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# Werner Heisenberg - Session VIII

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Interview of Werner Heisenberg by Thomas S. Kuhn on 1963 February 25,

Niels Bohr Library & Archives, American Institute of Physics,

College Park, MD USA,

www.aip.org/history-programs/niels-bohr-library/oral-histories/4661-8

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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.

### Heisenberg:

I had written to Pauli after coming from Heligoland. You remember that we spoke about this letter. This letter apparently is the second letter which I had written about quantum mechanics to Pauli and it was sent together with the paper itself. It says in the letter that I am enclosing the paper, but Pauli must send it back in two, or. three days because then I will hand it to Born. I have to go away to Cambridge and then Born will send it to the Zeitschrift. Now I always thought, and I had understood from van der Waerden who had studied these things carefully, that I went from Gottingen already in June. I thought that I left Gottingen in June and actually Born then gave the paper to the periodical, to the Zeitschrift. Now, this letter is dated, if I read it correctly — it's very difficult to read in spite of it being my own handwriting — the 9th of July, 9 VII, of this year. On the other hand, that doesn't fit with my remembrance of that time because I thought that at that time I was already in Holland and Cambridge. So I just don't know what has happened. It may be that I just meant VI and have written VII. I don't know. In any case, this date should be known to van der Waerden because he claimed he had so many evidences from Born and from letters and so on that there could be no doubt about the dates. So I just mention this. It's perhaps not very important, but still it's quite interesting because it's a letter written just shortly after this Heligoland trip.

### Kuhn:

Written from Gottingen?

### Heisenberg:

From Gottingen, and the letter says, "Since I came from Heligoland, I am more and more convinced that —." That kind of thing. Then there is also this letter in which I tried to explain to Pauli the perturbation theory which actually was more or less equivalent to introducing S and S^{-1} but it was still stated in the terms of the classical theory as an expansion, S = S_{1} + 2S_{2} + . . . .. It's a quite nice intermediate step between the final theory of canonical transformations and the theory which is still quite close to the classical theory. One can see how one just tries to bend away from the classical concepts, with some effort to begin with. At the end one suddenly sees that all things become simpler if you forget about classical theory.

### Kuhn:

Do you have any recollection at all about how the theory as you develop it in that letter relates to work that Born and Jordan may themselves have been doing at the same time on perturbation theory?

### Heisenberg:

Well, at least this is a letter, if I recall correctly, which I sent from Gottingen. So it must mean that at that time we discussed matters among ourselves. Still, I would think that it's quite possible that Born did find this story with the S to the minus first power from his general knowledge of mathematics. The mathematicians had long since known that this would work that way. At what time Born connected the two things I don't know. He had the knowledge to know about the canonical transformation, so at one instance he must have seen, "Well, after all, that's just the ordinary linear transformation, or unitary transformation."

### Kuhn:

In this period, the physicists had to study a lot of new mathematics, first with matrix mechanics, and then with the Schrodinger equation. One of the first examples of this is that, after Born pointed out to you that what you have been doing is matrices, you have to go look in some textbooks.

### Heisenberg:

Well, definitely. I, of course, tried to study linear algebra and I had once done a bit of it in this book of Weyl on relativity. But then I got some textbook from the GGottingen library. I don't know which one. Then I tried to study general linear algebra. It was not so clear at that time that one had to distinguish between unitary transformations and transformations of modulus 1, and that kind of thing. So only gradually one developed a detailed knowledge of these different possible schemes. Actually, of course, one automatically very soon saw that what one did was the unitary transformations, only the word "unitary" was not well known at that time, so one had to learn it. Well, as it is quite frequently the case in physics, you find in the mathematical, textbooks what you need. Still, you find it in a form which is a bit inconvenient for physics. Then you have to "prepare" this form, to change it a bit, to suit the problems of physics. At the end, of course, the two things go well together. So definitely after having heard from Born that this was just this business of unitary transformations in some kind of space, I studied these linear transformations. At that time —.

### Kuhn:

When you say unitary transformation in some kind of space, you are giving a fairly elaborate formulation — the one that presumably goes with the Hermitian forms and principal axis transformations. What's in the Born-Jordan paper itself is matrices, and one does not-necessarily phrase this as the problem of unitary transformations.

### Heisenberg:

No, probably not, no. But in the Born paper and in the Drei Manner Arbeit, Born already thought definitely of unitary transformations. Well, he spoke about Hauptachsen transformations, which of course, is not quite correct because Hauptachsen is something real and unitary referred to a complex basis. But these details only come out later. When the Dirac paper had come out on transformation theory, then I found it quite nice to see that it was essentially the square of the cosine between two directions which made the probability. In some way, I liked this comparison, because then the sum of the cosine squared is, of course, equal to unity. On the other hand, again I saw that it was really not a cosine, it was something more complex; it had to do with these complex variables. Anyway, I liked these anschauliche Bilder to understand somehow what probability meant and why the probability could be connected with these angles or with these transformation matrices.

### Kuhn:

Do you remember any of the books that one found particularly useful, in helping you or helping other people — books you recommended to other people, perhaps?

### Heisenberg:

Well, I don't even recall what book on matrix theory I did study. I must have looked into the library in Gottingen and tried to learn something. I think I then read some textbooks about matrices and then tried to figure out myself how matrices worked. Probably one had found, just by trying, that the unitary transformation is something especially simple. Then one found again in the textbooks that these had a special name called "unitary." But I couldn't tell you which book I studied. I just don't know.

### Kuhn:

I know that Schrodinger leans extremely hard on Courant-Hilbert.

### Heisenberg:

Yes, but did. Courant-Hilbert exist at that time?

### Kuhn:

Well, the first part of Courant-Hilbert comes out in 1925. So it certainly exists for Schrodinger. At what point it exists for you, I'm not quite sure.

### Heisenberg:

Well, I certainly have discussed about these problems quite frequently with Courant. Therefore I would even take it as probable that Courant has given me proof sheets of the book. As soon as the book was there, I certainly tried to study it. But still, the Courant-Hilbert had to do so much also with the differential equations, which was the Schrodinger line, so that I was, to begin with, not so much interested in this side of the problem. Later on, of course, I studied. the book of Courant-Hilbert quite frequently. It was, after all, written in a language which was suitable for the physicist. It was not in too abstract language. It was something one really could understand.

### Kuhn:

It was even more suitable than Courant could have known when he wrote it.

### Heisenberg:

Probably, yes, yes. Obviously, yes. I remember that once Courant told me that the mathematicians had known that there must be some Hermitian forms which had a continuous and a discrete spectrum at the same time; say some part being discrete, the other one being continuous. But no example was known until the Schrodinger model of the hydrogen. That was the first example in which the mathematicians could see such a thing. So he was, of course, very fond of this development.

### Kuhn:

I didn't know that that was the first actual —

### Heisenberg:

Yes, apparently it was the first example, but the mathematicians had known that it should be possible to construct such an example. But that again in some way made me dislike mathematics more than before because I felt, "Well, after all, these mathematicians prove that something exists but they don't show it." "The physicist is not interested in what exists mathematically. I want to see it on paper; I want to write it down."

### Kuhn:

I want to ask a very general sort of question about this year and to see whether it brings any reactions. You have talked off and on about the similarities between certain aspects of the period just before 1926 and the contemporary period in quantum theory. I think we both said in this connection that there is this period in which things did not seem to be going right and you will try an awful lot of different things. There's a larger variety of approaches than there usually is. That aspect I think we've talked over perhaps not exhaustively, but I think fairly thoroughly. Now what strikes me as we come to this year from the fall of 1925, with the Drei Manner Arbeit out, we enter into what I expect is a second sort of period, rather different from the one that has just gone. Now, after a period in which people have known that things were not right, there is a basic change produced. Maybe now things are right and, if so, this ought to change all sorts of things — one's feeling about the field, the sorts of problems that one picks, the one way one talks to other people about them, the way one feels about heresy. So I would say to you, "Think of that year, that year '25, '26." How is this different by virtue of the existence first of the matrix mechanics then of the Schrodinger equation, also? Here for the first time in many years there is really a chance to say, "We have the answer."

