Werner Heisenberg - Session III

Kuhn:

Well, I should think that in any case it will not now take us long, in view of the background we had laid down last time, to work through the remaining questions. Can you tell me a little bit about what the examining system was like, and what one would, in general, be expected to know, how many fields one had to present? How much room for variety was there?

Heisenberg:

Well, in our time the number of terms from beginning of studies to the examination was very much shorter than it is now. That actually, for instance, for myself it was only six terms from the beginning to taking the doctor's examination. Now usually it was perhaps eight terms at that time. But generally, it was much shorter than now, although there were absolutely no other examinations in between the beginning of the study and the doctor's examination. This is very different from the way it is now, because now they have the (Vordiploma) and the Diploma and so on. I think it's also very different from the system in your country where one has an examination almost after each lecture. You might perhaps say that the exercises connected with the lecture were some kind of examination, in so far as they enabled the professor to see how far the student had arrived in his studies. But otherwise there was, as I said, practically no examination before the doctor's thesis. At the doctor [examination], one had to know one Hauptfach and two Nebenfacher. In my case, for instance, the Hauptfach was physics and the Nebenfacher were mathematics and astronomy. There was a choice between several Nebenfacher — I don't know exactly what the rules of the game were. Usually you could select among a number of subjects just the two things which you could call the Nebenfacher. And in the Nebenfacher, there was only an oral examination, while in the Hauptfach, you had to write a doctor's thesis. So one had the doctor's thesis as the first piece. This was criticized by the professor and went through the faculty with the remarks of other professors.

Kuhn:

Was the entire faculty given an opportunity to do this?

Heisenberg:

I think it went through the entire faculty, yes. As a rule, most professors only wrote their name and indicated that they agreed and so on. But at least two or three would make a few more remarks. One of the professors would write a long text about it, and then the next one would perhaps write five or six lines and so on. But all the rest of the faculty had to see it, and that, of course, took considerable time. Therefore, the (Pedell) of the university, who took it around from professor to professor usually got a nice tip to do it quickly, you know. That kind of thing. On the other hand, there were only comparatively few students taking the doctor's examination, so the professors were not heavily overloaded with examinations, and all that kind of difficulties.

Kuhn:

When you say that your principal subject was physics, how much of physics did this mean you could expect to be examined on at a high level?

Heisenberg:

Well, physics meant, I think, theoretical physics and experimental physics — an hour or half an hour in each, but equal times for both. That was not on a very high level. In the examination on experimental physics, one had to know those things which were to be found in the practicum of the experimental institute, and, of course, one had to know about the general laws of physics in the different fields — thermodynamics, optics, and so on. But one had not to go into very special detail in any of these subjects. So the details were only asked in the theoretical physics, in the subjects on which one had worked for the thesis.

Kuhn:

Can I raise the, I hope not embarrassing, question about your own examination. You said something about it last time, and I may say that story is, in fact, in circulation, as you probably know, in international circles. This is perhaps a little out of the ordinary, but it seems an appropriate point to ask if you would say any more about it.

Heisenberg:

Oh certainly, I don't mind talking about it. The only danger in my telling the story too often is that I improve the story too much. But I think I will try to do it as historically as possible. My difficulties came in experimental physics. I had, as I told you, gotten from Wien, at his institute, the task to work on ... the Zeeman effect of hyperfine structure of the mercury lines. In this I didn't succeed simply because I didn't know what was expected from myself. The difficulties were more in the kind of administration than in the actual work. Well, actually I did get some equipment, let's say a Fabry-Perrot interferometer and that kind of thing. But, for instance, I did not know that to get my apparatus in better shape I could have gone to the work shop myself. I asked the people in the work shop, "Now could you make this and that for me," and so on. I had no idea that, as an experimental physicist, one was entitled to go to the work shop. So I tried to do everything myself by means of cigar box wood and that kind of thing. That didn't please the professor at all, naturally enough. So I never got anything very clear. Also he told me that I should photograph the lines, the interferometric lines. But I didn't know where to take my photographic apparatus from. I didn't know that I could go to the work shop or to the assistant, and ask him, "Well, could you give me a photographic apparatus?" So in some way, my problems came from the fact that simple the communications didn't work. I don't know why. Probably Wien thought "Well, the young man, he must find out himself. He must be a bit practical and do the things himself. After a while he probably will have learned it." But the actual result was that during these efforts, I lost interest very soon in the work. So I was engaged in theoretical work even during the time when I was in my room at the physical institute. So in some way, I never got interested in this experimental side of the question. Also I did not study, as I certainly ought to have done, those theoretical questions which had to do with the experimental equipment. For instance, later in the examination, Wien asked me about the resolving power of the Fabry-Perrot plates. There he expected that I could reproduce the theory of the resolving power — how it depends on the distance of the plates and so on. And this I had never studied. During the examination, of course, I tried to figure it out, but in this short time I couldn't really do the work myself. So he certainly realized that I simply had not been interested in it. And then he was angry, and then he asked me about the resolving power of microscopes. When I didn't know that, he asked me about the resolving power of telescopes, and I didn't know that either. That kind of thing. Then in some way he felt that I had too little interest in experimental physics. So then he asked me about the theory of the storage battery, and that I didn't know either. So I think he was perfectly justly quite dissatisfied with my knowledge. He thought that I should have a very poor mark; I don't know whether he wanted not to pass the examination. I expect that there must have been quite a discussion afterwards between him and Sommerfeld about the problem. Since I got through all right in mathematics and astronomy, there was no serious difficulty there, so I think they decided that I should pass with a rather low mark, and that was all.

Kuhn:

Do you have any feeling that some part of what this was about was the perennial battle between Sommerfeld and Wien?

Heisenberg:

I would say that it formed, perhaps, a kind of background in that sense that Sommerfeld always felt that theoretical physicists do some kind of "highbrow" physics. Wien felt that Sommerfeld forgot about the normal and decent part of experimental physics which everybody must know, and should know, and he wanted to insist that these things must be known to every student, even in Sommerfeld's laboratory. And I think he was quite right. I don't see any reason to complain. And Sommerfeld himself, I think, was somewhat disappointed that I had these difficulties. He had probably not realized that this work at the Wien Institute was not a success at all, because in some way I never got in touch with the real experimental physics.

Kuhn:

Did you, as a result of this experience, make a point of learning about resolving powers, for example?

Heisenberg:

Well, I did actually then learn about the resolving powers. I was a bit angry that I didn't know it. I felt, "Well, after all I have worked with these Fabry-Perrot plates, and I should have thought about it — why it works that way and not a different way." So I did learn about the resolving power of microscopes and things, and in some way I even had fun from seeing that by means of interference calculations, one can show that these things come out the way they do. So one might even say that in this later work on the gamma ray microscope and the uncertainty relation, I used the knowledge which I had acquired by this poor examination.

Kuhn:

That, of course, is why I asked the question. One may never know for sure, but it's at least worth pinning the information down. ... You said that when you had first started, you had very rarely read in journals, that you had tried to occasionally, but by and large you found that at the beginning there was too much special work required in order to read them. Now, at the next level, as you began to read journals, what journals could one take for granted as having been read?

Heisenberg:

Well, at that time I would say definitely two journals - Zeitschrift fur Physik, and the Physikalische Zeitschrift, which at that time was quite good. Later on it just closed. I don't know why it disappeared. But the Zeitschrift fur Physik was, of course, a very good and new journal and that was generally read at Sommerfeld's Institute. Later on, when I could read English — to begin with I couldn't read English — it was The Proceedings of the Royal Society that played a very great role.

Kuhn:

When did you actually learn enough English so that you read scientific papers in English?

Heisenberg:

Well, actually, I should say in Copenhagen. I might come to this point later on. When I came to Copenhagen, it was arranged that I should stay with a very nice old lady who played a big role in [Bohr's] Institute; that was Mrs. Maar. Mrs. Maar was a widow, and she had a nice house, and she had a habit of having young people from Bohr's Institute living with her. Oscar Klein had been the first to live with her, Kramers was in her house quite frequently, and I was either the successor of Klein or of Kramers, I don't know which. This was my first longer trip, for half a year, to Copenhagen. My first longer trip. She was very much interested in these young people and she realized very soon that it was very important for a young German to learn languages. I decided for myself that if I lived in Denmark that I wanted to learn Danish. At the same time, being at the Institute, I had to learn English. I first concentrated on Danish. Every day after lunch, she took one or two hours out of her day's work and talked Danish with me, and read newspapers. So I actually did acquire the Danish rather soon — not very well, but so that I could get along. At the same time, then very soon also, we took up English. After about ten or twelve weeks in Copenhagen, Bohr asked me to give a talk at the Colloquium, and I expected that this talk should be in Danish, so I prepared my talk in Danish. I was quite proud that I had now prepared a good talk, as I thought. Just half an hour before the Colloquium started, Bohr told me, "Well, it's obvious that we talk in English." That was, of course, very bad. Well, I tried the best I could, but I think it was extremely poor. But anyway, through Mrs. Maar, who really had done a lot of work with me, and was extremely kind to me, I did learn the two languages fairly well after a while. It was only from this time on that I really could read English without difficulty. I had read some English papers already in Munich, but only with some difficulty. I never had English in school — at that time we only had French in school. Well, I knew a bit of English from my mother. She had thought that I should learn English, so she had made a little effort while I was in school to teach me English, but not very efficiently.

