Werner Heisenberg - Session V

Kuhn:

This is the Pauli paper on the hydrogen molecule ion?

Heisenberg:

Yes. Well, in the paper itself, as you say, it's just stated what, according to Pauli, should be the stable state of this ion. He gets ionization energy and cannot compare this ionization energy with the experiments because at that time, the experiments were not available. Now, I wonder when the first experiments were available? I tried to find it out. You know a few years later there was this paper of Burrau, [Dansk. Vid. Selsk. (1927)], doing the thing by means of quantum mechanics, and there the experiments were used.

Kuhn:

Whose paper is it in which the correct values are used?

Heisenberg:

Well, that is not too easy to find. I think it is a paper by Smyth. ... And Franck and Jordan again quote several papers. ... I have not looked through all the details of the literature, but anyway it seems that the correct values have been known early in '25, or so.

Kuhn:

Do you happen to know whether the correct value is too large or too small, as compared with the Pauli value?

Heisenberg:

It was in that direction that the Pauli state was too high, too unstable. Therefore the hydrogen molecule which Pauli calculated was a thing which really should disintegrate by itself into hydrogen and a nucleus. This is probably the reason we were all pretty dissatisfied with the situation. Well, briefly the situation was this, that Pauli found out that he had different classes of solutions — some being dynamically stable, some others being dynamically unstable.

Kuhn:

But there was the ambiguous third class.

Heisenberg:

Ambiguous; well, in what sense ambiguous?

Kuhn:

In that he had not been able at the time the paper was published due to the mathematical complexities to decide whether it was stable or not. So that it always left a way out; if the problem was that he had too high an energy in the first calculation, there might have been a lower energy to be gotten from the anti-symmetrical solutions.

Heisenberg:

No. The disagreeable situation was this, and I think that is the reason why we were dissatisfied. Among those states which were unstable, namely those where the motion was in the middle plane, there was a state very much lower than the stable state which Pauli had calculated. So that to begin with, of course, everybody would have said, "Why shouldn't the molecule drop from the Pauli state into this lower state and then, of course, go into pieces, because that's not stable." But Pauli himself says, Well, there are some arguments from Bohr" — he quotes Bohr for it — "that the classes cannot go over into each other." Well, classically by continuous changes, of course, it could not; but quantum theoretically it's a bit difficult to argue. So I think our general feeling at that time was, "Well, this doesn't look too convincing; we get only a stable state of rather high energy which certainly doesn't look like the real state. Then the thing could actually, by emitting energy, go over into a lower state, and this lower state, by the way, has very much the energy of the real H₂⁺. This lower state, however, is dynamically unstable and will then disintegrate further." So this was a situation which, in some way, didn't look too convincing. It was not like a disproof by experiment, but in some way people felt, "Well, that doesn't look as it ought to." And that's probably the reason why we all, after a very short time at least, took it as an example of the fact that things don't work.

Kuhn:

That's terribly interesting and helpful.

Heisenberg:

Probably at the same time one knew already that then the helium things didn't work, and then one thought, "Well, the helium things don't work; here now we have a good calculation, but still it doesn't look too convincing. Things look a bit odd in this Pauli calculation." Then later on, of course, when the real value was found by (Witmer) or whoever it was, then it was quite clear that it wasn't consistent. I have here this paper by Burrau which was then the first calculation on the basis of quantum mechanics, and he makes some remarks in that direction.

Kuhn:

Very good. I will have a look at this and make a few notes. ... I've been able to go a little further on the cross field problems. Mostly I got that out of an overly quick look at what Pauli has to say about it here. ... When I say that the problem wasn't solved until quite late, what I mean is that there was no complete solution that didn't involve using perturbation theory. People were looking for a solution which would go through in some coordinate system directly as the Stark effect had. There were a number of quite interesting and good perturbation theory solutions; and I think the Klein paper and the Lenz paper are both in that category. They leave the following funny problem which Pauli emphasizes here as one which suddenly vanishes if you do the problem in matrix mechanics. There is a process that is always available to you when you — first you remember that in the old quantum theory one had these rather strange rules that forbid k = 0 and forbid m = 0 because the particle will run into the nucleus. Incidentally, that m = 0 exclusion is perfectly clear for the Stark effect, but it's always used in the Zeeman effect also where there isn't really any good reason to use it. This has puzzled me over and over. Sommerfeld has a very funny argument about it in Atombau that I'm convinced doesn't quite stand up; I wonder whether that rings any bells with you?

Heisenberg:

Well, I don't remember really, but I only remember that there have been many discussions about this k = 0 and m = 0 rule, and nobody was very happy about it. Everybody felt, "Well, there is something wrong with it." But nobody could really solve the problem.

Kuhn:

Well, now, apparently what happens with the cross field problem is that there is an adiabatic, or a mechanical, transformation you can carry out in which you start with your fields parallel to each other, move them out of parallel — perhaps also change the relative size of the fields, I believe — and then move them back parallel which will start you out in a non-forbidden state and wind you up adiabatically in one of the forbidden states.

Heisenberg:

Oh, I see. Yes, I think I remember that kind of thing. Yes, that's quite true. Who found that out, I mean, where did you get that from?

Kuhn:

Well, I get this information out of Pauli. He describes the situation, but the indication is that it was well-known and that he had not been deriving this for the first time. It's really in that connection and, not in connection with, I think, any of the later mathematics that he points to this paper of Klein and the paper of Lenz.

Heisenberg:

Well, this statement then should be found in either of these two papers, yes.

Kuhn:

Right. Now, I take it that it's something of that sort. People, I think, decide — and then it turns out to be quite wrong — that this is a problem that cannot be solved except in the perturbation treatment and that there it is showing a fundamental weakness of quantum theory. I do this in order to see whether this brings back discussions to you.

Heisenberg:

Well, at least it sounds very familiar when I hear it now. I would not have remembered it myself, but as you say now, I think that was the situation. One felt, "These cross fields make very disagreeable things with the state in m = 0." This state m = 0 was always a kind of stumbling stone, you know. One knew one had to omit it in one case and could not justly omit it in other cases, and nobody really knew what it was all about. So that I think at that time at least everybody was convinced, "Well, after all, this integral pdq is not really right; it's something which is approximately right or gives a right indication of what things are. But this m = 0 business shows, just as the Correspondence Principle does, that the whole thing is only a vague analogy with the classical situation. It is not the real solution."

Kuhn:

When you say you think everybody felt this way, would this even include Sommerfeld by '23, or so?

Heisenberg:

I should say yes. By '23 he must have recognized that things don't fit too well. He still would not take it from such a philosophical point as Bohr did, but still he felt, "Well, things are not all right."

Kuhn:

Good. Well, let me take you back briefly then to the Gottingen meeting and then proceed from there to your own days as a student and then as an assistant at Gottingen. I wanted to see whether we could go just a little further because we dashed off on other very, very fruitful problems last time. On the question of the importance of those meetings, you said that they and the appearance of Atombau were two great big steps.

Heisenberg:

Yes, yes.

Kuhn:

When I asked you about what made them quite so important, you spoke very well, and in quite personal terms, about your own sense of problems that a young man could solve and of the work to be done. I take it that that cannot have been the reason that they were felt so widely to be important. Other people must have, in part, known that there were problems to solve; in any case they were further advanced in their careers and would not have gotten that sort of thing out of it. Also, I take it it's true that although Bohr talked about some contemporary work of his own, he had been publishing steadily through this period, so that it can't have been brand new to people in the sense that Atombau introduced a lot of people to things they hadn't known anything about, or gave them a taking-off point. So I wondered were there, for example, a lot of discussions that went on in between the meetings, a lot of sharing of ideas? Was this what stimulated people, or what was it about what Bohr himself said?

Heisenberg:

I would describe the whole story perhaps in this sense, that up to the time around 1918 most physicists had in some way pushed quantum theory away. One knew, of course, about the paper of Planck and the papers of Einstein and so on, but still this was, so to say, a rather disagreeable feature of physics that was better not to talk about, you know. So nobody really liked to take these things seriously because one understood that then one got into all kinds of contradictions and troubles. I remember that Otto Stern once told me that when he had read about the first Bohr paper, that he had said to some of his friends, "Well, if that is correct, what Bohr says in his paper, then I give up physics. That's really no use." You know, that was the kind of tendency because up to that time one had this wonderful closed classical physics without any contradiction, with a perfect mathematical scheme, with the nice techniques of Hamilton and so on, and now all of a sudden somebody introduced a lot of contradictions into this scheme. Therefore, most physicists just preferred not to talk about it. Then there came the Stark effect, and the great success of the Bohr theory; that, of course, made some people listen. They said, "Well, all right; that must be something." Then gradually interest arose, and I think Sommerfeld did a lot by writing his book, so he aroused some interest, widely, but still not too successfully. Then there came the Bohr papers. First of all these papers were published at the place where they were difficult to be found; then it was partly in English, so people in Germany wouldn't realize too much about these papers. But gradually there came some interest at many places. I think in Gottingen the situation was just like that. They had heard about his paper; they had some connection, of course, with Munich and some with Copenhagen. So Born at some time must have decided, "Well, after all, now, the theory of the crystals is getting a bit annoying. I have done it so many years, why shouldn't I try something else? There is this Niels Bohr, and that seems to be exciting stuff. Nobody knows what it is all about; shall we not invite Niels Bohr?" Then there was Franck who had done some work in that direction, so they both decided to invite Niels Bohr for a meeting. And apparently, from this time on, perhaps as a consequence of the meeting, or perhaps from former ideas, he decided, "Now I will change my institute into an institute where we really do these things. When we really get into these problems, we might be able to do something in the research." So I think that is also the reason you stated in your papers why in Gottingen there was a clear change from one direction in theoretical physics to a new direction in theoretical physics just around the Bohr meeting. The Bohr meeting was a part of this change — an essential part of this change. So I think in some way you may say that this was just the time of a kind of break-through. Many people had been gradually a bit interested in these things, but many other people said, "Well, it's just so disagreeable." Then all of a sudden they said, "Well, there must be something in it. There is something; we don't know what, but now we shall try to do something about it." Still, after the meeting, I think, the real interest was limited to a few centers. There was Munich, of course; there was Copenhagen; very little in Cambridge — Cambridge only through the connection to Bohr. Perhaps there was a bit at Hamburg; I don't know whether Lenz had already gone to Hamburg at that time. Pauli was at Hamburg also for some time. But it just started, you know.

