Werner Heisenberg - Session II

Heisenberg:

Well, just to talk about Sommerfeld's lectures at the Institute —. I would first like to say that the lectures and the seminar are quite different. In the lectures, there are about 80 to 100 students. The most important part of the lecture was the exercises connected with the lectures. Professor Sommerfeld gave some problems and then these problems had to be solved at home and we would deliver the solved problems to the assistant. The assistant would then look through it, and one day a week these problems were handed back to the students. The problems were discussed at the blackboard and the students did not get a mark. Of course, the professor tried to get some impression of how good the student was in solving these problems.

Kuhn:

Was it Professor Sommerfeld himself who discussed the problems at the blackboard or did the assistant do that?

Heisenberg:

Usually he would be in the lecture room and sometimes the assistant would give the explanation, sometimes he himself would. Usually he would call on a student and say, "Well, you have solved this problem, could you explain at the blackboard how it is done?" Then the student would start solving the problem at the blackboard, and Sommerfeld would interrupt him, or the assistant would interrupt him, and say, "Well, this is not quite right. Now I will tell you that you had better do it this way." And this kind of thing. So it was a kind of permanent discussion between Sommerfeld, the assistant, and the student at the blackboard. For each problem we had about a quarter of an hour or twenty minutes at the blackboard, then the next problem would come. Usually we had about two or three problems each week. These problems were then solved, and the solution was fixed, and then the students knew what it was all about. Then they got the problems for next week, which they would solve at home, and so on. So this was a very efficient way of teaching the students to solve problems. I have learned a lot; the only thing which I did quite wrongly in the beginning was that my problems were always much too long. I didn't think of the poor assistant who could certainly not read twenty pages from each student... So I had to learn that one can solve such a problem on one or two pages and not on twenty pages. In this way, Sommerfeld had a very rigorous way of educating the students and told them exactly what they had to do — the emphasis being very strongly on the mathematics of it. So he was very interested in clean mathematics but in some way also he tried always to connect the mathematics with physics. He did not like to have any formula written down which was not understood in terms of physics. Later on, I was always interested to see how different the style in physics is at the different institutes. Primarily, in Sommerfeld's Institute, the mathematical scheme had to be quite perfect and according to the standard methods. But still, every formula had to be understood; that is, the student had to be able to say for every formula, "Well, in this formula, this term means such and such." You know that kind of thing. While later, in Gottingen, Born was more of a mathematician, and he would be interested in whether a solution actually existed and how you can prove that such an equation must have a solution, or can have several solutions. You know, these more the mathematical questions. The existence of solutions was never a problem to Sommerfeld. He always took it for granted that the mathematics would somehow work, even to the extent that he was not even afraid of inconsistencies in the mathematical scheme. He would say, "Well, if this mathematical scheme doesn't work, we can always assume there is a similar mathematical scheme which will work and still the physical content may be the same." So, the problem of very rigorous mathematics, that was not Sommerfeld's interest. He was a good mathematician, but in some way he was never interested in the proofs of convergences and so on. I should perhaps say it like this: to prove something in a strict mathematical sense was not Sommerfeld's problem. He would like to find out how things are, and also to find out what the mathematical connection is, but not how one can prove it in a strict mathematical sense. I remember a talk between Pauli and von Neumann much later, in which this opposition between the two possibilities came out quite clearly. Pauli himself was definitely, in this sense, a pupil of Sommerfeld; he was not interested in proofs. And von Neumann, being an excellent mathematician, of course was very interested in having rigorous proofs. Von Neumann told Pauli, "I can prove this and this," and then Pauli said, "Well, if a proof was important in physics, you would be a great physicist." You know, Pauli was always very shocking in this way. So I think that was always behind this Sommerfeld seminar. You should be able to describe nature in mathematical terms, but the mathematical foundations or the proofs were not important. What was important was the mathematical representation of nature.

Kuhn:

What techniques did Sommerfeld employ to make sure that people got this more physical knowledge? How did Sommerfeld train people that way?