Kuhn:

The French you had had in school, so you could read French?

Heisenberg:

Yes, yes, I had French in school, and I could read French. That was no difficulty. English was more difficult.

Kuhn:

Now then, to the journals — you say the Zeitschrift fur Physik and the Physikalische Zeitschrift, and then the next one for you would have been the Proceedings of the Royal Society, which you read regularly.

Heisenberg:

Yes, later on I did read them regularly. Yes, those were the main papers. And then there was the Annalen der Physik sometimes, but that was already rather declining at that time. I read practically no French journals; well, the Comptes Rendus, occasionally, of course. What was the American paper at that time? The Americans did also write for the Proceedings of the Royal Society, so I think there was not a special American journal which I would read. What was the journal?

Kuhn:

The Physical Review?

Heisenberg:

No, that didn't exist at that time. I don't think so. Well, in these early times it probably didn't play a very important role.

Kuhn:

It is very likely in this period that there would not have been very many people publishing there whom you would have wanted to follow. In experimental physics, you'd have been more likely to read it.

Heisenberg:

You don't know when the Physical Review started?

Kuhn:

I should, and I don't. I would say it was not only in existence then, but it had been in existence for some time. On the other hand, I don't know.

Heisenberg:

I certainly know that I should say after 1930, I have read the Physical Review quite regularly. Then it started to become the leading journal, but not much before that time. I couldn't say the exact date, but I would say that before 1925, I probably read the Physical Review either not at all or very rarely. But the English journal at that time was the Proceedings of the Royal Society.

Kuhn:

What about Phil. Mag?

Heisenberg:

Yes, I would occasionally read the Phil. Mag. and Nature; Nature and Phil. Mag., yes.

Kuhn:

But those were things that you might sometimes take up, but did not make a point of following?

Heisenberg:

No. But the Proceedings of the Royal Society. I probably have tried to read every time that it came in or least look through the titles and just see what has come off.

Kuhn:

Did this indicate that Sommerfeld made no great point about the desirability of keeping up with all the literature?

Heisenberg:

Probably not, but still he wanted to know always the new and exciting things. He didn't try to study carefully everything which came out; he did try to pick out all those papers which might be of interest for the special problem in which he was interested.

Kuhn:

But did he then look at a wider range of journals in order to be sure that he would not have missed anything?

Heisenberg:

I wonder how he did it? I should rather think not. I mean usually people read journals quite regularly only when they are younger. As soon as they get older, then they feel, "Well, the younger people shall read the journals, and they shall tell me what it is all about." Actually, for instance, at present I read journals only very rarely. I try to hear from my students what has come out and, of course, just once in a week I go down to the library and look through the titles a bit. But certainly I would miss many interesting papers if I would not hear about these papers through the students — not students, but through the younger generation.

Kuhn:

The reverse of the question then, in connection with reading journals, is selection of journals in which to publish.

Heisenberg:

Well, the principle, I think, in Sommerfeld's Institute was that one should publish in those journals in which the subject is treated most carefully and most frequently. So at that time it was obvious that this modern part of physics, Bohr's theory, was treated in Germany in the Zeits. f. Phys. Therefore, I also should publish in the Zeits. f. Phys. But, for instance, this work of turbulence was more old-fashioned physics; therefore, Sommerfeld suggested that I should write to the Ann. d. Phys. So it was published there. So it depended on the subject, and Sommerfeld would say, "Well, this Zeitschrift fur Physik; that is a journal for atomic physics."

Kuhn:

What about the Physikalische Zeitschrift?

Heisenberg:

Yes. I don't know why, but in some way the Phys. Zeits. had a different attitude; it was more bent in the direction of Nature, it had a wider frame. That's difficult to tell. Why do you prefer the one periodical over the other? Even nowadays I don't know why.

Kuhn:

Were there any striking differences in standards for refereeing or in the length of time that it took a paper to appear?

Heisenberg:

Well, for some time the Zeits. f. Phys. was known to publish very quickly and that was an argument in favor of doing it there. But I don't think there were very big differences. Anyway it went much more quickly than nowadays.

Kuhn:

What did "very quickly" mean in that time?

Heisenberg:

I think about four months between sending the paper and the actual publication of the paper. Something like that. One could easily check it. And then there was Die Naturwissenschaften, like Nature, where you could publish things within a few weeks. That is like the Physical Review Letters, where you actually try to do things very quickly.

Kuhn:

Well, my impression, judging by the pieces for which I go to Naturwissenschaften for this project, is that it was not often that quick announcements of new results in physics went through Naturwissenschaften;it was more likely to go to Nature for an important preliminary statement.

Heisenberg:

Well, that's quite true. I mean especially when one wanted to reach an international public, one would publish in Nature. That's quite true. But sometimes things did appear in Naturwissenschaften.

Kuhn:

Do you remember anything in particular that would illustrate that?

Heisenberg:

No, I don't remember anything.

Kuhn:

The only one I remember I want to talk to you about later so I will hold off for the moment. Why don't we now swing back toward physics. If we could, I would like to start out in a somewhat more general way before we come to the Zeeman effect. By 1923, at least around Copenhagen — I'm not sure now it was then in Munich it's perfectly clear that what I will call a "crisis" exists and is recognized with respect to the problems in quantum mechanics. It's clear in things that Bohr said, it's clear at least by what Bohr thinks that Born said, it's clear for many people in that 1923 Bohr Heft of Naturwiss. and in other places. But it is by no means clear to me when that strong attitude came, how it developed, and more particularly, where it developed. For it surely wasn't the same in different places. What I really want to ask you to do is to try, if you can, to forget what happened in the summer of 1922, which is probably important for this development, and tell me what was the state of mind of the faculty, of the students, about the state of affairs in physics and particularly in quantum physics in 1920, '21, '22.

Heisenberg:

I think I can say that quite definitely. I would say in Sommerfeld's Institute, first of all, people believed that somehow one could, by means of quantization rules — integral of pdq - actually calculate the stationary states. So this opinion was, of course, produced by the success that this scheme had in the Stark effect of the hydrogen and in the hydrogen spectrum in general, and so on; So actually, people thought, "Well, this seemed to be true, definitely true." On the other hand, one also realized that somehow one could not understand it. There was always a general feeling, more or less clearly expressed, that one cannot improve classical mechanics by adding new conditions to it; you know, that is in some way absurd. Also, it was recognized that the phenomenon of quantization obtained other puzzles which had not been solved, for instance, the light quantum business — are there light quanta or are there no light quanta. Then there had been —

Kuhn:

Let me interrupt to ask whether that was a serious problem for people in Munich?

Heisenberg:

Yes. I would say that this was a problem in Munich in so far as people saw that one couldn't have both at the same time. You can't say that light is waves and light are light quanta without making contradictions. On the other hand, I think, it was clear in Munich that somehow one had to take the contradiction and had to consider it as a part of physics for an unknown reason. One said, "Well, something hasn't been understood here, but in some way it looks as if there were light quanta and in some way it also looks as if there were waves, and we just don't understand what it is all about." But I think nobody in Munich would have dared to say there can't be light quanta because we have interference patterns, and also he wouldn't dare to say that we can't have interference of optical waves because there are the light quanta. So I think the Einstein paper of 1918 had made a very strong impression on everybody because one could see there that the light quanta are a reality and have to do with this business of the stationary states and so on. And still the waves as well have some kind of reality, and so one simply got into the habit of contradictions, as something which one must face. I mean one didn't simply say, "Well, this is all nonsense." That was the main difference between the Sommerfeld Institute and Wien's Institute. In Sommerfeld's Institute, the people dared to be inconsistent, to simply say, "Well, we know that it is inconsistent. Well, we can't have it, but we have to take it. We just see that nature is that way, and nature manages to get through it." That is a different question. But it wasn't so much a crisis to begin with, it was just a feeling that some things were difficult to understand. We apparently could calculate stationary states and when Bohr's paper came out on the Periodic System, the first idea was, "Well, now Bohr has actually succeeded in calculating the stationary states of all the different atoms." Everybody was very happy and said, "Well, that's just excellent." I think that was the general attitude. The idea that one really came into a crisis, namely that this calculation of the stationary states was simply wrong, did not occur to people in '20 and '21. I think the first instance when this occurred was when Pauli had tried to calculate the hydrogen molecule ion and didn't succeed. That made a strong impression on Sommerfeld and on many people in the Munich Institute. Then, of course, one tried to find excuses: "Well, why should it perhaps not go? Why should it not work in the hydrogen molecule ion, but only in the hydrogen atom?" But in some way that was the first moment when really this confidence was shaken.

Kuhn:

This does get us a little further ahead, but I think it is necessary to clarify this point. Would it be right to say that the people in Munich were considerably more comfortable in 1920 than probably people in Copenhagen were even then?