### Heisenberg:

Well, I have once, in giving a speech about these things, used the picture which I liked because it gives the right atmosphere. I might just tell this picture. It isn't too poetical. When you do some mountaineering, mountain climbing, you sometimes find yourself in the following situation: you want to climb some kind, of peak but there is fog everywhere. Well, you have your map or some other indication where you probably have to go and still you are completely lost in the fog. You don't know whether you have got the right direction or whether you get somewhere entirely on the wrong track and so on. Then the weather becomes lighter, and all of a sudden you see quite vaguely in the fog, just a few minute things from which you say, "Oh, this is the rock I want." In the very moment that you have seen that, then the whole picture changes completely because although you still don't know exactly the way that you want to go, although you still don't know whether you will make the rock, nevertheless, for a moment you say, "Oh, that's the thing, and now I know where I am; I have to go closer to that and. I will certainly see it. When I have seen it, then I will certainly find the way to go," and so on. I think this change has just taken place in this year. Up to that time, everybody was still prepared that things would turn out entirely different. But from the very moment, say, when this matrix mechanics appeared and especially when the Schrodinger paper appeared then everybody felt, "Well, now we are on the right track. There it is ahead and we have only to go in this direction, then we will certainly find everything we need." Of course, we also realized that we had not found it, so there may be surprises on the way. These surprises one must always reckon with. Still, it's an enormous difference when you have once seen the whole picture. The whole picture means when you have seen how things can possibly be connected at large. I think it makes such an enormous difference, at least from my own impression, whether I only see details, or whether I see the picture. So long as I only see details, as one does on any part of mountaineering, then, of course, I can say, "All right, I can go ahead for the next 15 yards," or 100 yards or perhaps even one kilometer, but still, I don't know whether this is right or maybe completely off the real track. When I have once the connection with the whole, then I know, "Well, that's the right direction." That was the change in '25 — from summer '25 on, we knew in which direction to go. This impression was very much increased when Schrodinger's papers came out. It was so interesting to see that Schrodinger's papers, to begin with, looked very different. But still, I had at once the feeling, "Well, this may be," — to use the picture again — "the same rock just seen from another side; otherwise both of us are completely wrong, because there is only one rock." You can see the rock from two sides, and apparently Schrodinger had approached it from a different angle, but still it must be the same rock. I couldn't doubt that it was the same one. That was the main change. I think that, more or less, most physicists who were interested in quantum theory did feel that way. Well, it's also nice that this change takes place all of a sudden and still only by very slight changes. In outer appearance, there is very little change from the one to the next stage. But still, these changes are absolutely essential because all of a sudden you see that the whole thing may be connected like that. As soon as you see that, then, of course, you can go in this direction and don't just flounder around.

### Kuhn:

I would like it very much if we could still make it more concrete. Think of things that other people felt in the oral conversations or particular episodes which will give this still more historical form, perhaps, than it has now.

### Heisenberg:

Well, I should perhaps say that before the summer of '25, of course, many people had the impression that the orbits of electrons are not very sensible concepts. But, still, the frequencies are, and the amplitudes are, and therefore people wanted to play with the amplitudes and the frequencies and not with the pictures of orbits. And by the summer of '25, one all of a sudden saw that the whole thing may be put together in a mathematical scheme which is consistent. That is, we may find mathematical schemes which just contain these amplitudes and just contain these frequencies. At the same time, of course, somehow they have to do with the old orbits and this "somehow" just meant a certain mathematical similarity. But besides this mathematical similarity, it's something in itself, something consistent and something which might possibly later on avoid all the contradictions just because it's consistent. There was, of course, from the very beginning the impression that if we find a consistent mathematical scheme, then it should sooner or later be possible also to avoid the contradictions in the way in which we talk about it. After all, mathematics is meant to be consistent; if mathematics is not consistent, then it's just wrong. Therefore, as soon as you find a consistent mathematical scheme then you should be able, sooner or later, to find also the right words to talk about it.

### Kuhn:

Do you remember where that was said? There are perhaps two stages here; first we find a consistent mathematical scheme and then utilize it for guidance in discovering what language to use so that we can talk about it consistently.

### Heisenberg:

Well, I wouldn't know of any special formulation. In this respect, I would say everybody talked back and forth about these problems and everybody hoped, of course, for some mathematical scheme which would do the trick, which would give a consistent picture. Still, to begin with, when I had this quantum mechanics, I was almost a bit disappointed that I was still so far from using the right words. Well, one knew at that time it is a continuous spectrum which was still lacking and this continuous spectrum has its special properties. Still, it was a bit troublesome to see an electron in a cloud chamber. You see the track and yet so far you have no mathematical formulation to talk about it. It was just the simplest classical concepts which looked so trivial and still you couldn't imitate them in quantum mechanics. At the same time you felt, "Well, that is a temporary trouble and if we only work it out carefully enough, then probably we will come to the right solution."

### Kuhn:

I wonder, for example, how Bohr felt about the idea of starting with the consistent mathematical scheme and then utilizing it to learn to talk consistently. To some extent, Bohr's own basic drives would seem to me to have been the reverse of that.

### Heisenberg:

Yes, there's no doubt. That is perfectly correct. Therefore Bohr would say, was a bit uneasy about the whole thing. He felt very strongly, "Well, there must be something in it," but at the same time, he also saw that one had not solved the problem of using the right words. This way of attack — that first you must have a mathematical scheme, then you will find the language — was, as you say, just opposite to his own way, to his own attitude. Therefore, he was very much worried and then hoped that one should, from the mathematical scheme, learn what it was all about. He was not so much interested in a special mathematical scheme. Especially he was not so willing to say, "Well, let us take for instance matrix mechanics and let's just work that out, then we must find, all the right answers." He rather felt, "Well, there's one mathematical tool — that's matrix mechanics. There's another one — that's wave mechanics. And there may be still other ones. But we must first come to the bottom in the philosophical interpretation." Still, of course, it made an enormous impression on Bohr that one could now do the calculation. That was a definite proof that one had found, at least mathematically, the correct solution.

### Kuhn:

Somebody has told me, and I'm not sure what the source of this is, that Bohr was himself convinced that one would reach the end finally by a whole succession of steps — something resembling successive approximations in the remodeling of the Correspondence Principle. His great surprise in this development — now he did not say this to us himself, I never had the chance to put this question to him — was that there was really only one big step. He had expected to do this by successive approximations. Does that remind you of anything?

### Heisenberg:

Ya. Well, the point was that mathematical schemes were not something primarily in Bohr's mind. Bohr was not a mathematically-minded man, but he thought about the connection in physics. He was, I would say, Faraday, but not Maxwell. Therefore, I can well imagine that he had the idea, "Well, we have the physical concepts and then we use this mathematical scheme and then we improve it a bit; improve it there." But it was probably a surprise for him that there could be just one new mathematical scheme which would do the whole thing in one step. Bohr probably had seen already before that time that this idea of doing it just in successive approximations will always lead into trouble. It's just always the Question of consistency which is asked. Either the thing is consistent, then its just one mathematical scheme; or it is not consistent, then it may look like many steps, but the inconsistency will come out at one point finally. You cannot avoid the inconsistency if it is there. That is a point which may not have been so much in Bohr's mind but which he at least had then realized by disagreeable experiences, by finding that he always got into trouble, say with the Compton effect, waves and particles, this experience with the conservation of energy, and so on. So Bohr, I would say, by successive disappointments, learned that you cannot do much with mathematical schemes which are not consistent. The idea of using successive approximations, each of which is not consistent but which still may lead a bit further must have proved to be a difficult task for Bohr at some time or another. What one really needed was a consistent scheme, and if it is consistent, then you can, of course, formulate it in one step.

### Kuhn:

I have the feeling that Bohr had been, from the very beginning, brilliantly aware of the conflicts between quantum mechanics and classical physics, and had seen more clearly than a great many other people the need for change and so on. He never lost sight of that. He never felt, as Sommerfeld I think had felt, that this was a position in which one could stay. In that sense, he was more eager to get rid of inconsistencies than almost anybody else for many years. On the other hand, there was a sort of "higher inconsistency" which he was quite willing to accept as part of the final picture.

