Werner Heisenberg - Session IX

Kuhn:

I notice how little we've tried to talk about Lande. From the point at which you start, he is the person who is perhaps working most closely on the same range of problems.

Heisenberg:

Yes. I do remember that I did exchange quite a number of letters with Lande. He came in from the very beginning in so far as he had invented these empirical rules concerning the level structure of anomalous Zeeman effect and so he was interested in this side of the problem. I do remember also that I had some discussions about this later paper, Abanderung der formalen Regeln der Quantentheorie," [Zs. f. Phys., 26 (1924), p. 291], where we discussed this "J verschwommen", you know, this j squared which should rather be J(J+ 1), and things like that. But as a whole, I would say that it was always a discussion about the formal procedure, the formal way to present experimental facts. It was not a discussion about what could be the final quantum mechanics, or at least that was in the background. The most important thing was in those discussions, "How will the empirical formula probably be?" "Are those formulas which we have already the correct formulas?" Of course, in my mind I tried to connect these things with the problems in the paper with Kramers — with the dispersion problems. I always felt that I must find how the amplitudes are. "What are the amplitudes there?" From this angle I was glad about the discussions with Lande, especially when we found that J(J + 1) was something important. It was so obvious that you could, by classical theory, never reach a J(J + 1). It again emphasized this necessity of multiplying matrices, I would say. Nowadays I would call it matrices. I remember that I tried once quite hard in the early stage to see whether I could get J(J + 1) out of the sum of the squares of the three angular momenta. I mean nowadays you would say that if M is the total angular momentum then Mx² + My² + Mz² gives J(J+ 1), if done properly according to matrix mechanics. Now I remember that I once tried to do it and didn't succeed. It was only later then, in connection with the Drei Manner Arbeit, that it became quite clear.

Kuhn:

Do you have any notion how early it was that you tried this before?

Heisenberg:

Well, that is difficult. I should say very probably in '24 when I wrote this second paper on Zeeman effect. I had written the paper with Sommerfeld about the angular momenta and I corresponded with Lande about the J(J + 1). In that period it must have been for the first time that I tried to do it that way. Since I did not know exactly the rules of matrix mechanics, that is it was not so quite clear how to multiply, somehow it didn't work out. Now I would say I was a bit unlucky. If I had done it well, I should have found that it can actually be done by means of matrix mechanics. Well, probably the reason is that one knew, of course, the matrix for the Mz. That was a trivial matrix. One did not know so well about Mx and My where the elements are out of the diagonal. Then it was not so quite clear how to multiply. Well, in matrices, of course, it's quite clear. I remember, then, when we wrote the Drei Manner Arbeit, I was very glad that that came out just as I had hoped. Therefore, I wrote this paragraph in the Drei Manner Arbeit. Also, I was a bit surprised that one could do that with the half-quantum numbers. I was not surprised completely, because I always knew that there were half-quantum numbers, but somehow it was a bit funny that these things could be done by integral quantum numbers and by half-quantum numbers. So indirectly, of course, the spinor problem was involved, but that we didn't know at that time. That is my strongest remembrance of the discussions with Lande. It was mostly about the formal rules and, when I agreed with Lande about the formal rules, I always tried to do something in the direction of the dispersion formula — multiplying matrices — but I just couldn't do it at that time.

Kuhn:

Then the one article that you publish with him is the one on the "Verzweigungsprinzip" ["Termstruktur der Multipletts höherer Stufe," Zs.f. Phys., 25 (1924), pp. 279-86. (18 May 1924)]. This is the notion that you somehow felt it was sort of a double core, a double Rumpf for the next higher element.

Heisenberg:

Yes, yes. Well, that, of course, was preliminary to the Goudsmit-Uhlenbeck idea. I remember that was always this problem of doubling at the place where one didn't know what to double. Just this side of the problem was then completely solved in the moment when one had the electronic spin. Well, I was not so terribly interested in this doubling business. I left that to Pauli and others. Only, once, I did this paper with Lande about the "Verzweigungsprinzip" in order to understand the Periodic System. Now, I don't know —. You have seen my correspondence with Lande. Well, actually you have given it to me.

Kuhn:

I've glanced at a little bit of it. I've made no attempt really to read through it. There simply has not been time for that.

Heisenberg:

Well, I could look through the thing and see what we discussed in connection with this "Verzweigungsprinzip," I would say it certainly was always in that formal direction. That is, we wanted to get correct formulas which we could apply to the empirical facts, and hope that it would fit, and to see how these formulas would look. That was a game which could be played without any understanding of the real physics. Perhaps it was important that at that time one had realized that one could play the game without really understanding. That is, one knew that there are some quite nice formal rules which seem to work and thereby you can do something which resembles classical physics only at a distance. It is different from classical physics, but not completely. At the same time, it works empirically. Well, that was successful in the case of the intensities, it was successful in the case of this J(J + 1), and the "Verzweigungsprinzip." So one tried to play with these rules. Land4 has certainly helped me in coming to think about the correct rules. The matrix multiplication stood already back there, but at some distance.

Kuhn:

Do you remember how he himself felt about this state of affairs in physics? He is not, by and large, a man to come out with so bold an idea as you often did in this period.

Heisenberg:

Well, of course, I would say he was, as you say, more cautious. He saw that one had some success with these formal things. Perhaps he was more of a phenomenological theoretician a man who wants to describe nature as it is. He just wanted to find out how nature is, what are the correct formulas. But he had not really the hope that one could find the whole clue to the thing that one could actually penetrate to the bottom and say, "Well, that is a new structure in physics." He was very able in finding the empirical rules, and finding out how nature actually worked. I think that was his main intention in this connection.

Kuhn:

Would you say that he was as much of a numerologist in this area as Sommerfeld was?

Heisenberg:

Well, perhaps of a slightly different type. Sommerfeld was just happy about finding integral numbers somewhere. That was not Lande. I would say he was closer to the experiment. He was a man who saw the experiments; he wanted to describe the experiments in terms of formula. Well, he was certainly not happy about this state of affairs in physics. He knew that integral pdq didn't work. That was quite obvious to him and still he didn't really attempt to do something entirely new there. Even now, as you know, he's not happy about the development and doesn't feel that the usual description of quantum mechanics in the textbooks is satisfactory. I tried to discuss this problem quite a few years ago with him, but without success. I couldn't convince him. At that time he was closer than Sommerfeld to the experiments. Sommerfeld liked mathematics, mathematical schemes and integral numbers. Later on, it was also important that things should fit the experiment, but he was not a man who could work from the experiment into the theory — who could take experimental facts and try to change them a little bit so they fit the formula, then see whether that still can be reconciled with the experiment, and so on. Lande liked this kind of phenomenological work. He was not so keen on integral numbers. This "J verschwommen,'" as we called it, was something rather different from that.

Kuhn:

There's one thing I think I should say. By all means there's no alter native to going ahead as I think we are doing but I think I should point out to you in honesty the most interesting thing for me that has come out of this part of the conversation so far this morning. Almost an incidental and an incalculable by-product of my having you tell about Lande is this remark about the earlier period when you were trying to get a J(J + 1) out of summing the squares of the components of the angular momentum. Now, I'm delighted to have that. It's a very important thing for me to know. It might equally well have not come out of my asking you about that. What sort of questions should I be asking you in order to make sure that we don't miss things? [Great laughter].

Heisenberg:

Well, that's just as difficult for me to know as for you. Well, I think now from this morning we came to that point which certainly is a part of the story. Quite a number of us, that is, Lande and I and Sommerfeld and Honl, all tried to play with formulas. Then we got a formula like the square root of L times L + 1 minus M² then one tried to make some sense from these formulas, to see how these things can possibly come out from some kind of decent mathematics. Well, at least I had always in mind that I should do something in the direction of the Kramers dispersion formula. That is, to multiply this amplitude by an amplitude which goes from this state to the next state — the matrix multiplication, which was not so well-known at that time. Therefore, it was a natural thing to try about the angular momenta, but still it was difficult.

Kuhn:

Well, let me ask you then a very different question. I'm not clear myself to what extent you had very much relation with him, but I do know that several of the people just a bit younger than you who were students at Göttingen mentioned particularly how important it was to them that he was often asked in the summers — and that's Ehrenfest. I talked to Maria Mayer, for instance, who spoke about the great difference between being a student at Gottingen in the winter semester when one learned from Born, and learned mathematical physics, and in the summer semester Ehrenfest was often there, and the whole way one took to physics was then different.