Heisenberg:

Well, that I wouldn't know, because I hadn't been in Copenhagen at that time. I've already told you about my conversation with Bohr in '22 where, at least in this special case, I was apparently still more critical than Bohr was. But how critical Bohr actually was, I don't know. One can simply say that already in his first paper in 1913, he's actually more critical than many people were later on. So he had some very critical remarks that this cannot be a consistent picture, but still it works somehow. I don't recall it exactly, but you will.

Kuhn:

I know that paper and those remarks. Good. Well, I'm eager as we go on to have you return to this point and to watch how things develop. But I take it that you would feel that at Munich the first strong doubts that maybe we can't even do what we have supposed we could do came with the Pauli paper.

Heisenberg:

Yes, the Pauli paper was a definite cut in the situation because there one saw that the old methods don't work anyway. And perhaps at this point I should come to my own first paper on the anomalous Zeeman effect. You remember that there had been this old paper of Voigt, I think from 1913 or so, and Sommerfeld had remodeled this paper to fit into his quantum theory by deducing, from the paper, formulas for the energy levels. Well, after my discussions with Lande on the energy levels and Lande's paper, Sommerfeld found that one could actually get these formulas for the energy levels as functions of the magnetic field. So that was quite a basis for many discussions. Then I remember that, after I had written this first paper, Pauli explained to me what had only been half clear to me, namely that what I actually had done was certainly not physics in the old sense. In the old sense, I would have had to solve a dynamical problem according to the strict laws of classical mechanics. I should have then quantized this model and so on. What I had done was that I had applied mathematical formulas so that they could be interpreted somehow as relations between angles of orbits and that kind of thing, not using strict mechanical laws, but rather using a kind of mathematical fantasy or imagination. This, of course, is not physics in any decent sense, but still —. So it was actually an attempt to connect physical pictures with mathematical formulas, but using unknown physical laws. Then, of course, you are out in the open sea, you can do whatever you like. But still, I felt at that time that the pictures did help me to get some notion as to how things probably are connected. If I recall correctly, I did derive from this first paper some empirical laws which later on also did prove correct — about triplet structure. Also I got an equation of the third degree for a triplet which later on perhaps could be compared — I don't know how well it does — with an equation of the third order which you get by solving the determinant of quantum mechanics. So this first paper, I think, is a clear indication that at that time, one was already inclined in Munich simply to leave classical mechanics, to simply say, "Well, we must follow the experimental situation, and our imagination. We must see how this experimental situation may be connected with physical pictures, but we cannot rely on classical mechanics, because that doesn't lead us to the real point."

Kuhn:

I think this is a very apt description of that paper — but it was not clear to me whether this is to be taken as an indication of your own special talents or the Munich vitality. Sommerfeld, I think, would not have written a paper like that.

Heisenberg:

No, no. I mean it was actually a mixture of many rather different things. You may also say, and I think quite justly, it was also a proof that my knowledge of classical mechanics was so weak that I didn't even realize where I actually went away from decent mechanics and where I did something which was still in agreement with classical mechanics.

Kuhn:

Let me ask you about one point in particular. In that paper you do your space quantization on the angular momentum of the valence electron, not with respect to the total angular momentum. You produce the total angular momentum and you discuss the precession of both the Rumpf and the valence electron with respect to the total angular momentum, but when it comes to space quantization, you use the azimuthal quantum number and not the total quantum number. Now this is a striking example of a place where you have all the mechanical pieces but you do something that looks unmechanical. I wondered whether you were bothered about that? Whether there were special reasons for doing it?

Heisenberg:

I think I must look through the paper again. No, I think I have it here. That is this one you mean?

Kuhn:

Yes, exactly. This, I think, is one of the papers that it would be throughly worthwhile looking at.

Heisenberg:

Yes. It presented a problem. It's quite funny to see it afterwards because after all, it was a very special subject, and in the whole picture of the atomic spectra it's not very important — this anomalous Zeeman effect. Still it was a point where we could get to the details of things. Let me see about this space quantization. Yes, there I have introduced the total angular momentum of the atom and its angle with the axis of the field. Yes, there were always these formulas with the cosine which were used to get the Lande formulas.

Kuhn:

Well, I think I'm right in saying that you do introduce the total angular momentum and you use it in evaluating the precession of both the Rumpf and the electron orbit, but not for the space quantization part of the problem.

Heisenberg:

Uh huh. That may be, yes.

Kuhn:

This is not in itself a point of great importance, but it's an illustration of just the sort of thing you were talking about, that is the senses in which this is and is not classically mechanically oriented. I thought it might provide more information.

Heisenberg:

Well, I remember that the criticism of Pauli did in some way also mean this point, but I don't know what the final outcome of this discussion was. It's a pity that we haven't got our letters because —. At that time, of course, one did not know about electronic spin, so one didn't know exactly which angular momenta one had to combine. Here I say the Rumpf and the electron. That, of course, was some help. I don't even recall now how I got the correct number of levels because after all, in order to get the right number of levels, you must do something else.

Kuhn:

But that's terribly important. You do it by means of what one will later call a sum rule. ... But that's a particularly interesting passage in the paper for various reasons. In asking about the space quantization of the two angular momenta, you say that the projection of the electron angular momentum onto the direction of the Rumpf angular momentum must be integral or half integral. You then set up a sum rule which leaves you saying parallel or anti-parallel as the only possibilities. Now, if instead of doing it that way, you would say, "Let's let the Rumpf line up," then there would only have been the two possibilities from the beginning. I'm very unclear as to why it was necessary to space quantize the electron angular momentum relative to the Rumpf rather than the Rumpf relative to the electron. It's possible that you started out by doing it the second way, but felt that you had to take care of the other possibility also, and gave only the more elaborate argument. It also happens, in this argument, that you point out that if there is such a thing as an anomalous Zeeman effect, then the Rubinowicz derivation of the selection rule cannot be right for the case of individual transitions, because in a transition in the anomalous Zeeman effect, you don't carry off exactly an angular Momentum of h over 2π. Therefore, it must be a statistical law only.

Heisenberg:

It does say that it should be a statistical law?

Kuhn:

I think I can show you. Yes. There's the sentence.

Heisenberg:

Oh yes, yes. Oh yeah. I had even stressed the physical importance of it.

Kuhn:

In this period various sorts of non-conservation are beginning to pop up again and again. It's here. It comes out again in a paper that you do with Born in which there is a final remark relating to the possibility of utilizing some such scheme to explain the paradoxes of the Stern-Gerlach experiment. It shows up again with the Bohr-Kramers-Slater. At some point, or again and again, I hope very much you'll say how people felt about these non-conservation ideas, where they came from, with whom were they popular and with whom not so popular.

Heisenberg:

Well, first of all, I would like to emphasize that paper of Rubinowicz as being very popular in Sommerfeld's laboratory. Sommerfeld, in some way, must have been closely connected with Rubinowicz. Has he been with Sommerfeld? Not in my time, but perhaps it was earlier than that. So I know also from discussions that Sommerfeld apparently knew Rubinowicz very well personally, and it may be that this paper of Rubinowicz had been written in Sommerfeld's laboratory. Sommerfeld did stress this point about the conservation in the spherical waves very strongly. So as soon as one had to go away from it, then one would always meet Sommerfeld's criticism. Now here one says that as soon as one goes away from the classical laws of emission of radiation, then that must be connected with this whole story of light quanta and waves. You know one knew from the Einstein paper that it has a certain meaning to consider this emission of waves as a kind of statistical average of the emission of light quanta. It was not as clear as it later on became in the Bohr-Kramers-Slater paper. But even in Einstein's paper, there were found quite clear and well-defined statistical laws of emission and absorption. ... And at the same time, everybody knew that when we talked about atomic models, then we thought of spherical waves being emitted and so on. So I think that it was at least a common way of talking about things that one said, "Well, these spherical waves must somehow mean the probability of emission of light quanta. We don't really know what it is all about, but still somehow that must be some statistical mixture of light quanta or so." And so from then on, one was allowed, if one got real contradictions to classical laws, to say, "Well, let's assume that the classical laws only hold statistically."

Kuhn:

It's a strange reversal though. Einstein's point is that, with respect to the emission of the individual quantum, you must expect conservation both of momentum and of energy. The statistics should enter only in the question of the total light emitted.

Heisenberg:

Yes. That is true. Yes, that formula in my paper looks very much like a sum rule.

Kuhn:

You come back to that formula later after Pauli has formulated the sum rules in the form in which they're now more generally put. Then you point back to this earlier thing, and say that you realize it's a mathematical law and not a physical law. I must say that I think that you give an awful lot to mathematics in order to come to that conclusion. This paper is just loaded with terribly interesting things of this sort that speak both for the state of the problem, and for the state of physics. Perhaps it would be best to continue talking about this at the moment in a fairly general way and you may then have more time to look at that paper.