### Heisenberg:

Well, I would say one should perhaps distinguish between two words which seem to be very close to each other. The one word is "inconsistency" and the other is "paradox." He felt so strongly that even when one had the final answer, there will remain a completely paradoxical situation which could not be handled by any of the usual concepts so that the whole philosophy of natural science should probably be changed in order to understand what happened here. Of course, this paradoxical situation looks like inconsistency, and it was very difficult to understand or to realize that one could have a theory which was completely consistent and at the same time contained all the paradoxes. Therefore, Bohr, I would say, went back and forth; he could not to begin with realize that this was the real chance — that one could include in a perfectly consistent theory all 'the paradoxes which he strongly felt were actually there. Therefore, because he was so much impressed by these paradoxes which were apparently unavoidable, he counted always on the possibility, "Well, these paradoxes may even, in the long run, mean some kind of inconsistency which cannot be avoided." On the other hand, in the course of the development, Bohr realized that an inconsistency is something still much worse than a paradox because inconsistency means that you just talk nonsense — that you do not know what you are talking about. A paradox may be very disagreeable but still you can make it work. An inconsistency can never be made to work. I remember that at that time we frequently quoted this sentence from Hilbert who had studied the inconsistencies of mathematical axioms and who had proved that if the mathematical system of axioms does contain an inconsistency — A equal to non A — then you can prove everything from this scheme. That we applied, of course, with great pleasure to physics. As soon as you came into a real inconsistency, then you could go anywhere. That, of course, is nowhere. Anywhere, nowhere, it's just an accident. Therefore, one learned in the course of time that a paradox was not the same as an inconsistency.

### Kuhn:

But that's a very difficult and not altogether clear situation. It seems to me terribly important what you're saying. For example, it might be quite difficult, possibly impossible, to produce an abstract formulation of the difference between a paradox and an inconsistency in a formal system. I think it would be absurd for us to get into the issue of whether that can be done or not. It seems to me that what you are describing may be a very important developmental stage in thinking about this, in which one begins to want to say, "No, that isn't an inconsistency, that's a paradox." Whereas before, the two things always seemed to be the same thing. Did this distinction, which you draw very successfully now, always exist in these discussions?

### Heisenberg:

Well, I should say that this distinction has come up during the discussions of the mathematicians in Gottingen. At least indirectly and unconsciously for the physicists these discussions may have contributed quite essentially to the development of physics. I remember that in being together with young mathematicians and listening to Hilbert's lectures and so on, I heard about the difficulties of the mathematicians. There it came up for the first time that one could have axioms for a logic that was different from classical logic and still was consistent. That I think was just the essential step. You could think just in this abstract manner of mathematicians and you could think out a scheme which was different from our logic and still you could be convinced that you never get out into the open sea. You always get consistent results. That was new to many people. Of course, it came also by means of relativity. One had learned that you could use the words "space" and "time" differently from their usual sense and still get something reasonable and consistent out. So I would say it is a consequence of this whole development — the theory of relativity, the axiomatization of mathematics — which made people think in these terms, which gave the possibility of distinguishing between paradox and inconsistency. That was, at that time, rather new and not obvious to everybody. On the contrary, it just came out of all these discussions. I could not say there was a definite moment at which I realized that one needed a consistent scheme which, however, might be different from the axiomatics of Newtonian physics. It was not as simple as that. Only gradually I think in the minds of many physicists developed the idea that we can scarcely describe nature without having something consistent, but we may be forced to describe nature by means of an axiomatic system which was thoroughly different from the old classical physics and even using a logical system which was different from the old one.

### Kuhn:

There is one thing about that formulation. It's the sort of thing that's implicit if not explicit in this Born article "Uber Quantenmechanik" of 1924 [Zs. f. Phys., 26, p. 379]. And it's the same thing really in your paper that is submitted on the same day, "Abgnderung der formalen Regeln der Quantentheorie" [Zs. f. Phys., 26, p. 291]. It again runs through Born's lectures on mechanics. This is the idea of a consistent but different formal system of rules. Would that idea itself have been familiar in Copenhagen in this period, in 1924?

### Heisenberg:

Well, perhaps not familiar, but still I think that Bohr would not have objected to it. Well, that's a difficult question. That's an interesting question. What would Bohr have said about it? Well, certainly Bohr did not object to it. I have discussed so many times with Bohr. Also Kramers would say, "That's all right, yes." They would feel, "Well, let these Gottingen people try in that direction; let's see what comes out." They said this not in the sense that one must necessarily go this way, that this was the only way out. Probably not yet. But still, Bohr knew that one needed something consistent. That he must have realized by that time. I don't know the answer.

### Kuhn:

What I really meant most to be getting at was less the question at what point one had the idea of a consistent axiomatic or quasi-axiomatic system which would be different from classical, but rather at what point you get the notion, or even begin to talk about the results in terms of a notion, that when I say consistent, I do not mean free from paradox. Because that's the tough one, and I'm not sure that any mathematician would admit that you could make anything out of that notion. But remember that the famous paradoxes like Epimenides' paradox about the lying Cretans, and the paradox of the barber who shaves everyone who does not shave himself, well, there's no reason to multiply these, are regarded as inconsistencies. That is, they are paradoxes because you know that there must be a way of reformulating the system so that these will cease to be inconsistent. They're not so damaging as the A equals non A; because you can still hope to find, ways around them. But their logical status in the system is, I think, finally an inconsistency. It was I who said that I thought that there was some higher sort of inconsistency which Bohr expected to have stay. And you introduced, the distinction between a paradox and an inconsistency, and I think that's exactly to the point. I think that catches exactly the spirit of what I had in mind. But if people talked about it in this way, this is a very odd and interesting way to talk about it.

### Heisenberg:

Well, I should say that behind this there was always the experience that at least in the theory of relativity, one had a consistent scheme which also contained its paradoxes. Of course, the paradoxes in relativity were much less dangerous than in quantum theory, and so they were almost harmless. Still, one had the experience that some people were so much worried about these paradoxes that they fought relativity to the utmost. There was the story of Lenard and Stark and these rather funny people, or disagreeable people. The fact that people were so much upset by something like the theory of relativity did show how difficult it was to take a paradox and be reconciled with it. Therefore, at least this was in the mind of the physicists: that there are situations in nature which can be described consistently and still which are very difficult to understand and which somehow are difficult to talk about. In so far, the relativity was a model for the new situation. Only the. new situation apparently was still much worse. I would put it this way. Bohr had shown in his papers and by the whole development of the theory, that there were paradoxes which cannot be avoided. Whether these paradoxes were inconsistencies or paradoxes was not decided, and also Bohr left this open for many years. Still, there was the example of the theory of relativity, that paradoxes need not mean inconsistencies. Now here the paradoxes apparently were much worse. But still, relativity reminded one that one was not forced to give up the hope to find something consistent. The consistency was at least always a hope which remained and which became stronger because the inconsistencies which one tried never worked. I would say it was a development of new hope during the time from 1918 until 1925. Perhaps to begin with, Bohr had hoped. — No, he has never hoped to get around the paradoxes. He had seen too clearly that these paradoxes are inherent. I don't know what his hopes actually were in 1918. Did you never discuss this with him?

### Kuhn:

Really, he never got to 1918. Occasionally, he just waved forward from —

### Heisenberg:

I would have liked to have known his answer to this question, yes.

### Kuhn:

I think, if one has the time to really work through that correspondence, there will be a lot to be learned. I don't think the situation is entirely hopeless. But there certainly are lost opportunities there. ... [A short discussion of the extent to which Bohr could recollect events from this period is omitted here.]

### Heisenberg:

I told you about Schrodinger's visit to Copenhagen in the fall of 1926 and how Bohr forced Schrodinger to acknowledge that one could not do without quantum jumps and so on. After that time, of course, Bohr was then terribly anxious to get to the bottom of things.

### Kuhn:

Did Schrodinger then say, "If I had known."? Id've heard this.

### Heisenberg:

I think I remember this, yes. Well, of course, I don't know the exact wording but I would say that this is what he said. I only remember that it was really a very hard fight between Bohr and Schrodinger. Schrodinger was ill and stayed in bed for some time. He had some kind of flu or cold. [Mrs. Bohr] would bring him tea, and Bohr would sit there trying to convince him. I think he really, in a kind of despair, at the end said that if one had to stick to these darn quantum jumps then he regrets that he ever had taken part in the whole thing. In some way he was extremely angry about this outcome, but he could not defend his position. He saw, at least at that time, that he could not really defend a new explanation.

### Kuhn:

There are a number of places to pick up that problem with him. I wonder which Bohr himself had particularly used in trying to convince him that one could not get along without the quantum?