Kuhn:

How large do you suppose Franck's role in that conversion of Gottingen may have been? That is, he had had previous contact with Bohr.

Heisenberg:

Yes, that certainly has played a big role; I don't doubt that that played a role. Naturally, Franck would be interested in carrying on his research on the energy levels, so he was interested in energy levels. I would take it that Franck finally convinced Born that he should take these things more seriously than he had done before. I could imagine that Born, being a good mathematician, didn't like that kind of technique which contained contradictions. So he could only with some difficulty be convinced by Franck that he should take these things seriously, but finally he saw that there must be something in it and that Bohr was a good man, and so he decided, "Well, now we'll have this meeting and then we shall see all about it." The meeting was probably meant just as an occasion to form an opinion about the current situation.

Kuhn:

That is very, very helpful. Now, let us get you to Gottingen. I think you told me before that the reason for your going there had been that Sommerfeld was away for the semester from Munich.

Heisenberg:

My first visit to Gottingen was just for this reason. He had gone to the States for one term to give lectures there, so I thought, "Why not go to Gottingen then and be acquainted with Gottingen."

Kuhn:

Was it your idea to go there in particular?

Heisenberg:

I think it was Sommerfeld's idea; he thought it was quite nice that I should get into a different atmosphere and then see what those people were doing, and so on. But I also found it a very good idea, so that was quite clear that I should do it. In Gottingen, I should perhaps say, I at once entered into a seminar of Born which, quite obviously again, was meant by Born as an occasion to learn all the techniques available for the modern quantum theory and possibly for inventing new techniques. So he not only studied with us the Hamilton and Jacobi technique, which was fairly well-known to us at that time, but then he also studied Charlier's Himmelsmechanik, the methods of Bohlin, and very refined schemes of perturbation theory, always with the idea to apply these schemes then in quantum theory and see what we could do about it. Obviously, one saw that in applying quantum theory to many-body problems one had to enter into horrible difficulties, because the many-body problem even in astronomy is a hopeless affair. We felt, "Well, what should one do about it; these are not periodic systems." Starting from this point Born thought, 'Well, we'll learn the methods of Himmelsmechanik, the book of Charlier, and it may be that there we'll hit on something which may be very useful for the quantization of helium, and so on."

Kuhn:

Did you have the feeling there that these people were really starting a considerable ways behind Munich, where you had just come from, on these problems?

Heisenberg:

Well, behind in that sense that they were not so well-acquainted with the experimental facts. That was the strength of Sommerfeld that he knew very many facts and tried to connect these facts. So in some way Sommerfeld was more in the whole experimental situation. Born appeared to me, when I came to Gottingen, as an extremely good mathematician who was interested in the mathematical methods of physics, but who did not know so many details. He had not so much feeling about how the things in atomic physics were. So I remember that, for instance, Fermi, who took part in this seminar was a bit unhappy about it; he disliked these mathematical subtleties, proof of convergence, and such. For example, we spoke about the theorem of (Bruins) that in an infinite neighborhood of a periodic solution there are always solutions which are not periodic; this kind of mathematical subtlety he hated. I mean, Fermi felt, "That's not physics." Still I must say that I learned a lot from these discussions, and I felt the time was not wasted. Just the contrary, I felt it was extremely interesting, and I learned a lot both about classical physics and mathematics, and also about what one could do and especially what one could probably not do in quantum physics. I would say just from these mathematical subtleties I had a stronger and stronger conviction that this was not the way of attacking atomic physics. You know, for instance, when you find such a theorem as that of (Bruins) which I have just mentioned, you can say, "Well, this theorem apparently has nothing whatsoever to do with the real situation in the atoms. The real atoms are quite stable and definite things, and there are no such troubles," you know. So this was, of course, not something you could write down on paper, but still it was a very definite feeling. I think also Born was quite satisfied with this feeling; it was not so that Born was disappointed. He felt, "Well, we must try our best; a negative proof, a proof that something does not work is just as good as a positive proof." And so far I felt this seminar of Born's very interesting, but I just mentioned that Fermi was not so pleased about it.

Kuhn:

You said that when you had done the paper, Pauli had pointed out to you that this wasn't the way to solve problems like this.

Heisenberg:

Yes, yes.

Kuhn:

Clearly after you work with Born in Gottingen, you know how to solve the sort of problem that's being done with the Hamilton-Jacobi techniques, and so on. To what extent did you learn those first at Gottingen? To what extent had you really had this material before you got there?

Heisenberg:

Well, I should say that already in Sommerfeld's seminar I learned some part of it, but I was not too firm in it. Only in Gottingen I became quite well acquainted with, I would say, the fundamental structure of it. In Sommerfeld's Institute one learned to solve special problems; one learned the tricks, you know. Born took it much more fundamentally, from a very general axiomatic point of view. So only in Gottingen did I really learn the techniques well. Also in this way Born's seminar was very helpful for me. I think from this Born seminar on I was able really to do perturbation calculations with all the rigor which was necessary to solve such problems. Of course, the result was for me, the negative one that one probably should not do it that way. Still, later on, through this technique I was able to formulate the correspondence in this more refined manner as we did it later on.

Kuhn:

Let me ask you just one more question about the seminar. This was the first time Born had given a seminar on this topic, so far as you know? I mean, he was really exploring this himself now, for the first time?

Heisenberg:

I would say that was his first seminar on these things, yes.

Kuhn:

You mentioned the emphasis on perturbation calculations. Now, I gather from a number of things that Born says himself around this time in his papers that there is some feeling — perhaps just with him, but perhaps at Gottingen generally — that a clue to the new quantum mechanics may come directly out of the general characteristics of perturbation calculations. That's to put it too vaguely, but it may already be too precise. Do you know what I mean?

Heisenberg:

Yes. I would say yes. That is quite true. Well, by doing the perturbation calculations so carefully one saw that there was a method of applying correspondence arguments to the single terms in these formulas. So each term can be translated by means of the Correspondence Principle. That, of course, came out only gradually, and that was, of course, essentially the basis of this paper of Kramers and myself in Copenhagen. Well, perhaps in Born's seminar people didn't talk about it that way, though it might be that somebody suggested already at that time that there are always these differential quotients and actually what one should have is a kind of difference quotient.

I remember that I did study this problem at Gottingen; I don't know whether it was in this term, or in a later term. I did attend a lecture — was it by Hilbert or by Bernays, by one of the mathematicians — on difference equations as distinct from differential equations. You know, equations of the type f(x + a) = F•f(x), something like that. So I had already that idea, and that probably came out from discussions with other people that the real quantum physics is a physics in which we have not a continuum but rather discontinuous states. So instead of having differential quotients, we must have something like difference quotients. I think it was also clear that the Ritz principle that the frequency is E₁ minus E₂ was something resembling the fact that in classical theory the frequency is dE/dJ , so it's a difference quotient. Well, actually that's probably already in the papers of Bohr on the Correspondence Principle — this comparison.

Kuhn:

Oh, yes. In fact that, you know, goes back into the very early days. It's certainly at least in Bohr's 1914 paper on the Stark effect. He formulates the earlier form of the Correspondence Principle that way. But I'm not clear that it's really until 1924 that you see the attempt to generalize that idea as you do, of course, by 1924 in a lot of places.

Heisenberg:

Yes, yes. That's, of course, difficult to say to what extent this idea did occur in the seminar of Born. I would think that probably some people have sometimes suggested that there for instance we have a perturbation formula in which we have a differential quotient with respect to the J, to the integral, and what we really ought to have is a difference quotient at this point. That I could imagine; but it was not stated very clearly; it was just vague talk of that kind at that time.

Kuhn:

I take it that because of the inflation Physikalische Berichte stopped printing these things for a couple of years, but I've got the winter '22/'23 course list. I don't have the '23/'24 which I would like to have.

Heisenberg:

But anyway this was this winter term in which I had been in Gottingen. I have certainly attended Born's lecture on the kinetic theory of matter; I occasionally went to Pohl's experimental physics just to have a look at what he did. I did go to Prandtl's lecture, Mechanics of Continua, on account of my interest in hydrodynamics. Oh, you have not the mathematical lectures.

Kuhn:

I think this time the mathematics is included there.