Heisenberg:

Yes. That was also certainly the impression that I had. I would say that in many ways, the physics which Ehrenfest tried to do was very similar to that which Bohr tried to do. That is, he wanted to understand things in the sense of physics, not as a mathematical scheme. He really wanted to see how nature does a thing and what the reasons are and so on. Therefore, his adiabatic principle was one of the cases where he could contribute something. He said, "If there's a quantization and then I can change the outer conditions slowly, what happens to the quantization?" Then it was very satisfactory to see that this quantization will not change by slow changes of the outer conditions. I remember that I don't think I had so many direct conversations with Ehrenfest. I had those when I was in Holland with him, but that was for only one or two days. Besides that, I have seen him quite frequently in Copenhagen and I think also once in Gottingen. Whenever he stood up in a discussion and would say something it was always in the following direction. "Let's forget about the mathematics of it. Let's ask what is the real physical content of what you say. What do you mean by that?" Therefore, Ehrenfest was not happy about such formulas like the things I discussed with Lande. It wouldn't mean much to him whether one replaced J² by J(J + 1). He would just say, "Well, it just means you haven't understood the thing." He was interested in such problems as the dispersion problem. Why is it that an atom would, under the influence of an outer light wave, not have a resonance at the orbital frequency, but resonance at the actual frequency. That certainly worried him very much because he saw that there was something wrong, but he couldn't give any answer. Well, nobody could at that time. Ehrenfest had a strong catalytic effect in physics at that time, since he always forced people to think about the physical content of what they say. I would feel that sometimes nowadays, for instance, we lack a man like Ehrenfest in physics because he was a man who didn't bother about the mathematics. He just wanted you to understand that what you say must mean something in physics. "What is it actually that you mean?" This side, nowadays is treated too little, I should say. Of course, Ehrenfest and Bohr were quite alike in this respect, only that Bohr was more constructive. Bohr had an imagination, a kind of intuition as to how things are. This whole story of the Periodic System was all done by intuition. Ehrenfest was a much more critical mind. Ehrenfest was always in despair over how dreadful physics was and that one couldn't understand anything, and everything that people say was just wrong. Of course, he was right in that way. Therefore, it was very natural that, in this Faust parody which I showed you yesterday, Ehrenfest would be Faust. You know, he's just unhappy about everything, everything's going wrong. Ehrenfest was, at the same time, also a man who had a very strong educating effect on the young people. For instance, when somebody had to give a talk in the colloquium, Ehrenfest would be extremely critical about the way it was produced. That is, for instance, you had definitely to ruse colored chalk. If you only wrote with white chalk, he would say, "Well, its a poor lecture. Apparently you haven't made use of that very good tool. You have to use different colors in the figures that you draw on the blackboard. That's no good." He would be extremely critical. He loved to quote this thing by Hilbert. If somebody made a noise with the chalk on the blackboard, then he used to tell the story of Hilbert. You know that story? Well, Hilbert was extremely sensitive. Apparently he was quite interested in music. He was extremely sensitive with his ears so if somebody made a noise with the chalk he said, "Well, that's impossible. You can't do that." And the story goes that again one of the students gave a talk and he made this kind of noise. Then Hilbert said, "Sie kennen ja nicht mal die Grundlage des Vortrags." Then the poor man said, "Well, I'm sorry, professor, but its not so easy." And Hilbert said, "Ich habe nicht gesagt es ist leicht. Ich habe gesagtes ist die Grundlage des Vortrags." So Ehrenfest would insist on all these things. The blackboard should be divided into different parts. Everybody who gave a talk had to know beforehand where to put his formula on the blackboard. Everything had to be prepared very well. I must say that I have always been very grateful for this education, which I got. Actually, when I have to give a talk, I do, as I did in the old times with Ehrenfest, think where to put this formula and that one and so on. This educating effect of Ehrenfest was very strong. Then also this extremely strong criticism, this honesty to say, "Well, we haven't understood," and "That is nonsense, what you say," and "Really you can't defend that because its a contradiction," was extremely helpful in seeing how difficult the whole thing was. Of course, it was a situation almost of despair because one couldn't avoid the paradoxes. That everybody could see. I wonder whether Ehrenfest did think of the possibility that one should still keep the paradoxes but still get a consistent mathematical scheme. Perhaps he had hoped for a long time that one could get rid of the paradoxes. Anyway, as I said, he had a very strong catalytic effect on the whole development.

Kuhn:

This seriousness and insistence on, "We don't understand," must have bothered some people greatly. There must have been people who found it very hard to have Ehrenfest around.

Heisenberg:

Yes, to some extent. As soon as somebody came with an idea which was a bit constructive, say the "Verzweigungsprinzip" or whatever, then of course, he would be a bit bothered by a man who would always say, It's just wrong." On the other hand, everybody agreed that the situation was very bad, but since nobody could offer a solution it didn't bother people so much as it could perhaps have. Obviously, also, Ehrenfest couldn't do any better. Ehrenfest in that way was much better than, say, people like Wien, who simply would throw away the whole quantum theoretical business and would say, "Well, that's all full of contradictions, therefore, forget about it." Ehrenfest would just never forget about it. He would say, "We have to think day and night about it just because it's so disagreeable."

Kuhn:

When I talked with Uhlenbeck, he said that he always himself had the feeling on the one hand that Ehrenfest was somewhat afraid of people like Born or Sommerfeld who had all that mathematical facility and could take an idea and turn it into mathematics so that you couldn't see the idea anymore. But then Uhlenbeck also said, "I think Born was also a little bit afraid of Ehrenfest," because, he says, "I think Born could put it into mathematics and then Ehrenfest would look at it and say, 'Yes, but what about the physics right there?'"

Heisenberg:

Yes, that is certainly so. I mean Born would have had some pleasure in working out this Bohlin method of perturbation, or some new feature in Charlier in perturbation theory. But Ehrenfest would have at once said, "Well, that's all right, but what does it mean in physics — in quantum theory. It can't be right." Therefore, Born, of course, was a bit afraid of the fact that Ehrenfest could disprove almost everything which was written down at that time. On the other hand, Ehrenfest probably was a bit sorry because he may have felt that the whole puzzle could only be solved by means of a new mathematical scheme. That is, just this separation between paradox and inconsistency. He probably has felt that the paradoxes cannot be avoided and then the only thing which remains is to avoid the inconsistencies and that then can only be done by means of mathematics. When Ehrenfest saw a mathematical scheme like the ones produced by Born, then, of course, he would at once point at it and say, "That's wrong and that's wrong." Therefore, when he had heard about this matrix mechanics —. Well, he had invited me to Holland and I told him about it. Then, of course, he saw that this was so new that at least one could not at once disprove it. Certainly one could not prove it, but at least he saw, "Well, that's something. It looks so different from the older things there may be some sense in it. Perhaps it's not possible to disprove it directly." But that was just in the very beginning, so it took some time until the things became clear. Did Uhlenbeck know something about Ehrenfest's position with respect to Bohr? Well, he admired Bohr, I should say. He was a good friend of Bohr.

Kuhn:

Yes, I think in some way he felt closer to Bohr than to anyone, any other major figure.

Heisenberg:

Yes, which is certainly correct. Also in his way of thinking, yes, yes. Yes, he didn't like too much the purely phenomenological way of arguing, and he didn't like Sommerfeld's mathematical schemes and Born's more complicated mathematics. Yes, I think that was a type of physics which was absolutely necessary at that time, otherwise the thing never would have come out. I think nowadays it is done too little. We have really too few Ehrenfests now.

Kuhn:

And Bohrs. You would put them together.

Heisenberg:

Yes, and Bohr in that respect. Every way, yes. It is really a trend in physics which comes from Faraday, I should say. When you look at the old papers of Faraday you see this. Faraday in some way was a theoretician as much as an experimental physicist, a man who could really go into the inner connections of physics. In spite of the fact that he had no mathematical scheme at his disposal, he could work it out so that he finally had understood.

Kuhn:

Well, let me raise another question that we've not really done perhaps. We may have done as much with this as we can. We talked once before about the spin. I want you to tell me about it at the time when it becomes an historical idea — the October paper of Goudsmit and Uhlenbeck. The idea is announced. I'd be interested in anything you may remember either about your own reactions or about other peoples, about the stages by which that gradually came to be accepted. This comes in right at the time of the working out of matrix mechanics. It can't have been immediately clear, or at least it may not have been immediately clear, that you weren't going to get all those results right out of matrix mechanics. So probably part of what it takes is convincing yourself that if you were going to get those results at all you would have to add something to matrix mechanics as they were adding something to classical mechanics.

Heisenberg:

Well, actually, I think that came already out at least for me from the Drei Manner Arbeit and from Pauli's paper on hydrogen in so far as one saw that, by means of rigorous quantization with matrix mechanics, one could only get integral angular momenta. On the other hand, the half angular momenta did work somehow. It did work with the rules M_xM_y, and so on. One saw that is something extra which must come in. So the half quantum number was something which is not so directly involved. Well, it was, of course in the harmonic oscillator where one got the half quantum. Still for the angular momentum, one did not get the half quantum and that was a problem of deep concern for us because, on the one hand, we saw that the angular momentum itself could be half quantum. Yet by quantizing p and q one did not get the half quantum. So one felt, "Well, there again we have the "unmechanische Zwang" and all these things. We have this doubling, and we really don't know what this doubling means. Tha'ts so funny and so disagreeable." Well, we were a bit unhappy but so many things were still not understood that we thought, "Well, let's wait and see what will come out later." Well, then the Uhlenbeck paper came. That was in the autumn of '25, I think, wasn't it?

