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# Werner Heisenberg - Session XI

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Interview of Werner Heisenberg by Thomas S. Kuhn and John L. Heilbron on 1963 July 5,

Niels Bohr Library & Archives, American Institute of Physics,

College Park, MD USA,

www.aip.org/history-programs/niels-bohr-library/oral-histories/4661-11

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### Abstract

This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Guido Beck, Richard Becker, Patrick Maynard Stuart Blackett, Harald Bohr, Niels Henrik David Bohr, Max Born, Gregory Breit, Burrau, Constantin Caratheodory, Geoffrey Chew, Arthur Compton, Richard Courant, Charles Galton Darwin, Peter Josef William Debye, David Mathias Dennison, Paul Adrien Maurice Dirac, Dopel, Drude (Paul's son), Paul Drude, Paul Ehrenfest, Albert Einstein, Walter M. Elsasser, Enrico Fermi, Richard Feynman, John Stuart Foster, Ralph Fowler, James Franck, Walther Gerlach, Walter Gordon, Hans August Georg Grimm, Wilhelm Hanle, G. H. Hardy, Karl Ferdinand Herzfeld, David Hilbert, Helmut Honl, Heinz Hopf, Friedrich Hund, Ernst Pascual Jordan, Oskar Benjamin Klein, Walter Kossel, Hendrik Anthony Kramers, Adolph Kratzer, Ralph de Laer Kronig, Rudolf Walther Ladenburg, Alfred Lande, Wilhelm Lenz, Frederic Lindemann (Viscount Cherwell), Mrs. Maar, Majorana (father), Ettore Majorana, Fritz Noether, J. Robert Oppenheimer, Franca Pauli, Wolfgang Pauli, Robert Wichard Pohl, Arthur Pringsheim, Ramanujan, A. Rosenthal, Adalbert Wojciech Rubinowicz, Carl Runge, R. Sauer, Erwin Schrodiner, Selmeyer, Hermann Senftleben, John Clarke Slater, Arnold Sommerfeld, Johannes Stark, Otto Stern, Tllmien, B. L. van der Waerden, John Hasbrouck Van Vleck, Woldemar Voigt, John Von Neumann, A. Voss, Victor Frederick Weisskopf, H. Welker, Gregor Wentzel, Wilhelm Wien, Eugene Paul Wigner; Como Conference, Kapitsa Club, Kobenhavns Universitet, Solvay Congress (1927), Solvay Congress (1962), Universitat GGottingen, Universitat Leipzig, Universitat Munchen, and University of Chicago.

### Kuhn:

As I said in the car, I think I want to talk mainly about quantum electrodynamics, but there are a few other things that partly I didn't know enough to ask, that partly have come up since. So I'll just start back and try to pick these up. The first one is a puzzle. You told me the story, which Dirac has also told me and which I had heard from somebody else also, about Dirac's not having heard your lecture at Cambridge, and so on. Since that time, through the good offices of Sir John Cockcroft, we have gotten from Kapitza the microfilm of the minute book of the Kapitza club. [The talk, entitled "Termzoologie und Zeemanbotanik," was delivered on 28 July 1925]

### Heisenberg:

I have seen the copies with Sir Cockroft. I saw Cockroft when I was in Cambridge so I studied the book, and I saw my notes on the lectures also.

### Kuhn:

Now there are two puzzling things about it. One of them is that I'm not quite certain from that title that you did in fact talk at this time about those new results.

### Heisenberg:

The point is this. I would believe that this was a kind of understatement concerning this lecture. After all, I had been interested in all kinds of level schemes, and so on, for Zeeman effect and for terms and multiplets, and whatever else. So I did consider my new paper just a continuation of the paper I had written with Kramers. I just tried to say this new scheme was a continuation of what I had done with Kramers, just a way of connecting the different levels together and saying what the amplitudes are, and so on. Therefore, I'm pretty sure that I did tell about the general scheme, but perhaps not only about this new scheme out also about the order things. At least that would be my interpretation for this.

### Kuhn:

This is, for example, a title that I think would fit at least as well or perhaps better a paper which you had recently written on a reformulation of the fundamentals of quantum mechanics for application to the anomalous Zeeman effect.

### Heisenberg:

Yes. I would believe that I had to refer to this paper. I would think that I have given a talk about all those things in which I was interested at the time, and since these things were for myself a kind of continuation. of all the papers on these two subjects, I just had them under these subjects. But I do not believe that I only spoke about these special subjects. Yes, I was also quite surprised to read it in here — it was the 28th of July, 1925. "Systematic errors in measurements of close pairs of spectral lines" by Babcock. But that means that Babcock had spoken about these things at the same meeting.

### Kuhn:

Exactly. I mean, it sounds as if it does. That's usually the way those work out. It sounds as if there would have been two talks at that meeting one of them may have been very short. Babcock's may just have been a short note. Dirac had originally thought, you see, that he was not even a member of the Kapitza Club, but he read a paper at the meeting after yours.

### Heisenberg:

But this paper had nothing to do with Dirac's q-number scheme yet.

### Kuhn:

No. And he was apparently away a good deal during that summer, so it's still possible that he wasn't at the meeting. But what was settled is suddenly somewhat more problematic again, and I'm glad to hear that you had already seen this.

### Heisenberg:

I had seen it, and of course I asked myself what the matter was. I'll put it this way: I was so much engaged with this whole problem that I could scarcely avoid talking about it. That's a point, I think, so I probably had not presented it as a complete theory or something like that. I did present it, but I believed at that time that it was just a continuation of these older attempts, but a more systematic continuation of which one could hope, but not know, that it would be a consistent scheme. Before you really have a definite proof that you have got a consistent scheme, then such new ideas go along the main road of such other attempts and you just try. You tell the people, "Well, I've tried this; I've tried that. It looks quite nice and consistent." So that is what I would suppose it had been, because Fowler definitely got the proof sheets of my paper. Well, it might be that I got the proof sheets when I was at Fowler's; I lived at Fowler's house. So I may have gotten two sets of proof sheets and I would have left the one to Fowler and the other one I would have sent Jack. I don't know. It may also be that I got the proof sheets only when I got back to Gottingen and then sent it to Fowler.

### Kuhn:

Is it possible that you actually talked more with Fowler personally about this and had not said anything at all about it at the Kapitza Club. I don't want to say I believe that — just is that possible?

### Heisenberg:

Definitely that would be a possibility, but, assuming this is so, you should remember that Fowler was interested in this new scheme, and he would have told me, "Well, after all, if you speak at the Kapitza Club mention something about the new scheme." Because, after all, I definitely had the hope at that time that this was a consistent scheme, that it was some closed theory. I had written letters to Pauli to that extent — that I believed it was possible I had a closed theory. So I think it extremely improbable that I would not have mentioned it there.

### Kuhn:

Yes, I would guess it very likely also that you had. That title certainly did not sound as if it was a paper that sort of took the main points to be the same main points and organizing principles that you used in the published paper. It sounds as if you would have talked about other things as well.

### Heisenberg:

Yes.