Heisenberg:

[Scans the list] Oh, now we have it, "Seminar "Uber Differenzgleichungen" by Courant and Siegel. That's the thing I had attended. So that makes the time scale quite clear; actually it was in this winter that I was already interested in difference equations. So the idea of changing differential quotients into difference quotients must have occurred, by that time, probably also in the discussions in the Born seminar. The Born seminar itself was probably not mentioned here on the list because that was a very private seminar which was in the evening in his house. Well, that is not mentioned at all here.

Kuhn:

How large a group was it in the Born seminar?

Heisenberg:

Five or six people, not more than that.

Kuhn:

Do you remember who was in that?

Heisenberg:

Well, there was Fermi; there was the mathematician (Carigiotto;) there was Jordan. I don't know whether Hund was there; it may be. Do you know whether Hund has taken part in this?

Kuhn:

Yes, he was in Gottingen that year.

Heisenberg:

Then he certainly would have taken part in the seminar. That's four people; I would say there were one or two more. Pauli was not in Gottingen, so far as I recall, at that time — at least not the whole time. Perhaps he was there temporarily. ...

Kuhn:

Being at Gottingen, how did you feel that it differed from Munich as a place to receive training in physics?

Heisenberg:

Well, in the respect that mathematics played for the theoretical physicist a much larger role in Gottingen. I felt Gottingen was a place in which the mathematicians dominated the field, for the mathematics institute was in some way the center of Gottingen. Experimental physics, of course, also was quite full of interest, and I would say my connection with the experimental physics was much easier in Gottingen and much nicer. I did learn from the Franck people, and I had discussions with Franck, so there was a close connection much better than in Munich. So the connection between experimental physics and theory was just as good as it could possibly be — better with the Franck institute than with the Pohl institute. Pohl always, to some extent, disliked these abstract things in quantum theory. He certainly disliked the idea that one should not be able to form models and so on. But still he was very helpful by his interest in band spectra and infra-red problems in crystals and so on. Franck naturally was extremely interested in all the development in quantum theory, but the field was dominated by the mathematicians. In some way mathematics formed the whole spirit of Gottingen. There was, of course, Hilbert; he was a very strong personality in spite of all his rather strange habits which are well-known. He was very strong in giving a direction to all the thinking in Gottingen. I think it's quite typical this famous remark by Hilbert that physics is much too difficult for the physicists. That was very typical because he felt, "Well, after all, only the mathematicians can really do the thing at the end."

Kuhn:

Did you see anything of Hilbert yourself? Did you follow his lectures?

Heisenberg:

Oh, yes. I did attend some of his lectures, and I was invited to his house occasionally — very rarely, but sometimes he gave parties at his house. He had a strong interest then later on. So when quantum mechanics was developed — now, that was two years later — he asked me to give lectures only for the mathematicians on the subject, and he was very interested in the thing. So he encouraged me a lot for my work. You know, Hilbert was a man who could see when something happened; he could see that there was something of very great interest. Also Hilbert had intense interest in Bohr's lectures. I remember that he discussed in the lectures. But then on the other hand it was quite obvious in Gottingen that the theoretical physicists would also go to the discussions about axiomatics in mathematics. So when there were discussions, for instance, between Brouwer, from Holland, and Hilbert everybody, of course, went because one knew that was something very exciting and very deep, and so on. The whole center was the mathematical institute at Gottingen, and, therefore, the whole thing looked rather different from Munich. In Munich it was Sommerfeld with his very great knowledge of details in atomic physics and an instinct for how things are, but Sommerfeld was rather separated from the mathematicians and strongly separated from the experimental institute because there things were a bit difficult.

Kuhn:

Had Sommerfeld entirely abandoned the experimental side of his own institute? When he first went there, there were experimental facilities; some experimentation was done.

Heisenberg:

He had experiments going on in the basement of his institute on X-rays, but only on the X-ray problem. That was an older tradition from Laue, I think. So there were always one or two rooms in the basement where there was a cathode-ray tube running. It was mostly Ewald at my time who did the experiments. I remember one of my first experiences was that I went down in the basement with the mechanic, Mr. Selmeyer, who is still even now alive in Munich — I saw him a few weeks ago. He's a very old gentleman now, of course. And this old mechanic, Selmeyer, showed me the apparatus which was just then working, that cathode-ray tube. Since I was a very poor physicist at that time, I tried to ask Selmeyer, "What is this?" and to point at the thing. Now, this was, of course at 40,000 volts, I just realized that before I could touch it I was taken by the neck by the mechanic and pulled back with a tremendous force so that I was lying down on the floor. I at first didn't know what had happened, and then he told me, "Well, you damned fool," and so on. He was perfectly right. That was one of the incidents by which I learned experimental physics. Well, that was in the basement, and that went on, but not with too full intensity. I should say that Ewald always did some experiments, and Sommerfeld kept up interest in these things, but not too intense an interest. So his interest came from the fine structure formula in the X-rays, and, of course, there were many discussions between Sommerfeld and Ewald and others of his group.

Kuhn:

I'm very grateful for this general remark about the much closer relations both with the mathematicians and with the experimentalists at G6ttingen. Actually working with Born did one see as much of Born as you'd seen of Sommerfeld? You speak of spending an hour a day, or something of the sort, with Sommerfeld.

Heisenberg:

Well, Born would not see the young students as much as that, so I had fewer scientific discussions with Born. On the other hand, Born had more private connections with the students; we had many parties in his house, and we had excursions to the (Heinberg). The whole style in Gottingen was less the traditional style; I mean, Sommerfeld was still the Herr Geheimrat and was a bit traditional, while Born tried to be everything else, but no Geheimrat. So we tried to play games in Born's house with Mrs. Born, and we played in the garden, and we went out to the (Heinberg). The whole thing was more intended as a kind of family life among the young people with the Born's. So it was on the one hand more, and on the other hand less, than in Munich.

Kuhn:

How large a group did this extended family make up? Was this again just the four or five?

Heisenberg:

Well, perhaps it was slightly bigger. I would say at these evening parties in Born's house we were perhaps ten or twelve. In this one seminar we were five or six; that was just those who were especially interested in quantum theory. The larger group included those who were interested in crystal structure. You know, Born had an intense interest in crystal structure, so all together it was perhaps ten or twelve, or so. It included the doctoral students of Born and assistants, and so on.

Kuhn:

Was the group of people doing interesting physics, active people, a somewhat larger group at Gottingen than it had been at Munich?

Heisenberg:

No, I would say that was more or less the same thing. There were always, of course some students who did some problems for their doctor's theses, or so, which were not too interesting. I mean, there must always be the average student who just wants to get his degree, but he cannot do very much in the research, so that kind of work would be going on in both places. I would say it was more or less the same in the size of the institute. Also, at Born's institute there were a few rooms in which experiments were being done. There was a room where Born did some experiments on molecular rays; he wanted to measure the speed of molecules heated up to a certain temperature, and that kind of thing. I don't know whether much has come out of it, but it was a kind of hobby with Born that he wanted to do some experiments at least.

Kuhn:

It was rather strange when I first ran into those experiments to notice the molecular beam techniques coming up here at just this time because at about the same time they were coming up at Frankfurt with Stern.

Heisenberg:

Yes, well, it was just the thing which was in the air; one could try, and so people got interested in it.

Kuhn:

I want very soon to talk about your own papers. We have gone over that lecture list for the winter term of '22. I wonder just whether you can remember other courses that you may have taken when you returned to Gottingen after you got your degree!

Heisenberg:

Well, I wouldn't recall now simply. I'm sure I would have gone to some lectures just for the interest of it, maybe to some of the mathematicians. No, I don't recall; if I would see the list, I probably could say.

Kuhn:

Maybe between now and the time you come to Copenhagen in July, we can dig out some source — a Gottingen list. We might ask you about that then. I would be particularly interested if there were any way of pinning down the mathematics' lectures you may have gone to. There's a story that floats around that somebody or other has told us — this jumps ahead again a bit, but it points to what makes, in a sense, a particularly interesting area — that when you first developed the non-commutive variables, someone in Copenhagen said to you, "Ah, just like Newton, you're making up the mathematics you need for the problem." And that when you got back to Gottingen, somebody said to you, "Now, what were you doing, sleeping in Hilbert's lectures?"

Heisenberg:

Well, I wouldn't recall that story; I think that must have been a very improved version. I had not realized that those things which I had written down on paper were matrices. I had never heard the lecture on matrices; of course, I knew to solve linear equations in a trivial way as one learns in school, but the general scheme that one has matrices and that matrices can be multiplied and that matrices can represent groups, and all that kind of thing, I simply had never learned. So when Born told me that this was really an example for matrix multiplication, I was very interested, but it was new to me. Then, of course, I started to read books on it, and it was very simple to find textbooks in which I could learn it. I might mention this point, that in my first paper on the quantum mechanics this fact that xy was not equal to yx was very disagreeable to me. I felt this was the only point of difficulty in the whole scheme, otherwise I would be perfectly happy. But this difficulty in some way worried me, and I could not solve it. I only felt that for this problem which I had worked out, the an harmonic oscillator, apparently I can get rid of the difficulty. I had written down, as the quantization rule the Thomas-Kuhn sum rule, but I had not recognized that this was just pq minus qp. That I had not seen. From that moment on I think I have learned one very important thing in theoretical physics — that if one finds a difficulty in a paper which one otherwise finds quite convincing, then one should not push the difficulty away, but one should rather try to make it into the center of the whole thing. That is, of course, some wisdom to which one only comes later.

