difference quotients. I tried to study classical mechanics very deeply and see how this mathematical scheme works and to see if I could not somehow get over to difference equations instead of differential equations. And that is the origin of this attempt to average between different states, and to make integrals, and then take the difference between the initial and final state, and all that kind of thing. Now clearly, from a later point of view, all these papers are more or less useless because they couldn't solve the problem, but as marking a tendency, I think they are quite useful because they show that that's the thing you have to do. And the pity was that the factor 2 of the electronic spin was mixed up with it because it had actually nothing whatsoever to do with it. It would have been a great relief if one had seen at once that this was an extra problem.

Kuhn:

But as it worked out, of course, it wasn't 'extra'. It's the central problem. More than anything else you are worrying about problems right there that are created by spin, aren't they? The anomalous Zeeman effect.

Heisenberg:

Yes. The Zeeman effect was created by spin but, for instance, the intensity rules and so on were not. They were only indirectly created by spin. So the rules of intensity could have been considered without speaking about electronic spin. But it could not be separated from it because there was a vector corresponding to the spin, and this vector had to be added or subtracted somehow. It was obvious that the two problems were entangled in each other, but still they were different problems from the physical point of view. Therefore, I would say this did delay the whole process of development. Kramers and I were extremely lucky in '24 that in our dispersion problem we could forget about the anomalous Zeeman effect. That was just so lucky that one did not have to do with these Clebsch-Gordon coefficients and the doubling of levels. We could say, "Let's speak about the reasonable model of atom which we have. There should be some dispersion of the atom and we will see how the dispersion will probably look." This unmechanische Zwang. Yes, it was a nuisance. He always disliked this factor 2. In Munich and in Gottingen one didn't worry too much about those things. Sommerfeld was quite happy in saying, "All right, we have two quantum numbers and in both cases we apply the Sommerfeld formula." And nobody could understand why one is justified to apply a formula when one introduces a new degree of freedom. It was absurd. But still, Sommerfeld wasn't too much worried about it. Nor was Born worried about it. Born knew there were some difficulties, but he felt, "All right, there are difficulties. Why not?" And it was only in Copenhagen that one was really worried about these things.

Kuhn:

Well now, clearly there were problems which Born, unlike Sommerfeld, took seriously. For example, the sort of trouble you two together demonstrate with the helium atom. That he does take seriously.

Heisenberg:

Yes, Born had realized that probably classical mechanics does not work for the atoms and we had to do something else. Also this tendency of replacing differential quotients by differences was very much favored by Born. I think I have heard Born say many times that one should try something in that direction. Also Born had suggested to me that I should listen to these lectures on difference equations rather than differential equations. So this was a tendency which was clearly represented in Born's mind. But Born was not too much worried about the anomalous Zeeman effect. It was a mathematical thing which appealed to Born's mathematical mind. Born felt that you should repair physics by introducing a new mathematical tool, namely the theory of difference equations. That would not occur to Bohr. Bohr would always say, "Well, first we have to understand how physics works. Only when we have completely understood what it is all, about can we then hope to represent it by mathematical schemes." But Born would argue the other way, and would say, "Well, perhaps some new mathematical tool is a decisive help in understanding physics."

Kuhn:

That was a fairly shrewd guess, wasn't it?

Heisenberg:

You mean "shrewd" in what sense?

Kuhn:

Well, that in the long run, a new mathematical tool did help.

Heisenberg:

Yes, it did actually help. I think generally Born is quite right in saying that without the new mathematical tool you can almost never hope to describe nature, because to describe nature means, finally, to describe it in terms of mathematics. Everything else is not precise, and you never know whether you have contradictions or not. But it is a question of how to get at it, and I would say both ways sometimes work. One can never hope to understand nature just by the mathematical tools if one has not gone into the real difficulties of the subject. After having gone through the difficulties and having a general notion of how things are connected, then you have a chance to do it by mathematical tools.

Kuhn:

Do you remember at all the relation of that first paper on the alteration of the quantum rules to the Born paper, "Uber Quantenmechanik"?

Heisenberg:

Yes, it is closely connected with this idea of having difference equations, and dispersion relation, and so on. Actually he, in some parts of the paper, repeats the arguments of Kramers and of myself.

Kuhn:

Well, that paper actually comes out or is at least submitted before your paper with Kramers. I think so.

Heisenberg:

Well, let me see. Yes, that's earlier than the paper of Kramers and myself, yes.

Kuhn:

Kramers' notes are already out and Born refers to these and says they are very important.