Kuhn:

Yes, the first one is in the middle of October. Now, I don't know to what extent you may have known about that paper before it appeared. Probably not.

Heisenberg:

I think I have heard about the paper from Bohr who passed through Gottingen. I think Bohr came on the way from Copenhagen to Holland through Gottingen. In Holland he had to give some lectures, I should say. I remember that I went to the station to get him there and on the way from the station to his hotel he told me about the electronic spin, about the paper of Uhlenbeck and Goudsmit. To begin with, I was rather critical and I mentioned this business with the factor 2 which didn't work out — the Thomas factor. I saw that Bohr was very strongly convinced so he did already change my own opinion to some extent. I felt, "Well, there may be something in it. After all, there is this factor 2, which we always had trouble with." Then one could at least understand why in our calculation of the hydrogen atom, or rather Pauli's calculation of the hydrogen atom, it does not work out with the half quantum numbers.

Kuhn:

But you think when you first talked with Bohr about this that Bohr himself was already pretty fully convinced?

Heisenberg:

Yes, I should say he was.

Kuhn:

He was himself not, initially convinced as you know. It appears to have required a remark of Einstein.

Heisenberg:

I see, yes, it is possible that it was Einstein. Yes, I see. Well, that I don't' know, but I have read that also ... At least in the old story, when Kronig was in Copenhagen, Kramers and I were not convinced by Kronig about the things. I don't know whether Bohr himself was involved with the problem at all. But at least nobody was really convinced and it was pushed aside. Then when this new paper came out —. Well, I heard about it through Bohr, and Bohr was convinced at that time. This story with Einstein must have been before. Do you know the details? Did he — maybe that he came from Berlin to —.

Kuhn:

I don't remember. It's all in the Pauli volume, either in van der Waerden's or in Kronig's piece. At various times I have memorized such details, but I don't remember them again now. I'm sure that book is around here if we want to check, but in some sense now it may not be worth your trouble.

Heisenberg:

No, only that I was rather easily convinced because, —. Well, I had the trouble with the factor 2. But on the other hand I saw the hydrogen calculation of Pauli had not given the factor 1/2, so I felt that there must be something to it. There must be something new coming into it, and if this was the spin of the electron then all right. So, I bad no reason to object against it. It only later came to my mind that I actually had discussed the matter with Kronig and had taken it as something rather absurd. I find it interesting that the three physicists, Kronig, Goudsmit and Uhlenbeck actually come from the same institute in Holland, Ehrenfest, and so on. I don't know what that means but its quite interesting that all this comes from this one point.

Kuhn:

Though I think Kronig didn't come from there then. I think Kronig was a student at Columbia and was traveling in Europe. He wound up there.

Heisenberg:

Oh yes, that's right. But originally he must have been Dutch, isn't he?

Kuhn:

By extraction. I think he was born as well as raised in the United States.

Heisenberg:

Oh, I see, yes. His parents may have come from Holland to the United States or so.

Kuhn:

He is, at that point, a traveling American graduate student.

Heisenberg:

Well, yes. He must have come from a rather international family because I was always surprised how well he spoke German. He spoke German almost like a German. He must have been also in Germany for some time. Probably he had traveled around, yes.

Kuhn:

But you don't remember in your own experience or with anybody else, a point at which it suddenly became clear that this had to be the right idea? Pauli was perhaps the last of all the important physicists to be convinced.

Heisenberg:

Well, I remember when Bohr spoke about it I thought, "Well, that may be." I didn't like it too well for two reasons. The one was the factor 2 and the difficulty there. The other was that I had the impression, "Well, after all, these things are so far from classical physics already that I don't see how a picture from classical physics could be so very helpful." That is, I could well imagine that this new quantum theory may invent such "doublications" of states somehow. After all, you can say that the electronic spin is just a "doublication" of states, and that it actually comes in as an angular momentum is a bit indirect. So the real solution of the spin problem was then actually in the paper of Dirac, I should say. There one knew why there is the factor 2 and so on. In some way, the paper of Dirac justified our general inclination to think of something rather abstract and rather unclassical. Later on, I remember that Bohr wrote a paper, at least spoke about a paper which he intended to write, that one could never measure the electronic spin in a direct way; but indirectly, of course, one could. That again came quite correctly into this general attitude that we thought, "Well, there are so many rather abstract and non-classical things that it is perhaps not possible to explain this 'doublication' just by an angular momentum of the electron." Even at the time, when Bohr tried to convince me that this was correct, I felt more, "Well, this may be a quite useful picture, but, after all, it is a quantum theoretical effect and not a classical effect."

Kuhn:

This whole range of problems finds us right now back in —. Well, we've never really talked much about the two papers of Pauli that come out at the very end of '24 and the beginning of '25, which again tie in with the whole question of spin but also get tied in with the question of resonance.

Heisenberg:

When you say two papers, you mean the paper on the exclusion principle?

Kuhn:

The second of the two [Zs. F. Phys., 31 (1925), pp. 765-83 (16 Jan. 1925)] though they're very close together, is the exclusion principle.

Heisenberg:

And the other one?

Kuhn:

The other one is the previous paper on the two-valuedness of the electron [Zs. f. Phys., 31 (1925), pp. 573-85 (Dec. 1924)] and the insistence that one has got now somehow or another to find two different quantum numbers that the electron can have and this has got to be utilized in the anomalous Zeeman effect. Well, not so much in the anomalous Zeeman effect, but in doublet separation.

Heisenberg:

Yes, in the doublet separation, yes. The X-ray: spectrum and the Sommerfeld formula and so on, yes.

Kuhn:

Those papers come out at the end of '24 and the beginning of '25. By the end of '26, they are classic papers, but I'm not clear how quickly people paid that much attention to them. If you took the one about the doubling with respect to the electron, it would be a perfectly good reason for throwing out everything that's gone on within the mechanical side or at least start that whole movement differently. I don't know whether it's too clear how important a paper that seemed to be. It doesn't have a great big immediate effect and neither does the exclusion principle paper. It's somehow too hard, perhaps, to fit in.

Heisenberg:

Well, I would put it this way. The first paper of Pauli was taken more as a phenomenological paper, like those of Lande and myself. That is, a description of what happens. Namely, in the X-ray spectra we have this funny application of the Sommerfeld formula which cannot be justified. What Pauli's paper does is just to give a systematic description of what happens in the X-rays. It was really meant as a phenomenological statement, and it was interesting that this statement could be formulated so simply. Well, in our present language one would say that one had to give a degree of freedom to the electron which is two-valued, which can either be plus or minus. Now this suggests something already like the electronic spin, but at that time, nobody thought about it. Then, when the exclusion paper came, that, I must say, did make a very strong impression on me. I felt that it is only now for the first time that we have really understood the Periodic System of the elements. So in the moment when this paper came out I understood, and I also felt that Bohr had understood, that Bohr's earlier ideas about having resonance in the closed shells were just all wrong, and that the real reason that we had closed shells was because of counting states. The trouble was that we didn't know what these two states of the electron mean, or at least we had no picture for these two states. Still, one could say, "The two states are there. That we can see from the X-ray spectra. Now we can explain all the shell structure of the Periodic System by means of this exclusion principle." Since the shell structure has always been linked up with the X-ray spectra, everybody felt, "Well, the theory of the Periodic System is now essentially clear. It is waiting for a final quantum mechanics which will come some day, but when this mechanical scheme is found, then the Periodic System must come out from itself." The trouble, of course, was then later, when Pauli wrote his paper on the hydrogen, that this 'doublication' was not in it. So it didn't come out by itself. Still, Pauli had this idea of the doubling in mind, so the electronic spin was not a revelation for him. He would say, "Well,that's perhaps a useful picture, but after all I have already introduced this new degree of freedom for the electron, and whether you call it angular momentum or not may not be so important." Well, of course, it was important. Later on he actually wrote a paper about the Pauli spin matrices. It was quite clear that it was important. I must say that this paper of Pauli on the exclusion principle has made a very big impression on me because I felt that now for the first time we have really understood the Periodic System. I thought that also Bohr had reacted that way, that he was very glad to forget about his resonance between different orbits because that didntt work out anyway. Also I remenber that then after the Pauli paper we very soon started to look into Bohr's theory of the Periodic System, and to ask whether or not some changes were necessary. I think they also bad to be made in the iron group or bie rare earth group. But I would not agree to your statement that this paper on the exclusion principle was not recognized at once. At least for a small group of people it was recognized at once as the final solution of the Periodic System problem.

Kuhn:

Was there anything else that one could do with it at that point? Did it begin to solve problems?