Kuhn:

That's a very nice point. Let me ask you again about leading figures both among the students and the faculty during those three semesters that you were at Gottingen. With regard to Munich, you point to Pauli and to Wentzel as the two relatively senior students, and you've told me something about the interests of each. Are there similar things to be said about the people in Gottingen?

Heisenberg:

Well, there was Jordan; I think I had many discussions with Jordan, and I realized that he was very good. I mean, he was certainly one of the best students there and understood a lot about this quantum theoretical business. Then there was Hund; I was very good friends with Hund. We always used to go on walks together and hiking on Sundays, and we also had many discussions. So I would say those students with whom I had most contact were Jordan and Hund. Then there was Heckmann, but Heckmann did not take part in this kind of research; he was interested in the crystals. Then I saw occasionally (Carigiotto) who was a mathematician; he was much more senior than I was. Then I had good contact with Blackett; Blackett at that time was in Gottingen. He was, of course, an experimental physicist belonging entirely to Franck's group, but I found it very nice to be together with Blackett. In some way we could get along together very well. Our contact was not so frequent as with the others simply because Blackett was married, and therefore he had a family life. I remember that I was in Blackett's home quite frequently, and so we had many nice discussions on the problems which were going on. Among the theoreticians I should say Jordan and Hund and (Cargiato) and, only rather rarely, Fermi. I had some discussions with Fermi, but it must have been that Fermi was not — I would say — in a good period of his young life. He may have had personal problems; I don't know what. At least he was always a bit shy and for himself, and it was not too easy to get into contact with him. Still, I liked him as a rather different type of a physicist. I remember that when quantum mechanics had come in '25, in the spring of '26 I made my first trip to Italy with one of my Gottingen friends; that was Drude the son of the theoretician Drude. He was a good friend of mine too. Coming back from Sicily with Drude I decided, "Now, I must see this Fermi," who had been in our seminar and by that time had become already some kind of professor in Rome. So I visited Fermi on the way back from Sicily and we had a nice discussion, I think it was already on the exclusion principle and the Fermi statistics. That was the time when Fermi worked on his Fermi statistics, and so that was a very nice discussion which we both remembered later on as, I would say, the beginning of our real conversation. While in Gottingen we never had a real conversation; we met in the seminar, and we met occasionally on the streets, but not in that way that we really got in touch.

Kuhn:

Did anybody in that year in Gottingen have any idea how good Fermi was going to turn out to be?

Heisenberg:

No, I would say not. I would say everybody said, "Well, he's a good student; he understands all these things." But he didn't have that force which he later showed — the force to take things into his own hands and do them. That at least I couldn't see, and I don't think Born has seen it. No, he was a bit of a shy fellow, you know; he had very little contact. Maybe he had difficulties with the language; I don't know how much German he really could talk. We, of course, couldn't talk Italian, and nobody came to the idea to talk English at that time, you know; that was quite different. Well, Fermi must have spoken some German, but in some way he was a bit shy, and I think he didn't like the whole atmosphere of the country. Well, I mean, there is almost in everybody's life — especially when one is very young — periods in which one is unhappy and feels that everything is so difficult, and so on. So that might have been that way.

Kuhn:

He was apparently extremely insecure in that period at Gottingen.

Heisenberg:

Yes, yes.

Kuhn:

Laura Fermi says something about it in her book. He felt he needed encouragement and support of a sort that he did not get and was much impressed by this whole group around him who knew so much.

Heisenberg:

Yes, that may be, yes.

Kuhn:

I take it that it was, in some sense, going to Ehrenfest then which helped him a great deal, because if I remember correctly — and I may not — he was, in fact, only in Gottingen for a semester.

Heisenberg:

Yes, I think that was so.

Kuhn:

He stopped his fellowship, which was for a whole year, at the end of the semester and went back to Italy.

Heisenberg:

I see.

Kuhn:

Then he spent half of the next year, I think, with Ehrenfest and was then much encouraged and did continue and picked up from there.

Heisenberg:

Well, it may be that Fermi came to Gottingen just in a too early stage of his studies; it was perhaps that he did not have the preparation for it, and so he couldn't really take part in the game. I don't know.

Kuhn:

What was Blackett himself actually most interested in when you talked physics with Blackett?

Heisenberg:

Well, we spoke about energy levels of atoms; you know, the Franck-Hertz business, and I think also resonance fluorescence. I do not know what kind of paper he did at that time; he certainly had some equipment in the institute and did some experiments, but it's more this experimental side of quantum theory. I think also that while Blackett was there that the Compton paper came out and that we had some discussions on the Compton effect. When did the Compton paper actually appear?

Kuhn:

The Compton paper appeared quite late in '22.

Heisenberg:

Late in '22; well, that would fit exactly with that date, yes.

Kuhn:

The paper comes out while Sommerfeld is in the United States.

Heisenberg:

I see, yes, yes. Yes, well, that fits well together with this scheme. I think I had some discussions with Blackett on the Compton effect. Of course, people fought back and forth when they heard of this explanation by means of the light quanta. This explanation by the way was, I think, first given by Debye.

Kuhn:

I'm not sure which of those two papers actually came out first. It's not in the first of the Compton papers which reports the result, and then both Compton and Debye give the explanation independently, and I'm not sure in which order. I think there's no question that it was quite independent. How did people feel about that?

Heisenberg:

Well, that added to the material in favor of light quanta, of course. Now, even up to that time, people felt, "Well, there is some truth in the light quantum story; there is some truth in the wave story." And now, again, one had the fact which accumulated material for the light quanta. All right, it just added to this feeling that the whole thing is deeper than one thought and how these things are connected nobody really understood, especially in scattering. That was such an exciting thing because, in scattering, when you have a wave, this wave should have one and the same frequency everywhere, and now you had the change of frequency with the angle, which was quite absurd from the wave picture. But people wouldn't draw the conclusion: "Nay, we have to drop the waves all together," because if one would drop the wave all together then one had no interference. The next step was, of course, that one said, "Well, if we have a Compton effect, what about interference? Does it mean that (scattered light can never interfere)?" Then, of course, one realized that the recoil in most cases was more than could be connected with interference, and so on. Well, all these discussions then started. I think it was a great time of the Gedanken experiment. One thought out an experiment which put the two sides in the strongest opposition to each other. One said, "Well, now we have a complete contradiction. What will nature do if we ask her that question?" Now, of course, in most cases one couldn't ask that question because the experiment was too difficult, but then from such a Gedanken experiment you would perhaps find another experiment which could actually be carried out. I don't know at what time one really thought about the Bothe-Geiger experiment, but it must have been pretty soon that people said, "Well, if the light quanta are correct, then there must be always, at the same time, a recoil electron."

Kuhn:

Well, of course, the Bothe-Geiger experiment is, at the time the Compton paper initially comes out, still two years off.

Heisenberg:

It is still two years off. Yes, yes; it's still two years off, so there are still two years between.

Kuhn:

Well, I find this very helpful. It may be all that can be done, but you are giving me a great big generalization about what, to some extent, must have been happening, and I'm sure it's right. On the other hand, it isn't true that everybody felt the same way.

Heisenberg:

Of course not, yes.

Kuhn:

In some places people must have been saying, "I told you all the time it was really particles." And in other places people must have been saying, "It just isn't true at all; there's something the matter with the experiment. At least Duane, you know, and his students for awhile couldn't even duplicate the experiment and were sure it was wrong. I wonder whether we can come to something that happened — something that will give more —.

Heisenberg:

Well, I must say, that at that time I do not remember any case where somebody would fight for the one side alone, that somebody would say, "I believe in the waves and the light quanta are just wrong." Or that other people would say, "There are only light quanta, and the waves are just wrong." There is one exception; Bohr himself. And that was quite interesting. When he had written the paper together with Slater and Kramers, Einstein had, apparently written a letter and had criticized it and said that he thought the light quanta had more reality than Bohr was willing to give to the light quanta. Then Bohr got quite upset. He once said, to me, "And even if Einstein would send, a telegram and would write to me that now he had, definite and unavoidable proof that the light quanta exist as reality, even then the telegram could only reach me by radio on account of the waves which are there." So Bohr in some way saw the reality of the waves as a very strong thing, and he was not willing to take the light quanta as more than a kind of — well, at that time — statistical conservation of energy business. Only later on, of course, he saw that these two things can actually be combined in a very subtle way. I would say that even in 1922 there was nobody who would dare to put all his weight on only one side. The Compton paper, of course, was exciting. It was a very interesting contribution to the light quantum side of the picture, but people would say, "Well, after all, that the light quanta somehow exist we have known already since Einstein." So the whole point is the "somehow." Of course, we learned something very essential about the "somehow," but nobody would say, "Now we know there are light quanta."

Kuhn:

You speak of the manner in which Gedanken experiments crop up with respect to a problem of this sort, and I take it that that's very much what was involved in the background of the Bohr-Kramers-Slater paper.

Heisenberg:

Yes, yes.

Kuhn:

Can you think of similar things that were going on in Gottingen, I mean, did the Gottingen group take this that seriously? Would the same sort of discussions go on there?