Heisenberg:

Well, I should first say what kind of mathematics he taught the students. For example, in the course on mechanics, he would teach them how to solve differential equations involving time, and how to derive from the differential equation a law of conservation. He did not treat the group theoretical side of the problem which nowadays everybody would start with. He rather first told them mathematical tricks — how to solve the problem. Such a trick was that you have to take the equation of motion and multiply it by the velocity and then integrate it and then you can find the law of energy conservation. So he wood teach them these kinds of tricks, but not teach the general way of solving differential equations or the underlying group theoretical principles. In electrodynamics he would teach the solution of partial differential equations — the linear differential equations — and how you can solve them by means of exponentials. He would never teach general rules, general principles, according to which you can always do that kind of thing. He would rather teach them that there is always some trick with which you can do the problem, and the group theory came only as a trick. He would say, "Now here we have a problem which has rotational symmetry." But then he would not say, "Now consider the group of rotations;" he would say, "Since we have rotational symmetry, then, of course, it's a nice trick to introduce polar coordinates; then you will see that things work out." You know he was in some way always fond of these tricks, but he did not try to look behind the tricks and to see why does this trick work, and why doesn't any other trick work. And so in this way you might say it is not a good education; but the funny thing is, that just instinctively one did acquire a feeling why one had to use this trick here and the other trick there. So, in some way, one did acquire a feeling, for instance, for the immense importance of group theory for all mathematical interpretation of physics. Now, to speak about Sommerfeld's seminary. I do not mean the seminar courses, but rather just one of the three or four rooms in Sommerfeld's Institute. There was one room there where young physicists were allowed to sit and obviously they were only those who were really interested in science and wanted to do something themselves. They were students who perhaps later on would get a doctor's thesis, and so on. When you came to his Institute, you would find perhaps five or six people sitting around in the room reading some textbooks, and there was an assistant at the desk. Actually, during my first couple of semesters with Sommerfeld, Wentzel was at that desk. He was the assistant. Pauli was a kind of secondary assistant. We would then sit in the seminary, and if you had a question, you could go to them and ask them whether they could help things. So in this way, I came into discussions with Pauli. Actually, one spoke about new developments in physics in the seminary, and then, of course, I would ask Pauli what his opinions were. I should perhaps also say that this seminary was a kind of market place in which to exchange views about the most modern developments. One got a feeling of a very exciting and interesting development taking place about which you had to hear the latest news every morning. Perhaps somebody would come and say, "Well, have you looked at the recent issue of the Physikalische Zeitschrift or the Proceedings of the Royal Society? There is a paper of — ," and so on. Quite frequently, if somebody brought the news of this kind, say news from Copenhagen about quantum theory, then people would stand together at the blackboard. Pauli would be asked what he thought about this latest news; he would try to analyze it at the blackboard, but other people would interrupt him and so on. And so we tried to get a common opinion on the recent developments. We heard about these developments either by new periodicals which came in, or by letters which Sommerfeld had gotten. If he had gotten a letter from Einstein or Bohr or others of this group, then he would usually hand the letter to Pauli and say, "Well, Pauli, here look, Einstein writes this — what do you think about it?" So this was the eternal life in the Sommerfeld Institute. Then, of course, there were special seminars — now that was a different thing. There, of course, Sommerfeld tried to get information about the most recent developments himself. That he did by turning to a student and saying, "Now here you have the paper of Mr. Kramers. You give a talk at the seminar next week and explain to us what Kramers actually means by his paper and what you think about it."

Kuhn:

Were these topics really handed out from one week to the next?

Heisenberg:

Well, I should say perhaps about every two or three weeks. In 1920, in the first, or perhaps the second, term in which I took part, I got, rather early, a paper by Kramers on the quadratic Stark effect of hydrogen. That was done by the standard method — the integral of pdq — and so on. Sommerfeld wanted to see whether he should believe or should not believe what it was all about. I only remember that I gave a very poor lecture because Sommerfeld afterwards told me, "Maybe you have understood it yourself, but you certainly haven't explained it to the others." He probably was perfectly right. But this seminar didn't impress me too much. I don't know why, but I have learned much more from these informal discussions in the Institute to which sometimes Sommerfeld would come himself. Well, at least it was a rule that those few students who really were interested in the game would sit out in the seminary in the morning — say 9:00 til at least 1:00 or half past one. During this time there were these discussions and also during this time people were called in by Sommerfeld to his room to discuss things with him. So I should say that almost every morning, but at least every second morning, I was called in to Sommerfeld. I had to tell him about what I had tried in my own work, and what I thought about Lande's paper, and so on. In this way, Sommerfeld has really made an enormous effort to get his students into the game — to get them interested, to get them to take part in the scientific life, and, of course, to suggest some work which they had to do.