Heisenberg:

No, not yet. I would say that only happened when one could connect it with the problem of symmetry in matrix mechanics or wave mechanics. I should say that this idea that there is room for only one electron in one state — that was again one of these funny formal rules which looked so different from anything one knew in classical physics that one really couldntt understand what it meant.

Kuhn:

It could, for some people, have been sufficiently strange and different and ununderstandable to be a reason to forget about it.

Heisenberg:

Well, I would say perhaps it was taken by some people in a similar fashion as Planck's paper in 1900 was taken by many physicists. They said, "Well, after all, he does get the right law of heat radiation, but since it doesn't fit in with anything else in physics, what can we do about it." This idea of having only one electron in one orbit doesn't fit in with anything in other physics, so it was difficult to say what it meant.

Kuhn:

Well, particularly since in order to get the law in the first place, you've got to invent an extra quantum number with respect to which the exclusion is to be enunciated.

Heisenberg:

Yes, so in this respect it belonged to these funny empirical rules which you just can invent and you don't know what they mean. Still, the thing works. Since one had got accustomed to funny rules at that time, one didn't mind it. So at least a number of people saw that this was very important. I'm sure that Bohr did take that view and considered it as the real solution of the Periodic System problem. Well, Pauli perhaps was not so glad about the electronic spin just because it was too classical again. He preferred his degree of freedom which one could consider as something only quantum theoretical. Later on he saw how important it was to interpret it this different way.

Kuhn:

Now let me ask you what has come back to you about this whole set of ideas, which also includes the exclusion principle and statistics, that comes into that resonance paper.

Heisenberg:

Yes, the resonance paper. Of course, there I had a number of very exciting experiences when I worked with that paper. First of all, that this symmetry did provide a clue to the Pauli principle so that one could say, "If two things must always be connected anti-symmetrically, then there can only be one electron in each state."

Kuhn:

Can I ask, do you remember what you started out to work on when you worked on that paper? You can't have been working on all the problems you solved.

Heisenberg:

No, and I should also add that for quite a considerable time I did mix up Bose statistics and Fermi-Dirac statistics. Well, first of all, Fermi-Dirac statistics was not known at that time, there was only the Pauli exclusion principle. Somehow I always got mixed up between Bose's statistics which produced a different way of counting states, and the Pauli exclusion principle. And only when I wrote down the equation for two electrons which were equal did I see that there were two solution, one symmetrical, one anti-symmetrical. Then I first thought, "Well, one has to take the symmetrical solution in order to get the Bose statistics, so that must be the one which gives the right Pauli exclusion principle." It was at a rather late stage that I saw, "No, that is just the other way around. In order to get Bose statistics, you must take the symmetrical one, and in order to get Pauli's exclusion, you must take the anti-symmetrical one." I'm not even sure whether that is quite clear in my first paper. It was probably clear in the second paper, but perhaps not quite in the first. I would have to look into the paper. At least I did see clearly that there were two sets of states and the important thing was, of course, non-combining sets of states. So I should say at least in the second paper it was quite clear that if one forgets about the spin, then one has two sets of states, the symmetric and the anti-symmetric, the one being the orthohelium, the other the parahelium. If, however, one included the spin, then one was left with only one set of states, namely the anti-symmetrical, and that then did just what Pauli had said. This all came from studying two equal systems being in resonance which had been a favorite problem of discussion for a long time. It had been in the Drei Manner Arbeit, but it had been discussed much earlier in connection with dispersion. Just as with the two pendula where the energy flows from one to the other, I said, "All right, I have two hydrogen atoms, one here and one here. What happens? That is clear. You get resonance only if this is a lower state and that is a higher," and that kind of thing. We discussed these kinds of problems frequently in Gottingen and tried to do something with it. Therefore, it also came into the Drei Manner Arbeit. But only when I applied it on such a practical problem like the helium atom with the two electrons, only then I saw that you could follow this up by the difference between orthoehelium and parahelium. I remember that it was a very great help empirically in finding these things, to see that the ground state belonged only to parahelium and not to orthohelium. Orthohelium had no ground state. Well, that again showed the connection to the symmetry properties. The symmetry came out quite clearly only when these papers of Dirac and Fermi appeared. Yes, that also had to do with —. Now let me see. I did tell you that I was, in the spring of '26, together with (Brochard) Drude and we did a tour in Italy. On the way back I saw Fermi in Rome, and I think that Fermi told me about his new statistics in agreement with the Pauli exclusion principle. He told me that when' one applied Paulis exclusion principle one got something which is somewhat related to the Bose statistics, but which is definitely different from Bosets statistics. It was a kind of complement. He told me that the relation between his statistics and Boses was something like plus and minus. So that I knew from Fermi. The paper had not appeared at that time. It must have been April of '26 and that certainly must have influenced my paper on this resonance business. ... Do I not quote my conversation with Fermi?

Kuhn:

No, you dont. Thats interesting though, because as a matter of fact, Fermi's own first report on it is submitted in February, '26.

Heisenberg:

February, '26, already, yes.

Kuhn:

On the other hand, what I think may not yet be clear, even if you talked with him about that, is that youve got any occasion to get involved with it, that you haven't got everything you want with Boses statistics on the one hand, which are by now out for a while, and with the Pauli principle on the other hand.

Heisenberg:

Well, I only remember that it was for a considerable time mixed up in my mind. I couldn't make out what was in Boses statistics, in Fermis statistics; "Are they the same; are they different? What 's it all about?" I had not seen any paper of Fermi by that time but Fermi did tell me in April, '26 about his ideas and I found them interesting. That I know. But when I worked on this resonance, I started the whole thing just from doing proper calculations on matrix mechanics. I had forgotten about the statistics. Then when I saw that there are these two systems, I started remembering these discussions in statistics and I had the impression that they must have to do with it. I should, really look into the paper and see what I did state about the Pauli principle. I think in the second paper, at least, I must have stated quite clearly that the Pauli principle is now obeyed in the helium spectrum, and everything is fine, and that must. be identical with the statistics of Dirac and Fermi. On the other lnnd, I was not interested in the theory of gases. I was interested in two electrons and not in many electrons. Therefore I could forget about Bose and Fermi statistics. I could not forget about the exclusion principle. So that perhaps is one of the reasons. I was interested to get a clear formulation of Pauli's exclusion principle, but I was not primarily interested in gases. Therefore I could leave it open whether the final statistics of the gas was Fermi or Bose or whatever.

Kuhn:

So in the first paper, I'm quite certain that I'm remembering correctly when I say that there you dontt mention Fermi's statistics. You say that if one insists on the Pauli principle, then the N factorial possible wave functions are restricted to the one wave function which will not combine with the others. This changes your method of counting in such a way that you get Einstein-Bose statistics. There's no talk yet of Fermi statistics. This does enter in the second paper.

Heisenberg:

Yes, that is just it. I do mention the Pauli principle because I need that. I do also mention Bose's statistics with the factorials, but it is still not quite clear which is which. In the second paper it's quite clear.

Kuhn:

Clearly, you are aware of Fermi's statistics, though you don't mention them in the first paper and the whole thing goes through as though there were just the Einstein-Bose statistics at that point.

Heisenberg:

But I must have seen the following thing: I do remember that already in the first paper I wrote about the orthohelium and parahelium. Then I think I also mentioned that if now one added the spin to it, that then the one spectrum gets a triplet and the other gets a singlet. Now the point is that if you postulate Bose statistics for the whole thing, then the orthohelium would be a singlet and the parahelium a triplet. But since I had the Pauli statistics and the exclusion principle, its just the other way around, the orthohelium is a triplet and the parahelium is a singlet. But I think by that time I must at least formally have it in the paper — that the whole thing must obey the Pauli statistics. But I don't quite recall how that looks.

Kuhn:

Well, that the whole thing must obey the Pauli principle is surely in the first paper. There's nothiug about any relation to Ferm'ts statistics. I think you see this, at this point, as being the same thing as saying that we impose Bose statistics on these electrons. I think you see that choice of the wave function which will give you the Pauli exclusion principle as simultaneously giving you, for particles of this sort, Bose statistics.

Heisenberg:

I see. Yes. Well, it was probably this then. For a system of two electrons, everything was quite clear in that paper. But how the extension would be for several electrons, that was not clear. There I reckoned with the possibility that for several electrons one would get the Bose statistics and not the Dirac statistics. That should be at the end of that paper.

Kuhn:

Unfortunately, I don't have the paper itself. What I have is largely some incomplete notes of my own here. According to my notes you discuss briefly the case of N identical particles. 'In general if we have n partial systems which are identical there will be a degeneracy of N factorial in the system. When you add the interaction, it lifts the degeneracy and gives you N factorial partial systems. But of these, one and oniy one contains no equivalent path; this is the only one that occurs in nature.' And that, you say, is the Pauli principle. But you simultaneously say that it also reduces the statistical weight from N factorial to 1, and this gives the Bose-Einstein statistics.