Heisenberg:

Well, for instance, they did in connection with these discussions on the resonance fluorescence and the experiments of Hanle and others in the Franck institute. So these Franck experiments — resonance fluorescence — have an obvious explanation by the wave picture. You have a resonance between the incoming wave and the oscillator, then you have outgoing waves, and so on. The Compton paper, of course, suggested why these things ought also to have an explanation in terms of light quanta. What would you say if the whole thing would be done by light quanta; how would it look as pictured in the light quantum language? So we tried to translate and to see, "Well, can we do the same thing also by means of light quanta." Therefore, my paper which I later did in Copenhagen on this resonance fluorescence was also to some extent a result of these attempts of translating. One said, "Well, after all, we must always have the two pictures somehow; we don't know how, but we are allowed to use the two pictures to the utmost and to see how much can be done with the one picture and the other." Now, space quantization, of course, then belonged to the light quantum side of it. That was the discrete steps of quantum theory. Therefore, one felt, "Why not use that?" I think just in these years — at least I, but I think many of our group — had come into the habit of playing with different pictures. The idea was always to say, "Don't use one picture, don't believe in one special theory," but rather say, "We must play between light quanta and waves and space quantization and no space quantization and always play around and get the feeling of how it might be." Especially in the sense of a Gedanken experiment we ask, "What would nature do if we asked her this question" From this period I think this paper on the resonance fluorescence was written, and that's well understandable there. But to what degree this same attitude developed among others is difficult to say. I would say nobody in Gottingen would object again st that kind of talking — that kind of vague talk, "vagues Geschwatz," as one said in Gottingen. Yes, I remember one term which goes in that direction. When later Sommerfeld and I wrote this paper on the intensities, we had to replace sometimes j² of the classical theory by j times j + 1, and so we had to introduce a quantum theoretical j which was the square root of j times j + 1. This is, of course, a very disagreeable quantity to write on paper — the square root of j times j+ 1. So we used to call it "j verschwommen." You know, that means a vague j which is not really taken seriously. It has a kind of criticism in it; that means "vagues Geschwatz." It's all this vague talk, and nothing is really good solid physics; still it seems to have some meaning.

Kuhn:

I'm just wondering which paper this is. That is, I don't think this is the multiplet intensity paper with Sommerfeld because in the first place that's earlier. That's done almost immediately after the Rumpf model.

Heisenberg:

I should say it must be that paper because L times L + 1 must have appeared in that paper.

Kuhn:

No, I don't think so. That is, the paper on the intensity of multiplet lines and their Zeeman components is done in 1922. It's submitted on the 26th of August, 1922.

Heisenberg:

Yes, but how could one avoid in that paper writing down L times L + 1; I mean, there must be such a formula because, after all, there were the correct quantum mechanical formulas in that paper already.

Kuhn:

I don't think you'd have gotten those until after the general formulation of the g factor, which is 1923. Landé produces a J with a tilda over it —.

Heisenberg:

Yes, "J verschwommen," yes, that was just it.

Kuhn:

Which is exactly this. You must all have been using that, and I'm sure something of the sort comes out in your late '23 and '24 papers. I think perhaps it's not in a paper with Sommerfeld.

Heisenberg:

May I try to have a look at this paper? [Interruption] Then we had it in the discussions with Lande a bit later and there we had this "J verschwommen," and that was again an example of where one started playing with different pictures.

Kuhn:

This is terribly much on the track of this question that I wanted now to ask you again for this period. Again this attempt to trace the change in feeling over time about the state of quantum mechanics. Already the sorts of things you're saying are very clear in the literature in '24 and becoming clear in some of the literature in '23, but I think are not quite the same in Gottingen, Copenhagen and Munich. That is, the development of this notion that we are ultimately going to have to get a basic alteration. Now, let me ask one thing. When you say people played with different pictures simultaneously and tried to confront them with each other, was the feeling that the purpose of this is to find still another picture which will eliminate this, or was it thought that one would go on forever doing this?

Heisenberg:

No, I would say that so far as I have spoken to people, everybody hoped that someday somebody would find the real picture which is behind it. I mean, we spoke about the real atomic mechanics as being some kind of difference mechanics instead of differential, abandoning the continuum of variables for discrete variables, and so on. So we spoke about quantum mechanics as something which rust come some day, and the playing between different pictures was only meant as a study to prepare this new thing to happen. Sommerfeld was not too happy about it because he had for some time hoped that these methods with integral pdq were the final methods. So it was a disappointment for him that these methods perhaps had to be abandoned again. So far Sommerfeld hesitated a bit to go into this playing with pictures, and I noticed that in Copenhagen people were so much more willing to play with pictures than in Munich. Born looked at the whole thing a bit more from the outside. I think I realized in the first term at Gottingen that all this atomic business was a bit foreign to Born yet. I mean, he had been interested in the crystals, and all these things which were in Sommerfeld's books and in Bohr's papers were new to Born, and he had to learn it. He learned it as an excellent mathematician who knew that mathematics was a thing which one really had to understand and could understand — contradictions in mathematics were nonsense — they didn't exist — and so on. But Born was quite willing to agree with this playing with different pictures because he would say, "Well, after all, there are contradictions, so something must be wrong. We must look into the future for a final new scheme of mechanics."

Kuhn:

Was it already fairly clear in his seminar in '22 that one had to look for room for a fundamental change? He's terribly clear about that in the Atommechanik in '24.

Heisenberg:

In '24, yes. Well, certainly there were remarks in that seminar in that direction, but how strong these remarks were, I don't know. At least the confidence in integral pdq was already shaken at that time.

Kuhn:

Again on the same track. There is one terribly important idea that one begins to see in the literature in this period, though I'm not sure I can pin it down before 1924. This is the idea that the new picture, whatever it is, is going to have to be a picture which works only in terms of observables. You don't enunciate this as though it were a great new idea of your own, but people point back to your first matrix mechanics paper as though it were. It's clear in several places. Born in the Atommechanik in several places says just the same thing. There are also a few references to it in the Kramers' paper, though they're very mild references. Now, I'm terribly much interested in knowing how that idea develops and where it comes from. It's first most explicit in Gottingen; is it a Gottingen idea or a Copenhagen idea, or everybody's idea?

Heisenberg:

I would say in Gottingen it was closely connected with the interest in relativity which had been in Gottingen. There was Minkowski, and Minkowski as you know, has been very interested in special relativity. When one spoke about special relativity, people always said, "Well, there was this very famous point of Einstein that one should only speak about those things which one can observe, that actually the time entering in the Lorentz transformation was the real time." And in some way that was an essential turn which Einstein had given to the Lorentz idea. Lorentz had the right formulas, but he thought that was the apparent time. Einstein said, however, "There is no apparent and no real time; there is just one real time, and that is what you call the apparent time." So this turning of the picture by saying the real things are those which you observe and everything else is nothing was in the minds of the Gottingen people. Now, would say the primary experience for many physicists' work in that field was the negative image of this idea of relativity, namely, that in the integral pdq business you had introduced many things which certainly could not be in the experiments — like the orbital frequencies. So one had the feeling that it could not make sense that you have orbital frequencies which have a certain value according to this picture. You can calculate what the value is, and still this frequency never shows up in any experiment whatsoever. That must be nonsense. Now, of course, if you really take that criticism seriously, then you come very soon to the other view, "Well, why not say that all the things which should be handled in theory are just those things which we also can hope to observe somehow." That was perhaps wider spread in Gottingen than in Munich on account of this interest in relativity, and the point in relativity was emphasized quite strongly by Minkowski and such people when they gave lectures on it. I remember that when I first saw Einstein I had a talk with him about this. Einstein just explained to me that he did not agree with this point of view; I think I told you that. After some colloquium in Berlin, I went to Einstein's house; he said that he wanted to talk to me about quantum mechanics. I told him that this idea of observable quantities was actually taken from his relativity. Then he said, "That may be so, but still it's the wrong principle in philosophy." And he explained that it is the theory finally which decides what can be observed and what can not, and, therefore, one cannot, before the theory, know what is observable and what not. On the other hand, of course, he agreed that as a heuristic principle it was extremely important. It was a way of finding what one should probably put into a theory.

Kuhn:

Do you remember when that conversation was?

Heisenberg:

I should say the summer '26, or the spring '26.

Kuhn:

Can you recapture any specific conversations, or anything that would indicate when the idea of trying to restrict oneself to observables became more important. That is, the interpretation of Einstein is very old.

Heisenberg:

Yes, yes.

Kuhn:

The problems of quantum mechanics are in some ways fairly old, yet at least in the published literature I don't know anything before 1924 that begins to make this plea. The logic of the situation is very clear, and you've given a very good exposition of it, but that transfer of ideas was not immediate and automatic.