Heisenberg:

Yes, I must simply study it carefully again. I just looked through it once here, and I didn't study it carefully. But I now see my difficulty with Rubinowicz. Sommerfeld certainly has pointed out this to me very clearly and he said, "Well, there is this Rubinowicz paper and then you get into disagreement with it." And then I used this very weak argument of only statistical conservation because one knew the Einstein paper and at the same time knew the spherical waves. I would say it was a kind of argument like in the Bohr-Kramers-Slater paper, and that must have been in the mind of many people. At that time, I had not seen Bohr yet, so I could not possibly have discussed it with him. But apparently many physicists, in some way, thought, "The spherical waves are a reality, and the light quanta are a reality. We don't know how they are connected, but anyway there must be some kind of statistical connection."

Kuhn:

You used models, or a model, very strongly in this paper. The paper is, in a sense, about a model. I wonder how Sommerfeld felt about that. It's rather noticeable in much of his own work how far away from models he will often stay, and some of his reluctance to use the Correspondence Principle has to do with that.

Heisenberg:

Yes. That was a strange feature which I never quite understood, because if one believed in the models, then one must also be able to do some kind of calculation of the intensity. A model which never gives the intensity is not real physics. I think that Sommerfeld disliked this kind of qualitative physics, physics which was made by feelings and by intuition and so on. What he wanted is at least clear mathematical procedure — integral of pdq and so on — and by this procedure you get at the right formula for the levels. But first to say, as in the Correspondence Principle, that you take an average between two things and somehow the experimental value is in the neighborhood of that average — that was a kind of physics which didn't appeal to him. And he did not realize that this was perhaps a very essential progress, because the model is just a kind of thing which shows how things are connected, but is not something very fixed, very rigid. So I always liked Bohr's Correspondence Principle just because it gave that kind of lack of rigidity, that flexibility in the picture, which could lead to real mathematical schemes. Well, Sommerfeld disliked any non-rigidity. He wanted to have things fixed mathematically, and so he disliked the Correspondence Principle. There had been quite a number of discussions between Sommerfeld and Pauli just about the Correspondence Principle, and Sommerfeld never liked it. In some way, he never felt that it was good.

Kuhn:

Can you reconstruct or remember more about those conversations?

Heisenberg:

I think that Sommerfeld liked it at one point — when Bohr had succeeded in deriving definite selection rules, like the delta L being only plus or minus 1. Then Sommerfeld felt, "Well, this is something precise and strict, and this must be true." He perhaps didn't, even then, like the way it was found, but I would say that, probably instinctively, Sommerfeld felt that this was part of group theory — the rotation group, by means of the Correspondence Principle, required that there was a selection rule. He would never have expressed it that way at that time because one didn't know about group theory. Still, the idea to Get definite selection rules appealed to Sommerfeld. Psychologically he would have reacted this way: "Let's forget about Bohr's Correspondence Principle, and let's just simply state clearly that there is a selection rule, and only these transitions are possible." He felt that that was a clear statement. While these more weak statements — that the classical intensity is not too far off the quantum theoretical — he didn't like.

Kuhn:

How did Pauli feel about this?

Heisenberg:

Yes, that is interesting. How did he feel. I think he was more in favor of the Correspondence Principle because he was more critical against the models. He would say, "Well, after all, these models are only vague talk. We don't know why they work so well in some cases, and therefore the Correspondence Principle is just an indication about the weakness of the model." Perhaps he would put it that way.

Kuhn:

Well, you know this goes with something you said before that puzzles me a bit. Granting that the Correspondence Principle tells you that you cannot take the model altogether seriously, there is nevertheless a sense in which the Correspondence Principle is a much more modellm@ssig approach than Sommerfeld's approach. And when Sommerfeld discusses the Correspondence Principle in Atombau, at a time before he is yet giving it a central place, but still as late as 1923, he said, "After all, Bohr's success does indicate that we may have to take models seriously." So there is the other sense in which the Correspondence Principle is the place that is allowing one to use models in fact. You might say that Bohr is for models in one sense in which Sommerfeld is against them.

Heisenberg:

Yes, perhaps one can put it that way. When you speak about the model, you mean something which can only be described by means of classical physics. As soon as you go away from classical physics, then, in a strict sense, you don't even know what a model could possibly mean because then the words haven't got any meaning anymore. Now this was a dilemma. Because if one said that one used a model to calculate the levels and then at the same time one goes away from classical physics by introducing integral pdg, then one does something which already is inconsistent. Now, having this inconsistency, Sommerfeld wanted to go into rigorous mathematical laws which in some way went away from the model, while Bohr tried to keep to the picture while at the same time omitting classical mechanics. He tried to keep the words and the pictures without keeping the meaning of the words, of. the pictures. Both things are possible in such a situation because your words don't really tackle the things anymore. You can't get hold of the things by means of your words and so what shall you do? But Sommerfeld's escape would always be into the rigorous mathematical scheme, while Bohr's escape would be into the philosophy of things. Perhaps this is the fundamental difference between the two people. Sommerfeld was never a philosopher. He would never —. He was really not interested in philosophy, but interested in mathematical laws, in strict laws of nature. But he was not interested in these vague, problematic features of nature where you can possibly not use the ordinary words to describe the situation and so on. I remember I sent to Sommerfeld my later paper about the Uncertainty Relations, "gber den anschaulichen Inhalt der quanten-theoretischen Kinematik und Mechanik." Then Sommerfeld replied with the remark, "Your paper may be quite good, only I dislike the title. You should have called it 'gber den unanschaulichenInhalt." That shows his way. I think that is probably a good description., I think Bohr was, from his youth, interested in this limitation of our way of expression, the limitation of words, the problem of talking about things where one knows that the words don't really get hold of the things. And this kind of thinking was quite foreign to Sommerfeld. It would not occur to him.

Kuhn:

Now I'm doing just what I said not to do, but you mentioned a terribly important point that I would like to check while we're at it. Bohr said to us just a little bit about this very early interest of his in the use of words and spoke of an old idea of his in which he utilized Riemann surfaces to point it out. Did he talk to you and the others at the institute about his ideas on this?

Heisenberg:

Well, he definitely talked to me about it several times.

Kuhn:

How early would that be?

Heisenberg:

Well, these discussions with Bohr were mostly, of course, at the time of the Uncertainty Relations. That would be 1926 and 1927, but maybe already earlier. That I don't quite recall. At least I would say that Bohr's interest in these things had been much earlier. I remember one of these sailing trips which we made from Copenhagen. You know Bohr had a sailing boat together with Bjerrum and Chievitz, and so on. Bohr spoke about his philosophy in connection with the Uncertainty Relations and there one of his friends told him, "Well, didn't you tell us exactly the same things already twenty years ago?" So these friends remembered that he had talked in a very similar manner already very early. So I cannot doubt that he had talked about these things already, say in 1913. Then also I remember that he told me once very many details about his study of the philosophy of James. James was one of his favorite philosophers and especially the work called "The Streams of Thought." That had made a profound impression on Bohr, and he always explained to me that this was the only way of talking about language. Bohr said that when any word is produced, this word raises something into the full light of consciousness, and at the same time, it raises many other things which are only in a shaded light and are almost completely covered, and all these things enter in consciousness at the same time. Therefore, a word is such a complicated thing that one could not possibly hope to just copy it by a mathematical letter, because the mathematical letter can then only mean, let us say, that thing connected with the word which is in the center of consciousness. That kind of thing, you know.

Kuhn:

Do you remember at all when he told you this?

Heisenberg:

Well, I would say it should have been around '27, '28, '29 or so. I went away from Copenhagen already in the autumn of '27; on the other hand, I came back to Copenhagen almost every autumn. But we had most of these discussions in '26 and '27. So this should probably be around '27. Perhaps around the Brussels Conference, the Solvay Conference, in '27, which was a very important conference.

Kuhn:

I asked this for a particular reason. Professor Bohr also talked to us a bit about his interest in James, and he insisted that at least some of it went back quite a long way. On the other hand, Rosenfeld, who looked over the transcripts said, "Well, that's got to be wrong, because I remember reading James with him in 1931 or '32." It could be that both of these are right, that they read something else, and that Professor Bohr had already read this part on the stream of consciousness, which is what he particularly referred to. But I press this point only because I'd like to be sure as to whether some part of that does go back at least into the twenties.

Heisenberg:

Here I'm not absolutely certain because, of course, I have spoken to Bohr so often. I cannot guarantee that these discussions about James have not been only after '32. Because, in the years after I left Copenhagen in '27, I was together with Bohr practically every autumn, then a few times in this skiing hut here in the Bavarian Alps. So I saw him so frequently that it's extremely difficult to remember when this discussion was.

Kuhn:

If we may, let's come back to the Rumpf model. Let me ask you this. Can you tell me more about how that came into being? That is, you told me about this first work in the Sommerfeld seminar, in which you arrived at half quantum numbers, presumably for the doublet. But there's a whole lot that goes on with respect to this problem between that point and the time when you published the paper on the Rumpf model. I wonder how much of this one can still get hold of. For example, there is Sommerfeld's own work on the Voigt formula. There is certainly the Lande papers in which he gives g factors — not the general formula, but the factors for doublets and triplets which you use in the Rumpf model. You introduce your paper by laying out these known regularities which you're going to derive. And I wonder whether you would at all remember discussions of these earlier developments. What sort of work were you, yourself, doing on this Zeeman effect in this time? At what point did the modellmassige approach begin to come to mind?