Heisenberg:

Yes. [Heisenberg reads in Born's paper.] That was, of course, the main point that one could combine Einstein's statistical theory with the Correspondence Principle. And so here he tried' something very much in the same direction as Kramers and I later did, only he didn't know about these extra frequencies — the Raman effect. But, besides the Raman effect, it was certainly just entirely in that direction and shows again this tendency of having differences instead of differential quotients.

Kuhn:

How did people in Copenhagen feel about that paper? How did they feel about your paper of '24, in which you introduce +this integral between j + ½ and j - ½, and also the sum rules?

Heisenberg:

Well, the general opinion, I would say, was this: One said, "Well, one must try in that direction and all these papers will probably contain some tools, but it's clear that these papers don't give the final solution. It's just something moving in the right direction. But the final solution must be deeper than that." So one just tried to get step by step more nearer to the final solution. In this way the papers were considered as some step forward, but it was clear that they did not contain the final solution.

Kuhn:

What is also striking is that that whole group of papers that appeared in '24 — the Bohr-Kramers-Slater paper, this paper of yours, the Born paper, and a number of others of the same sort, particularly on the question of the doubling of the states — could scarcely have been written two years earlier.

Heisenberg:

No, and also, I should say that one can scarcely imagine that such papers would be written now, for instance. Because if now people would write papers of that kind, everybody would say, "Well, that's quite unclear; that vague talk; that's of no use. The paper's certainly wrong. Why write it?" It is a rather unusual state in physics that people would dare to write papers of that kind. It was again this strange situation that everybody agreed by that time that physics did contain contradictions; not the real physics of the world, but the physics which was made in the institute did contain contradictions and it couldn't be helped. In such a situation, one is willing to take papers which only go somewhere in the right direction, even if they don't reach the goal. For instance, about this thing which I tried with the anomalous Zeeman effect in integrals — that shows that we may understand such terms as L(L+1). Apparently these terms are there, so we get better into the right region. It reminded me of the game which children play in which you hide something in the room and then the child walks around and you say, "There you are quite cold, now you're getting warmer and so on." And as soon as a paper got warmer, so to say, one had the impression that it was more satisfying. One would say, "All right, that's a help."

Kuhn:

Which of these papers did you think were warm?

Heisenberg:

Well, this paper of Born was pretty good. The Kramers' paper was good. The Born paper was the proof of Kramers'. Everybody had the impression, "Yes, yes, we must try in that direction." People could perhaps criticize, "Well, after all, it's not so much more than in Kramers' paper. Kramers did all the right things that did mean anything. But still, it definitely goes in the right direction." So I would say there is a clear progress, step by step, from the Ladenburg paper, the Kramers' paper, this paper of Born, then Kramers and my paper — every paper going a little bit further than the last one and a little bit further in the right direction. Everybody realized that was the right direction.

Kuhn:

There must have been some people who were terribly skeptical about this. For example, Sommerfeld, I would imagine, didn't like it a bit. Is that correct?

Heisenberg:

Yes. That is quite true for the following reason: Sommerfeld had for some time thought this was the solution to everything. At the time when one could calculate the Stark effect, then he thought, "Well, this is the solution, and now we know how to handle atoms." But when it came out, as in this letter from Pauli to Sommerfeld that all this was some kind of illusion — that it did just by chance work so well in the hydrogen — I mean it was a complete miracle that it did work so well in hydrogen — then Sommerfeld was in some way a bit disgusted. He didn't like it anymore. All this stuff was too complicated. He only liked it when it became clear mathematics again. Sommerfeld was a man who only liked clear mathematical schemes. So he liked the old classical mechanics even if it contained integral pdq because, in itself, an integral is clear enough. Then again, he liked quantum mechanics when it was quite clear. But this intermediate stage, where the paper could not possibly be clear, but where one had always to mix things which were clear with other things which were not at all clear — that he disliked. So he certainly didn't like this paper, and also I wouldn't believe that he liked much my paper with Kramers. But he had to agree that he couldn't do it any better. Of course, that he knew quite well. Still, Sommerfeld was much more interested in this development than many other physicists. People like Wien would just say, "Well, it is just all nonsense. Forget about it. Somebody must later on do the real physics, but it's all nonsense they talk." So a man like Wien would simply not take this seriously. He would say, "Well, all right, people write wrong papers, why should these papers be taken seriously?" But as you say, it is certainly true that Sommerfeld was least inclined to take part in this development. Born was inclined to do it because he was interested in the possibility of perhaps finding new mathematical tools.

Kuhn:

Did he talk about new mathematical tools?