Heisenberg:

That means simply that I have not understood the thing completely. Yes, I remember that, later on, I was a bit ashamed that I had not clearly understood the thing. I mentioned it before that I had the impression that in spite of everything being clear for the two electron system, I had not really understood how it would be for the N electron system. Only the papers of Dirac and Fermi made this point quite clear. Yes, that was exactly the situation. In this first paper on the resonance there were so many new points coming in that there was a good chance not to find out.

Kuhn:

This is still one of the most exciting of all the many papers that I have been reading, exactly because of the number of new sorts of things. Now look, you insist in this paper, and you insist in your next couple of papers, that now a great big unsolved problem with the new quantum theory is to understand why the Pauli exclusion principle has to work. Why one is forced to restrict oneself to this one solution out of the N factorial solutions. Its a perfectly reasonable problem. I'm not sure now what one says about this problem with respect to fundamental particle theory, but that there's a very long intermediate period in which one says, "These particles have Einstein-Bose statistics or these particles have Fermi-Dirac statistics," and it becomes a God-given property. You no longer ask the question, "Why is it that we are forced —."

Heisenberg:

Yes, well, actually, one —. I think the historical cause of this is that in quantum mechanics one saw that one has really no way of telling. You could always do both and you could just decide about which statistics to use. On the other hand, when the Dirac paper came out later on, one saw that the spin, and also the statistics, were connected with the Lorentz group. I think the final answer only came much later when one had come quite deeply into the connections between the Lorentz group and the exchange quantities and so on. Then one saw, "Well, particles with spin 1/2 must have Fermi-Dirac statistics. Particles with integral spin must have Einstein-Bose." But that you can prove only by means of the quantization of waves and all this business, so that is connected with PCT theorem, which is very modern stuff now. Only very lately one has really understood why it is. In these early stages, first one thought, of course, that that is a very important problem that we must solve. Then one learned in quantum mechanics that there is absolutely no way of telling because you can write down mathematical schemes which are perfectly consistent, and you can have it either way. I think that came out most clearly by the papers of Klein, Jordan and Wigner. There are three papers which I always considered as very important papers. I think they came in '27 or '28 or so. There one saw simply you have two different rules of quantization of waves. First of all, you learned that when you start from the quantization of waves, that is, when you start from the Schrodinger picture, you do not get all the N factorial systems. You get only one, either the Einstein-Bose or the Fermi, but not anything else. That I found already was a very exciting statement that if you started from the Schrodinger picture, you are bound to one of these two statistics, but you cannot get anything else, any of the other systems. That again showed that this equivalence between the two pictures of waves and particles was in a strange way connected with the idea of having Bose or Fermi statistics. From then on one learned that this thing had to do with the Lorentz group and then one came into all the troubles. Ever since we have worried about the Lorentz group so I need not talk about that. I think it was quite interesting that in this first stage one thought one had all the N factorial systems. Then one saw that one could not decide within quantum mechanics, but if one wanted the equivalence of the two pictures — Schrodinger and particle picture — one had at least to restrict the whole thing to the two schemes, Einstein or the Fermi-Dirac. Already at that time Dirac's theory of the electron had come out, and then one soon learned the thing must have to do with the Lorentz group. I might make one remark. This doubling of states which Pauli first had called the unmechanical doubling, was actually connected with the Lorentz group. But later on, as you know, one had found doublings which had not to do with the Lorentz group, say the iso-spin doubling, neutrons and protons. This doubling itself was something which Pauli liked. Therefore he was not too happy about the electronic spin. The idea that one should be forced, in such a discontinuous theory as quantum theory is, simply to double, to confront an alternative, either this or that, appealed to a very fundamental feature in Pauli's philosophy. Now I wonder, did I ever show you this letter of Pauli in connection with our elementary particle business where he was for some time extremely enthusiastic about the whole thing? Then there come a few sentences where he says, "Verdoppelung und Symmetrieverminderung. 'Das ist des Pudels Kern'. That is, "The fundamental principle from which all nature is produced is doubling of states and then, later on, reduction of symmetries." He adds, at this point, "Verdoppelung ist ein alter Zug des Teufels." In the whole medieval philosophy of the Alchemist the devil was the one who would double things. Then he adds that the devil is, of course, the one who always makes doubts, hesitations, and the word "Teufel" has to do with "Zweifel," which, in the old time, meant doubling, i.e. you can do either this or that. So Pauli says that to be put in front of an alternative and to double the possibilities is an old and most fundamental feature of the devil. In this way, the devil has created. the world. Pauli loved to talk about these things. Well, if I have not shown you this letter of Pauli, I really should show it to you. Its very interesting for the psychology of Pauli. Pm sure that this side of his philosophy must have played its role already in '24 when he wrote this paper on the "unmechanische Zwang". Therefore, he wasn't too happy to have this dissolved into a rather trivial angular momentum of an eleotron. In so far, he also approved of the doubling which I then tried in the iso-spin case and therefore also the doubling which occurred in the theory of elementary particles.

Kuhn:

That letter I have not seen. Well, in some way itts appropriate that I haven't because it obviously gets into much more recent development. But you're clearly also right that it must reflect back on attitudes at these earlier points.

Heisenberg:

Yes. Its so funny that Pauli in some way had some especially good relation to the devil. I would say, of course, also to God. I did probably tell you about Dirac's philosophy — there is no God. Did I tell you that story? I think it reflects also on the philosophy of Pauli. Since I have just spoken about his attitude with respect to the devil, I must tell another story. This happened during the Solvay Conference in '27. There we lived in the same hotel and the younger people of the group sat one evening together drinking a glass of wine or so. Somehow the problem had come up about religion and natural science. Dirac was a very eager defender of the view that religion was just nonsense, was opium for the people, it was just made to make people foolish, and so on. He argued rather strongly. Well, Dirac was a very young man and in some way he was interested in Communistic ideas, which, of course, was perfectly all right at that time. Pauli listened to it, and while Dirac became very angry about religion, he never said a word. He just sat there, you know his way, smiling a bit maliciously. Then finally somebody said, "Well, Pauli, you never say a word to this discussion. That is your opinion on it?" Then Pauli said, with a very malicious smile, "Yes, you know this Mr. Dirac has a religion. This religion is that there is no God and Dirac is his prophet!" I do remember long discussions with Pauli, especially once when we took a boat from Langelinie, in Copenhagen, to the harbor and had a nice time. All of a sudden, I don't know why, Pauli came to the problem of religion and discussed the existence of God. He really was deeply interested in the question of how far one conveys meaning in using such words as "God." He, of course, at once would admit that a language never is suited for discussing these things, and so on. I remember another sentence in one of his letters. I had told him about the discussion I had had with some theologians. Then he said, "Ja, uber Deine Theologen, zu denen ich ja in der archetypischen Relation der feindlichen Brüder stehe." That's very typical of him. He did think about these fundamental problems in tens of devil and God. At the same time he knew, of course, that these were very vague symbols by which one could not really express what one meant. Still he used it.

Kuhn:

Had that interest in that way of talking gone back a long way with him? Does that go back to the period when you first knew him, or does that come only later?

Heisenberg:

Well, I remember that I once made, being a student, a short trip on bicycle with him and Laporte — the three of us. It was only for a few days. Actually we came through Urfeld, if I remember right, we came to Garmisch and [???], and had a few nice days in the mountains. There I had some discussions with him on these problems. But I remember that when one really started to come into these problems, I would say the atmosphere became so tense that it was disagreeable to continue. I could see that this man was so engaged in problems of that kind that it was really better if one did not touch it. So we started a discussion, and he could see that I could understand him in this plane, and from this moment on he had a strong confidence in me. But also in some way, it was agreed that we should not talk about it. So I think for at least ten years more we never took up this discussion again. We only knew from each other that we both were also interested. in this side of the world, not only in mathematics and physics. So that made my relation to Pauli always different from the relation to many other students, because we had in this short trip just once discussed this point. Then we could see at once, "Well, here things become serious, better not talk about it." So, we never touched it again. Well, only then, of course, in this problem in Brussels, when he said that to Dirac, I could at once recognize what he meant. Then we had this discussion on the boat in the harbor of Copenhagen. Again, this side of Pauli comes out extremely strongly in these enthusiastic letters about the theory of the elementary particles. He was, I would say, for one or two months in a completely euphoric state. "Now all problems are solved." Later on he just —. There came an opposite extreme. Disappointment. Still, it was so clear when he was io much engaged in physics that it was in connection with this philosophical side of the world.

Kuhn:

How far back does the influence of Jung go?

Heisenberg:

Well, I do not know from Pauli himself, but I would think just from the time very soon after he came to Zurich. But how close the connection was I dont know. That I couldntt tell. But I would say his interest in philosophical problems has certainly been earlier than his encounter with Jung. Only Jung did hit the point, you know, in Pauli. Pauli was inclined in this direction, and therefore he could listen to Jung and hear what this man Jung actually meant, which many. other people just didn't see.