Heisenberg:

Well, I think the general story is like this. Actually, this Lande work had been done also in Munich to some extent. I told you that Sommerfeld had given me the problem. He had written a short paper on the multiplication law of the Zeeman effect, where he had simply used the fact that any frequency was a difference between two terms. Actually, the Lande formulas were in some way also derived —. Well, I had also found these formulas and also it was absolutely correct that Lande should publish it first because he was the first. Still, Sommerfeld, who had this paper on the Voigt theory for himself, felt a bit sorry about me that I had not written anything in spite of having done so much work. Sommerfeld felt that I had done so much work with it that I should also publish a paper. So he told me, "Well, now you have done so much with these things. Phenomenologically, the things now are being written by Lande and by myself, but will you not try to do the model of it, because now it must be quite simple to find a model which should give it." Well, the idea was that since, in the case of the Stark effect, it had been so simple to derive the exact model, and since now it was clear that the general principles of Bohr's philosophy — energy differences give the frequencies — (did) work, the optimism was, "Well, it must be quite simple also to find the correct model for it." I mean the difficulty in Zeeman effect you can only have the normal Zeeman effect formula, that was not so clear at that time. So Sommerfeld thought, "Well, now this young man can try a bit with the models so he learns something." And I did realize that the explanation by means of a model really didn't work in some way. It worked only if one did things which were really not justified from classical mechanics, or at least I felt that the whole thing was a bit weak. On the other hand, I also felt that this was interesting and it looked as if it contained a number of things which looked like real physics. You know it was this standard situation in an undeveloped field of physics where you feel that you have gotten hold of some parts of reality, only you cannot rationalize it to the end. You cannot really get a perfectly clear picture. And, on the other hand, at the same time I felt, "Well, the picture is so interesting, why not give it to others, even if it's not clear." I mean that at least would not be my philosophy to such a paper. I mean I don't know how I felt at that time because clear and unclear is always such a difficult term. I would say if one knows that one has gotten hold of some part of physics, why should not other people also try their best to take part in it. And so the paper came out in this sense, that I tried to do my best using this material of Lande and of Sommerfeld, to work back to a model. And the idea was there should be a picture behind it, just as there is a picture behind the Stark effect in the hydrogen which everybody knew. Well, that was at the beginning of many other developments.

Kuhn:

Yes, it certainly was. All sorts of important work stems from this paper.

Heisenberg:

Yes. And still it is quite unclear. I did realize now when I looked through it that there are many things in it which are such that if one really now asks, "What did you actually mean by this," then it's very (difficult to answer). But I will look carefully through the paper. I think it's worthwhile to answer questions in detail.

Kuhn:

As you read it, if you can keep in mind that what I would most hope for is not so much a contemporary explanation of what is in it, but anything that it may bring back to your mind of things that went on while you were writing it, of problems that bothered you, of things that you tried to do but couldn't do, of the points that seemed stronger and the points that seemed weaker at the time. This is the most helpful. It's a very different way of reading a paper from the way you would sit down to read a contemporary paper. I know with my own students I have a terrible time, if they have had training in the sciences, making them read a paper as a historian, instead of reading it as a scientist. One has to put oneself in a very different frame of mind in order to get the sorts of points that one's then most concerned with.

Heisenberg:

Well, I would describe the state in which I was when I wrote the paper perhaps in the following sense: What quite frequently happens in physics is that, from seeing some part of the experimental situation, you get a feeling of how the general experimental situation is. That is, you get some kind of picture. Well, there should be quotation marks around the word "picture". This "picture" allows you to guess how other experiments might come out. And, of course, then you try to give to this picture some definite form in words or in mathematical formula. Then what frequently happens later on is that the mathematical formulation of the "picture," or the formulation of the "picture" in words, turns out to be rather wrong. Still, the experimental guesses are rather right. That is, the actual "picture" which you had in mind was much better than the rationalization which you tried to put down in the publication. That is, of course, a quite normal situation, because the rationalization, as everybody knows, is always a later stage and not the first stage. So first one has what one may call an impression of how things are connected, and from this impression you can guess, and you have a good chance to guess the correct things. But then you say, "Well, why do you guess this, and why not that?" Then you try to give rationalizations, to use words and to say, "Well, because I described such and such." The picture changes over and over again and it's so nice to see how such pictures change. May I give one example from later times — this so-called multiple production of particles in elementary particle collisions. Now this possibility occurred to me in 1936. I remember quite well that I actually attended a very annoying chemical lecture and thought about the elementary particles just to pass my time. Suddenly I saw that in the perturbation theory you might have that kind of divergence which, on the one hand leads to the well-known divergencies of the field theory and then it also led to the assumption that when two particles collide at high energy then you can get any number of particles. Now, when I tried then to make some kind of picture out of it, I did guess the probable number of particles which would come out and the way in which the cross sections would vary at extremely high energies and all these kinds of things. And I published papers about these guesses. Then later on, the picture changed tremendously. First of all, at that time one didn't know anything about the pi mesons and I thought always about mu mesons. Now actually, it was the pi mesons and not the mu mesons. Then I always thought that these pi mesons, or mu mesons rather, should come out all at the same time as these particles. Later on, one knew that they are resonance states, so that many different particles come out and they disintegrate later on into π's. Then, quite recently, there came this story of the Regge-poles. One knows now that if you demand a certain behavior of the cross section at extremely high energy — if you say that the cross sections become constant — then you can say that the Regge-poles behave in such a way as the Geneva people have found. But if you say that they go logarithmically, then you have a slightly different Regge behavior, and so on. But the funny thing is that through all these changes the actual experimental situation looks still extremely near to what I guessed at that time. Well, if one gets into such a picture, one sees experimental connections rather clearly and they look all quite reasonable. But as soon as you try to rationalize it, then you have, of course, a greater chance to make one mistake after the other. This, of course, means that the time is not ripe for doing it in perfectly rational terms, but still nature itself has such a close connection in itself that one can guess it. One sees how things are connected. That is a situation which has occurred to me so frequently that I take it for granted that this is the situation for almost every theoretical physicist an this world. He has some pictures of the world, and if he studies carefully what the experiments show, he has a good chance to guess more or less correctly how things are. But the rationalization may take him ten years or much more. It's a long process. And that is exactly also the situation with this paper. This paper is certainly not good at all because there are so many mistakes in it, there are many wrong things, but still it contains connections which all have some reality in them.

Kuhn:

... Did anyone suggest to you that for a man who had really published previously only one short note, that this was a terribly speculative thing to be associated with so early in life?

Heisenberg:

Well, I'm sure that many people would have thought that way but I —

Kuhn:

Did you feel as though you were taking a chance in publishing a paper of this sort? This is not meant to be a remark about the paper — I'm inclined to think that I'm a great deal fonder of this paper than you are.

Heisenberg:

Well, I don't think that I did reflect much about this point. I just felt that this was extremely interesting stuff, and after all, I had done something with it. I felt that in some points I had had some success, so why should I not publish a paper. I didn't think too much about the consequences of my paper. I mean it didn't occur to me that some people might criticize me for it. I just felt, "Well, after all, it's very interesting, and why not publish it?"

Kuhn:

This paper enters into the 1923 edition of Atombau but in a somewhat odd way. The treatment of the paper is sketched in the Nachtrag. On the other hand, when Sommerfeld develops the anomalous Zeeman effect in the earlier parts of the chapter to which he attaches this model as an appendix, there are certain problems he handles extremely differently. In particular when he talks about doublets, instead of using half integral quantum numbers, he uses a new selection principle which is that delta m shall be zero or plus or minus 2.

Heisenberg:

Oh. Which principle did you call it?

Kuhn:

The selection rule for the changes in the magnetic quantum number. Under Rubinowicz's argument, it must be plus or minus 1 or zero. But, as you say, for doublets you are led to half integral quantum numbers. Rather than do this, Sommerfeld here utilizes the selection rule that delta m shall be plus or minus 2, that is he doubles all the m values, so that all the half integral quantum numbers must become integral quantum numbers.

Heisenberg:

Oh, that I don't recall at all. Did he double the quantum in order to avoid the half quantum number?

Kuhn:

In 1923. But later, there is the appendix in which he does use half-integral quantum numbers. There must have been discussions over points of this sort and I wondered whether —.