Heisenberg:

Oh yes, he definitely would. We always spoke about how somebody must invent a new quantum mechanics. I think that was already a slogan which was discussed. Instead of saying quantum mechanics, we would say difference mechanics or discreet quantum theory, "discreet" meaning that only difference quotients would enter, and no differential quotients. Then nobody knew what was really discreet and what was not discreet because time could scarcely be discreet and space could scarcely be discreet. All this was unclear to the utmost, but still we spoke about this possibility of having a quantum mechanics. Therefore, also the term "quantum mechanics" means some new mechanics. I might just have a look at what Born said. [Reads in the paper]. Well, he starts with using this argument from the dispersion theory. So by that time this argument was a widespread argument which everybody knew. It had to do with this argument of Pauli about the Franck-Hertz experiment. Oh, I see here he quotes the paper of Bohr-Kramers-Slater, yes. About this paper of Bohr-Kramers-Slater — there I was not quite clear about Born's attitude. I felt once, when I discussed this matter with Born, that he was a bit angry that I had quoted too much the Bohr-Kramers-Slater paper in connection with the probability interpretation of waves. He felt that the probability interpretation of waves was really his paper on the collision problems. Well, I had always stated it in this way, and I think it's also quite fair: Born did get the correct interpretation of the quantum mechanics. That is, he knew that the Schrodinger waves were not real waves but they were probability waves and that these waves in configuration space, not in real space, had to be interpreted statistically, as probabilities. Still, I felt that the central step was made by Bohr-Kramers-Slater in the earlier paper in that sense that the waves got this strange kind of reality. The waves were something which was just in the middle between an actual reality and something which was only mathematics. And this intermediate position of waves, which were a physical reality in the sense that they produced probabilities for decay or emission, and, at the same time, were not completely real, were not completely real like the electromagnetic waves, that I found so extremely interesting and attractive.

Kuhn:

You did find that attractive?

Heisenberg:

I found it extremely attractive, because I found that this idea of having such intermediate kinds of reality was just the price which one had to pay for understanding quantum theory. By that time one knew that one had to pay a high price and you could not get any cheap solution. Cheap solutions could not be found. When I saw the papers of Bohr-Kramers-Slater, I had the impression that this was the kind of price that might be sufficient to get it. So I was a bit skeptical with the conservation of energy. There, everybody felt, "Well, that's very dangerous. You can get on the wrong track." But still, this idea of having the waves which were just not quite real, but almost real, that was the thing of the right kind. So I would again use the term, "It made sense to me." It sounded correct. I should also believe that when Born later on gave his statistical interpretation of the Schrodinger wave that he was also influenced by this paper of Bohr-Kramers-Slater which he quotes here at this point.

Kuhn:

It's interesting to me that in '24, in both Gottingen and Copenhagen, it is clear that people know the thing's all screwed up. This may not have been the feeling in Munich, but if you remember any conversations in Munich about this, I would like to hear them. The physicists are willing to take more drastic steps than they have ever been willing to take before. The contrast just with '23 is marked. Yet, they are not really going about it in the same way in Gottingen and Copenhagen. How would you describe that difference?

Heisenberg:

Well, the emphasis in Gottingen was more on the mathematical side, on the formal side, and in Copenhagen the emphasis was more on the philosophical side, I should say. This is true in the following sense: For Born, a description of physics would always be a mathematical description, so his attention was concentrated on the idea of how the mathematical scheme to describe these funny things which we see in our experiments would look. Bohr's approach in Copenhagen would be different. Bohr would ask, "Well, how can nature avoid contradictions? Now we know the wave picture, we know interference, we know the Compton effect, we know all that — how can our Lord possibly keep this world in order?" And so he wanted first to understand how contradictions are avoided, how things are connected, and he would say, "Well, only when we have sufficiently understood that, only then can we hope to put it into forms of mathematics. Of course, Kramers was, in some way, a man who could play on both instruments. Kramers understood perfectly well what Bohr said, and at the same time Kramers had perfect control of (Copenhagen) mathematical schemes, which Bohr had not. Therefore, Kramers could easily work both ways, and Kramers certainly had all these things more or less in mind which Born has in this paper. If Kramers and I had not written this other paper together, thus if the Smekal-Raman effect had not been found, then Kramers probably would have written a complicated paper on the dispersion theory which would contain many of these statements which are here in Born's paper. So Kramers would know both sides, but Bohr would always worry about the final inconsistencies of the whole thing. These inconsistencies were not even removed when the quantum mechanics was developed. In my first paper on quantum mechanics, and in Schrodinger's paper which had come out, it was clear at that time, also to Bohr, that this mathematical scheme, either quantum mechanics or wave mechanics, did lead to the right description. But Bohr was not satisfied before '27, before this uncertainty business came up. Bohr's worries were not easily satisfied by mathematical schemes because he would say, "Even the mathematical scheme does not help. I first want to understand how nature actually avoids contradictions." On the one hand, you see an electron moving in a cloud chamber, so there is something like an electronic orbit. You simply can see it. At the same time, there is the question, 'Is there an electronic orbit in the hydrogen atom or is there not?' The electron is there, there's no doubt, because it can come out. Does the electron move around? If yes, what is the frequency in that orbit? If no, why do you have the orbit in the cloud chamber? So these kind of worries were, for Bohr, of the most troublesome nature. He just didn't know what to say about it and was unhappy about it.