### Heisenberg:

I think it was especially Planck's law. He just tried to show that without quantum jumps one could just not get Planck's law. He used more or less the argument of the old Einstein paper from 1918, which was a perfectly clear-cut argument and very difficult to get around. Well, as it was, Schrodinger had the impression that now he had such an entirely new picture and, after all, he does get the correct frequencies by his picture. Why should one not forget about Planck's formula, or, in some way at least, get around it. So, to begin with, Bohr's ar bent was not too convincing for Schrodinger. In that way Schrodinger was a bit of a Viennese; he would say, "Well, after all, we don't know, we don't worry." That kind of "Schlamperei." That was just contrary to Bohr's spirit. Bohr would always try to go definitely to the bottom. Bohr would come to the point where one had to say, "Well, this cannot be decided; but at least this far it is clear." The trouble was that even Bohr at that time, of course, realized that we had not the right words yet to describe the thing. So after Schrodinger's visit we had innumerable discussions about the problems. These discussions were always of the following type. I was, I would say, the optimistic one. I said, "Well, after all, we have the mathematical scheme now. We must only do it carefully. I would like to stick to the old notions of matrix mechanics; then we will come to a complete understanding." Bohr would start from the paradoxes and would say, "Well, there are these many paradoxes and these paradoxes are not helped by the new mathematical scheme." Probably Bohr has thought of the possibility that the paradoxes would remain as inconsistencies. Then, of course, the problem came, "Do we have a mathematical or physical scheme to predict what will come out from any experiment?" If we would be able to predict for any experiment what comes out, then it's a question of the experiments. Do the experiments fit or do they not fit? The trouble was that, up to that time, one always thought that for one single experiment you can get two kinds of predictions, depending on whether you do it this way or that way. That is, of course, what one would call an inconsistency. Well, one of the famous examples, which has been discussed many times, was the electron going through two holes. You know that kind of thing. There one had the impression that from doing it the one or the other way one gets different answers and therefore one had no consistent scheme. Now I tried, of course, to show that we do have a consistent scheme; that is, for any given experiment, we do know the answer. The trouble was, that to begin with, say in October or November when we discussed these things, we were not able always to give the right answer because the thing was not worked out well enough.

### Kuhn:

These are discussions which begin immediately and go on steadily from the time of Schrodinger's visit. That was in August?

### Heisenberg:

I would say September. I should believe that Schrodinger was. in Copenhagen in September, perhaps the middle of September. After that time the discussions went on and on. I remember that sometimes Bohr and I would disagree because I would say, "Well, I'm convinced that this is the solution already.". Bohr would say, "No, there you come into a contradiction." Then sometimes I had the impression that Bohr really tried to lead me onto "Glatteis," onto slippery ground, in order to prove that I had not the solution. Now, this was, of course, exactly what he had to do from his point of view. It was perfectly correct. He also was perfectly correct in saying, "So long as it is possible that you get onto slippery ground, then it means that we have not understood the theory." I remember that I sometimes was a bit angry about it, which was, of course, natural.

### Kuhn:

This is terribly important ground that we're on now. I want to make it just as clear and detailed as we can. As you describe this, I get the feeling that you're saying, "I already thought, perhaps not in full detail, I saw where we were coming out. Bohr was very skeptical and we were already philosophically in very different positions." If that's at all right, I'd like to get you to describe the nature of that difference more fully. What sort of answer did you think you already? saw that Bohr thought was perhaps not the right way yet to go at this?

### Heisenberg:

Well, I would rather describe it in the following terms. I had the impression, "Now I have seen the connection of the whole thing. 'Seen' means seen in the fog, as in this other picture. Therefore, I cannot doubt when I only go in this direction, I will also be able to work out every detail. I don't know exactly yet how to do it, but still I will be able to do it. Then everything is all right, so far as the experiment doesn't contradict." Bohr had not had this experience, so I would say he was not so much impressed by the new development. He had a strong impression of what had happened, so he also felt that there must be some truth in it. Still, his strongest impressions were the paradoxes, these hopeless paradoxes which so far nobody has been able to answer. These paradoxes were so in the center of his mind that he just couldn't imagine that anybody could find an answer to the paradoxes, even having the nicest mathematical scheme in the world.

### Kuhn:

Now what will you point to as, at this time, the paradoxes that most concerned him?

### Heisenberg:

Well, there were problems of resonance fluorescence. A very central problem was that of the two holes. You know what I mean — an electron emitting radiation and then you have interference patterns. Do you or do you not get an interference pattern? Or, for instance, when you have alpha rays —.

### Kuhn:

How long do you suppose that had been a terrible paradox for Bohr?

### Heisenberg:

Well, I think until February, '27.

### Kuhn:

When do you suppose it began to be a terrible paradox? One can say that's a terrible paradox right back to 1905 with the photoelectric effect. One can say that it gets to be a terrible paradox only when with electron diffraction it becomes perfectly clear that you have to take this dualism as fundamental. I'm never clear when Copenhagen began to think that that was really going to be a terrible problem.

### Heisenberg:

Well, I would say that it has always been considered as a very disagreeable problem. But to begin with, when all the things were still in such a preliminary stage, everybody may have hoped, "Well, after some time, when we have more experiments, and know more about it, then we will find a solution." The very strange situation was now that by coming nearer and nearer to the solution, the paradoxes became worse and worse. That was the main experience. In spite of now having a mathematical scheme both from Schrodinger's side and from the matrix side, and in spite of seeing that these mathematical schemes are equivalent and consistent and so on, nobody could know an answer to the question, "Is an electron now a wave or is it a particle, and how does it behave if I do this and that and so on." Therefore, the paradoxes became so much more pronounced in that time. That again was a gradual process. You couldn't pick out a definite time and say, "From then on the paradoxes were so important." But only by coming nearer and nearer to the real thing to see that the paradoxes by no means disappeared, but on the contrary get worse and worse because they turn out more clearly — that was the exciting thing. Then of course, I would say that, like a chemist who tries to concentrate his poison more and more from some kind of solution, we tried to concentrate the poison of the paradox, and the final concentration was such experiments like the electron with the two holes and so on. They were just a kind of quintessence of what was the trouble. And as you say, actually this quintessence was very easily seen already in Einstein s paper of 1906 or so. It was old stuff, but still, you could concentrate it more and more and see what the fundamental problem was. To this fundamental problem it looked as if the new mathematical tool did give no clear answer yet. One just had no way of really talking about it. That was the stage in the autumn of '26.

### Kuhn:

Were there other paradoxes besides the one with the two holes? Were there other thought-experiments or other aspects of these paradoxes that you kept coming back to? You speak of the resonance fluorescence. Is this particularly the thing that you had worked out yourself — in the zero external field case the atom nevertheless acts as though there were a magnetic field.

### Heisenberg:

Yes. That again was one of the central parts. One said, "Well, after all, it must be possible to turn an atom continuously from one position to the other." At the same time one says, "There are only two or three positions. So, what is the matter? Is it three, or is it continuous? After all, three is not equal to continuum. That everybody knows. What is it?" There was also the paradox of the polarized light. Say you have a light quantum polarized in this direction. Then you have a Nicol prism and then behind the Nicol prism the light is only polarized in this direction. What has happened to the light quantum? Is it turned around? What has happened? So there were a number of experiments which were, of course, related to each other. You could vary the experiments a bit. But there were always such central questions on which you could put your finger and say, "Well, there something is still wrong." In these discussions in the autumn of '26, we always spoke about problems of this kind. We tried to find out what will probably happen if you do this or that. Now in the case of resonance fluorescence, we had the answer. The answer looked funny enough, but still we saw that this is an answer. It's a possible answer. Then we tried to see how it was from the Compton effect — you know the scattering from an electron. Now the wave in different directions has different frequencies. Would you get an interference pattern from these different waves? Now, of course, you cannot have interference between two waves of different frequencies. What happens, and so on. We talked back and forth about these problems and sometimes got a bit impatient with each other about it. I would perhaps try to say, "Well, this is the answer." Then Bohr gave the contradictions and would say, "No, it can't be the answer," and so on.

### Kuhn:

Let me make sure that I understand one aspect of these conversations. There are always at least two sorts of problems that can be arising here. One of them is, "Do we know what will happen experimentally?" The other one is, "Do we know how to fit our theory to what we know happens experimentally." My impression is that the, experimental question was also open.