Kuhn:

This went on for you for really from your first semester?

Heisenberg:

Yes, I think that went on for the first two years, for the first four terms. After these four terms, I went for one term to Gottingen because Sommerfeld was away in the States. Then I came back again for the sixth term to Munich to get my doctor's degree and during that time I worked on this turbulence question, which was an entirely different thing. After that, I went to Gottingen to be with Max Born... I had four semesters with Sommerfeld in Munich, then one term with Born and Franck at Gottingen, and then again one term with Sommerfeld at Munich. Then I became an assistant of Born in Gottingen. So altogether I was five terms with Sommerfeld here in Munich. These first four terms were, in some way, the most interesting because in these four terms I learned most from the discussions with Sommerfeld and Pauli and Wentzel. I did also take part in the general physics colloquium, but that I found difficult because there people would talk about quite different subjects which, of course, I hadn't learned yet: spectroscopy, experimental techniques, and all these things. Of course, my whole education was extremely one-sided and always specialized in these modern theoretical problems. There was always some interest in this Institute, and in Sommerfeld himself, for mathematical techniques: how to solve an integral and how to go into the complex plane, and so on. For instance, Sommerfeld would be delighted about the present development of the Reggi-pole. He would say, "Well, that's just it!" And actually, the whole Reggi-pole business goes back to a paper of Sommerfeld and Hopf in the very early period, which is also quoted now. So Sommerfeld and Hopf did actually do just such a transformation from the angular momentum to the Reggi-poles.

Kuhn:

You speak of having spent mornings in the seminar room. What would you be reading as this was going on?

Heisenberg:

To a large extent I would be reading classical mechanics or thermodynamics or whatever I had in the lecture. I read in order to get enough material to solve my problems. For next week I had, say, to solve some problem on thermodynamics and so I wanted to see whether I could do it. So I would read the textbooks on thermodynamics or whatever else. At the same time, I would still try to read, once in a while, also an actual newly published paper. But usually the paper would be too difficult for me. I found when I had to read newly published papers that I always had to go back to other textbooks in order to understand them, so I think most of the time I did actually read textbooks and mostly textbooks on the material of the lectures. I also read books from other lectures. In the afternoons I would attend lectures on mathematics, on group theory, on the theory of functions, or that kind of thing; then I would also try to get from the library some book on the theory of functions — that kind of thing. So at least in the first two or three terms, I think I almost never read new papers, but mostly I read textbooks in order to learn what it was all about. Then, of course, I read a paper only when I had discussed it with Pauli or Wentzel, and they had told me, "This is a very interesting paper. Try to understand it."

Kuhn:

Do you remember at all which books were particularly used? What would you have used for mechanics? What would you have used for thermodynamics or for electromagnetic theory?

Heisenberg:

I see. For electromagnetic theory we used a book of Abraham. That was a very good textbook. Now in mechanics — what did I actually read in mechanics? I did once study Charlier, Himmelsmechachanik, but there was still another textbook on mechanics. I think, of the textbooks of Planck, I only studied Thermodynamics. We did not find these books very suited for the student. Yes, for mechanics I used Mueller-Prange...I think that was quite a good book on mechanics. But it's all old-fashioned mechanics. I mean in modern textbooks people would probably start with the group theoretical aspect, but that was not so at that time.

Kuhn:

But it includes some Hamilton-Jacobi theory?

Heisenberg:

Yes, yes, oh yes. Sommerfeld placed very much emphasis on the Hamilton-Jacobi thing. So apparently we did read it, also simply from his book on Atombau. That was a book which was very much studied in Sommerfeld's seminary and actually was also made at the Institute. That is, Sommerfeld didn't write it all himself; he would have his assistants write some part and then he would correct it. So actually, in some way, it was the common work of the whole Institute.

Kuhn:

This first edition was already out when you arrived, and the second one must have been pretty nearly done.