Heisenberg:

Well, the half quantum number was, of course, a point of many discussions. because the half quantum was something which was very much against Sommerfeld's way of looking at things. Sommerfeld liked integral numbers, as I told you. He liked precise mathematical laws and integral numbers. So the half quantum was for him just something awful. He disliked that intensely, but, of course, he saw on the other hand that by means of this half number, one could get order into the anomalous Zeeman effect. I did not recall, as you say, that he actually then tried simply to multiply by 2, which, of course, is a formal way out. This is, according to my opinion, not attractive at all, but in some way he liked the integral numbers so much so he must have come to it. I had completely forgotten that he had done that. Well, I can look it up in Sommerfeld's book. But anyway, I do recall that we had many discussions on the half quantum numbers and I got my first help from Kratzer, as I told you. He told me, "Well, in the band spectra, it looks as if the half quantum number is something very useful and probably fits better with the experiment than integral numbers." But I remember that for a long time, even in the Sommerfeld Institute, the attitude of the others was, "Well, this half quantum number of Heisenberg is quite an interesting, but certainly wrong idea. For such a young man it's very nice that he thought about it. There may be something in it. But certainly that can't be true because if you start with half integral numbers where do you end?"

Kuhn:

Were you aware of the discussions of zero point energy, and of the possibility of a half quantum number coming in there?

Heisenberg:

Sometime later, yes. I think that came out of a discussion with Pauli, but I don't know exactly when. The zero point energy in solid bodies — there you could actually see the half quantum.

Kuhn:

Historically, some of those discussions are quite old. They go back to Planck's second version of his theory in 1911.

Heisenberg:

I do remember that Pauli once told me, and it made a great impression on me, "Well, you may be right anyhow with your half quantum number. There is this old paper on the specific heat problem — something about the equilibrium between the solid state and a liquid — where you could actually see that there was a zero point energy." And I remember that he then told the argument also to Sommerfeld, who then said, Well, there may be something in it." But nobody really liked it. Still everybody said, "Well, there may be something in it." Still, I don't know when this discussion with Pauli took place. It may have been as early as '22, but certainly not much earlier. Yes, I remember that Kratzer was in favor of the half quantum in band spectra because it fitted better with his experiments and then Pauli brought this argument about the specific heat. So there was gradually growing a certain sympathy for the half quantum number. But it was only in the quantum mechanics that it really came out, and everyone knew what it was all about. And it was also only then that one realized the connection with the representation of the rotation group; that was a much later stage.

Kuhn:

There is another odd thing that happens in the next paper which you do with Sommerfeld, which is the Correspondence Principle treatment of intensities.

Heisenberg:

Oh yes. Does that contain already the spin? No? But there was the Rumpf and the electron and the combination of angular momentum and that kind of thing.

Kuhn:

Yes, except the paper quite scrupulously avoids any real use of models. That is, it supposes that one has the following motions, and it simply sets up an abstract Fourier series. You start out with the Fourier series for the ellipse. Then you let the ellipse precess in its awn plane. Then you tilt it out of its plane, and watch what happens to the various Fourier components.

Heisenberg:

Yes, you just introduce angles. You have two vectors, which combine to a third vector. Then you project these three vectors on some direction in space. You calculate all the cosines and so on. Then you get certain classical formula with the total angular momentum, the orbital angular momentum, and the momentum of this extra thing. Then one tries to translate these formulas into quantum formulas by replacing L² by L(L + 1). Yes, I remember. It was that kind of thing.

Kuhn:

In that paper, until almost the end, there is no mention at all of the Rumpf model and only in the most indirect sense would one want to say that use was being made of it. However, there are a number of changes that have come on, at least with respect to Sommerfeld's thinking. For one, and I wonder if you could enlighten me at all on this, Sommerfeld has been very reluctant to adopt Lands idea that Sommerfeld's inner quantum number is the total angular momentum. He mentions it occasionally in Atombau, but by and large, he treats this simply as the inner quantum number, an index of multiplicity. In this paper, from the beginning, one takes the inner quantum number to be total angular momentum. Again, very little use is made of your model until the end. And then there is the rather strange remark that this, in certain respects, is incompatible with your Rump model, particularly in that it is the total angular momentum, and not the electron angular momentum alone, that is quantize with respect to the field direction. But there is the remark at the end of the paper that "We've corrected the calculations on the basis of the Rump model." Again, clearly Sommerfeld himself is to some extent being converted about a number of things here. The consistency, inconsistency relations are fascinating in what they indicate about the problem and the state of mind, and I wondered again whether you remembered any conversations with him or points at which he changed his mind or anything of this sort that has been going on at the time.

Heisenberg:

Well, I should perhaps say that for Sommerfeld again, the center of interest was not the model — whether the inner quantum number means total angular momentum or whatever. The center of interest for Sommerfeld was that one has integral numbers as ratios between intensities. The intensity ratio of the two D lines was 2 to 1, and that kind of thing. That appealed to him. He was happy that one could, in this case, use the Correspondence Principle to guess such integral relationships. On the other hand, he saw — that came by many discussions — that this idea of combining angular momentums was a tool to derive such formulas just by guess-work, by always guessing from a classical formula to a quantum theoretical formula. He probably would just not put much emphasis on what this inner quantum number meant. Of course, in this picture, that vector which remained constant in time, and only could be changed by means of an outer field, could only be the total angular momentum if you believe in the ordinary classical conservation laws. But since even these conservation laws and everything else was in doubt, there was always a state of vagueness about such concepts. For Sommerfeld, these pictures of the total angular momentum were just pictures by means of which one could derive empirical laws about integral relations between intensities. So he didn't mind very much whether this was called the total angular momentum or inner quantum number. It was only later on that one could realize, "Well, after all, the conservation laws must be correct, and therefore this must be the total angular momentum. There's no doubt about the meaning of these things."

Kuhn:

What part, at this time, did Pauli play in this work? Was he already deeply interested in spectroscopic and atomic problems?

Heisenberg:

Oh yes. I think all these things were always discussed with him. He came from this X-ray business; the number of levels didn't fit; you had the two kinds of doublets in Sommerfeld's formula. And Pauli insisted that this was really Schwindel. He would say, "Well, that's complete Schwindel. Either the Sommerfeld formula is correct, and then the number of levels must be correct; or, if the number of levels is not correct, then it means that we have a new degree of freedom. That degree of freedom must mean something and you have to say something about it." Of course, he did not come to this anschaulich model of spin, but he did come to the doubling of states. ... Well, Pauli certainly did take part in all these discussions. I told him what I did, and I wanted to know his opinion and I think he was quite interested. But he never took part in it. I would say one of the main reasons why Pauli never published anything in this field was because Pauli would only publish things which he could rationalize completely. He would always wait until he had come to the very end of the game so that he could say everything in perfectly rational terms, and therefore, he would not publish a paper on this subject. He would say, "Well, it's not quite clear, and I'm not interested in 'atom-mystics.'" Still, he was very interested. There's no doubt about this. But he didn't publish anything.

Kuhn:

What about Wentzel? Was he also a continual participant here?

Heisenberg:

Well, he took part in these discussions, but I would say to a lesser degree. I remember that he was interested in the dualism between waves and light quanta. That was a problem which worried him more than others. I remember frequent discussions with Wentzel about whether one could not derive the interference pattern by means of a quantization of the path of light quanta. That must have been an idea which had come out in a paper of an American physicist. Duane. Yes, Duane. That was a paper which fascinated Wentzel and Wentzel tried to do some work on it himself. And I remember many discussions on these things, but I do not recall whether Wentzel published anything. Did he publish at that time?

Kuhn:

I'm not sure. I don't know.

Heisenberg:

Certainly the paper of Duane was a problem of concern to Wentzel. I remember one discussion with Pauli and Wentzel and I sitting together and saying, "Well, what does all this quantization of the light quanta on these paths mean?" It was such a funny idea that the periodicity of a grating could be used like a real mechanical periodicity, so that you could apply the integral of pdq. Very nice idea, a very brilliant idea, because it's so against normal possibilities. But Wentzel was not too much interested in these problems of the anomalous Zeeman effect. He didn't take much part in it.

Kuhn:

Lande's clearly the person outside of Munich doing most on this. How did one keep in touch with him?

Heisenberg:

Just by letters, yes, yes. He usually stayed at Tubingen at that time, and there were always letters going back and forth.

Kuhn:

Before Lande got much concerned with details of spectrum, he had written some papers on crossed orbits in the helium atom, combining quantized angular momentum. Sommerfeld was initially much interested in it and then rather rejected it. I wonder what the attitude of Sommerfeld, of the group, towards Lande's continuing work had been.

Heisenberg:

I think generally, Sommerfeld was a bit critical against Lande. He felt that Lande was not very clear and he couldn't understand him too well. I remember that his reactions to letters of Lande was sometimes a bit angry. He said, "Well, this Lande always comes with these complicated things and it's always so unclear. I don't know what the man means." I didn't look into the details of these discussions, I only saw some reflections of the discussions in the mind of Sommerfeld. Sommerfeld, of course, believed that Lande had something, and that he should publish it. He also told Lande that he would be glad if Lande could publish these things about the anomalous Zeeman effect. In some way, though, Sommerfeld was a bit critical against Lande that I do remember. He was critical for reasons which are unknown to me. Perhaps Lande's way of writing letters was not too apt for Sommerfeld's way of thinking. I don't know.