Kuhn:

You say that the problem of the photon was terribly on Bohr's mind, in '23 and '24., but it does not seem to have been very much on his mind before. Can you help me out on this?

Heisenberg:

Well, I could imagine that for some time Bohr was also induced to take the whole scheme more seriously than one should have, because of the enormous successes. There was the Stark effect and the Stark effect did contain so many details that it was really difficult, even for a very critical mind, to say that a theory which gives so many details still is fundamentally wrong. That probably was not even possible for a man like Bohr. So for some years he apparently believed that this integral pdq business would finally solve the problems. Of course, by doing his Periodic System, I think he changed his mind in two ways. One thing was that he did realize that essentially his models were a correct description of what happened. He could actually give some kind of understanding of the Periodic System. At the same time, he realized that classical mechanics didn't really work, as Pauli writes in these letters. Well, Bohr didn't have a real explanation of the closed shells, and he only could get pictures which sounded reasonable, but he didn't really understand. He couldn't really understand. Probably for Bohr, just through his work with. the Periodic System he developed that state of mind where he did start worrying about problems, but also perhaps that may have been in consequence of our discussions in Copenhagen and in Gottingen at these lectures. He did see that the whole theory, on the one hand, was extremely successful, and on the other hand, was fundamentally wrong. And that was a contradiction which is very difficult to bear, especially for a man who has formulated the theory. So he was in a continuous inner discussion about this problem. He always worried, "What has happened? Did I make a mistake? What could one change in the theory? It works so well here and still it contains contradictions." At a later time, he learned to remind one of his very first paper in which he actually pointed out the contradictions. I think in his very first paper he said that this theory was clearly very far away from the closed and harmonic state of the classical theory. Well, nature was not as simple, and one had to take it so. And he must have forgotten this statement in the later papers by the enormous success of the early part of the theory, especially in the Stark effect, and then only later on he got back into the worries.

Kuhn:

How were his relations with Born? Did he think well of Born's work? What were the relations generally between Copenhagen and Gottingen?

Heisenberg:

The relations were rather close. Bohr was glad that in Gottingen he had now a team of physicists interested in his work. He had to get people interested because most physicists at that time did different things — they did acoustics or hydrodynamics or whatever else — but they didn't worry about atomic physics. So he was glad that there was now a group of good people who could do something with him. Still this mathematical attitude in Gottingen didn't appeal to him too much. So I remember that he once criticized the book of Born — of Born and Jordan.

Kuhn:

The second one — the matrix mechanics.

Heisenberg:

Yes, matrix mechanics. Bohr said, "Well, under the hands of Born, everything gets so complicated." So for him, complicated mathematics was an unnecessary degree of complication which he disliked. However, he realized that these Gottingen mathematicians are very good and that he probably could profit very much for his own theory by this mathematical scheme. Born himself was quite a bit worried about the criticism which this Gottingen style received by Pauli and other physicists. Well, at his eightieth birthday Born quoted a letter from Pauli where Pauli was very angry about the Gottingen "Gelehrigkeit," the Gottingen "Formalismus." He was a bit even offended, I think, by this criticism, because after all, this formalism later on proved extremely useful. But there was definitely this difference in spirit that the Copenhagen people wanted first to understand physics, and then later see how much one can describe it by mathematical means. In Gottingen the idea was to find a good mathematical scheme, then you will understand physics by itself. I think the future has shown that the Gottingen people were not so wrong. After all it was extremely difficult to understand the real situation without the mathematical scheme.

Kuhn:

In some way, you could say the wave equation approach was a more physical approach. The matrix mechanics is surely a highly new mathematical approach.

Heisenberg:

Yes, wave mechanics was a more physical approach. Wave mechanics did actually start from entirely different physical ideas which only partly proved right. Yes, yes. Yes, that's quite true. I remember that when wave mechanics penetrated into Gottingen that it made a lot of excitement. I remember the following discussion. I was called to a room where Franck and Born were sitting together. Franck brought a new letter from Elsasser, I think. And Elsasser told about this idea that the de Broglie waves could actually be taken as waves which made interferences. It was an idea of Elsasser that you could explain, I think, the Ramsauer effect, or such things, by means of this interference.