Heisenberg:

I might perhaps mention quite a modern paper which I just saw a few days ago, but which I think describes a situation which is very much similar to that one. In the last Geneva meeting Chew was asked to give an exposition of his ideas on the S matrix, and I just got a copy of it. Unfortunately, I have sent it back; actually you should have a look at it. Chew says the following. He was attacked at the meeting with the accusation that he didn't believe in field theory anymore. You know, his so-called declaration of independence that one should only talk about the S matrix and forget all field theory. Then he said, "Well, I have been a very diligent student of field theory for many years. I have worked out problems in field theory, I learned it, I have taught my own pupils to do so, and so on." Then he says, "But all of a sudden I realized that whenever I did a thing which was relevant for experiment, I only did it with the S matrix. I never handled anything else but the S matrix, and all the other things I could just as well forget because I didn't actually use them. What I did use was always some connection between S matrix elements, dispersion theory, and so on." So he describes in nice words the process which was exactly the same at that time 110 years ago, namely, that one has realized that, after all, the only thing which we then finally deal with are the frequencies which really are observed, are the intensities which really are observed, are some phases and interferences with amplitudes which really are there. So it's no use talking about these orbits because you never use these orbits, and that was the point. It's a kind of frustration — why do we always talk about things which are not there? You know, that kind of experience? Now, you ask me did I have any special conversations. Well, I certainly have had conversations with Pauli in that direction. One of us would say, "Well, why do we always talk about these darn orbits and we never see the orbits, we never see an electron go around, we never measure that frequency. What's that all about?" Then, of course, you could argue that after all you see the energies and so on. But I cannot remember any special conversations, so I would rather describe my own situation in those years very much like Chew described his situation. It is always this problem that you are just gradually pushed away from something. It's just gradually; you cannot easily pin it down to just one definite conversation; that is the point. So this "gradually" may also be different — it is probably different for different people — the one more, the other less. But gradually people had to move away from it.

Kuhn:

When you went to Copenhagen, did you find that this feeling was equally present there?

Heisenberg:

Yes, yes. It was definitely present there, yes; very much so, yes. Especially this conversation about the fluorescence there. If I may just interject a remark about a much later time, namely, about this paper of Chew. For myself, with this S matrix business I had exactly those experiences of Chew a long time ago when I wrote these papers on the S matrix in '43. Therefore, I did actually for a number of years work on the S matrix. But then I later on came back from this idea to some extent because I felt that to figure out the S matrix from just this abstract notion of having nothing but the S matrix was mathematically too complicated. There must be a way behind it of getting the S matrix somewhere from some kind of field theory which is simpler than the S matrix itself. Therefore, I finally adopted a point of view which is, I would say, intermediate between the extreme field axiomatics of (Wightmann) and the extreme S matrix point of Chew. So I finally came on the way passing through Chew's point of view back half way again to the field theory. Again, I may be wrong; nobody knows the answer yet, but it's quite interesting how things may change. Even in quantum mechanics one can say that finally one did not work only with observable quantities because one actually had to introduce — and did introduce — the Schrodinger wave function. The Schrodinger wave function itself is certainly not what one would call an observable in a decent sense of the word; it is some mathematical tool behind the observables, and a tool by which you can calculate. So the Schrodinger function is just a very nice interpretation of this statement of Einstein that it's only the theory which decides about the observables. Well, it's probably this situation which also again happens in every new stage of physics.

Kuhn:

I will come now, if I may, to some of your own work at Gottingen, and particularly these first two papers that you do with Born. One of them is the paper on phase relations, and the next one the paper on the helium atom. The problem of phase relations was a problem that took me totally by surprise when I first ran into it. But I now begin to see that it comes up in a number of places in these years, and that Schrodinger refers back to it himself. This paper, you remember, is the one in which you say, "There can only be certain phase relations between the electrons finally in a single atom." And you think from perturbation theory that you have shown that the electrons must stay in phase with each other. Was that a comfortable idea? Was it an important idea as things developed later?

Heisenberg:

Well, it had to do with this, that one knew from classical mechanics that a normal solution of a many-body problem is not a periodic solution. So to have a periodical solution you must do something special, and the most obvious thing you should try is, of course, a phase relation between electrons. Therefore, the interest in phase relations came first of all from having reasonable solutions at all, and secondly, from the idea that the closed shells of Bohr should be due to the phase relations because before Pauli's paper had arrived, one didn't know how to explain the closed shells. So the hope was that by means of phase relations, one could explain closed shells and perhaps also explain that there were quantized solutions at all. Born, quite correctly, had stated in the seminar that if we took the phase relations — and that we must do from the present state of physics — then we must study those papers of the astronomers which dealt with the problem of phase relation in the planetary motion and deviations from the phase relations. That is, what happens if you make small perturbations around a phase relation. Born knew — because he had a very good knowledge of all these things — that the astronomers had done a lot of work on these things. That was Bohlin's methods and so on. So he thought, "well, the physicists apparently have to study that now." At that time, of course, one still hoped that by applying classical mechanics to a many-body problem and then picking out those solutions which were real periodic solutions, namely, solutions with phase relations, then one could hope to apply integral pdq. In the course of time, of course, one came away from it, but that was still in the old spirit of the integral pdq business. As I told, still at the Gottingen meeting Bohr did believe in the phase relations and explained his closed shells by means of phase relations.

Kuhn:

Did he? That, you see, I had not realized.

Heisenberg:

Oh, yes. At that time he still believed in the phase relations. The Pauli paper was definitely later. When did Pauli's paper appear, on the Pauli Principle?

Kuhn:

It was submitted within a couple of months after you and Kramers submitted the joint paper. It's late in '24.

Heisenberg:

Oh, yes. So it's definitely much later than this period. Because Pauli introduced an entirely new principle, namely, the principle of having only one electron in each orbit; that was something entirely different, and had nothing to do with phase relations.

Kuhn:

I'm interested that it was particularly the question of closed shells that was connected with this because nothing is said about that at all in this paper.

Heisenberg:

In my paper on the phase relations with Max Born? I see.

Kuhn:

That doesn't mean that that was not what was in your mind because you have no occasion to apply it to that. It must also have been involved with the problem of the helium atom.

Heisenberg:

Born was very conservative in some ways; he would only state things which he could prove mathematically. He thought that our statement about how to give a phase relation was a correct statement, but whether it would actually apply to quantum theory, and how, and so on, he would leave open because he knew that that was a difficulty. I also know that Pauli criticized this idea of the Phase relations rather early. I don't know whether that was already in '22, but I remember that he several times told me, "Well, these phase relations of Bohr — that is swindle. That I don't believe; that is not the real reason for the closed shells." But at what time that was, I couldn't recall.

Kuhn:

We've already said a little bit about the helium atom problem. This becomes for some people just what you said earlier you thought the Pauli paper on the hydrogen molecule ion was the first sample of — the case where one can really do the problem far enough to show that one is getting wrong values and that it's not going to get better.

Heisenberg:

Yes. Well, I would say at that time that was already the intention of the paper. I mean, in some way people feel uneasy about the old methods and say, "Well, it doesn't really work out; it shouldn't be that complicated," and so on. Then one finally decided to try the opposite — to try to prove that it's wrong by working it out consistently with the old methods and see that one does not get the right results. That then is what had happened in this paper with Born. Probably at the time when this paper appeared, I should say, many people thought, "Well, it couldn't possibly have been right." For instance, the Compton effect and these things already at that time were in the air and people felt, "Now, it can't be true in the old way." So one went away from the integral pdq just around that time, and the paper, of course, fitted in quite well with it. For my mind, however, this paper was not the first definite proof; it was a kind of step in the many proofs one had already. As I said about the Pauli paper, at least there was a definite uneasiness about the results of the paper. The paper didn't look right in the results; you couldn't exactly say, "It is wrong, but still it didn't look right.

Kuhn:

In the end of the paper on phase relations there is a very leading remark. You suggest that this view about phase relations runs into exactly the same problem that had been raised by Einstein and Ehrenfest for the Stern-Gerlach experiment. You remember that their big problem about the Stern-Gerlach experiment is that if, [adiabatically], you turn on a field the atom ought just precess where it is. Where is the energy coming from to flip it into one of the allowed positions when you have a field? And you suggest that there is the same problem here. Suppose, in the case of two rotators, you start out with no interaction between them and turn it on gradually; where does the energy come from that is going to be necessary to make them obey? You suggest again here statistical energy conservation.

Heisenberg:

I didn't recall that at all. I should say that when people discussed these discrepancies between wave picture and particle picture, light quanta and waves, and so on, then the idea of statistical conservation was, more or less, the only way out which people had. [Looks at the paper.] Well, we say actually two things that are quite interesting. I don't recall it at all, but I see we say, "We are inclined to assume that the mechanical equations are not fulfilled." That really says, "We hope for a real quantum mechanics." Then we say energy and momentum may be only conserved statistically. Well, they were the two ways out which everybody had in mind at that time. One didn't know how one could possibly keep the complete energy and momentum conservation together with the wave picture and all that. Oh, at the same time one also felt that sometimes one has to replace this mechanics by quantum mechanics.

Kuhn:

When you worked with Born on a paper like this, since you did not have the same sort of regular discussions that you had with Sommerfeld, I take it one probably had to make special appointments.

Heisenberg:

Yes, yes, yes. One had to make special appointments. I think it was more like this: he would give me a special part of the problem and say, "can you think about that, and we'll discuss it then next week on Monday morning?" Then I would try to do my mathematics and keep this picture in my mind. I would go to him on Monday mornings and show him what I had done, and then he would criticize it and so.

Kuhn:

Did he simultaneously present those things that he had done in the meanwhile, and did you discuss them together?

Heisenberg:

I would say yes. It's very long ago; I couldn't even say that, but I should say yes.

Kuhn:

Excuse me for pushing so hard.

Heisenberg:

No, no; it's quite interesting, yes. Did we mention this method of Bohlin?

Kuhn:

Yes, yes.

Heisenberg:

That was the point; I remember now.