### Heisenberg:

Yes, well, in some cases, of course, the experimental question was open. The point was that one thought out experiments which were very subtle and therefore had not been carried out yet. In those cases, of course, one just didn't know what the answer was. On the other hand, one had the impression already that if one would find a consistent answer from the theory, that is, if one could show that, for instance, quantum mechanics of Schrodinger mechanics does lead to a definite answer, then we did scarcely doubt that this would come out of the experiments. So we weren't so much worried about the experiment, but we were more worried about the theory.

### Kuhn:

Was there, for example, a real question as to what would have happened if you had done the two-hole experiment at very, very, low intensity? This is ultimately done and you get the statistical distribution of a single photon. I take it that for some people that experiment had to be done before they would believe that it was going to work all the way down to one photon. Was that question even open in these discussions? Was there a real possibility that if you did this as a one photon experiment you would find that if it went through this slit it went straight ahead and if it went through the other slit it went straight ahead?

### Heisenberg:

I think that we would have believed already at that time that we do get the correct interference pattern. There could not be any doubt that an electron would suffer some diffraction from the edge of the hole. That's easy enough. But then the whole point was, "Do we get on the screen behind it just an even distribution or do we get the interference between the two spherical waves?" By that time, I think Bohr and I were already convinced that we do get the interference pattern. It just can't be avoided. At the same time we felt very uneasy about it, and didn't know what it meant. Again, it was a question of getting consistent answers from the theory. As soon as we got consistent answers, then we would not doubt that the experiments would probably show the same. In the earlier stage, it was a question of the experiment. For instance, when the Compton effect was found, that was a surprise. At that time, I think most people would have thought that in the Compton effect the frequency is identical with the original frequency. That was really a surprise that the frequency can change. From the Einstein theory of light quanta, people could have known it before. At that time it was a question of experiments, but not in '26. In '26 it was more or less clear that the experiment would come out as the theoreticians wanted it to come out if only the theoreticians knew exactly what to believe. That was just the point: "Do we know exactly what to predict?" The difficulties in the discussion between Bohr and myself was that I wanted to start entirely from the mathematical scheme of quantum mechanics and use Schrodinger theory perhaps as a mathematical tool sometimes, but never enter into Schrodinger's interpretation, which I couldn't believe. Bohr, however, wanted to take the interpretation in some way very serious and play with both schemes. For instance, we did agree — that was important after Schrodinger's visit that if you had atoms only in the first excited state, that is, if through a Franck-Hertz experiment you take care that you have a beam consisting entirely of atoms in the higher state, then you would have the spontaneous '28 emission of radiation. Schrodinger would say that you would get no frequency, you would get no radiation, because you always needed an upper and a lower state to get the frequency. So in this point we were quite convinced that the quantum theoretical answer was the correct one. We did agree on many experiments which —.

### Kuhn:

Do you remember other points of disagreement and agreement of that sort? It is terribly interesting to know more about the sense in which Bohr did want to use the Schrodinger interpretation and, on the other hand, the circumstances in which he clearly knew it was not to be used.

### Heisenberg:

Well, this experiment which I have just mentioned was, of course, a part of a larger group of experiments connected with the dispersion problem of Kramers and myself. Bohr believed, and we all believed, that the physical interpretation of Kramers and my dispersion formula given in the paper was correct. So from an atom you can only have such lines which according to the Einstein conditions can come from this level and not from the Schrodinger idea of using interferences. Now let me speak of other experiments. Well, of course, there was no disagreement between Schrodinger and ourselves concerning the interference pattern behind the two holes. Now I wonder what Schrodinger would have said to the light quantum aspect of these? Of course, we were also convinced that if we have the two holes here and here, we have,say,a source of light behind them and a screen in front, then we do knock out single electrons so the complete light quantum is finally found there. I donut know what Schrodinger would have thought about this point. Well, the trouble was that Schrodinger's picture had not been worked out completely. Schrodinger saw that he would get into difficulties. Again, it was the question of having light of extremely faint intensity. That happens then? Do you find the whole energy somewhere and so on. I wonder whether the Bothe-Geiger experiment was known at that time?

### Kuhn:

Oh, I think it must have been. That was really done before the end of '25 — the preliminary results — and then the relatively full ones in '26.

### Heisenberg:

Now, what can we say about the other experiments? I wonder whether we have discussed the Bothe-Geiger experiment with Schrodinger in '26? I couldn't say that. I also wonder how Schrodinger would have explained —. Oh yes, there was this question of the wave packet which spreads out into space. I mean Schrodinger always hoped that he would somehow succeed in keeping these wave packets together, and we would always insist that these wave packets would run out into the open and then somehow would be contracted by the act of observation, but that was completely unclear at that time. There we didn't know what to say. We just felt that the wave packets do spread out and that can't be helped. One should not try to improve on this. Our general attitude at that time was to not try to change anything in the mathematical scheme, especially not try to improve such very disagreeable findings as the spreading wave packet. While Schrodinger obviously, from his way of talking about it was forced to try to see, "How can I keep my wave packets together?" Still, as I said, I just wanted to forget about wave packets and about waves because I felt, "Well, I have the quantum mechanical scheme and I will first try to follow that to the extreme and to see whether I cannot hope to predict everything from that scheme. Later on I will try to understand what the waves of Schrodinger mean." I, of course, had always in mind the old theory of Duane that one could get interference by quantization, and. I hoped that the mathematical scheme would be clever enough to do it by itself without the physicists thinking about it. And it did to some extent, but only by means of rather complicated transformations. Bohr and I tried from different angles and therefore it was difficult to agree. Whenever Bohr could give an example in which I couldn't find the answer, then it was clear that we had not understood what the actual situation was. I think I told you before that in the end, shortly after Christmas, we both were in a kind of despair. In some way we couldn't agree and so we were a bit angry about it. So Bohr went away to Norway to ski. Earlier he had thought of the possibility of taking me with him but then he didn't like it. He wanted to be alone, to think alone, and I think he was quite right. So I was alone in Copenhagen and then within a few days I thought that this thing with the Uncertainty Relations would be the right answer. I tried to say what space meant and what velocity meant, and so on. I just tried to turn around the question according to the example of Einstein. You know Einstein just reversed the question by saying, "We do not ask how can we describe nature by mathematical schemes, but we say that nature always works so that the mathematical scheme can be fitted to it." That is, you find in nature only situations which can be described by means of the Lorentz transformations. Therefore, I just suggested for myself, "Well, is it not so that I can only find in nature situations which can be described by quantum mechanics?" Then I asked, "Well, what are those situations which you can define?" Then I found very soon that these are situations in which there was this Uncertainty Relation between p and q. Then I tried to see, "Well, let us assume there is only this possibility of having p•q> h/2π. Does this make a consistent statement? Can I then prove that my experiments never give anything different?" I remembered then my old discussion with (Bockert) Drude came in at an essential point now. I did remember, "Well, yes, (Bockert) Drude told me how I could observe the orbit." Then I saw very soon, "Oh, no, now I can save it because I see that by the light quantum hitting the electron I can preserve the Uncertainty there." Well, I did, as you probably know, write the whole stuff in a long letter to Pauli. Dented to get Pauli's reaction before Bohr was back because I felt again that when Bohr comes back he will be angry about my interpretation. So I first wanted to have some support, and see whether somebody else liked it. Now Pauli's reaction was extremely enthusiastic. He said something like, "Morgenrote einer Neuzeit," now it becomes day in quantum theory. So I was very happy about Pauli's reaction on it. When Bohr came back I showed him a paper which I had written — I had written it up formally as a paper — and I showed him Pauli's reaction. I did realize that Bohr was a bit upset about it because he still felt that it was not quite clear what I had written — not in every way clear. At the same time he saw Pauli's reaction, and he knew Pauli was very critical, so he felt it should, in some way, be right. So actually Bohr went out to the country for reasons which I don't know. It must have been pretty warm at that time. And I also went to the country to a different place, namely to the place of Mrs. Maar — I think with Foster. I remember that Bohr and I once met while we were out walking — the two places are not very far from each other. I don't know whether we agreed to meet or whether we met by coincidence, but there was Bohr and Oskar Klein on the one side and I was on the other side and the three of us had a discussion. Bohr found some trouble in my paper. Apparently he didn't quite agree with my analysis of the gamma ray microscope because I hadn't taken the aperture of the microscope into account properly. That is, you could also have a microscope of a small aperture, and then it is not really the momentum itself of the light quantum which is important, but the uncertainty of the momentum which is important. It had actually been not quite clear in my paper. I didn't know exactly what to say to Bohr's argument to begin with and so the discussion ended with the general impression that now Bohr again, has shown that my interpretation is not correct. Inside I was a bit furious about this discussion, and Bohr also went away rather angry because he saw my reaction, whether I had expressed it or not. So it was a bit of a tense situation at that time. Well, a few days later we again met in Copenhagen, and Bohr tried to explain that it was not right and I shouldn't publish the paper. I remember that it ended with my breaking out in tears because I just couldn't stand this pressure from Bohr. So it was very disagreeable. Then, of course, after a few days we could, at least in this special case, settle everything. We both agreed then that if we just did it slowly it must now come out. Then it was really in some way quite easy because after a few days again we agreed that the paper could be published if it was improved on these points, and I had to agree that these were quite important improvements. So the paper came out in the form which you probably know. There was at the end a remark that Iliad discussed the thing with Bohr and definite improvements had come in by the discussions with Bohr and this was the result.