### Kuhn:

A paper which appeared in 1924, and which I gather got a good deal of attention from Jordan and Born at least, was the Van Vleck paper on correspondance treatment of absorption. [Phys. Rev. 24 (1924) pp. 330-365]

### Heisenberg:

Well, I would say that the attention came about mostly through personal talks and conversation. I felt that the people to whom I talked at the time were quite excited about the possibility, especially when Born and Jordan's paper came out, that one could write pq - qp = ih. This appealed to people because they would say, "Well, that sounds so simple; it looks very nice," and so on. So I should say it was a combination of Born and Jordan's paper on the one hand, and Dirac's paper on the other hand, which really made the whole thing.

### Kuhn:

I meant to be going back just a little bit earlier. Van Vleck wrote a paper in '24, actually appreciably before this work of yours was done, on a correspondence principle treatment of absorption. I guess it was really, even before your paper with Kramers. This paper comes very close to having the dispersion formula in it and I gather Born and Jordan were quite interested in it, particularly in connection with the work they did on a-periodic systems. Jordan says that it was really in trying to work out the Van Vleck paper better that they began to talk also a bit about schemes of transition probabilities or amplitudes.

### Heisenberg:

May I have a look at the paper? I do not recall the paper now, but it may quite well be that I knew it well at that time. Was this paper quoted by Born and Jordan?

### Kuhn:

They cite it; they cite it well along in their paper. Not in their matrix mechanics paper; this is in an earlier paper. Another version of the paper also appeared. It appeared both in the Physical Review and somewhere else.

### Heisenberg:

That was later than Kramers' first paper on dispersion. Or was it simultaneous with Kramers?

### Kuhn:

No, it's a little later. That's submitted in October and Kramers' came out in the middle of the summer.

### Heisenberg:

Oh, he speaks about Kramers' formula.

### Kuhn:

Well, if this rings no bells with you, that in itself is an answer. Jordan, in talking about some of the work that he and Born had been doing gives certain particular emphasis to this paper. I had known of its existence but had not yet paid any particular attention to it. I just wondered if it was a paper that you remembered having been of any particular interest.

### Heisenberg:

No, I only knew the Kramers paper; and then of course when Kramers and I worked on dispersion we started just going ahead. I knew that Van Vleck was very well acquainted with all these new developments, and when I came to the States a few years later I had long talks with Van Vleck and I always considered Van Vleck as being one of those who really knew the whole thing. But I do not remember this paper.

### Kuhn:

Well, that in itself answers the question quite well. Again now, still back in the matrix mechanics period, one question which was on the outline but which we said very little about. While you mere working, and particularly then after your first paper and during the course of the preparation of the Drei Manner Arbeit, I wonder what other things the three of you tried that you didn't succeed in. Clearly you must nave tried the hydrogen atom. Did you go back and try the hydrogen atom again? You had, of course, tried that first.

### Heisenberg:

I certainly tried again on the hydrogen atom, but I did not succeed. And as you know, Pauli came out while the Drei Manner Arbeit was being prepared, so there was no need to do it then. I think Pauli wrote to me in October that he had done the hydrogen atom, and that was more of less the same period that we worked on the Drei Manner Arbeit.

### Kuhn:

Did you make any attempt, for example, to find a relativistic formulation or to examine any of the relativistic properties?

### Heisenberg:

No, on the contrary. As far as I was concerned, I was a little bit disappointed that Jordan at the end of this paper would go into the relativistic things. I had the strong feeling that in bringing in relativity one brings in an entirely new feature, which perhaps was again a new difficulty and would involve new and foreign difficulties, difficulties which one really should separate at that state and at that time from the rest of the problems. So I at that time felt that one could probably change Newtonian mechanics into quantum mechanics, but one should leave out relativistic features because that brings in some entire new things which I was afraid of tackling at that point. Of course, later on we got engaged in the problem and from thence quantum electrodynamics started. I felt that you had to bring in the quantization of wave fields, which was a bit funny — different from quantization of mechanical motions — and, what was worse, that you had to use the Lorentz group instead of the Galilei group. I had a strong feeling that this becomes very dangerous. So I was glad that for sometime one could keep the two problems quite separate. I also was very glad that when Dirac and Jordan worked on the theory of transformation that all this could be done without going into relativity problems. I had, at that time at least, the impression that non-relativistic problems could be solved completely and that there was a closed scheme. As soon as you introduce the Lorentz group entirely new things come in, and then of course you just don't know what happens.

### Kuhn:

You speak of the problem of introducing the Lorentz group as to some extent a separate problem from the problem of quantizing waves. How did that idea itself strike you?

### Heisenberg:

It just belongs to this point. I was, to begin with, afraid that one should introduce the Maxwell theory, and Lorentz group, and so on. On the other hand, I could see at once, of course, that when you quantize Maxwell waves you get the light quanta, so there must be some truth in it. One couldn't doubt that. But just how much truth — that was a problem. Then there was this interpretation of wave mechanics by Schrodinger which worried us considerably, and I told you about the discussions which had taken place in 1926 here in Copenhagen. Really then for some time I had the feeling that this Schrodinger picture after all was all right; you might be able to talk about waves. But then you would have to quantize the waves as well, that is, you would nave to introduce a letter 'h' always by adding new concepts. You could never do with the classical concepts alone, but whenever you go into quantum theory you must introduce the letter 'h', and at the same time introduce all this notion of probability, amplitudes, and so on. So I was very glad when I saw in the paper of Klein and Jordan and Wigner that actually the unrelativistic theory did allow this transformation, that you could start from the quantized waves and then go over to the Schrodinger scheme for the particles. I found that this was the solution of the Schrodinger problem. I mean the Schrodinger problem in the sense that Schrodinger said, "Well, why don't you talk about waves alone and forget about all the orbits of electrons and so on, and then everything will be all right." Well, it is all right, but only when you introduce 'h' and introduce all the difficulties with probability and so on.

### Kuhn:

I am mixed up, because to some extent you seem to be talking about probability on the transformation theory, but then there is also the problem of the second quantization, or the quantization of waves, which comes really a year or more later. To some extent the transformation theory would itself take care of this problem of showing what the Schrodinger theory was about, without going over to the question, of second quantization.

### Heisenberg:

Yes. Of course I always protested against the use of the word 'second quantization.' I never liked it because I felt there is never any second quantization. You can either, quantize, which means you introduce 'h', and the concept of interference of probabilities or you don't quantize, and then you have a classical theory. But it does not make much difference whether you quantize a wave picture or whether you quantize a particle picture. Therefore I was glad to see that you can actually do either the one or the other and transform in between both. Therefore I also emphasize that what you would quantize in the second quantization are not the Schrodinger waves. What you quantize is something which looks like Schrodinger waves but only for a three-dimensional problem. For instance, helium you can treat by having a Schrodinger wave in a six dimensional space. That's perfectly all right; but this six dimensional space should never be quantized, the wave should never be quantized. You could also treat helium by speaking about Schrodinger waves as being just material classical waves, three-dimensional waves. Then you could quantize these three dimensional waves and you would actually be able to prove that the scheme which you get is then finally identical with the scheme of the six-dimensional waves of the Schrodinger equation. Therefore I hated the word 'second quantization' because you never quantize twice; that's just not true. It is true that when you introduce the Schrodinger waves, it looks like a quantization, but actually it is not a quantization when you use the three-dimensional Schrodinger waves. So when Schrodinger did his so-called classical picture, that is, a three-dimensional meta-wave in interaction with forces, the forces are a kind of refraction index for the waves and so on, this was a very nice classical picture out had nothing to do with quantum theory. It only looks like quantum theory, out it is not quantum theory. That is a thing which you may quantize, and then you get the real quantum theory, namely, the six-dimensional theory of the helium, for instance. So you probably will never find the word 'second quantization,' or at least only with criticism, in my papers.