Kuhn:

In thinking about that paper, I realize also you do refer back to the earlier paper that he had done with Pauli, on perturbation methods, the year before. Almost certainly there would have been an earlier seminar while Pauli was there, or certainly he had done important work on the perturbation theory before you got to Gottingen, though only just before.

Heisenberg:

I think one of the origins of this paper was that Born had given to me, in the seminar, the problem of giving a talk about Bohlin's method. I remember that all of a sudden, I should say, I had to study about Bohlin's method; I went home with two volumes of Charlier's Mechanik and that type of thing. It was very hard to study all the details of Bohlin's method. I think it must have been because I had to give a talk about the method of Bohlin in the evening seminar at Born's house. After I had given that talk, Born suggested that we should try together to work on this problem of what we should do about it in quantum theory, and so we agreed to write this paper together, and that was then the outcome of these discussions.

Kuhn:

These are both quite different papers from anything that you had done while at Munich.

Heisenberg:

Yes, and in a quite different style, yes. Here we use very elaborate and rigorous mathematical schemes which are found in textbooks useful for the astronomers; it's an entirely different style. At that time I knew then the whole picture of classical mechanics and all these methods and tried to learn the details of it and to apply it.

Kuhn:

Did you feel good about this sort of work also, or did you feel impatient that there were problems about the Zeeman effect you wanted to be working on instead?

Heisenberg:

Well, I remember that I looked on such formulas like this always already with the hope that I could change them into difference equations. You know, such equations where one had differential quotients looked so obviously wrong, and so one had the feeling, "Well, after all, in the real mechanics you should have differences there and not differential quotients." So I found it nice to get into the whole mathematical scheme of classical mechanics so closely that I had a clear picture in my mind of how this whole scheme worked because then I could hope to change the picture in such a direction that someday it could become a real quantum mechanics. I never believed that this could really be the solution of problems in quantum theory, and I think also Born did not believe it. He just felt that if one worked along the old scheme one would have to take this problem seriously, but, after all, probably one should not follow this line at all, one should invent something new.

Kuhn:

But he does, at least in '24, emphasize that a way to discover what new to invent is to push the old techniques just as far as they will go?

Heisenberg:

Yes, that I think is quite a sound principle in all stages of physics, and that was probably his intention. He wanted just to say, "Let's do the best that is possible along the old lines and see how far we come. When we get to points where we can see that doesn't work, well, all right, then we know where we are." That's very much the principles along which, for instance, now a man like (Wightmann) works. He wants to push the old axioms as far as he can, and only when it's definitely disproved will he be happy about it.

Kuhn:

These two papers are the ones that grow out of that first semester at Gottingen, but when you get back there again there are suddenly, I guess, three papers on the quantum theory of molecules.

Heisenberg:

Oh, yes. But that was a side track I should say. Well, in some way Born was Interested in molecules, and molecules was one thing one talked about in Gottingen. But that was not in the main line. I remember one paper on the hydrogen molecule where I tried to get this anti-symmetry of the hydrogen, and that was not right actually. I had missed the point that it can be a triangle, which one later on saw. That had to do with developments which rather came from the crystal theory of Born's. I think Hund had been interested in molecules, and he had introduced — was it he? I'm not sure — the deformation of an atom in a crystal, so one should introduce deformability, or such a constant, and then, of course, that would play a role in forming a molecule or crystal. So for some time I thought it was quite nice to take part in this problem. But that was not my main interest. There were several papers on molecules. I remember this one about the hydrogen, but were there others?

Kuhn:

Yes. Well, the one about hydrogen, which is actually not hydrogen but water, is the third. It's one you do alone. That's "part two;" there's a "part one" that you do with Born, which is on the influence of deformability of ions on optical and chemical constants. Then there's also a paper on the quantum theory of molecules. The first one, on the quantum theory of molecules' [Ann. d. Phys. 74 (1924)] is submitted in the very end of '23, and the "part one" of the next paper, ["Uber den Einfluss der Deformierbarkeit der Ionen auf optische und chemische Konstanten," Zs. f. Phys. 23, 26 (1924).], is submitted in 1924. Those are terribly different; they're both on sort of the same subject, but they're terribly different papers.

Heisenberg:

Well, I would say these papers come just from Born's line of interest. I mean, Born was interested in crystals, and therefore also in molecules, and he tried always to improve his calculations a bit. Then he found that this deformability was a kind of thing which might help to improve the representation of the experimental effect. Since I was his assistant he just wanted my help for doing it. So he induced me to do it. I do recall this second paper, and the third. I do not recall what the first one was. Do you recall what the first one is?

Kuhn:

I've got a few notes on it. Because it was somewhat off the track, I did not look at it terribly carefully. Well, in fact, because I was lazy about this one, what I've mostly got is photostats of a few pages of it. But I think that includes the introduction to the conclusion which will tell you just what the paper was about. [Professor Heisenberg looks at the pages.] That's really mostly an attempt to develop the perturbation theory for molecules.

Heisenberg:

Yes. A very general kind of perturbation theory for molecules. Oh, yes, now I remember quite well. That was a kind of hobby of Born I should say. Born always felt that for the molecules one must have a systematic theory where one first considers the nuclei as fixed, and then you consider the motion of the nuclei, and all that must give a consistent picture. From this picture you should be able to derive the band spectra and whatever else. I think that Born has come back to this problem later on, and if I am not quite wrong, I should even think that the doctor's thesis of Oppenheimer in Gottingen was just on this problem. So Born again and again tried to give a very nice mathematical scheme for such a complicated system which consisted partly of very heavy things like nuclei and partly very light things, the electrons. It was not my main interest; that was also suggested just by Born, and was, of course, his interest.

Kuhn:

I wanted to ask you if that would be equally true of the second paper, [on the influence of the deformability], because what perhaps impressed me most, outside of a biographical point about this, is this. This [first] paper is a very formal development of the successive terms in the perturbation calculations, and so on. There is never a reference to experiment, or any attempt to compare anything. Now the other paper is in spirit totally different. It's quite informal; it's full of what references to experiment can be found; it's the first paper in which — and this is where my own irrelevant biographical interest comes in — I have seen an attempt to use spectroscopic measurements and measurements of the quantum defect applied to the thing not in a pure atomic state and to a non-spectral problem. This is what I did in my thesis for van Vleck on the theory of solids. And there is a good deal of pushing for particular experimental results. It's hard to believe that the same man was deeply involved in both of these papers.

Heisenberg:

May I have a look at it? Well, this [first] paper was mostly, I should say, Born's. I mean, I was asked to help Born, so I did, but that was not my primary interest. Now this [second] paper. Well, I would say that is probably an outcome of discussions with Fritz Hund at that time. Hund was on the crystal side; he was one of Born's pupils working on crystals and also molecules. Hund had probably spoken to me about deformation and such things. I wonder whether I quoted Hund; did I in this paper?

Kuhn:

I'm not sure. There are a lot of references to literature in there, but not sure that I —.

Heisenberg:

Is that the whole paper, or is this just —?

Kuhn:

No, that's just the very beginning of it, and there are some notes of mine, but they probably wouldn't show a quotation. My impression is Hund's own work on molecules has not begun to come out yet quite at this point, but that may be quite wrong.

Heisenberg:

I remember that there was this one point which I found interesting, that the quadratic Stark effect and the deformability are the same things. The quadratic Stark effect was a spectroscopic issue, I mean, you could talk about the Stark effect and the quadratic Stark effect and could calculate it by perturbation theory, and some things had been done. That, of course, I knew well already from the Bohr lectures. Then I had, probably by discussions with Fritz Hund, understood that when an atom is deformed by electric fields in a crystal, then again this deformation is just made by an auto-electric field; in other words, you have exactly the quadratic Stark effect. I found it a nice idea to combine spectroscopic things with things in a crystal. Now, I don't know whether somebody else had done it before, but at least I was struck by this idea, and I found it a nice problem to work on. So I wrote this paper. It was an attempt to connect things outside of spectroscopy with the spectroscopic fact. I would say the paper was clearly an outcome from the frequent exchange of ideas among different people in Gottingen. I mean, there was this line of Born's about interest in crystals and so on, so I had discussions with his pupils, and so this paper came. I might mention another thing. I would say in Gottingen we had a rather wide education in physics in the sense that we heard about many different parts of theoretical physics. I mean, Sommerfeld was more specialized; he was just concentrating on the atoms. In Gottingen one was interested in the solid state; one was interested in liquids; one was interested in ferromagnetism. So, for instance, also the later paper on ferromagnetism actually had its origin in these years in Gottingen because I once heard the lecture of Born on magnetism. He explained the theory of Weiss on ferromagnetism, and then he mentioned — and that was, of course, the decisive point — "There must be forces between the magnets in the crystal which put the magnets parallel, but the ordinary magnetic forces are certainly much too weak, and we do not know where these forces come from." Now, this remark was a thing which I kept in mind. I knew from Born that if one would just use the magnetic forces, you would get a Curie point which was about a factor 100 or 1000 lower than it actually is. Still this Weiss theory of ferromagnetism was such a simple theory so that was easy to keep it in mind and to remember it. So I would say in Gottingen we had a rather good "allgemeine Bildung", a general education in physics. The interest in ions and solid state physics and molecules came from the same source as the interest in ferromagnetism and that kind of thing. This is also connected with the fact that Pohl was very interested in the solid state, in the optical problems of the solid state. So Gottingen has done a lot for my general education in physics, and this paper is just one example for it.