### Kuhn:

As I remember that note though, it is left that Bohr has pointed out that there are places which need improvement. It isn't clear I think in that note that very many changes have actually yet been introduced.

### Heisenberg:

Well, do you just by chance have this paper here? [Heisenberg examines the last pages of "Anschaulichen Inhalt ..." Zs. Phys. j (1927) pp. 172-98. (Eing. 23 Marz 1927)] So it was so that the original text of the paper was more or less unchanged, but there was this final note added to it. I don't recall this quite, but when I write at the head of this final note "Nachtrag bei der Korrektur" it almost looks as if the paper had been sent to the printer before we had agreed on this. But this I wouldn't believe because usually I never sent a paper away before I knew that Bohr would agree to it. Also, the date is too late, yes. The 23rd of March shows that this was at the end of our discussions, but probably we decided that it was not wise to change the whole trend of the paper and only it was reasonable to add this. Then the "Nachtrag" was sent to the printer simultaneously with the paper.

### Kuhn:

You say it was not a good idea to change the whole trend of the paper and clearly fixing up the argument about the gamma ray microscope was not going to change the whole trend of the paper. Also what you say about the disagreements with Bohr does indicate he was bothered by something more fundamental, and I'm not sure that I see as much as I would like to what the issue between you was.

### Heisenberg:

Well, one thing of the issue comes up quite clearly here because here it says, "Vor allem beruht die Unsicherheit in der Beobachtung nicht ausschliesslich auf dem Vorkommen von Diskontinuitaten, sonder hangt direkt zusammen mit der Forderung, den verschiedenen Erfahrungen gleichzeitig gerecht zu werden, die in der Korpuskulartheorie einerseits, der Wellentheorie anderseits zum Ausdruck kommen." Now I always refused to talk about wave theory in this connection. I wanted to do everything from quantum mechanics and therefore I did not like to think about wave theory at this point. I agreed about the interpretation of the gamma ray microscope — that not only the discontinuities were important, but also this problem of the aperture and interference. I, to begin with at least, was satisfied to see that if the discontinuity is there, then the discontinuity may introduce the necessary uncertainty and so on. The main point was that Bohr wanted.to take this dualism between waves and corpuscles as the central point of the problem, and to say, "That is the center of the whole story, and we have to start from that side of the story in order to understand it." I, in some way would say, "Well, we have a consistent mathematical scheme and this consistent mathematical scheme tells us everything which can be observed. Nothing is in nature which cannot be described by this mathematical scheme." It was a different way of looking at the problem because Bohr would not like to say that nature' imitates a mathematical scheme, that nature does only things which fit into a mathematical scheme. While I would say, "Well, waves and corpuscles are, certainly, a way in which we talk and we do come to these concepts from classical physics. Classical physics has taught us to talk about particles and waves, but since classical physics is not true there, why should we stick so much to these concepts? Why should we not simply say that we cannot use these concepts with a very high precision, therefore the uncertainty relations, and therefore we have to abandon these concepts to a certain extent. Then we get beyond this range of the classical theory, we must realize that our words don't fit. They don't really get a hold in the physical reality and therefore a new mathematical scheme is just as good as anything because the new mathematical scheme then tells what may be there and what may not be there. Nature just in some way follows the scheme." This way of turning around came from my first long discussion with Einstein about which I told you. He had explained to me that what is observed or not is decided by theory. Only when you have the complete theory can you say what can be observed. The word observation means that you do something which is consistent with the known physical laws. So long as you have no laws in physics you don't observe anything. Well, you have impressions and you have something on your photographic plate, but you have no way of going from the plate to the atoms. If you have no way of going from the plate to the atoms, what is the use of the plate? That was an argument which had made a strong impression on me — that was the discussion with Einstein. So in this case I now used this argument so to say, a inst Bohr. I would say that that was the main difference — that we just in the course of these weeks or months, had realized that actually our position was not so different or at least that the two positions could be completely reconciled and there was no real trouble anymore. So we did convince ourselves,that we now had a scheme by which we could predict every experiment. We did not doubt that nature would also follow these predictions. That's of course the next question. I have seen a paper by (Wiener) in which he discussed what would have happened if, for instance, the ground state of the helium atom would have come out experimentally different from what quantum theory has calculated. ... I found it interesting because it is a very American question. I would say that nobody in Europe would have asked this question. It is a question which comes out from the pragmatic philosophy. If you take always the pragmatic things as primary things, that is, the facts as the primary thing, then, of course, you must be prepared that such a thing like the normal state of helium comes out differently. In the European version of such theories, one would always think, "Well, a theory means a statement about the connections. A correct theory of nature is a correct statement about the connections between different experiments." Now, of course, there are wrong theories. That nobody can doubt, but still when the theory is right at many points, then it means that you have a very high probability that you have found the right connections. But if you have found the right connections, then it's impossible that one experiment can all of a sudden drop out of this game and say, "Well, now here, nature is something different." So in other words, if in the case of the lower states of helium there would have been a complete disagreement one would have at once asked, "Well, what about the next state of helium? How could it be that the next state comes out right but the lowest does not?" Underlying these discussions was the conviction that once one has found a consistent picture of all the connections, then nature will always comply with this picture. Nature must make sense. Somehow nature must make sense because otherwise we couldn't understand anything. History shows that we can understand nature somehow and so finally in history always nature has made sense. Finally we have understood, and then not a single experiment has ever contradicted this connection. In this sense, we were convinced by that time, "Well, now we have a consistent scheme and so since we know that nature complies with this scheme at very many points, we cannot doubt that it will also comply with it at all points."

### Kuhn:

Well, now, I take it from what you say that you were not necessarily happy with the idea that perhaps one still had to take the wave particle dualism as fundamental.

### Heisenberg:

Yes, yes. I didn't like that too much, no.

### Kuhn:

You were happy about the situation but to some extent happy because you were convinced that one did not have to talk about dualism in order to explain things.

### Heisenberg:

Well, I wouldn't exactly express it that way. I was convinced that the mathematical scheme did allow one to predict every experiment. I agreed that it was convenient also to speak about waves because I saw that we have the interference so it's very convenient to talk about waves. But it was not essential to do it. I was more or less convinced that if somebody wanted to he could probably do the whole thing in the Schrodinger way — using only words like wave and so on. Then, if he does it carefully enough, that will work as well. So briefly afterwards I wrote these lectures which I gave in Chicago in 1929. There I think it was always done with the two possibilities. It was not the dualism in the sense that you needed both, it was rather a dualism in the sense that you may do it either way. You can either start from a wave picture or you can start from a particle picture. Each of the two pictures can be carried through to the end and will give the correct answers. At the end you discover that, after all, you have done the same thing, just in a different language. I think that these lectures at least were clearly written in the sense that they showed not that we have dualism, but that you have the two possibilities. That was a point which I think Lande always had misunderstood. Lande fights so much against dualism in quantum theory. I always tried to explain to him when I exchanged letters with him that we have no dualism. We have a unified theory. That is, we have one mathematical scheme which just allows many transformations but we have just one mathematical scheme which gives apparently the correct experimental answers. The fact that we can use two kinds of words to describe it is just an indication of the inadequacy of words, which is a natural thing which we know already from relativity. Why should we worry so much about it? I know that, besides Lande, many other physicists had been upset by this situation, and they felt it was a dualistic description of nature. I never felt that.