### Kuhn:

That's a very nice way of putting the point. Now, to come back to this time still before the Schrodinger equation, did you worry about a-period processes while you were doing the Drei Manner Arbeit, or was that simply —?

### Heisenberg:

Well, I certainly worried about it, out I couldn't solve it. I always knew that this was a danger in the background, and I at least felt that someday we had to solve a-periodic problems; I also could easily see from the ideas of Born and Schrodinger that this might be a problem which you could tackle much more easily by means of Schrodinger mathematics than by matrix mathematics. But anyway it did worry me a great deal, but I couldn't solve it. We could, of course, just say we can have continuous matrices and so forth, out that was not sufficient.

### Kuhn:

What was the impact on this, then, of the Dirac q-number approach? This was somehow so close and yet so different. I wondered to what extent did any of you try from the start to work with the abstract algebra Dirac was developing.

### Heisenberg:

Well my impression was that it was very nice, and therefore a very important abstraction, insofar as it did bring out those features were essential and put them apart from the other features which were not on the other hand, for practical calculation, I preferred matrix mechanics because there I could write down something; but I could see that there was a nice point for this abstract language. It's the same process which you always find in mathematics; you speak in an abstract way about a group and so on, but still if you want to write something down on paper then you write down a representation of the group. It was more or less the same thing. I admired Dirac's being able to do the things in this abstract manner, and I felt that this was very good because then you could make it independent of any special representation, but still for the practical calculation I never used it.

### Kuhn:

Dirac seems to be one of the very few people who was ever able to solve problems with q-numbers directly. It still leaves me gasping to follow the manner in which he did that.

### Heisenberg:

Yes. Well, I think it's a problem which occurs quite frequently in modern mathematics. Some people can actually do problems without writing down representations; they can do them in a very abstract manner, most people have to write something down on paper.

### Kuhn:

I said to you, in the car that it was inexcusable bat necessary that I did not know either the Dirac transformation theory or the Jordan papers when we talked [in February], but that I now realize that those must have been really central, starting perhaps with the Born Stossvorgange paper. But in setting up the problems which were discussed here in '26-'27, is there really anything you can remember about early feelings about those papers: the deeper sense they gave one of the role of probability as simply one very striking thing; or the sense in which the Schrodinger equation now becomes a derived equation rather than one from which you start; the notion of the wave function as a probability amplitude and as a transformation function. All of these are to some extent new elements. There have been bits of them before quite clearly, but I, at least, reading them, get a sense of a depth of insight into the nature of quantum mechanics that has not come previously. I just wondered how you felt about them, talks that they may have stimulated with Pauli or with Bohr or with Born.

### Heisenberg:

First let me say that it made a very great impression on me that one now had a mathematical scheme from which one could understand why there are so many different ways of putting the mathematical scheme. In the early part of this Drei Manner Arbeit, for instance, and also in the paper which Born had written, with Wiener, he tried to do something of this kind, but in some way he didn't get through and did not find a way, for instance, of treating continuous problems. But now, by means of the transformation theory, we had this complete flexibility; we could change from one scheme to the other and even to a third scheme. One could see that at the center of the problem there was a kind of abstract algebra or group theory and then you had so many different ways of expressing the thing. So in that way I was very happy about the development. At the same time I remember that Jordan used this transformation theory for deriving what he called the axiomatic of quantum theory. He wrote down axioms — what is this, what is that probability, and so on. This I disliked intensely from the beginning because I felt he was introducing into quantum theory that kind of concept which mathematicians use and which is too far from physics. You will remember that Born was always a little upset when some physicists criticized his mathematical attitudes; he told you about a talk he had with Pauli on the train from Gottingen to Hanover when Pauli had criticized him tremendously about "Gottingen Gelehrsamkeit." And in some way I again felt that this axiomatic scheme was leading us a bit away from the physical content of quantum theory. I could not object to it, because after all it was correct physics, but I felt a bit uneasy about it. So did Bohr, I should say. In some ways we would probably nowadays say that this was the final formulation of the mathematical substance of quantum theory. Well, perhaps I should say that there's always the following element in it. When you axiomatize a theory, as for instance Newton had done in classical mechanics, you say 'these are my assumptions, these are my axioms,'; then the whole thing is consistent and all the rest follows. Then from this very moment on you don't know whether this whole scheme has anything at all to do with nature because then it's closed. You maybe lucky and it may actually fit to nature in a very large number of observations; all right, but you never can say how much it fits. I mean, in some way you have lost contact with nature; there is something which is closed, in itself. I felt that this was what was going on, that this was what was going to happen; therefore I felt uneasy about it. Still it was absolutely necessary in the development.

### Kuhn:

Now does this mean that you felt happier with the Dirac paper? The result in the Dirac paper are almost identical, but the whole spirit of the paper is very different.

### Heisenberg:

Yes, I was more happy with the Dirac paper than with the Jordan paper; that's quite correct. Because Dirac kept within the spirit of quantum theory while Jordan, together with Born, went into the spirit of the mathematicians. Still the two papers were identical in all essential points.

### Kuhn:

There is very fundamentally in the postulate system, or axiom system, of the Jordan paper, but not in the Dirac paper, the idea that if you have two variables that have a kinematic relation classically, then there must be a quantum mechanical probability relation between them that is independent of the dynamics of the situation. This seems to me to have been quite an important novelty. The probabilistic interpretation of the wave function up to that point has depended very much on the dynamic of the situation as it is put into the Schrodinger equation itself. I gather Pauli had some role in this formulation of it. Jordan acknowledge conversations or something of the sort. I just wondered whether you had been in on any of those or remembered any discussions of that idea, which seems something of a key idea.

### Heisenberg:

I remember very little of it. I remember that I always believed one could not distinguish so well between dynamical and kinematical connection. Actually I think my first paper was called Kinematical and Dynamical Connections. But I do not know of any special discussions which took place there. Maybe between Pauli and the others.

### Kuhn:

No, you would not necessarily have been involved, but I know you were closely in touch with Pauli yourself, at least by mail, in this period, and I just wondered whether anything had come from that. Jordan also introduces the idea that a little later proves quite important: that the fundamental way of recognizing what the conjugate impulse to a given variable is, is in terms of the probability function, exp. 2 i pq/n. This must be the probability function relating the two and this is really the definition of a conjugate variable. Just a little later, in the second part of the Neue Begrundung, he then recognizes that you can then have variables that are conjugate to each other that don't obey the commutation relations. You see, it's that which ultimately enables him to get anti-commutation and to handle Fermi statistics. That really goes back into this new definition of conjugate variables.

### Heisenberg:

Yes. I do remember a little of this development. I only know that when I first heard about the anti-commutation relation I was very surprised that this would work on account of, say, the Poisson bracket story in classical mechanics. I thought it should always be the commutator; but then I could see that the anti-commutator was all right and of course that meant one step further toward rather abstract connections, one step away from classical physics. One could see that this had now happened, but I had not seen it in the early stages. That was definitely a surprise to me when I heard it. Of course it came about by the distinction between Bose statistics and Fermi statistics; one knew that Bose statistics had this representation as quantized waves and therefore it was not unnatural to hope that there should be a similar representation with the Fermi statistics. But still it was quite a surprise.