Kuhn:

I think most of the people who know that side of Pauli, many of whom would have described aspects of it as highly mystical, would also say that that was not something that you had. They would not expect to find that same sort of appreciation of a mystical approach to nature in you also. Would that be a mistake?

Heisenberg:

Well, I find it difficult to know what other people think about me.

Kuhn:

Well, what I really meant was with regard to the later Pauli attitude on points of this sort, would you feel comfortable and at home with them yourself? I think many physicists did not.

Heisenberg:

You mean many physicists would disagree with Pauli on this side of the world, or what would you say?

Kuhn:

I think they would indeed disagree, but that's a free privilege for anybody. I think to some extent they would be uncomfortable about the fact that anybody half as able and as critical as Pauli should himself have adventures which seem to them not only not physics, but almost a denial of physics.

Heisenberg:

Yes, yes. Well, did I tell you the following thing? When Pauli had died, I was asked to write this memorial volume. Weisskopf had asked me. Then, actually, originally I had written an article on Pauli's philosophical views, but this article was not accepted. Weisskopf said, "Well, this article is very nice, but you know we don't like to discuss this side of Pauli so much. We want to see Pauli as a physicist." So actually I was a bit angry about Weisskopf, but, well, I had to take his opinion, and apparently other people agreed. Afterwards I did publish my article of Pauli's philosophical views. I first then published it in German. May I give you a copy? Later on it did appear in a rather obscure periodical in the United States because there were still some people in America who were still interested in it, but not the physicists. These were people of a different structure. Still, I like this article on Pauli's philosophical views. I think that I had succeeded in describing very accurately how Pauli's mind was constructed. I also hoped that I had made it clear to many people that I liked this kind of mind, and that my own mind is not so very different from that of Pauli. I may just have it here.

Kuhn:

I would be very grateful if you would. Well, that I'm delighted to have. I should have known that this existed, but I didn't.

Heisenberg:

Well, I hope that I have characterized this side of Pauli correctly. I discussed this paper with van der Waerden who knew Pauli well and he agreed and said, "Well, that is exactly like Pauli was." Actually, I did quote very many things from Pauli, partly in his papers, partly in his letters, so that I think it is quite a correct picture. But I know that many physicists don't like this side of Pauli. I would say Pauli would never have made such ingenious physics as he has done if he had not had this side, you know. In order to invent the exclusion principle and all these things, one must be more than just a formal physicist. So I always loved this side of Pauli. This side of Pauli was really the first basis of an entire understanding between Pauli and myself. Although, as I said, we practically never talked about it until rather late and we were both rather old people. I just mentioned it because, in this first paper on the two-valuedness of the electron, undoubtedly this side has played some role for Pauli. It also fitted this role very nicely that he became Mephistopheles in our Faust. That's absolutely right to the point.

Kuhn:

Its almost a perfect role, including the Pauli effect.

Heisenberg:

But I was also surprised to see that even a man like Weisskopf, who first of all is a brilliant physicist and then also is a man who knew Bohr and Ehrenfest and all these people so well, would rather not like to speak about Pauli in these terms. I wonder how that is? I mean, why is it something one should not talk about, or why is it a feature which, so to say, spoils the picture of Pauli? Not for me, but for many physicists.

Kuhn:

I don't know. I've talked further to Weisskopf about it. In what little conversation I've had with him that would have any reference to this, I do rather think that Mrs. Pauli is not eager to have this side I know because I've talked about microfilming the letters. Weisskopf has said that he thought there might be a problem with some of the more recent letters and that he thought Mrs. Pauli would rather have the more philosophical side, for the time being, withheld.

Heisenberg:

Well, of course, I sent Mrs. Pauli both this thing and also several other things which I had written about Pauli. She wrote very nicely back, but I could not see from her reaction whether she approved or did not approve of it. I would think if she did not approve the story, I would have felt it from the letter that she sent to me, from some remark in that direction. So apparently she was quite happy about the way it was discussed. Quite aside from Mrs. Pauli, you know physicists really do very serious things; they think about the structure of the world. After all, that's what we do. So then why is it that so many physicists are in disagreement with that way of thinking, also with this side of a man who took these things seriously it was not for Pauli a kind of funny game. It was certainly not meant as opium; it was the contrary of opium for Pauli. Pauli was so extremely sceptical that he very soon reached that point where he becomes sceptical against sceptics — where it turns around. That is a point which is unavoidable for everybody who wants to be consistent. That is apparently a point which very few people like to reach. It's very disagreeable to reach that point. It's very important if one is consistent and then, of course, one sees that rational thinking is only a limited approach to the world. Well, why not take it as it is? Pauli certainly tried, wherever he could, to do things rationally. He was a rationalist of the purest flavor. Still, at the same time, especially when one is so rational, one must see where the limits are, because there are limits. That can't be helped. Well, now we come to different things and you want to go back to physics again.

Kuhn:

I must say that I don't find it surprising that physicists, by and large, react this way. I think for very many of them some of this comes through, perhaps in ways you will thoroughly disagree with, in this book of mine. For most of them it would in very many ways be a real denial of the techniques and value systems that they have been brought up with.

Heisenberg:

Yes, well, I have studied your book already and it gave me great pleasure to see the way how you use the term paradigm. This whole comparison which you do between revolutions in science and revolutions in politics is a very interesting parallel. Certainly, one learns a lot from it. Yes, the necessity is to break away those things which seem to be obvious and which actually are the basis on which you stand. One always, in such a situation, is forced to cut the branch on which one is sitting. That can't be helped, because after all, one never can rest. There is no solid bottom. One is always somewhere in the middle and one can get some clarity around oneself but one can never hope that these fundamentals will rest forever.

Kuhn:

But God help one if one educates,scientists to think that what they are always supposed to be doing is sawing away at the branch that they're sitting on. That must be reserved for very special circumstances and people must not feel comfortable while they're doing it.

Heisenberg:

Yes, yes.

Kuhn:

It would be to raise a generation of lemmings.

Heisenberg:

Well, science is a very funny thing, you know. Its a very funny attitude of the human mind. But Pauli, just by his very structure, was forced to realize this situation. And Ehrenfest was as well. He knew that we must, so to say, always be in despair about our situation. Out of this despair we must do something which leads a little bit further, and that's all we can do. We certainly cant hope to solve the problems once and for all. That,s just out of the question. By the way, just to come to more modern discussions, that was a point at which again I have been apparently misunderstood by very many physicists. In regard to my attempts toward the unified field theory, many people must have thought from some very foolish newspaper talks that now I believed that I had solved all problems of physics. I have never believed anything like that — as foolish as that. The only thing I felt was that since all elementary particles are connected in nature, they can be transmuted to others. Therefore, we must find some mathematical description for this spectrum of elementary particles. This mathematical description then will be very important for a kind of unification between electrodynamics and gravitation and elementary particles. Still, for instance, I was always convinced that biology would never be included in such a scheme. This mathematical formula, if correct, would certainly not be sufficient to derive the existence of a flower or of a bird. So I would always say that natural science will always consist of some closed schemes which, just by being closed, also must be limited. Newtonian mechanics is a limited description of nature and in that limited field it is perfectly accurate. It can never be improved. All attempts to improve Newtonian mechanics ae just fruitless. But you can come to parts of physics where the concepts of Newtonian physics donut apply. You just can't do anything with these words. Then you have to go for something new. So I'm convinced also that in elementary particle physics we can hope to calculate the masses of the elementary particles. But in order to derive the existence of a living cell, we need quite new concepts. For instance, the concept, life. This concept life is not contained in physics or chemistry, and doesn't occur in any of these descriptions. So whenever we come into other regions than those of elementary particles, we must take new concepts and we cannot hope that we can cover those objects by the concepts of elementary particle physics. But apparently some people have misunderstood that and then they quite justly get very angry.

Kuhn:

This is a story I guess I just don't know. I certainly have not heard anybody accuse you of having solved all problems of the universe, life included. You do raise here a question in what you say about Newtonian physics which is related to the historical development of the interpretation of quantum mechanics. Would you say, for you now, that Newtonian physics was still an entirely valid structure to be utilized right along side of' quantum mechanics but in mutually exclusive regions?