### Kuhn:

Well, you say that at a fairly early stage of the game you and Bohr reached entire agreement on this?

### Heisenberg:

I should say that by March in '27 we had already reached complete agreement. So there was only a short period of perhaps ten days or so in which we really disagreed rather strongly.

### Kuhn:

If I remember what you've just read me from that note, the note says that Bohr has persuaded you that it's not just the discontinuity, but also the jointly particulate and wave nature that is responsible for these uncertainties. Doesn't that need to mean something a little bit different from saying that we can take this result and talk about it either as a wave or as a particle, getting the same result either way? Doesn't that put the paradox of the dualism into a more central position?

### Heisenberg:

Well, to some extent it does, but I could perhaps say that at that time I had understood that it doesn't do any harm to my own explanation if I do it that way. I felt, "Well, one might also do it that way. Why not?" Therefore, I didn't want to protest too strongly against it. I said, "All right, it may be of some help to play always between both pictures." For me the essential point was that I had understood that by playing between the two pictures, nothing could go wrong. So I didn't object to playing between both pictures. At the same time I felt it was not necessary. I would say it was possible but not necessary. For explaining the gamma ray microscope to physicists, it was useful to play between both pictures. That I could see. But it was not absolutely essential. You could actually use both languages independently. Therefore I was very happy shortly afterwards about this paper of Klein-Jordan and Wigner. It's a series of papers in which they actually started by the Schrodinger picture, not only the Schrodinger formulas, but rather the Schrodinger "anschauliche" interpretation, the picture of having waves in three dimensional space and for these waves certain equations of motion. So everything looked like a classical wave theory. But then, in the end, the waves are quantized, so for the waves now one gets commutation relations and so on. This I liked very much because now I could see, "All right. There is an entirely different picture to start with and if I quantize that picture — that is, if I make this picture open to the same restrictions as the particle picture — then the two pictures become equivalent." That was exactly what I wanted. That was perhaps a bit later. I don't know when the Klein-Jordan-Wigner papers arrived, 'but they probably appeared also in the summer '27, shortly after this paper.

### Kuhn:

In these talks that you and Bohr had day after day in '26-'27, who else would have been involved in those? Was this pretty much just the two of you?

### Heisenberg:

In the last stage, say around February and March, Oskar Klein was very much involved. But in some way I would feel that Oskar Klein thought it was his duty, being an old friend of Bohr, that he must defend Bohr against the young man Heisenberg. Perhaps it was also a bit of an issue of who finally clarified the whole thing and so on. So Oskar Klein wanted to help Bohr and I was perhaps sometimes a bit too harsh and too quick with saying something, I don't know. So Klein took part quite frequently in these discussions and also helped to clarify. After all, he's a very good physicist. I don't know exactly whether the paper of Klein-Wigner-Jordan later on was also a consequence of these discussions. It may be. I wouldn't be surprised if that was the answer. Perhaps Klein, from taking part in all these discussions, felt it was a good idea to start from the Schrodinger picture entirely and see how far one can get from this picture into quantum theory. Then he discovered together with Jordan that it was actually possible to get everything just from that picture. I think besides Bohr, Klein, and myself, there was nobody in these discussions; only Pauli by correspondence. I would write Pauli about it and ask his opinion, but I don't think that he did contribute much to it in that stage. Actually everything was done within the three of us. Kramers was not there in Copenhagen at that time so far as I can recall. If Kramers had been there I have no doubt that Bohr would have discussed everything with Kramers. At the same time I remember that I did some paper together with Foster on the Stark effect of helium. [J. S. Foster, "Application of Quantum Mechanics to the Stark Effect in Helium," Proc. Roy. Soc. Lond. A, 117 (1927), pp. 137-63. (Received 8 Aug. 1927)] That must have appeared around that time. think that must have been roughly the same time, perhaps a little bit later. ... It may 'also only be a paper of Foster in which he quotes that we did some theoretical work together.

### Kuhn:

In that case, it will not be on my list.

### Heisenberg:

I see. Then it must be a paper by Foster which probably was published in the Physical Review or the Proceedings of the Royal Society and then that will contain a reference to our common calculations. We did some calculations, in common, but since he had done all the experiments probably he has published the whole thing and then just made a reference to common calculations.

### Kuhn:

Let me say — I think this is not the place to do it — we have gone over much too quickly the papers on resonance which really come in before this, and I do want to go back in our next talk and ask you to tell me just as much as you can about the development of that whole range of ideas. There's a whole group of papers there, two on resonance, one on the helium atom, and the one on "Schwankungserscheinungen.["Mehrkorperproblem and Resonanz in der Quantenmechanik," Zs. f. Phys., 21 (1926), pp. 411-27 (Copenhagen, 11 June 1926); "Spektra von Atomsystemen mit zwei Elektronen," Zs. f. Phys., 39 (1926), pp. 499-519 (Copenhagen, 24 July 1926); "Schwankungserscheinungen and Quantenmechanik," Zs. f. Phys., 40 (1926/27), pp. 501-06 (Copenhagen, 6 Nov. 1926); "Mehrkorperproblem and Resonanz II," Zs. f. Phys., 41 (1927), pp. 239-67 (Copenhagen, 22 Dec. 1926).] But the first of the two resonance papers, which is also the first of that whole group, is the one I'd particularly like to talk about because it really contains almost everything that comes later. I sit there reading it with my mouth hanging open because of the number of new ideas that all of a sudden get tied together here.

### Heisenberg:

Have you the paper now with you? I would just like to see —.

### Kuhn:

No, unfortunately, I've got my notes on that paper, but I do not have the paper itself.

### Heisenberg:

I might have it here. I must look and see whether there are any copies left.

### Kuhn:

Well, I would point out to you some of the sorts of things that I have in mind to ask. Some of the questions I asked about it came in here and it was really that a whole lot of new things suddenly enter together and get tied together here. It seems incredible to me that you were worrying about all of them when you started that paper. It seems to be much more likely that it starts off in one corner and gradually spreads out.

### Heisenberg:

Yes, I think I must read this paper because otherwise I don't recall exactly what happened.

### Kuhn:

That's really why I thought I would just break in for a minute now to suggest that we ought not take that up at this point but it would be terribly worth your having a look at it and the paper itself is this —.

### Heisenberg:

This is after quantum mechanics?

### Kuhn:

Yes.

### Heisenberg:

Oh, yes, yes. I remember the paper. That was — it had to do with problems of two electrons. Of course, my general intention was to do the helium problem and then I discovered that before I could do the helium problem I must say generally what happens if I have two systems which are equivalent. The Pauli principle then comes in, and so I tried, first, in a general fashion to work out what kind, of new problems come in. As you say, there was both the Einstein statistics and the Pauli or Dirac-Fermi statistics and the question of having energy going over from this [electron] to that [electron]. It had to do with the older paper on the fluctuations, on the "Shwankungserscheinungen."

### Kuhn:

But that's not an older paper. It's later.

### Heisenberg:

It's later. Well, I thought it was — ... Well, I should have it in the library at home because at home I have the Zeits. f. Physik already from the Drei Manner Arbeit on, so then I certainly have it at home. So we can try it tomorrow and not today.

### Kuhn:

Good. Excellent.

### Heisenberg:

If you remind me tomorrow, then I can just look in my own library. Yes, I remember quite well this paper was also full of excitement for me because so many new things came up. One studied the behavior of two electrons and one saw that now the mathematical scheme contained new properties, like the symmetry, that one could see. Also I felt already that the problem of the fluctuations could come out, but as you say I did it later. I didn't know, I thought the other one was earlier.

### Kuhn:

Well, those two papers are very closely related one to the other.

### Heisenberg:

Yes, no doubt, yes.

### Kuhn:

But the one which picks out all of these really quite divergent pieces and —. No, this is really terribly exciting to read. One has that feeling that it's a little bit like when one reads thermodynamics and suddenly finds that from a few simple assumptions one is getting so much physical content. Somewhat the same thing has happened here in a quite surprising way.