### Kuhn:

That that turned out to be the way to do it?

### Heisenberg:

Yes. At least, this was a part of the development in which I did not take part; when I saw it I was of course very happy to see it, but I had not taken part in it before.

### Kuhn:

But let me say that the notion that the commutation conditions need not be fulfilled by variables that are canonical in this other sense that Jordan introduces is already in the transformation theory in the Neue Begrundung which you were presumably very much concerned with in the work on the uncertainty principle.

### Heisenberg:

Yes, but my attitude would probably have been that I would have said, "Well here again some of these mathematicians try to find the most general scheme; well, what's the use of it. After all, you should only be forced into it by nature and if you are not forced, why try it?" This may be quite wrong, but still it's a very natural thing to feel.

### Kuhn:

Both Dirac and Jordan in these separate papers come out very firmly with the idea that you can only get probabilistic information. Now so far as I can see that is the first time that anything of quite this sort has been said, and of course it does lead directly in to the next, and in a sense, final stages, that you get to later in the year with the uncertainty principle. But I was surprised to find that clear a statement and I take it that this is related to the thing that Pauli is quoted as saying: "You can either talk 'q' language or 'p' language but if you talk them both together you —." What sort of response from you or others or Bohr did that particular formulation, which does come in both those papers, call forth?

### Heisenberg:

I should say that one did put these remarks into the same region where one puts other remarks to the effect that one has to divide the phase space into cells of size 'h' each, but the form of the cell is not very important. You can make the cells round or square, very long or very narrow, and that kind of thing. So everybody knew very well in some way that after all the form of these phase cells is not so important, but the size seemed important. The whole problem was: in what language could you express this fact; how could you state it; how does it relate with the experimental situation? Because, after all, in the experiments you saw electrons moving with a certain velocity at a certain point and so it looked as if the electron should have a momentum and should have a position. This whole thing was in kind of fog; one couldn't see clearly what it was all about. But everybody felt there mast be something of this kind. Pauli once wrote to me that he wanted to leave the walls of the cell free with only the size fixed, but how could he do this mathematically? You have to say-something about the walls of the cell; you can't just leave the walls open. So there was much talk about it, but without any clear notion. Certainly these uncertainty relations were not something entirely new to everybody; it was something everybody had expected. Only this special formulation with average error, that kind of thing; that was perhaps new and did come out of the transformation theory. Therefore I liked to apply the transformation theory to transformations from one instant to another instant of time, which was new at the time. I remember Bohr was a bit surprised that one could use it that way; of course then he agreed about it. But there one could see quite clearly that if you make the one more accurate you lose some accuracy at the other end, and so the absolute minimum which you can achieve is a Gaussian function. On the other hand, I would say the main effort which had to be made at that time was to understand that it's not the problem to describe the experiment as it seemed to be, but rather to say that only those things exist in experiments, exist in nature, that do fit intc our mathematical schemes. You know, for some time the idea was that we had to find a mathematical scheme to fit the experiments; the experiment: seemed to show the electrons having a certain position, having a certain velocity. Then all of a sudden you say, "Well, only those things exist in the experiment which do fit to our theory." You turn it around, you know. And this turning around was a real effort; that one should dare to say, "Well, nothing else happens ever in nature, but only those thing: which do fit with the mathematical scheme."

### Kuhn:

Was that as a program consciously and explicitly formulated?

### Heisenberg:

This turning around, you mean?

### Kuhn:

Yes, were you aware of it and did you talk about this as the new way of going at this problem?

### Heisenberg:

Well, I remember that once I had a long discussion with Niels Bohr in my room in the institute. I lived in (Harald Bohr's room). This discussion went up till about half past twelve at night or something like that. And then I was very excited about the discussion; I was half angry: about it. I went through the (Faelled park) for a run, you know, for one hour's walk and then I felt, ""Well, after all, why not simply say that only those things occur in nature which fit with our mathematical scheme". It occurred to me, "Why not just turn it around?" Then, of course, in the moment that you say that, you must say, "Well, after all, you see electrons moving there and what do you do about them?" Then you start thinking, "Well, could you not try to measure it more accurately," and then you come into these arguments with the gamma ray microscope and so on. So I think this turning around of the (impression), at least for me personally, came just in that night at the (Faelled park). But then from that time on I tried to see whether the experiments will go together with the idea; then I remember this discussion with the young Drude in Gottingen about the gamma ray microscope and tried to prove it there, and so on. And, as you know, in discussing the gamma ray microscope, I first made a rather bad mistake which then later Niels Bohr corrected and so on. That I told you already. But I would say the main effort was really to reach that point where you feel now you have to turn around. That is not so trivial. Later on it looks quite trivial but it isn't to begin with.

### Kuhn:

This is a terribly important point, both as a point and as a story of this particular night. This is brand new. We did not get this last time.

### Heilbron:

I'm a little handicapped because I'm not quite sure what you did talk about last time. Do you remember by any chance what the content of that conversation with Bohr that evening may have been?

### Heisenberg:

Well, you know we always discussed problems and what do you say in quantum theory about such a thing as an electron track in a cloud chamber. You cannot quantize it because it's not a periodic motion and still it's a motion and it has a 'p' and it has a 'q' and what shall you do about the 'p' and 'q' and so on. Why does it fit into the continuous spectrum? At that time, Bohr was very much inclined always to use the Schrodinger picture; that is, to go forth and back between wave and particle picture. That was a thing which I didn't like too much because I felt that at least quantum theory seems to be a consistent scheme and so we should be able to talk about nature by only using this scheme and not introduce any other schemes even if they are mathematically connected. So I was very happy about the transformation theory which just existed at that time. Well, this idea that one could turn it around occurred after this discussion and what was the actual content of this discussion it's very difficult to say. It's so long ago.

### Kuhn:

But again, we've said one thing that I had begun to wonder about and that I would really like to pin down more. Part of what was at issue in the differences of opinion that went on in this year had to do with the fact that Bohr was thinking more and more about the dualism and that for you, you didn't want the dualism, you could transform from any one to any other.

### Heisenberg:

Yes, for me it was clear that ultimately there was no dualism and after all, we had a closed mathematical scheme and this scheme was just one scheme and not two schemes. At the same time, I did realize by means of Dirac's and Jordan's papers that this scheme, which was a complete and unified scheme, if I may call it, was very flexible, and therefore, if there was dualism, this dualism just represented that flexibility of the scheme. You could also call it not dualism but pluralism or whatever you may call it. Because after all, you can transform it into many other schemes. Therefore I was always a bit upset by this tendency of Bohr, of putting it into a dualistic form saying, "Here we have the waves and we can work with the waves and here we have the particles and we shall play around with both." In some way I didn't like it so much. Perhaps also I didn't like it because I didn't want to go too much into the Schrodinger line of thought. I just wanted to stick to the matrix line.

### Kuhn:

In that sense, one would go on to ask, there are still important elements of the dualism as against pluralism left in the principle of complementarity. How do you feel about it in that more refined form?

### Heisenberg:

You mean nowadays?