Kuhn:

This I take it showed up not only in the course work, but also in the subjects talked about as people got together.

Heisenberg:

Yes, yes.

Kuhn:

Was there anything like the cafe? You spoke of a cafe in Munich that had been frequented. Was there a similar institution?

Heisenberg:

No, there was no similar institution. Well, there was a cafe of Krone und Lanz, but I very rarely went. I would say these talks took place during the walks on the Heinberg. I mean, there was much hiking and walking around; always on Sundays there would be some groups together. On these hiking tours, of course, we would also occasionally discuss physics, so that was the "pendant" to the Hofgarten.

Kuhn:

Well, I think this is just the place at which to stop for today. There are a couple of papers that come out while you're still at Gottingen that I want to talk about, but they're papers that point directly toward this next range of topics. That is, the first of them is the paper with Lande on multiplets which gets very much into the violation of the Aufbau principle. The one that comes after it is the one on associating an interaction with two energy levels rather than with one, which, of course, gets right into the heart of the situation. So those papers, and then the transition to Copenhagen and those issues would be ideal things, I think, to start off with next week. (Recorder turned off) If you're going to talk about conversations with Kronig in Copenhagen, I'm going to turn the machine on again.

Heisenberg:

Yes. Well, I just want to mention that I do remember that Kronig once told me about the idea that the electron could have a magnetic moment and that that should be the solution of these difficulties. I think it went that way that at first I felt it was very odd, and I didn't like it just because it was odd. Everybody considered the electron as a nice sphere having no angular momentum, but then I also heard that he had told it to other people. I don't know whether it was Kramers or Pauli; they also disliked it, and they had some arguments about this factor of 2, that it didn't fit with the factor of 2 in the splitting of the levels. So in some way I pushed it away, probably not because I really could criticize it from very good reasons, but just because it looked so odd, and I didn't like it. So I think I agree with van der Waerden that at that time one did first push it away for psychological reasons, namely, that the electron should not be such a complicated thing as having an angular momentum. Then secondly, one had real reasons, namely, this factor of 2 which didn't fit with that model, or at least at that time it didn't seem to fit with the model. So one used the real reasons to support psychology at the wrong point, instead of saying, "Well, after all, this is perhaps the solution to all the troubles with the factor of 2." I don't know why; I only remember that I was not the only one to criticize it, and perhaps the main mistake of Kronig was that he didn't really fight. I mean, if you have a good idea, then you must not only pronounce it, you must fight for it, because your ideas are never liked by the other people. That's a normal thing.

Kuhn:

Let me check one thing. It may be that this is in the van der Waerden paper, and I've forgotten it. You're quite sure that you were well aware of the problem of the factor of 2 before the Goudsmit-Uhlenbeck paper actually came out? I mean, I know you very quickly wrote Goudsmit saying, "What about the factor of 2?" They'd never heard of it; they didn't even know how to show that it was wrong by a factor of 2. But I wondered whether that came after their paper or whether it had already been a reason for —.

Heisenberg:

Well, I should emphasize that at this point I may be mistaken; I mean, that's very difficult to remember for certain. But I would believe that when Kronig told me his idea, I had already, beforehand, made some calculation, which I would have called a calculation about the interaction between the Rumpf and the electron. And from these calculations, I had found that one got the splitting roughly all right, but there was this problem of the factor of 2. I think that I had that in mind already; I'm not quite sure. It may, of course, be a later interpretation of the things.

Kuhn:

Well, that's very useful. One could look at the papers from that point of view.

Heisenberg:

But I would say, at least psychologically, I didn't like the idea of putting a magnetic moment on the electron, and therefore I was glad to find an excuse for abandoning it; I would put it that I don't know who took part in this discussion. I remember that it was in the library of the Copenhagen Institute that Kronig told me, and I think there was a small blackboard on which he drew some pictures about it. I just said, "That's a very funny idea and very interesting," but in some way I pushed it away. Kronig certainly did not really fight for it; he did not say, "Well, you must now believe that is the solution," and so on. If he had pushed the point very strongly, he might have convinced me because after all he had good arguments, and the factor of 2 is not so decisive. If one would have pressed the point, one would probably have seen that there may be some subtleties about it with relativity and so on, as later Thomas had shown.

Kuhn:

That was shocking to get a factor of 2 out of a relativistic correction, wasn't it?

Heisenberg:

Yes, yes. That was very implausible. I mean, it was very nice; we admired then, of course, the work of Thomas when he had actually found it. Up to that time I thought that this factor of 2 was a good justification for not believing this idea of the spinning electron. But, as I said, Kronig did not really push the point very far, and I don't know whether I was present at his discussion with Kramers. I must have been present at some discussion, but probably there have been other discussions at which I was not present. Did you ever talk to Kronig about how he felt?

Kuhn:

In fact it was Mr. Heilbron who talked with him, and not I. You know he says something about it in his article in the Pauli volume. Mr. Heilbron was not really able to get much more than has already been printed in there and in the van der Waerden article. I have a hunch which may be quite wrong, that I'd like at least to try out on you. You suggest reasons for brushing it aside and emphasize the fact that after all the electron was supposed to be a point particle, and it shouldn't have that sort of property. Now, I wonder about one other reason for brushing it aside that may, with the work that was going on in Copenhagen at this point, have been quite important; and it may have had nothing to do with it. I wonder how you feel. All of you in Copenhagen at that point were emphasizing I think two things. One was another particular way of solving these problems in terms of non-mechanical forces, using two quantum levels for the interaction instead of one. So there was definitely another approach that you were using.

Heisenberg:

Yes, but a purely formal approach, of course. We just attached two quantum numbers. I mean, we could not give any mechanical picture for explaining these two quantum numbers.

Kuhn:

No, but isn't it also true — and this does get into something we must come back to — that you had a notion that this was the route to the new and very different quantum theory. What I would then really be asking you is, was it possible that one reason for brushing this idea aside was because it was too classical?

Heisenberg:

Well, that is certainly one element in it, yes. Oh, no doubt. I mean, at that time one was already accustomed to the fact that quantum theory is very different from classical mechanics, so one felt that it was not at all necessary that there should be a classical picture to something which happens in quantum theory. So we felt that if quantum theory multiplies the number of states by 2, that must be explained some way, but by means of quantum theory, not by means of classical pictures. And you may even say that later on then the Dirac theory of the spinning electron shows that it is almost more a quantum effect than it is a classical model of a spinning electron. The interpretation by means of the spinning electron is a picture which is only very partly correct. For instance, you can use an entirely different picture; you can say that you have a multiplication by 2 in the Dirac equation, but this multiplication means actually that the electron is not moving on a straight line, but is moving in circles — this spiraling motion. That is, I think, a picture which Schrodinger liked later on. So, that an electron would be a body which spins around an axis is not the only possible classical picture, but it is one classical picture which certainly has been of enormous help later on in understanding these things. As you say, the fact that one was already so faraway from classical mechanics made it much easier to throw away, to brush away, a classical picture because, after all, classical physics is not correct anyway, so therefore why bother about such rather queer and odd picture as a spinning electron.

Kuhn:

Let me try to put you even one step beyond that. It is, if one looks at the set of problems which convinced people that they had to make a great big break, remarkable that several of them could, as of that point, been solved within something very close to the old quantum theory by introducing electron spin. An awful lot of the problems which made the main pressure for a break and which were responsible for the sort of really deep rethinking that was going on could really have been taken care of. What do you think would have happened if the idea of electron spin had been taken seriously 6 months before your paper on matrix mechanics?

Heisenberg:

Well, I don't think that it would have shaken the general attitude. I mean, all right, one would have seen that there are problems which can be interpreted still rather classically, but by that time already the whole scheme of integral pdq was so suspicious to many people that I don't think it would have changed the situation fundamentally. Well, somewhat later we had a similar situation with respect to the quantum conditions in general. You remember this discussion with Schrodinger and Wien. Schrodinger all of a sudden said, "Well, should we not simply explain the old Ritz formula not by energy levels, but by simply saying, "There are vibrations in the atom of a cloud, and then it's obvious that the difference between two frequencies should again be a frequency, and then we get rid of all this nonsense of quantum jumps and so on." But by that time one knew already so much about the quantum jumps, about the paradoxes of quantum theory, that one could not save the situation by such pictures. So I would feel that if Goudsmit and Uhlenbeck would have come out two years earlier or if we had believed the Kronig idea, even then the situation would not have been entirely different. But it is correct in the other version, that is, that this belief in classical pictures made it much easier to brush aside that idea of Kronig. One said, "Well, after all, never mind."

Kuhn:

I have just a little hunch that a number of you, probably including yourself, would have immediately tried in the first place to see what thing would do for the anomalous Zeeman effect — that it would have done beautifully — and see what it would have done for the helium atom. That it wouldn't have done so well, but it would have done a good deal.

Heisenberg:

No, it wouldn't have helped at all in the helium.

Kuhn:

Not at all?

Heisenberg:

No, practically not at all. Well, it would have helped with the number of states; in that sense it would; but not with the position of levels.

Kuhn:

It wouldn't have given you the quantitative picture, certainly not.

Heisenberg:

No, no, no.

Kuhn:

Even the qualitative picture was evading the-old quantum theory, and it would have given you that.

Heisenberg:

Yes, that's just it. I mean, there were already so many points at which one felt that the old scheme had to be abandoned.