Kuhn:

Most of the correspondence in this period then was between Sommerfeld and Lande?

Heisenberg:

I would think so. I think my correspondence with Lande came somewhat later. But you gave me a number of letters which I did exchange with him. That was a bit later. I think the first correspondence was always between Sommerfeld and Lande. It may also be that there was some kind of slight tension, in some sense, because Sommerfeld had published this one paper about the law of multiplication which was a bit too trivial. Later I heard much criticism that Sommerfeld shouldn't publish a paper as trivial as that because after all, to discover that one can multiply two numbers and so on is not worthwhile. It may be that Sommerfeld also was angry because Lande did take this problem up, and did it more successfully than he, himself, had done it. I mean Lande actually found out how the levels would be, while Sommerfeld just gave this general law and didn't find out the levels. After all, it should have been possible for Sommerfeld, if he had taken the care, to derive the levels. So it may be that he was a bit angry that Lande had been cleverer than himself.

Kuhn:

Well, not clear what it would take to take that next step. One of the things that is clearly involved with it, in Lande's case, is the recognition that the inner quantum number is the total angular momentum, and what this means about the selection rules. The selection rule for total angular momentum ought not to be the same as the one for the electron angular momentum. That piece of the puzzle would have been less likely to be in Sommerfeld's hands. To what extent did you, yourself, also get involved with the X-ray problem and also with the problem of higher multiplicity?

Heisenberg:

Well, the X-ray problem I always heard from talks with Pauli and from Colloquium. The X-ray problem was a standard problem discussed in the Sommerfeld seminar and so on, and in the Sommerfeld Institute. So I would simply hear about it, but I was not engaged with it myself. The problem of higher multiplicity came very soon. Well, one heard about these higher multiples being discovered. I think there was work of Catalan and the Spanish people. And then, of course, the question at once arose how one could explain these multiplets in the same scheme. Then very soon one came to this idea of adding angular momenta. This paper with Sommerfeld — the second one — must have been already on the higher multiplets.

Kuhn:

It will apply equally well to higher multiplicities simply by giving the Rumpf a greater angular momentum. There is, I think, no attempt yet to compare it with data on the multiplets. He talked really in detail only about doublets and triplets.

Heisenberg:

Yes, but I recall that very shortly afterwards, Sommerfeld continued that kind of work together with Honl, and there was a formula of Sommerfeld and Honl that was explicitly made for these multiplets. My paper with Sommerfeld was probably written still starting from the idea of doublets and triplets, but by the time the paper was almost finished, the first multiplets appeared. Then Sommerfeld continued with Honl because I was away then in Copenhagen. So that probably is the history of the thing. But it must have been almost simultaneously so I should say that while we were just finishing these papers then already the first multiplets came out.

Kuhn:

Sommerfeld apparently got a copy of this work of Catalán from Catalán before it was actually published. I don't know whether you would have been there when he brought that back and first looked at it.

Heisenberg:

Well, I remember that I once got a copy of a paper from Sommerfeld, and I don't remember whether it was already a printed copy or whether it was typewritten or something like that. I remember it especially because we made some joke about it, about learning Spanish. It was written in Spanish, at least the title was in Spanish: "Estructura del espectro del escandio." And then we said, "Well, Spanish is very easy: we put an "e" in front of every word and then we will be speaking Spanish." This very foolish joke remains in my memory, and I think that was a word which was exchanged between Pauli and myself. But I don't recall more than that — whether it was actually the printed paper or the typewritten; I can't say. At least Sommerfeld was interested in it very early; he was a good friend of Catalán, so I think they very soon started working this out.

Kuhn:

I had not realized either quite how late the multiplicities —. But for certain people this was just an eye-opener, and a quite sudden one when it begins to happen.

Heisenberg:

Oh yes. It was very important because one saw that this idea of having multiplets having to connect angular momentum in some scheme, was a very general idea and did play a great role in all the complicated spectra. Well, you must remember that at that time this idea that every spectra line was just a difference between two levels was not at all generally accepted. I remember that from Bohr's lecture in Gottingen. I think I went home from the lecture room together with old Runge, the mathematician. He was very interested, and said, "Well, it's of course very nice what this Bohr tells, and apparently, in some cases, this scheme works. But think about these thousands and thousands of lines in the iron spectrum. There's not the slightest hope ever to explain these things by levels." In some way he simply rejected the idea that all these lines should be just the differences of two levels.

Kuhn:

Would it widely have been rejected as late as that?

Heisenberg:

Well, that I don't know. I would say "widely", what does it mean? Many people just said, "Well, we are not interested." Other people would say, "Well, we don't know. Maybe, maybe not."

Kuhn:

Let me ask you just two or three things that are in this period. You mentioned that, when you talked to Bohr in the summer of '22, the background for that talk was that you had been thinking about the dispersion problem. How did you come to be thinking about it? Was this a problem that was bothering people in Munich? It bulks so large a little later.

Heisenberg:

Well, I think that was the result of these discussions on the dualism between waves and particles. That problem was in Munich quite frequently. I told you about Wentzel's interest in Duane and so on. One always thought, "Well, there is this idea that the spectra line is an emission of the light quantum, a difference between two energy levels. That's all right. At the same time, it is a spherical wave, and you see from the Correspondence Principle that even the waves are all right. On the other hand, the frequency of the wave is already wrong, because neither in the initial nor in the final state is the frequency right, it's just right in the middle between both. Now, what's the matter? The mechanical model has the wrong frequency." I think that was a statement which had been discussed in Sommerfeld's Institute and also in talks between Pauli and myself. So we tried to visualize, "Now there is a hydrogen atom and the electron turns like that, but what is the frequency of this electron? Isn't it a scandal that this electron goes around with a frequency which is different from the optical frequency. What's the matter there?" So from there the way to the dispersion argument was not very far. I couldn't say that I had discussed this argument quite clearly with people like Pauli beforehand but —. I think actually it didn't occur to me before I heard the paper of Bohr and Kramers, because I hadn't known that Kramers had done so carefully the quadratic Stark effect. But when I saw that he had simply done the Stark effect so that there he had an electric field and that meant that the electron cloud of the hydrogen atom is just displaced a little bit. Then I said, "Well, now if the electric field moves, then the cloud follows at the same frequency. And then there must be resonance when you come to the frequency with which the electron moves. But that's the wrong point." You know, it's a very obvious argument when you always play around with the light quanta and then, of course, you get to contradictions.

Kuhn:

Well, there must be a little bit more to your argument than that in that this creates a problem for the Stark effect which would apply equally to the first order Stark effect.

Heisenberg:

Yes, that was one of the difficulties. This is just it. That's just the point. But in the first order Stark effect you can say, "Well, after all, there the electron has these degeneracies so there is no slow precession. Only when you apply an electric field does this slow precession start." This was very clearly described by this paper of Lenz which Pauli later on used, for quantum mechanics of the hydrogen atom. So from the paper of Lenz and from similar arguments, we had always a very clear picture of what happened in the first order Stark effect. So in the first order Stark effect you could say, "Well, there the whole type of motion is different, so it's not the same thing as in dispersion." While in second order Stark effect, you have just that kind of deformation which you must have when you move the field around, and that's a slightly different thing.

Kuhn:

This problem of the wrong dispersion frequency — the wrong resonance frequency is a scandal in a sense that even Pauli's paper on the hydrogen molecule ion isn't. I mean here is a very, very basic contradiction in a problem which you should be able to do by quantum mechanics. There's some exchange between Bohr and Sommerfeld about it in 1916. But it seems to die out again very much.

Heisenberg:

The contradictions between this Bohr-Sommerfeld quantum theory and classical theory were so terrible that one had to find excuses. Now on the one hand, one saw that the Stark effect came out very well — the first order Stark effect. So this, in many ways, was, of course, a pure miracle and one couldn't understand it. Therefore, one had to find excuses as to why the things worked there and do not work at other points. Now in the hydrogen molecule ion, of course, one could say, "Well, that's such a complicated thing and it only works for such mechanical systems where one has very simple periodic motions." And, in the case of dispersion, Bohr had some excuse by saying, "Well, as soon as the reaction from the radiation comes in, when you get some(stopping)(power) of the emitted radiation, then the mechanical laws cannot further be applied." So I remember that also in our discussion on the (Heinberg), Bohr first tried to use these kinds of excuses. But, of course, during the discussion he talked himself away from it a bit. He felt that this was only a rather lame excuse, not a really good thing. That was a very common situation in physics at that time, that in order to understand anything, or to believe that one had understood anything, one had to find excuses. Otherwise you could just drop everything — you could drop the Stark effect and the hydrogen atom and then where are you? Therefore, these excuses prevented you from taking seriously these very bad contradictions. So such an excuse could block progress for a number of years, and perhaps it was very good that it did block progress at one point because thereby it made possible progress at other points. Because if you block progress by criticism too early, then you can't get anywhere.

Kuhn:

Yes, you leave those problems until there are no fruitful areas elsewhere.

Heisenberg:

Yes, yes. That is probably what had happened. I didn't know of discussions between Sommerfeld and Bohr in 1916, did you say?