### Kuhn:

Nowadays, but it, after all, goes back to Como and it goes through all the measuring problems that Bohr worked out before and in the years immediately after Como.

### Heisenberg:

Well, I should say that it is quite clear nowadays and it was already quite clear in those years that the two pictures, wave and particle picture, are the two most important pictures which we nave and also those two pictures about which we can talk (in ordinary) language. We have got the words 'waves' and the words 'particles,' so we have got a language by which we can talk and in so far it's quite nice to talk about dualism. There are other ways of transforming but they are actually more abstract, not so definitely connected with our pictures. In so far, I don't object nowadays very much against the dualistic description if only people keep in mind that actually they mean only one theory. I remember a discussion with Lande a few years ago in which he actually thought that quantum theory was a dualistic theory. But that was a misunderstanding since actually it is a very unique or unified theory not dualistic, only it looks dualistic when you translate it into ordinary language. So some misunderstandings by some people may have come from this emphasis on the dualistic nature of the interpretation. But Einstein's difficulties in 1927 at the Solvay Conference were actually directed against this idea of turning the question around. So Einstein did not believe that one could claim that only those things existed in nature that did fit with the mathematical scheme. So he always tried to disprove this fundamental assumption. And therefore his discussion on the light quanta which comes out of this later, and all these nice experiments.

### Heilbron:

Did you yourself spend much time trying to untangle these puzzles of Einstein? It is somehow rather curious that Bohr seems to have been the one to do it.

### Heisenberg:

Well, Bohr was, of course, most anxious to untangle the thing, but I think it was a kind of fight with some [???] people who have [???]. Well, Einstein usually put the question rather early in the day and then, of course, the problem would be discussed very eagerly among Bohr and Pauli and myself. I think it was always the three of us. But then Bohr would remain alone in his room for a few hours and Pauli and I would discuss it and in the evening we would come together again and say, "Well, what do you think now about it." But mostly I would say it was Bohr who was very eager to give the correct answer by at least late in the evening.

### Kuhn:

Well, now after Solvay, you spoke very impressively of the sense in which the burden of responsibility shifted and now it was up to the opposition to make a case. So far everything had been knocked down. Now at that point Bohr does not stop doing measurement problems at that stage of the game and I've just been talking earlier in the afternoon with Casimir, who says when he was here in '29 and '30, problems of this sort were still very much on Bohr's mind. And, of course, this goes on into '32 with the paper with Rosenfeld. But I take it that you yourself did very little more after '27.

### Heisenberg:

Yes, I felt after all, after '27 that things were more or less solved and it's up to the other side to disprove it if they wanted to and therefore I just felt, "Well, now I shall try to apply it to other problems." Well, at the same time I started teaching; I became a professor in Leipzig. I had to learn classical physics which I didn't know at all at that time, so I did make many mistakes in it in giving my first courses, in thermodynamics and that kind of thing. So I tried to find nice applications of quantum theory and there came the paper on ferromagnetism and then we had the applications. Well, Bloch was my assistant at that time. There were applications of theory of conductivity and so on. And already a few years later then I started to get interested in the relativistic side of the problem. Of course, everybody was very excited when Dirac's paper on the electron came out, but again I was almost horrified to see what entirely new problems would now come because then we had the negative energy problem and the holes and whatever. In some way I had hoped that we would have a few quiet years in which we could just apply the old scheme to many problems like conductivity and crystals and ferromagnetism or whatever else.

### Kuhn:

I want to talk again about the Dirac paper and the reactions to it. I don't want to let you get quite that far ahead yet. On the Uncertainty Principle paper, at the end of it, you have a note about the discussions with Bohr which have convinced you of certain things that need to be changed. The note sounds as though these discussions probably had taken place at a time when it was too late to change the paper or when yo had not changed the paper. I'm not at all clear from it whether you actually revised the paper in the light of these discussions with Bohr, or whether you let it go the way it was, and simply said that there are revisions that need to be made.

### Heisenberg:

Well, actually it was this. There was, as you know, for some weeks a rather strong disagreement between Bohr and myself and there was some tension. That was after Bohr came back, because I felt that now all problems are solved. Especially Pauli's letter had convinced me that that would be so. But Bohr felt that the problems had not been solved. He was not too happy about this idea of Uncertainty Relation and so on. Then he had shown that my discussion of the gamma ray microscope was not correct and so in some way that did prove for Bohr that I had not solved all problems, at least not correctly. Still, I felt that now the problems are solved. I had made a slip, and so on, but after a few weeks of tension we discovered that the differences were so small so that it was really not worthwhile to talk too much about the differences. Then Bohr suggested, "Well, let's do this." He agreed then that it was a good idea to talk about the Uncertainty Relation. He agreed that this was a way of formulating things which was very sensible and on the other hand, I did agree that he was right in the gamma ray microscope, so we decided that I should just add this note which clarified the point and then we would possibly write something together or Bohr alone would write something about it. There was finally quite an agreement about it. But you could, of course, see from this note at the end of the paper that there had been some difficulty in arranging it.

### Kuhn:

If I remember correctly, that note was actually added in proof. Had you sent the paper in before Bohr got back and before these discussions took place and then you added that in proof?

### Heisenberg:

Does it say "added in proof?" Does it say that?

### Kuhn:

I think it does and I'm pretty certain that I have it here.

### Heisenberg:

I would have imagined that it was added before it was sent to the printer, but it's difficult now to remember. It was so long ago.

### Heilbron:

Well, wouldn't it have been rather unusual to have sent it in before Bohr had approved?

### Heisenberg:

Oh, certainly, I wouldn't have sent it before Bohr had approved of sending it. No, no, that was not the problem, out there could have been something of the kind that I would have suggested to Bohr, "Well, you see that Pauli agrees completely with the paper, so would you not agree that I send it to the printer." Then he would say, "All right," but at the same time in his heart he would not agree.

### Kuhn:

It was added in proof.

### Heisenberg:

It was added in proof. So probably the situation was as I described it just now. That is, that I suggested to Bohr that now I want to send the paper to the printer because Pauli has approved of it and everything seems all right. Then Bohr probably said yes, and so on and then I had sent it away but certainly with his approval. I would never, never have sent a paper without his approval. But then in the meantime, Bohr got more and more dissatisfied and he would discuss it over and over again, you know, that kind of thing. But anyway this phase of disagreement was only a very short duration, I should say. Perhaps two weeks or so.

### Heilbron:

What was the real core of his disagreement?

### Heisenberg:

I should say that he had thought himself into this scheme of dualism. He had come to the idea that we always, needed two pictures, we had to play between the two pictures and you know his mind was still less mathematical than mine, so he was not too much impressed by mathematical consistency or non-consistency. He would simply say, "Well, have I understood how the thing works?" And he would say that to understand means to use the two pictures, waves and particles, and to play back and forth between the two pictures. Now, here was a paper which tried to go entirely on the one line, namely on the particle line, and simply apply on the particle line these ideas of transformation using the flexibility of the mathematical scheme, so he had felt, "Well, this man forgets one half of the picture. If you only talk about the particle side, you forget one half of it. It may be consistent, but it's not the real story."

### Kuhn:

Do you remember whether in this connection he used this Riemann surface?

### Heisenberg:

The Riemann surface picture. I don't think he would have used it just in that connection. He definitely spoke quite frequently about the Riemann surface analogy, but I don't think it played a special role in these discussions.