Kuhn:

He also had the Davisson-Kunsman curves — the old curves.

Heisenberg:

I think this was rather early; I should say around '24. Did the Davisson-Kunsman curves already —?

Kuhn:

The Davisson-Germer curves did not exist yet. But the Davisson-Kunsman had existed I think since '22 or '23. And they weren't really sort of a set of maximums but they were odd enough so that it was possible to exclaim.

Heisenberg:

At least Franck, in this discussion, started to propagate this idea of having matter waves. Born, in some way, was very skeptical and said, "Well that's too odd. That's absurd that now the electron which we can see in a cloud chamber, is to be a wave — what do you mean by that?" Then, of course, the discussion came to the Compton effect where we see that same kind of absurdity — we had to have light quanta as well as the waves. Everybody was pretty upset after this discussion. Nobody dared to have definite opinions. Everybody said, "Well, maybe there's some truth in it — what does it all mean?"

Kuhn:

Had the paper of Elsasser actually been published at this point or were they looking at it to see whether it should be published from Gottingen?

Heisenberg:

Well, I would say that it was before it was published. Elsasser had suggested the paper and Franck was now worried about [whether or not it should be published, whether or not it was sensible, whether or not it was absurd.] Then, of course, we knew about the de Broglie paper — no, the Einstein paper. It was the Einstein paper which came first. Was it Einstein first or de Broglie?

Kuhn:

Well, it's a little hard to date. The second of the Einstein papers mentions de Broglie and it is from the second of the Einstein papers that Elsasser picked up the references to de Broglie. Einstein had seen an unpublished copy of the thesis. Well, by the time Elsasser got out he was able to get hold of the thesis itself, presumably in the Annales de Physique.

Heisenberg:

At least this discussion was definitely the first time that I realized that wave mechanics could be a reality, that there could be some real physics behind the interference of matter waves. It made a deep impression on me so that I even now know exactly in which room in Gottingen the conversation took place. It was quite nice and when we had Born's eightieth birthday, we actually did go to this room and then we said, "Well, here is where we discussed that thing with Franck and Elsasser."

Kuhn:

See that paper was actually submitted on the 18th of July, 1925. So it's significantly before you had heard anything about Schrodinger.

Heisenberg:

Yes. It's definitely before Schrodinger, yes. I would have even thought it was still earlier. I see.

Kuhn:

Well, there may have been appreciable discussion on it before that.

Heisenberg:

But still, I would now conclude from this date that this discussion about which I told you must have taken place, say, in May, '25, or so. It was certainly before I had this quantum mechanics. Well, at that time, nobody knew what one should believe about it, but my impression was that there one sees how complicated all these things are and how far we are still from an understanding of all these problems. But I did not really want to go into this side of the problem. I just thought that it was very interesting that someone should try it. Then I remembered this Duane paper — the quantization of interference, the derivation of interference by means of quantization. I thought that it might have to do with this Duane stuff. I also think that it occurred in the discussion that someone said, "Well, we are accustomed to quantize periodic motions; now if an electron passes by a grating then it's a periodic motion somehow, because there comes always again and again a line of the grating. Therefore, why not quantize that?" This, of course, was the Duane idea more or less. One could see that all these things did belong together in a reasonable way, but in a way which was not understood at that time.

Kuhn:

Well, I'm surprised that at this point in '25 you really took this set of ideas that seriously. Which ones did you know? The Einstein papers?

Heisenberg:

Well, we did know the Einstein paper by that time, but the Einstein paper was more or less taken as some very queer idea. Then we knew about the Bose paper. Then we knew about the Duane paper and that did play, I think, a large role in the discussion at that time. So we knew that there was something in it — in the quantization of translational motion if it was in a periodic grating; this connection of interference patterns with quantum theory. But it was all what one should call vague talk. We didn't know what to make out of it. It definitely made a great impression on me, and I felt that it was something serious. But my reaction from it was, "Well, we must first try to understand things like the hydrogen atom. If we understand the hydrogen atom really, then there must be a consistent way to go over to translational motion, to motion in a cloud chamber. Then we can simply ask what happens if such a thing goes past grating, and then it will probably come out." So I definitely favored the Duane idea to get rid of the material waves. In some way I didn't like the idea of the material waves at that time, and I rather preferred the idea of quantization of translational motion.

Kuhn:

I think this is an excellent place to stop. And. I think that next time, when it is feasible for us to get together, I think we will really start with matrix mechanics.

Heisenberg:

All right, good.