Heisenberg:

Yes, well, I did take part in discussions about the second and third editions — discussions taking place again between Wentzel, Pauli and Sommerfeld. The question was should this be put into the book, should this be taken out, how good is it actually, and so on... Wentzel, I think, has formulated some sections and Sommerfeld would then revise it. But more or less Sommerfeld did do the writing. I would say 80 percent was due to Sommerfeld and only perhaps 20 percent due to the others. You might ask Wentzel about this. I just see here a question: "Who were the leading teachers among the professors?" Now leading, in this case, means leading for me, because I don't know about others. But I did attend lectures of the mathematicians Rosenthal and Voss and Pringsheim and Lindemann. I would say by far, the best lectures were those of Rosenthal; and I did have some benefit from the lectures of Voss, I would say. But neither from Lindemann, nor from Pringsheim did I learn anything.

Kuhn:

What did Voss lecture about?

Heisenberg:

I think it was theory of functions, analytic functions, that kind of thing. And that was a good lecture from which I could learn something. But Pringsheim lectured on convergence — epsilontic, as Pauli would call it — and I didn't; know at all what he was talking about. I didn't understand what he meant. I had the same difficulty with Lindemann. But there may have been many other very good professors, but I don't remember the lectures. Well, yes, I did also attend lectures of old Seeliger, the astronomer, but from these lectures I didn't profit anything. I didn't know what he was talking about.

Kuhn:

Would these other lectures also involve problems as the Sommerfeld lectures had?

Heisenberg:

No, not all of them, but some of them. For instance, the Pringsheim lectures did involve problems and the Rosenthal lectures did involve problems, but not Lindemann and not Voss and not Seeliger. But as a rule, I would say that one only learns something from lectures where there are problems. It is extremely important that one should try to solve problems. Now I always tell my sons, "Now then, if you attend any lectures, please take those that require solving problems, else you don't know where you go." Just listening is of very little use.

Kuhn:

Particularly if it is a very good lecturer.

Heisenberg:

Yes, that is quite right. Particularly if the lecture is good because then everything is too smooth. Yes, that is a very good remark. That's like in music: if the performance is too good, you really don't enjoy it, because it just goes by and you never can penetrate into the heart of it. Sometimes a poor performance is better to enjoy it because you can look at those things which were wrong and analyze them.

Kuhn:

I hadn't thought about that, but I see exactly what you mean.

Heisenberg:

Well, yes, the related sciences were mathematics, astronomy, geology, chemistry. Yes, chemistry. I should have mentioned Herzfeld, who is now in Washington. He was a very good lecturer, and I learned a lot from his lectures. I think he was a good lecturer because he was a poor one, just to use your paradox. You know he would change his mind and say, "Well, now, this was wrong." So in this way he was not a good lecturer, but just because of this one could learn a lot from him. Indirectly, he was a very good lecturer. I had more advantage, more benefit from the lectures of Herzfeld than from many others.

Kuhn:

What did you take with him, do you remember?

Heisenberg:

Physical chemistry. It was essentially on (van't Hoff's Law), thermodynamics of reactions, and equilibrium between different phases.

Kuhn:

He gave this in a pretty highly theoretical fashion, I take it.

Heisenberg:

Well, yes, pretty high; not too high. You had to write down the equilibrium condition. It was more or less only the second law of thermodynamics which was involved, so it wasn't too bad.

Kuhn:

He didn't assume a detailed prior knowledge of thermodynamics?

Heisenberg:

No, he actually tried to teach that to the students. Well, he expected that they had had one lecture of thermodynamics beforehand, so they knew what the first and second laws of thermodynamics meant. Then he would explain how to apply it. He did not use much of the kinetic theory of matter, statistics, and so on. He would mention it, but primarily he would give a phenomenological description of equilibrium and chemical reactions.

Kuhn:

In the nature of the case, did you also take Wien's experimental physics?

Heisenberg:

Yes, I did, but without much benefit. I found that was kind of show, nice to look at, but one couldn't learn anything. Or to put It in very extreme words, what I do remember from this lecture is just that the room was dark and that there was a spot of light on a scale, and the light would move around on the scale and then it would stop at 15. Well, what benefit had you from that? Of course, if you really would have understood what the experiment was, it probably was a very good experiment that gave much information, but for the student who doesn't know what it is all about, it's really nothing.