Kuhn:

1916 or '17. ... You apply the classical perturbation to an established Bohr orbit, calculate the dispersion, and you get rather good results. And just let this go. Now it's perfectly clear that it has to be wrong. Bohr immediately or shortly, picks it out, or points out, that it gives good results but it has to be the wrong answer to the problem because the whole approach will obviously lead to the wrong dispersion — to the mechanical frequencies for anomalous dispersion. At that point, there's some talk about it. Then there's just not very much done with this problem. Some people must be worrying about it, others not. Your whole point about excuses seems to me very much to the point, and this is very useful to know the way in which people blocked off that problem. But that is such a key problem then with respect to Kramers' work and your own paper with Kramers.

Heisenberg:

Well, that, of course, did make things really very much clearer. Yes, that also what I felt, that is, that from that time on one had a general idea of how things could one day come out. Yes, but as you say, in 1916 it was just too early and people would say, "Well, let's wait for the future." Well, one sometimes pushes away a problem because one feels that one can't solve it yet and so it has to wait.

Kuhn:

Because it will finish this period for the moment, may I ask you just a couple of questions about Sommerfeld? Then that would be a good point to call a halt today.

Heisenberg:

That's good, yes.

Kuhn:

People who worked with Sommerfeld published some joint papers with Sommerfeld, some papers by themselves; Sommerfeld publishes some papers in which he acknowledges help from other people. How did work go on with him on a paper? What determined the question of authorship? It must have been terribly hard under those working conditions with all this talk to decide what the proper way to label a particular paper was.

Heisenberg:

Well, I would say that this was simply settled by Sommerfeld himself. He would decide who would publish which paper and generally people agreed that his decision was a just decision. Everybody realized that in such a state of affairs where everybody talked to everybody, it would be very difficult to disentangle it completely, and so when Sommerfeld had said, "Well, you publish this and you publish that," then everybody was happy and didn't worry about it. I have never heard any disagreement with Sommerfeld's decision. ...

Kuhn:

The fact that a paper comes out as Sommerfeld, or as Heisenberg, or as Sommerfeld and Heisenberg, does not necessarily indicate that it was worked on very differently. You might have had just as much discussion about a paper that appeared jointly as about a paper that appeared under one or the other names.

Heisenberg:

Yes, I would say that the amount of contribution from the two sides would be very similar in the two cases. ...

Kuhn:

Well, take this paper on the intensities of the Zeeman components. Do you remember who actually wrote the paper? There must have been a lot of discussions and work at the blackboard, I suppose.

Heisenberg:

Yes, I think Sommerfeld wrote a large part of the paper. It may be that I have at home still the manuscript of the paper in his handwriting. He wrote it by hand. I would say that probably he has written most of it, probably after having some notes from myself. I don't know whether I corrected it afterwards. But I do think, especially in that case, that there are manuscripts in Sommerfeld's handwriting — at least some parts of the paper.

Kuhn:

I guess my last question is really, "Is there anything else you can tell us about Sommerfeld?" For example, you mention somewhere that he forbade you to play chess. This is a man who himself bulks so large that anything that will help to make him more of a person and to round out the picture —.

Heisenberg:

Yes, he had strong views about how young people should behave. So he was, in that way, very old-fashioned. For instance, I recall that Pauli — I don't know for sure whether it was Pauli — was always a bit late in the Institute in the morning. He didn't come before 12 o'clock — he would work at night. And then Sommerfeld once asked Pauli why he came so late and Pauli said that he worked so well at night. And then Sommerfeld told him, "Well, this is a mistake. You do not work well at night; you work very much better early in the morning. So I think tomorrow morning you will come at eight o'clock to the Institute." So Pauli would try to come at eight o'clock. Sommerfeld would always have very definite opinions as to what people should do and should not do. And so also about this game of chess. He said, "Well, you shouldn't waste your time by playing chess. If you do have that kind of effort, then you'd better do physics; if you want to have some recreation, you can go skiing." So he had definite opinions as to what people should do and should not do and that was quite clear for him. So in this way he was an old-fashioned Geheimrat with very definite views on morals, on politics, on general behavior and so on. Well, Pauli used to say about him, "He looks like a Husaroberst." He had this mustache, a strong personality, and strong views. That also resulted in his being an extremely good teacher because also by this side of his personality he had a strong influence on the young people; they wouldn't dare to object to his statements. And that was perhaps also one of the reasons why everybody accepted his decision about who should publish a paper; simply because one knew at the same time that his decision was just as good as any decision that could be made. He would try to do it as justly as possible. So he was accepted. He had a great deal of authority. At the same time Sommerfeld was very charming. To begin with, when you looked at him, you could perhaps feel that he was a bit harsh — like a Husaroberst. But in discussions very soon one could discover that he was very friendly and took very much interest in each young fellow, and his whole personal life. He wanted to see whether the young man was on the right track; and if not, then he would try to do something about it. So one could be pretty certain that if one came into the hands of Sommerfeld, you would finally pass a doctor's examination and would probably be just on the track which was possible and reasonable for one's life. He was an educator in every sense of the word.

Kuhn:

Did the number of Pauli's idiosyncracies, the sort of thing that is illustrated by your story of his coming at 8 o'clock, make any problem in his relation with Sommerfeld?

Heisenberg:

Well, Sommerfeld had the attitude towards Pauli, "Well, there is a young man, extremely talented, extremely good in physics and so on, but at the same time, a bit endangered by his strange habits and a bit spoiled perhaps by wrong education." So he had to do something to put him on the right track. And this he tried with Pauli. Pauli at once recognized that there was an old gentleman who took an extreme interest himself, in Pauli, because he knew that he was in some way a genius. At the same time he said, "Well, in order for you to become a genius, I have to educate you. You have to come at eight o'clock in the morning." So Sommerfeld didn't change his mind about what people should be like. Sommerfeld thought, "Well, there's a young man with, an enormous gift, and one must try to get the best out of these gifts, and therefore one has to put him on the right track."

Kuhn:

Did Pauli come at eight o'clock?

Heisenberg:

Well, for some time he did. I don't think it did last very long. No, I think that Sommerfeld was the only physicist who had never been criticized by Pauli. I mean Pauli certainly did criticize Einstein, and everyone else, without any hesitation. But with Sommerfeld it was different. I had been told once that even five or six years later that Sommerfeld entered the room and Pauli was nice at once; a thing which Pauli would never do from his normal habits. I think the main trick with Sommerfeld being such a good educator was that he loved the young people, and that was really the point. He had an enormous interest in his young people — fortunately not too many — perhaps five to ten young people in his Institute — and that was his whole life. He would really be interested in every one of these young fellows and try to get him on the best way and teach him physics and so on. And if a man has this interest in the younger generation, then the younger generation doesn't mind if he has too strong views about what should be done or not.

Kuhn:

Is anybody able to teach that way anymore?

Heisenberg:

Well, I can't imagine it. Now in Germany it is almost hopeless because there are too many students. For instance, my eldest son has studied law in the University of Munich. He was, even in the exercises, always together with 800 other students. Now, what then? He never has talked to any of the professors. He just listened and he has talked to a few assistants. I think in his six years of study he had perhaps had three or four conversations with a professor. Now he has passed his examination. It's really dreadful. It's a consequence of the too great number of people. ...

Kuhn:

Do you suppose the consequences are more serious in physics than in law because of the nature of the field? That old sense of the apprenticeship relation in higher education in physics.

Heisenberg:

I could imagine that the understanding of physics really worsens by this nonexistence of a real tradition. I would never have understood physics if I had not had occasion to have so many discussions with people like Sommerfeld and Bohr and Pauli, although he was my age. Let's say Sommerfeld and Bohr. Also Born, but more Sommerfeld and Bohr. Now these young people, even if they get finally a professorship themselves, they probably have never had the occasion to discuss with people of this standard. One can only learn the real connections, the real substance of physics, by having all these discussions. The subject itself is too difficult. Physics is very abstract and difficult, much more than old physics, I would say. To speak about the present time, when I talk to young people, especially also young American physicists in Geneva at our last conference, there are so many extremely well-gifted people. But I still find it difficult, very often, to find a language by which I can talk to these people. When I use my own language, then I feel that they think, "Well, that's a bit funny, the old gentleman talking. He uses terms which really don't mean anything in physics. It's all vague talk." I must try then to translate in their language and simply use just those very specialized notions that they have developed. But one definitely sees that the tradition is not close. They don't even understand the way we talk about things. We had a very nice discussion about one and one half years ago with Bohr at the Solvay Conference at Brussels in 1961. There, of course, was not the real young generation, but there were excellent physicists from the States like Feynman and Gell-Mann and these people. It was very interesting to see that when they talked they used a very different language from that of Bohr. But still during this week which we were together every day for about six or eight hours, a certain adaptation of the two languages came about. People suddenly recognized that when people like Bohr said something one could really understand what he meant, especially a man like Feynman, who has so many interests of the general life. So it was very agreeable to see how gradually, gradually this kind of communication came to be.