### Kuhn:

Hund said something to me that I think must tie into this picture and I ask you whether it seems likely that it represents the same thing. When he first came up here in'26 Hund was doing his first molecular spectroscopy paper, which is the first paper in which he makes use of wave functions. He says that he shows this to Bohr and he doesn't really remember exactly what Bohr said, but he had in it the usual Gottingen disclaimer of the physical significance of wave functions, but they're easy to use as mathematics. Something of this sort, which is no longer in the paper. And he says Bohr says, "No, you shouldn't say that." "There's something really more physical about the wave function than this allows." And he says that that was the first time that he got any idea that there would be physical significance to this function. That is the beginning of the same period in which your own discussions with Bohr must have been taking place and I wonder whether that doesn't illustrate also the attitude of Bohr.

### Heisenberg:

Oh, yes. That fits exactly into the picture. And also the Klein-Jordan-Wigner story fits in quite well because I felt that Klein-Jordan-Wigner had just cleared up this point. They have shown that you can use the wave picture. All right. But then it's not the Schrodinger waves. So these Schrodinger waves which you use for calculating the stationary states of helium are not a classical picture. They never play any role as a classical wave picture. So if you have a classical wave picture, then there are those waves which Klein-Jordan-Wigner would quantize after wards, not the Schrodinger waves in many dimensional space. The Schrodinger waves in many-dimensional space are not the things which you should use in a classical picture. I think it also helped in improving the discussions between Bohr and myself, because Bohr then also saw, "Well, after all this classical picture has to be quantized again before you can actually use it."

### Kuhn:

Dirac was here in that first full year when you came up and was here during that fall. Professor Hund tells a story, I believe in his piece in your Festschrift, of Dirac's having ,made a bet that within a year one would understand what spin was all about.

### Heisenberg:

Oh, yes, yes. There was a theory about it.

### Kuhn:

Dirac now has no recollection at all of this, and is a little dubious. Hund is not sure whether he heard the bet, or whether he heard about it from you. Do you remember about that at all?

### Heisenberg:

Not very well, no. No, I remember there was Pauli's idea of the spin. That was a bit earlier. That was — well, when was the Pauli paper?

### Kuhn:

The Pauli paper is '27.

### Heisenberg:

Not earlier?

### Kuhn:

No, because you see the Pauli paper depends on the Jordan papers to some extent.

### Heisenberg:

Well, the paper which Jordan and I had written on the Zeeman effect, was that after? That's earlier?

### Kuhn:

Yes, that's quite shortly after the Drei Manner Arbeit. That's the spring of '26.

### Heisenberg:

I see. Well, Pauli's paper was earlier than Dirac's or was it later than Dirac's?

### Kuhn:

Well, it's earlier than the Dirac electron.

### Heisenberg:

Earlier than the Dirac electron, ja.

### Kuhn:

It's fairly early in '27, and Dirac's electron paper is fairly early in '28. There's almost a year in between the two. If there was such a bet while Dirac was in Copenhagen, it would be before at least the submission of the Pauli paper.

### Heisenberg:

Well, by that time I was not in Copenhagen because I went to Leipzig in the autumn of '27.

### Kuhn:

But you were here during the year in which Dirac was here in the fall.

### Heisenberg:

Yes, yes.

### Kuhn:

The bet itself is unimportant; the important issue is whether Dirac was deeply concerned about the spin problem. As Hund tells the story, he says Dirac almost won the bet because just over a year later he got the explanation of spin. Dirac has no recollection of having been very much concerned with what the explanation of spin was and therefore the whole question as to whether there was such a bet or not becomes more important, not for the bet, but —.

### Heisenberg:

For the role in the development. I see. Well, I don't recall. No, I don't know. I remember that the Pauli paper with this doubling was, of course, something which was widely discussed and one had the impression, "Well, there's something still in the back of it." It's not the end of the story, it's the beginning of the story.

### Kuhn:

Did Pauli also feel that way about it?

### Heisenberg:

Well, I don't know. Well, nowadays the difficulty is that when you think about such an old question you nowadays come into such a problem by concepts which are certainly more modern like group theory, where they speak about the two valuedness of the representations, of the Lorentz group which, of course, we didn't know at that time. The Dirac paper did come as a complete surprise to me. There's no doubt. I knew Pauli's theory of the spin very well and I thought it was a very convenient scheme. I did not feel it was something very excitingly new. I just felt it was very convenient, very nice. But that one should use it in the way Dirac did — to take the square root out of the Hamiltonian —. That was entirely new to me and very foreign to me so I was very surprised that this would work out. But I don't know about a bet, no.

### Kuhn:

In the question of the bet, this is what is at issue for me: if you take the Dirac paper as it is written, it simply would not be correct to say that Dirac used the Pauli theory to take the square root out, because what Dirac says in the paper, in so far as the paper can be taken to represent his thought, is that he is looking for a relativistic wave equation and he adds the further condition that if the transformation theory is to be preserved, which is his basic postulate, then it's got to be a linear equation. Then he does this and is in effect surprised to find that he gets spin. He doesn't put spin in at all. He gets it out.

### Heisenberg:

I should say that's a way of representing the paper. We must ask Dirac.

### Kuhn:

I have asked him, and I think he now thinks that he was not looking for spin when he did that. He was looking for a relativistic wave equation, a linear relativistic wave equation.

### Heisenberg:

But he must have known at that time that at least Pauli had deduced such a funny quantity sigma, which has a property that the sum over "i" of iπ^{2} is just the sum over pi squared. And that is such an interesting property that he must have seen at once that such doubling might do it.

### Kuhn:

Well, I think he surely uses the Pauli spin matrices at some point when it comes to working out his own four by four matrices. But I'm not at all clear that he's thinking about spin at all when he starts on that work.

### Heisenberg:

Yes, you're probably quite right that he did not try to introduce a spin, he just tried to take the square root of the energy because he felt that was necessary. Actually, it was not necessary. That was not correct what he thought, but still, that's what he tried and he did find the spin in that way, so he felt that now he has found a proof why there must be spin. So he really felt that he had given the reason for having the spin.

### Kuhn:

Well, was that problem of the reason for spin one that was much discussed at the time of the Pauli paper and in Copenhagen? It was now a bother?

### Heisenberg:

Yes. It was a kind of a bother. In the early times we had this nice electron which had complete spherical symmetry and now all of a sudden one had introduced dissymmetry of the electron, so one had to ask, "Why should the electron have this kind of lack of symmetry?" Therefore, people were not too happy. Of course, you could say, why should the electron be symmetrical, but: still, you always preferred the symmetrical things before the unsymmetrical ones so one had to look for some kind of explanation. Of course, nowadays we know that we can have all kinds of particles, symmetrical and anti-symmetrical, but still, people felt that there should be some explanation for it.

### Kuhn:

Then you would say that whether there was a bet or not, there could have been a bet.

### Heisenberg:

Oh, definitely there could have been.

### Kuhn:

This sort of issue, at least, was a live one.

### Heisenberg:

Oh, yes, yes. One hoped that somebody would find a good reason for the spin. Yes, that was definitely so.

### Kuhn:

Was there anyone with whom you were acquainted with that preferred the Darwin wave? I can guess you did not like that very much.