Heisenberg:

Well, I would not say in mutually exclusive regions. I would say there is a definite realm of phenomena which can also be described by Newtonian mechanics. That is all those phenomena where we can forget about very small things, and can forget about very big velocities. And since it is a closed axiomatic system I think it should be left as it is and it can never be improved. Of course, it doesn't cover the whole physics. There are other schemes. Already Maxwell theory is entirely different from it and again that is a closed scheme and cannot be improved. Quantum theory, in its present state does certainly include Newtonian physics in some way. That is, it is a wider scheme which also includes chemistry and, in so far, it is certainly wider. The concepts for quantum mechanics can only be explained by already knowing the Newtonian concepts. That is, quantum theory is based upon the existence of classical physics. This is the point which Bohr emphasized so strongly, that we cannot talk about quantum physics without having already classical physics. So I would say Newtonian mechanics is a kind of a priori for quantum theory. It is a priori in that sense that it is that language which enables us to say what we observe. If we have not the language of classical physics, I dont know how we should speak about our experiences. I once wrote an article. I wonder whether you have seen that. That was something which Pauli also introduced me to. It was an article in this Swiss periodical Dialectica — 'Closed Axiomatic Systems in Physics.' Well, I tried to describe the role of Newtonian mechanics and Maxwell theory and so on. I found it interesting that there are only very few of these closed, systems. What exists so far in the history of physics is Newtonian mechanics, Maxwell theory including special relativity, quantum mechanics, including Newtonian physics as a limiting field, and the theory of heat. I think the theory of heat is a nice example of how entirely different concepts connected up with the old concepts. The theory of heat really is just the concept of robability, nothing else. This concept of probability can be put upon classical mechanics, it can be put upon Maxwell theory. So we can make heat radiation and so on. One sees that here the concept of statistical behavior is sufficient to cover an enormous range of phenomena if one connects it with other parts of physics which one already knows. So I took this as a separate kind of closed system, but there are only these few systems so far. If, now, my wishes with respect to the elementary particles of physics will be fulfilled, then all these four or five schemes are actually connected within one schemee. Still, there are other parts of nature which certainly are not contained in the scheme, for example, biology or psychology. There may be schemes that are wider than the older ones so that the older ones are sub-spaces of the whole thing. lie can imagine there's a kind of mathematical space where there are sub-spaces and these sub-spaces can then be talked about and ordered by concepts which are somewhat simpler than the total thing. Would you agree with this general desoription of our theoretical analysis of physics?

Kuhn:

You catch me in a position I'd rather not be in. I think I have to say honestly no. I don't think I would agree. On the other hand, I would be reluctant at this point,, to get very deeply into this. Let me go just this far perhaps. I think theres also perhaps here something that goes back into the early days of the interpretation of quantum mechanics, which I should also like to come to. What bothers me a little bit is this. You pick out these various fields which you can think of now as closed axiolatic systems. It seems to me that wheneverone has stopped doing research with a system, one knows just everything it will do now, and one knows also what it will not do, and in those areas one is using another system and it's in those areas that one is doing research. Then one has the option of crystallizing this now past doctrine which is no longer being used except perhaps for engineering applications. I would say, "All right, now this is now a closed book, and a logically donsistent scheme." One can't, in a sense, do anything else with it. One either does that or one discards it. It has exactly lost that openness and uncertainty at the edges which is characteristic of a scheme that is being used to do research.

Heisenberg:

No, but may I say one thing. I do not agree with this point. For instance, Newtonian mechanics is closed in that sense as I described it, but still its open to research. For instance, all the recent progress in hydrodynamics, say turbulence and statistical turbulence, all that is really part of Newtonian mechanics and the modern part which is developed further. This fact that a system may be closed in my sense does not mean that you cannot go on with research in it.

Kuhn:

But will you accept the statement that it is not finished for research in the sense that there may be all sorts of fascinating problems of applied mathematics left to be done, but, in the sense that one does not expect to learn more about the world or something new about the world, it is finished for research?

Heisenberg:

Well, that could perhaps be said, yes. Yes, it's a bit radical to say it that way, but at least I can connect some sense with this statement.

Kuhn:

Now what strikes me is that there are many more systems to be found in the history of physics which would satisfy your criteria. You could have Ptolemaic astronomy...

Heisenberg:

Yes, well, of course, that is a very phenomenological description of the world. Ptolemaic astronomy is a very good one for the phenomenological aspects because it works very well, but it does not use the idea of laws of nature or such things. ... Well, I should perhaps say this. To my criteria of closed system, of course, there belongs an axiomatic mathematical description. You start out with definite axioms which can be proved to be consistent and so on. That criterion already is perhaps not so easy for Ptolemaic astronomy. The trouble is that Ptolemaic astronomy does fit experiments very well if applied quite phenomenologically. That is, you say, "If I don't describe planetary motion well enough then I add another epicycle to it and so finally I can get any accuracy." But if I stick to the original idea to have all these cycles, and perhaps cycles and epicycles, then I certainly do not get agreement with the facts.

Kuhn:

Well, depending upon how far Itm willing to stretch my observation. If I let my velocities get high enough or my dimensions get small enough, then for Newtonian physics I also have difficulties. Your sense of closure has to also say that I will not go in certain directions in my observations.

Heisenberg:

But the trouble is this. And for this reason I insisted on a closed mathematical system of axioms. When you have a number of axioms as Newton had in the first pages in his famous book, Principia Mathematica, then the words are not only defined by the ordinary use of the language, but they are defined by their connections. That is, you cannot change one word without ruining the whole thing. Everything is bound up. And just because of this an experiment which cannot be described by this axiomatic system means something more radical than for Ptolemaic astronomy. In Ptolemy's case, if the orbit didn't fit, he could add other epicycles. But if an experiment does not fit in Newtonian physics, you don't know what you mean by the words. That is the point. As sopn as you come to velocities, near the velocity of light, then it is not only so that Newtonian physics doesn't apply, but the point is that you even don't know what you mean by "velocity." Well, as you well know, you cannot add two velocities ant so on, so just the word. "velocity" loses its immediate meaning. That, I think is a very characteristic feature of what I mean by close system; that is, when you have such a system and you get disagreement with facts, then it means that you can't use the words anymore. You just don't know how to talk.

Kuhn:

O.K. That I entirely agree with. But I think you look too narrowly at the group of systems within which one can have that experience. I'm perfectly sure that this is what happened to people who had trouble with the Ptolemaic system and that when you are now looking back and not seeing the Ptolemaic system that way, but seeing it as a phenomenoligical theory, this is in large part simply because you are too far now away from it. Just as you say, the problem one runs into in Newtonian mechanics when the velocity gets too high is not well-described as the 'velocity is getting too high.' One wants to say that one doesn't know what velocity is anymore. I want to say with respect to a nice little phrase like 'the stability of the earth' exactly that same sort of problem happens in the transition out of the Ptolemaic system. As you see perhaps in the book, I am not very happy about taking out a sub-group of these important discarded theories and saying, "Now these few are still with us altogether in the only good sense in which they ever were with us." I would suppose that somehow or other in the long run quantum mechanics must be the substitute for Newton in the sense that Newton is the substitute for Ptolemy and Aristotle.

Heisenberg:

Well, I quite see that you look at this problem from the historical point of view, and I certainly would agree that I do not know how people will talk about these problems say 1000 years from now. It may be that there the language and the concepts have changed so much that they would not use the Newtonian concepts at all anymore. They would just have different words which fulfill all the functions of the words in Newtonian physics which we now have. In this long run, I agree.

Kuhn:

Well, let me ask you one question and then try to take it back to a more historical question. Then you now speak of Newtonian system as an abstractly formulable system, do you suppose you really use implicitly what you already know about quantum mechanics. That is, this would not be quite the same Newtonian physics that one would have written out as an abstract system before 1925.

Heisenberg:

Well, I agree that probably a textbook on Newtonian physics nowadays will already be written slightly different from a textbook 50 years ago. In that sense, you are certainly right. Still, I would say the engineer who has to do some construction on a big engine will use the same kind of argument as one has used 100 years ago. ... Then I give lectures on mechanics to the students at the University,as I do quite frequently, we have very good, use for words like "position" and "momentum" and "mass" and so on. We have to connect all these words in the way that Newton did it in his first book and then we are quite successful in dealing with engines and with the planetary motions and so on. That gives a consistent picture and actually I would teach this picture to the students without reminding the students of relativity or quantum theory and so on. Of course, I cannot take these things out of a mind, so I will perhaps, for instance, enlarge upon the group theoretical side of Newtonian physics because I know later on in quantum theory this group theoretical aspect is such an important aspect. In so far, the modern development will have some influence on this teaching. Still, I would teach it as a closed system, as something which is independent from all the later development. It is still extremely useful nowadays. I don't really object against bringing in this engineer. Its this practical side of the problem that is quite important.

Kuhn:

You have indicated that Bohr has developed more fully than anybody else the view that one must talk about quantum mechanical things in classical terms. I was trying to remember just what you had told me about these discussions with Bohr in 1926 and to think again about that note that you put in at the end of the paper on the "Anschaulichen Inhalt." I take it that the difference in opinion in these discussions was related to the question as to what apparatus, verbal and otherwise, one had to carry with one from the pre-mathematical quantum mechanical formulation. Perhaps part of what is meant in saying that it isntt. just the discontinuity but also the dualism, is that we cannot get as far from a classical vocabulary or a classical way of looking at things when we are trying to learn how to solve the equations to make them relate to experiments as one would wish. It seems that you wanted to get further from a classical vocabulary than Bohr was willing to permit. Is this right and can you elaborate more on the nature of the disagreement?