### Heisenberg:

Yes, that is exactly as you say. One had at that time the impression that now we have entered into a new field and wherever you go you just can collect the nicest material. You are all of a sudden in a world of new possibilities, of new connections which you haven't seen before. That was certainly the actual position. That was summer '26, just before the — . That's right, yes. After the first Schrodinger paper. So one could use the Schrodingerformalism to help a bit with the mathematics, I think.

### Kuhn:

Well, there may be another sort of use of it in here. I want to wait till you've looked at it. I might simply mention an interesting question to me. In this paper you start out by saying that very little has been done so far with more than one electron problems in quantum mechanics because after all the mathematical techniques have just been too difficult; recently Schrodinger, has produced this new procedure, which makes great progress on the questions of mathematical manageability for the multi-electron problems. You then point out, however, that we've got to be careful about Schrodinger's interpretation, and you discuss this in some length. Then you go ahead and do your problem entirely with matrix mechanics, until very close to the end when you say that it may be worth writing down, while you're at it, the Schrodinger wave functions also. You write down the symmetric and anti-symmetric functions but there's no simple answer to the question as to what the devil all this talk about Schrodinger is doing in this paper after all.

### Heisenberg:

Well, I think I know the answer. The point was that at the same time when I wrote this paper, I thought already of the helium problem. I had realized that in order to calculate the shift of levels in the helium atom I needed the matrix elements and the matrix elements I could only calculate, sensibly, from Schrodinger theory. To do that from matrix mechanics alone would have bean extremely difficult. Since I knew that later I would be forced to use Schrodinger's tools in order to get the matrix elements, I thought that I could already write down here how the connection is to be made later on. But after all, this paper had to do with matrix mechanics so I didn't want to mention Schrodinger's approach too frequently. Still, I wanted to mention it in order to use the Schrodinger theory in the next paper on the helium.

### Kuhn:

Of course, there is an additional possibility. A number of these ideas emerge more straightforwardly from the Schrodinger approach than they do from the matrix mechanics approach. Well, the production of symmetric and anti-symmetric wave functions from one electron functions is somehow or another quite a straight forward procedure. It was at least possible that some of these ideas developed in this paper were ones that you had first developed thinking about wave functions.

### Heisenberg:

Oh, you mean that I first thought about wave functions then have translated them into quantum mechanics.

### Kuhn:

I've got no notion that that was necessarily the case.

### Heisenberg:

Well, I don't think that at that time the translation from the one to the other was so familiar to me. Well, of course, it was in some way. One knew how to calculate matrix elements. Then there was this paper of Born in the background — you know, in the Drei Manner Arbeit one had the "Hauptachsen-Transformation," and I think I had realized that these "Hauptachsen" were something very similar to the Schrodinger function. Well, it may quite well be that Schrodinger's paper definitely had some influence on this paper. But I don't believe that I would have started to work on Schrodinger's theory because in some way the mathe matical tools of Schrodinger were not so familiar to me — spherical harmonics and so on. I could do it, but I could do it only with some labor. I didn't like too much to enter into this problem of the spherical harmonics. I rather felt that if I could do without it, I'd rather prefer it. Maybe that for the symmetry —.

### Kuhn:

Why don't we simply keep thins question open? I raise it now because if you do look at the paper this may then suggest something as you do. I might point out one other thing. Do you remember in the Drei Manner Arbeit when Born comes back to the question of perturbation theory in' degenerate cases with the treatment that you give in Hermitian forms. You don't carry it at all far, you simply point out that it can be carried out. You give one example, in which you write down the secular determinant and make the following remark [p.589. "Dieser Fall liegt vor, wenn zwei ursprunglich gleiche, nicht entartete Systeme ... durch irgendwelche Krafte gekoppelt werden."]

### Heisenberg:

Yes, yes. That is quite true. That's the kind of thing of which one had in mind at that time, yes; but whether we had actually done some calculations at this point, this I don't know.

### Kuhn:

Well, it seems strikingly clear that you can't have done very much with that then. That equation and that remark, after all, contain everything that's in the later paper. But on the other hand, clearly you aren't seeing any of it.

### Heisenberg:

No, that's quite true, yes.

### Kuhn:

So the whole question is what is the relation between that pregnant statement with which nothing whatsoever is done and this brilliant later paper? One caild point back and say, "Well, look they must all have known it all the time," which would be absurd.

### Heisenberg:

Yes. Well, the point is that we probably have in Gottingen quite frequently discussed a system containing two equal systems. First of all; there is the old classical experiment which you show in every lecture — two pendula being coupled by some piece of rubber. It was a natural thing to discuss it in quantum theory and we certainly have tried to discuss it already very early in the time before quantum mechanics, especially in connection with dispersion theory. We always say, "Well, let's assume we have two oscillators. There must be resonance in that sense, and the energy goes from here to there. So this was a mechanical problem which was in the mind of physicists in Gottingen and also in Copenhagen. It may be that we have just touched this problem in this secular determinant here. Yes, I'm quite surprised to find it here.

### Kuhn:

I didn't notice it when I first went through the paper. I noticed it accidently later. Well, I looked back, because you referred back for the mathematics to this paper. I was looking back and. I suddenly saw this remark and thought, "By golly it's all here." It clearly isn't all there either in the sense that you cannot have been seeing what you wrote in that paper.

### Heisenberg:

We had not seen all the implications, no, no.

### Kuhn:

The qualitative implications perhaps not at all. The qualitative implications — what it says to the picture that is so exciting.

### Heisenberg:

Yes, I cannot say how far we actually got here. We were quite familiar with secular determinants by that time. You saw in this paper I wrote with Jordan that secular determinants were used, so that was a natural thing; but that two equal systems would produce this kind of splitting that was not —. Yes, it is clearly stated here, there's no doubt, but how far we have carried it, I don't know. You know, when we wrote the Drei Manner Arbeit our general situation was this: we saw that we had entered a new field and you could pick new things just wherever you went. Therefore, we just took what came on our way but without following it further because we realized that to follow it further would take some time and we would have to do some work. So we just saw now that the problem of the two equal systems coming into resonance is an interesting problem .and will lead to that kind of thing. We just mentioned it and said, "Forget about it, we'll do it later." So it must be a remark of this kind. It's always the situation when you have entered into an entirely new field. You don't know where to go because there are too many different problems which are opened up and you have to stick to a few of then to do them properly. But it may be that we discussed it among ourselves. We had already in mind, "Well, when we have finished the paper, then sooner or later we must try the helium and two equal systems." How long time is it between this paper and the helium paper?

### Kuhn:

November, 1925 to June, '26.

### Heisenberg:

Yes, seven months. Yes, and there were other papers between.

### Kuhn:

Yes, though not very many.

### Heisenberg:

The Zeeman effect paper with Jordan.

### Kuhn:

Really just that one and the one for the Mathematische Annalen. That was a slow year.

### Heisenberg:

Yes, yes, I remember.

### Kuhn:

In that year were you able to get a lot of the new theory into your teaching?

### Heisenberg:

You mean whether I taught about my new theory? I would say no. I did some teaching, some discussing, at the seminar of Hilbert. So I did give some colloquia and that kind, of thing, but not official teaching, not teaching to the students.

### Kuhn:

Were the graduate students at Gottingen getting this new theory quite quickly?

### Heisenberg:

Not at that time, yet. No, I would say not before '27 or '28 and at that time I was not in Gottingen anymore, so I think I never did any teaching on quantum mechanics in Gottingen. My first teaching on quantum mechanics was in Leipzig. I started in Leipzig in the autumn of '27, if I recall correctly, and then I started also very soon teaching all these things. ... I came to Copenhagen in May, '26, and then I stayed until the autumn of '27.

### Kuhn:

Was von Neumann in Gottingen while you were there?

### Heisenberg:

No, I don't believe so. I met von Neumann first in Berlin when he was a teacher in Berlin.

### Kuhn:

But you would say really that in this first year or so this was not yet being taken up to any great extent by the graduate students.

### Heisenberg:

No, not yet, no. That came later. I would say not before '27. After '27 everythingms clear and then it could come into the general lectures. Well, I don't recall when I did give my first lecture on quantum mechanics but that may have been pretty early in Leipzig. My first lecture in Leipzig I think was just classical mechanics but then it was decided that I give some special courses. Well, I simply don't know.

### Kuhn:

Good. Well, I think this would be an excellent place for us to cut this off how.