### Heisenberg:

No, I did not like it very much. At least I did only feel that this was an example of the flexibility of the theory, that you could always transform it from the one to the other side. Well, one could see that the Darwin picture finally was equivalent to the Pauli picture, but I never liked it very much.

### Kuhn:

Did you remember whether Bohr liked it?

### Heisenberg:

No, I don't know.

### Kuhn:

We have not talked much about your transition to Leipzig. That was somehow a part of a major re-shuffling of the location of the prominent young physicists, wasn't it? Pauli goes to Zurich, you go to Leipzig, Debye goes to Leipzig. Jordan then takes Pauli's place. There's almost an air as though somebody had sat behind the scenes and pulled strings as to what we should now do.

### Heisenberg:

Well, I should say that one had noticed that people at many universities by this time had discovered that some very interesting and new development is taking place and there are a number of young people who have taken so active a part in the development, so we should offer them good positions and try to get them for our universities. I first got a call to a minor professorship in Leipzig which I didn't take. Then I got a call for this Zurich professorship, which later Pauli took, and then Debye tried very hard to get me to Leipzig and so I followed finally Debye to Leipzig and Pauli took the professorship in Zurich.

### Kuhn:

Did you actually turn down the professorship in Zurich?

### Heisenberg:

Yes.

### Kuhn:

Why did you turn that down?

### Heisenberg:

Well, there were two reasons. One reason was that, my father felt, "Well if you take your first professorship in a different country from Germany, it may be difficult for you later on to come back to Germany and it might be more advisable to start in the old country." The second reason was that Debye had a very suggestive way of talking and he said that I should be in his place and he talked quite a lot to me and explained now nice it would be if we would work together in Leipzig. So finally I followed Debye.

### Kuhn:

So actually you had the opportunity in, Leipzig before you turned down the call to Zurich.

### Heisenberg:

Well, yes. I had actually the two calls at the same time. I got the call to Zurich and practically at the same time the call to Leipzig.

### Kuhn:

This was the major call to Leipzig.

### Heisenberg:

Both were very good.

### Kuhn:

I mean you spoke of first turning down a minor appointment to Leipzig.

### Heisenberg:

Yes, that I had turned down. That was earlier than both others, yes. That was an Extraordinariat at Leipzig. That I felt I should not take. Then actually the professor in Leipzig, Des Coudres, had died and then Debye had taken the chair in Leipzig and he suggested that I should take the official chair of Des Coudres in Leipzig which was a very good professorship. At the same time I had gotten the offer from Zurich to this professorship that Pauli later on took and then I had to decide between both and so I did decide for Leipzig.

### Kuhn:

I hadn't realized that those two had come at the same time. Well, now I take it from what you say that your new duties at Leipzig actually made a considerable difference in your mode of work and so on. You had much more teaching to do.

### Heisenberg:

Yes. Well, I had to start by doing a lot of teaching and that was the first time that I had to do the teaching, so I had to learn classical physics much better than before and that kind of thing, which I did with some pleasure. I felt, "Well, after all, one day I have to learn all these things and it's nice to do it." I liked teaching. I found it nice to have young people around. Of course, to begin with it was a very modest affair in Leipzig.. I had just one assistant and in the seminary [by 'seminary' Heisenberg means that common room in which pre- or postdoctoral students sat and worked or read or discussed] only one or two students and then, of course, gradually it grew.

### Kuhn:

Didn't it grow pretty fast?

### Heisenberg:

Oh, yes. Within a few years it was a large group. Many young people from your country came and then I had quite a group there. Bloch came very soon, Peierls, Placzek, Halpern, Teller, Feenberg, Nordsieck, Weisskopf, Landau, Houston and Eckart for some time. It grew quite quickly, yes, yes. For some time there was also a rather close cooperation between Berlin and Leipzig. At that time, Schrodinger was in Berlin and there was also London and Wigner. I remember that when I came to this idea of the explanation of ferromagnetism, I went to Berlin to discuss the matter with these people because it was kind of an application of the London ideas on the quantum chemistry.

### Kuhn:

This question of quantum chemistry is one which I've talked some about with Hund and he indicates what I had only known vaguely before how troublesome for a while the difference between his own approach and the London approach was. There was until the early thirties a good deal of something close to friction over the fact that neither of these people could see the value of what the other was doing.

### Heisenberg:

That is quite true, yes. Of course, one could see that there were two methods of approximation making different assumptions and it was very difficult to prove in which case one method was better than the other one. Well, in the case of ferromagnetism, I had actually used the London approach but also there very briefly afterwards Bloch and others could show that the other method of Hund would work just as well. So I think Slater then has worked entirely with the Hund method. It was difficult to see. There were some attempts to connect the two approximations and schemes but I remember that they went into very clumsy mathematics so you couldn't handle that kind of more general scheme, which could contain both things.

### Kuhn:

Do you remember any particular episodes in the debate about the two? Was Leipzig mostly committed to Hund's approach because he was there?

### Heisenberg:

No, I wouldn't say that. Actually we did study both approaches. I remember that I once came back to the seminar and I had just seen a paper, a very clumsy mathematical paper of some Russians who gave a more general scheme which in the one case did contain the Hund approach and in the other case the London-Heitler approach and so we thought, "Well, what about ferromagnetism?" We could at once see that ferromagnetism would be contained in this more general scheme, but still we never really could follow it because you had to write so many things down and it was no use trying it. I don't know what Hund thinks nowadays as to which scheme is better.

### Kuhn:

Well, his impression is that after about '31, after the Slater paper one could at least see how the two were related one to the other and could see the validity in both and also that they had both advanced far enough so that they were giving the same results which initially I gather they did not always do.

### Heisenberg:

The Slater paper had the very great success in that one could, after that paper, avoid using this rather complicated group theoretical concepts, of group character and so on, and actually one could just do with anti symmetry and these old symmetry schemes of Hund. So Slater did simplify the whole situation a lot. I don't know whether you recall in this Faust parody which was played in '32 here in the institute; there was a short scene where Slater is seen to kill the dragon of group symmetry, "Das indizes-beschuppte Vieh Es starb an Antisymmetrie. So that shows the importance of the Slater paper.

### Kuhn:

That raises a whole other area which is the area of the reception of group theory. In our earlier talks you kept saying, "Then we didn't know about group theory, so this all became easier or more obvious when one did." Still and all, many people's first response to the Wigner paper was to throw up their hands at this awful new mathematics.

### Heisenberg:

Yes, yes. That was the situation. On the one hand, I could see that Wigner had, by his method, solved certain problems which I could not properly solve. You know I had written something about molecules and so on. But in the Wigner paper I could see that all was much better mathematics and that it was clear and my paper was not clear at all. So it was definitely an improvement. Still, it did involve many new mathematical techniques, which so far no physicists had ever known. So we had to sit and learn group theory and read Schur's papers and that kind of thing. Everybody was a bit exhausted and felt, "Well, it's just awful that we have to learn all that stuff."

### Kuhn:

Did you in fact then sit down and learn it?

### Heisenberg:

Oh, yes, yes, I did, yes.

### Kuhn:

Hund says that he did not.

### Heisenberg:

Oh, I see.

### Kuhn:

He says he really didn't learn it until much later. I mean he learned something from it. He's already worked out some fairly elaborate but still more physical techniques of his own for doing a number of these things and he says that it was really Only later when he had to teach something about it that he did. He went on the whole using his own techniques.