Heisenberg:

Well, I think that is perfectly right and at the same time it also is true to say that just by the discussions with Bohr I learned that the thing which I in some way attempted could not be done. That is, one cannot go entirely away from the old words because one has to talk about something. I saw that very clearly in this gamma ray microscope. In the gamma ray microscope, you must say what happens in your microscope. Now if you talk about the microscope you must use some words and there at once one uses the paradoxical version of nature; that is, one uses contradictory words. One says, "There I have a wave which makes a nice diffraction pattern on my photographic plate and so, therefore, and only therefore, I can see my particle. On the other hand, I have no wave. I have a light quantum hitting the electron and the light quantum goes through the lens." So I could realize that I could not avoid using these weak terms which we always have used for many years in order to describe what I see. So I saw that in order to describe phenomena, one needs a language. The language can only be taken from the historical process. Well, we do have a language and that is the situation in which we are. Then we know that this language has been improved by classical physics. It has been made more precise and so on. Therefore, we actually do use these precise terms and then we actually learn by quantum theory that we have used them in a too precise manner. The terms don't get hold of the phenomena but still, to some extent, they do. I realized, in the process of discussing these problems with Bohr, how desperate the situation is. On the one hand we know that our concepts don't work, and on the other hand, we have nothing except the concepts with which we could talk about what we see. We want to talk about what we see. Of course, it also occurred to me at that time that, if one distinguishes the natural language and the scientific language, the natural language is very weak but is much more stable than the scientific language. The scientific language is a precise language in which you know what every word means. And just in the very moment when it has become very precise or completely precise, in that moment you don't know how far it touches nature. Therefore, you are always in this dilemma. If you use a precise language, that is a language which can be transformed into mathematics, then you don't know how this mathematical pattern fits into nature. You don't know whether you can get hold of nature. Or, if you use your natural language, then by the very definition you know that you have got hold in nature because that's the only use of natural language. There you know that you can touch nature and there you see that it is quite vague and you never can get it quite precise. I think this tension you just have to take; you can't avoid it. That was perhaps the strongest experience of these months — that gradually I saw that one will always have to live under this tension. You could never hope to avoid this tension. In Newton's time, one had probably hoped that one could avoid this tension n that one could just make a precise language and then everything is clear. In some way already Maxwell theory showed that that was not possible.

Kuhn:

: This may be a little unfair of me, but it is at least the point of view from which I originally asked the question. That you have just said seems to be excellent and very much to the point. I also get some feeling that, at least in 1927 in the Uncertainty Principle paper, this is not yet your point of view.

Heisenberg:

Not yet completely.

Kuhn:

Is this a lot of what Bohr is still pushing you on?

Heisenberg:

Well, what is clearly in that paper is my own misunderstanding that one could not use the words "position" and "velocity" in the same manner as one had done before. So these words ceased to get hold in the phenomena. Now the general attitude that one still has to keep the words a that the words are so important that one has to keep them in spite of the fact that they have these limitations that was Bohr's point. Bohr would insist, "Well, in spite of your Uncertainty Principle, you have to use the words "position" and "velocity," just because you haven't got anything else." Well, this was Bohr's side of the picture which came out during the discussions and which probably in the paper were not so clear to me as they were a few months later. It was just in this stage of development that one gradually became accustomed to the idea that we never really can get out of this atmosphere of despair and hopelessness because we never have words by which we can really do the thing. But we have themathematical scheme and we have the words of classical physics which are vague, but still they are quite useful.

Kuhn:

Then would it be fair to say that in that paper you still have hopes of avoiding the paradoxes?

Heisenberg:

Not really. I would say not really anymore. At least I waild have felt that the price which one would have to pay was so enormous that nobody would be willing to pay the price. Perhaps you remember that later on I tried to compare this point in relativity and in quantum theory. In relativity, to some extent, the actual language has adjusted to the mathematical scheme. People say that two events are simultaneous with respect to such and such a system. In quantum theory, language has never adjusted to it. That is so interesting. The mathematiciazis have shown that it could adjust to it by changing the Aristotelian logic. You have to pay that price. You have really to be willing to give up Aristotelian logic and then you can finally come to a language in yhich you can actually imitate the mathematical scheme. So far, nobody has ever been willing to pay that price. Now that was not so clear at that time. But still it was clear that probably the only sensible thing to do was to use the old words and always remember their limitations. Also, one could get along quite well with it. Perhaps the most important success of the Brussels meeting was that we could see that against any objections, against any attempts to disprove the theory, we could get along with it. We could get anything clear by using the old words and limiting them by the Uncertainty Relations and still get a completely consistent picture.

Kuhn:

Now when you say, "We could do this," by the time of the Brussels meeting, how big is this group?

Heisenberg:

I would say at that time it was practically Bohr, Pauli, and myself. Perhaps just the three of us. That very soon spread out. Schrodinger was not satisfied. He wouldn't like it. I don't know how quickly the idea spread. At the Brussels meeting it was really just the three of us, I should say. Born would agree that it was good to use this language, but he probably would not have been quite sure that everything would work out all right. I don't know how happy he was about the state of affairs. It may also be that he was quite happy. The real fight was between Einstein and Bohr. Probably you have been told many times of this meeting. Usually, in the morning at breakfast, Einstein would have invented a new experiment by which he definitely could disprove the theory, and he would say, "Well, there you can disprove it. Certainly it doesnt work." Then Bohr would be in despair and would discuss the thing, and by the evening, again, Bohr would be on the winning side. He would say, "Well, this is the interpretation and there you see it can work." Einstein would be in despair and the next morning he would come back with a new example. Ehrenfest finally said, "Einstein, ich schame mich fur Sie." "I am ashamed for you because these discussions are just like those about relativity, and now I see that Bohr is right and you dont believe it." I remember Ehrenfest saying, "Ich schame mich fur Sie."

Kuhn:

This was at Brussels?

Heisenberg:

This was at Brussels, yes. So Ehrenfest also was at least on our side. He definitely felt, "Now the Copenhagen interpretation is the correct interpretation." The climax came with this experiment on the light quantum. You remember that. It is described in this volume on Einstein's seventieth birthday. That was such a nice case because Bohr could defeat Einstein with his own weapons by using the general theory of relativity. But Einstein didnt give up. He was not happy; he was not satisfied with it. He never liked it. I did discuss these problems once more, shortly before Einstein died, in 1954. I was in Princeton and I spent a whole afternoon with Einstein. Well, he just felt it was not nice physics. He disliked it. He could have no objection. He did not approve of any of these attempts like Bohm or so on. He just said, "No, that's nothing. That's not the, thing I'm after. But I dont like your kind of physics. I think you are allright with the experiments; there's consistency; but I dont like it."

Kuhn:

I think that bothered Bohr terribly until the end of his life.

Heisenberg:

Yes, oh yes. That he could not convince a man of the quality of Einstein, yes.

Kuhn:

And a man who had done so much to make all of this possible.

Heisenberg:

Yes, oh yes.

Kuhn:

You said that you thought that the Como meeting had not been nearly so important as the Brussels meeting.

Heisenberg:

Well, in Como there were some very informal talks and I think I had to give a lecture. Schrodinger gave a lecture. Certainly the Como meeting did a lot to spread the knowledge of this new scheme to many physicists. So it was the first time that a great large group of physicists would listen to that kind of thing and would hear that now there is a development which is going on and which seems to be in a state of clarification. The Brussels meeting was the one where really the details were discussed end where one had to fight. There Einstein tried very hard to disprove the theory. He was so dissatisfied that he really insisted on the fact that there must be something wrong and he was always very angry when he found that he had not come through with it. That was a real hard fight which started at breakfast in the morning. I used to follow Einstein and Bohr on our way from the breakfast to the meeting, which was about five hundred yards down the street. They would talk to each other in a very energetic way, discussing it all the way. At the breakfast, usually, Einstein was on the winning side because then he had a new problem and Bohr would try to think about it. Then during the lunch time, of course, Pauli and I discussed new problems.. In some cases, the answer was simple but there were a few cases like this light quantum that the answers were far from being trivial, but were rather deep. It was clear that at the moment when Einstein brought in the weight of the box with the light quantum, then gravitation came in because weight means gravitation. So one had to use such general ideas as general relativity. By the way, that was so exciting because it was an attempt to disprove the theory and then finally one saw that the attempt had failed. In so far now, this group, Bohr, Ehrenfest, Pauli, and myself, felt that they were on the right track, that they had a good concept and no lack of clarity anymore. So we were all quite happy and felt that now the game was won.

Kuhn:

I have heard it said that several of the younger people at Como were not impressed with Bohr's papers.

Heisenberg:

Well, that is quite possible because Bohr was never a good speaker. Bohr always would speak with a very soft voice and when he had to say very important things then he would speak especially softly. You know that kind of strange technique which had to do with his whole psychic structure. Its not easy far younger people to realize what such a lecture then means. So probably the Como meeting had just spread the news that there are the people in Copenhagen who really believe —.