### Heisenberg:

Well, I felt that when I had seen the Wigner paper, I had to learn it. So actually, I took the book of Schur and studied it very carefully and learned what a group character is and so on. So afterwards I had the impression that now I knew at least what people were talking about and I would in case of an emergency be able to do the calculation myself. Still, I was very happy that Hund would produce some easier schemes He would tell in the seminary about some other schemes and then I would occasionally just comment by saying, "Well, in the book of Schur you would find this and this lemma, and he would say, "It's all right.."

### Kuhn:

Was van der Waerden's role at Leipzig important with respect to the group theoretical formulation?

### Heisenberg:

Yes, I would say that van der Waerden's role in Leipzig was very import because he had a tremendous ability of understanding quickly what the people were talking about and then he knew all these things so well, so he would, by a few sentences of explanation, clarify at once a complicated situation at our seminar. So van der Waerden's participation in the seminary was extremely helpful. I feel that I have really learned a large part of my mathematical training from van der Waerden, just by discussing with him. I admired first his extreme knowledge. Well, he knew chemistry so well and he knew so many mathematical things and also he had an enormously quick understanding of questions, of problems.

### Kuhn:

Do you remember any particular occasions on which he made important contributions to the seminar that would illustrate this?

### Heisenberg:

Well for instance when we spoke about the two-valued representation of the Lorentz group when the Dirac paper when spin came out, then van der Waerden at once could point out that the mathematicians know two-valued representations of the Lorentz group with such and such properties and that's apparently what the Dirac matrices are and so the understanding at Leipzig of the Dirac paper was very largely due to van der Waerden's help. Well, we spoke about the Weyl spinor business. The Dirac spinor was the thing which everybody discussed, but then there was Weyl spinor business which van der Waerden knew. The others did not know about it, but then there was Majorana. He was in Leipzig and Majorana found his Majorana particle, which has no charge but still had the spin 1/2, and that, of course, was to be represented by Weyl's spinor. So we learned a lot from van der Waerden just in that respect.

### Kuhn:

Were people able to communicate with Majorana when he was at Leipzig?

### Heisenberg:

Well, it was very difficult. Of course, people tried to talk to him and he was always very kind and very polite and very shy. It's very difficult to get something out from him. But still, one could see at once that he was a very good physicist. When he made a remark it was to the point. I presume that was his last paper that he had written on the Majorana particle. He died very shortly after that, yes.

### Kuhn:

He was pretty much in isolation for a year or so before he died.

### Heisenberg:

In isolation in Leipzig, you mean?

### Kuhn:

No, no, he was back —.

### Heisenberg:

He went back to Italy but I think very shortly after that he died.

### Kuhn:

I'm not sure just how long he was back. My feeling was that he had bee back for a while, that he'd gone back to his home.

### Heilbron:

I thought it was while returning to his home.

### Kuhn:

From Leipzig?

### Heilbron:

That was what I thought, but that may not be correct.

### Kuhn:

You may be right. I've got the chronology oh that a little mixed up. On the Dirac paper, the holes were clearly a problem but my impression is that nobody paid very much attention to it at the beginning.

### Heisenberg:

To the Dirac paper about the electron, you mean? Oh, no, no.

### Kuhn:

Excuse me, I mean the negative energy levels were clearly —.

### Heisenberg:

Oh, ja, the negative energy levels and then the problems of the holes and so on.

### Kuhn:

Well, it's two years from the Dirac electron paper to his theory of the positron —.

### Heisenberg:

Of the holes, yes. The first great impression of the Dirac paper was that he could derive the Sommerfeld formula and so that he now had finally the Sommerfeld formula but with the correct attachment of spin and inner quantum number. So this was such a success that people first were enthusiastic about it and tried to learn it and only later people discovered that these negative energies are not too nice and what do we have to do about it. So you say it took two years until one got into the question with the holes. So far the negative energies were just an unanswerable problem. People did worry about it, but felt, "Well, as soon as you introduce a Lorentz group, you introduce many new and unexpected features so that is out in the open again. So one worried about the negative energies but still the Sommerfeld formula came out so well so it should contain some truth.

### Kuhn:

Then what was the reactions to the hole theory?

### Heisenberg:

To the hole theory — well, in the first paper on the hole theory, Dirac claimed that the holes were the protons. I remember that when this was discussed in Leipzig that several people, among them myself, said, "well, this just can't be true because there is symmetry between the two masses. If there are holes, they should have the same mass as the protons. Dirac made some comment to this point, but that was "faule Ausrede," that we didn't believe. And the symmetry could not be spoiled by some extra interaction; so that we did not believe, the protons. But then if one did not believe the protons, one should have concluded at once that therefore there must be positive electrons, but you know, that's a step again that is difficult to do. So we just said, "That this should be the proton, that we can't believe If there would- be positive electrons, then it would be all right, but there are no positive electrons apparently, so we don't know."

### Kuhn:

Were you prepared that easily to take the idea of an infinite sea of filled states?

### Heisenberg:

Yes, I should say that didn't worry us too much. 'One felt that after all, that's rather an abstract notion and you shouldn't take it too seriously so that might have some meaning. Yes, that didn't worry us too much.

### Kuhn:

I take it that it worried Bohr a great deal.

### Heisenberg:

You think so?

### Kuhn:

He was pretty clearly dead set against —. Dirac makes the remark that this wouldn't affect the validity of Maxwell's equations and Bohr says, "What about the static interaction of the electrons?" and Dirac sort of says, "Well, you throw that away, it's only deviations that matter. Well, this is the sort of mathematical formalism that Bohr would probably not like.

### Heisenberg:

I would agree that Bohr would, of course, not like such abstract mathematical schemes and therefore he would always try to find the physical content of it. To begin with, as you say, the physical content would just be absurd, because it would destroy all electrodynamics. But in Leipzig it didn't worry us too much. I don't know when we discussed matter with Bohr. Well, we didn't take it too seriously. We felt that it may contain some truth but only after the positron had been discovered. Then, of course, the situation was different.

### Kuhn:

Do you remember how word of the positron first got to Leipzig? There's a particle that's discovered several times. Did the Anderson paper make any impression or did it take the Blackett paper?

### Heisenberg:

No, I think it was the Anderson paper. I do remember that we discussed the Anderson paper on our skiing hut at the Bavarian mountains. Somebody had brought this Anderson picture with him and we discussed it and we tried to convince Bohr that after all there was a positive electron. Bohr would say, "How do you really know where the electron comes in? Could it not come in the other side and then it actually might be a negative electron?" And so there were some arguments and it was not quite clear what the answer would be. But at that time it was clear that if there was a positive particle, it should be the brother to the electron and this would actually prove the idea of the hole theory.

### Kuhn:

Well, Anderson had not seen the relation of his discovery to the Dirac paper.

### Heisenberg:

No, that was only seen by others then, yes, yes. But I would say that by the theoreticians at that time it would be seen, because we did never like the idea of the holes being the proton, so if the holes are anything, they should be positive electrons and if there is now a positive electron, why not say it's the same thing.

### Kuhn:

Do you remember what season of the year, or what months these conversations at the skiing hut took place?

### Heisenberg:

That was the beginning of March. Which year I should know, but that you can look up.