Kuhn:

And there was no great effort to make sure that you would know what it was about?

Heisenberg:

Well, at least this effort wasn't successful in my case. Well, he tried to make some very spectacular experiments which then did impress the students because they just remembered what had happened there; but still, regarding the physics of it, I would say one should listen to such a lecture only after having studied theoretical physics for four terms or so. Then you knew what was the problem, and what kind of natural law should be checked or disproved and so on. Then you could understand what it was all about. Do you, nowadays in the States, have these great lectures of experimental physics or do you not have anything of the kind?

Kuhn:

One has great big lectures, and they do include demonstrations, but there is no separation between the course in experimental physics and the course in theoretical physics at the elementary level. Students in their first year at an American university do not have the mathematical preparation for a course like Sommerfeld's...

Heisenberg:

Well, I remember Sommerfeld setting the rule: it was given as a rule by Sommerfeld, I remember that he said, "My first course in theoretical physics," that's the course in mechanics, "should be attended by students who are in the fourth or in the fifth term of their studies. That is, the first three terms should be devoted entirely to differential and integral calculus and that kind of thing, and only when the student really knows about these things and can solve simple differential equations, only then he shall attend the course on mechanics." That was his rule. Actually, I did attend his course in mechanics in my first term, but only because I had learned the calculus earlier, so I thought that I could follow. I could actually follow, so I had no difficulty in solving his problems in mechanics.

Kuhn:

Was one supposed to start his theoretical physics course with the mechanics course?

Heisenberg:

Yes. He had a cycle of six terms. That was a rather long period. He would start this mechanics, then the next term would be thermodynamics, and then electrodynamics, and then one course on mathematical methods in theoretical physics, then optics, and then atomic theory. And then it would start again from the beginning.

Kuhn:

By this method, some people would have to wait quite a long time before they could start.

Heisenberg:

Yes, well actually it meant that one had to learn some of these subjects just from textbooks, without attending lectures. If one had learned in one or two terms Sommerfeld's general method of doing things then you could, say, learn electrodynamics from the textbooks if you had no time to attend the lectures. So this was the math idea. Then later, it was arranged so that there were always two courses having a period of six terms but with a difference in phase, so that every third term the cycle would start again. For instance, Sommerfeld would give mechanics now, then he would give mechanics one, or one and a half years later. So in this way one could cover the whole cycle more easily.

Kuhn:

I've been cheating a little bit. I have here, taken from the Physikalische Zeitschrift, a list of the lectures offered at Munich during the years you were there. I deliberately wanted to see what came to your memory first. Could you look through this list and indicate which lectures you heard?

Heisenberg:

Yes, I can tell you exactly. Here is my first term, winter 1920/21. I took Sommerfeld's course Mechanik. I also went to Wien's Experimental-Physik, of which this was the first part. It treated mechanics and optics and fitted well with Sommerfeld's lecture. I did occasionally attend the seminar which Sommerfeld gave with Lenz and Ewald and Herzfeld on x-rays, but I didn't understand much about it. At this seminar he also spoke about the spectral lines and the anomalous Zeeman effect, and so on. I did also attend the courses of Graetz, but only for a short while. Sommerfeld told me, "Well, these courses of Graetz are just a kind, of general survey." ... Sommerfeld said, "You'd better let that go." Well, that was probably all — except for the mathematics lecture. I didn't attend Herzfeld's lectures the first term. Now the summer term, let me see, yes, I did attend Sommerfeld's lecture on hydrodynamics. That was actually the starting point also for this later work of the turbulence.

Kuhn:

Would the lectures on hydrodynamics also be attended by 80-100 people?

Heisenberg:

Well, not quite as many; but I should say 60 people.

Kuhn:

Where did those people go? I mean there were only four or five of them that were going to be doctors in physics.

Heisenberg:

Well, there was, for instance, an institute of (Prandtl) on hydrodynamics and they would later on possibly go into aircraft factories... So I would suppose that these people would go into industry and engineering, but I don't know. So far as I recall, I was the only Sommerfeld student who actually worked seriously on hydrodynamics. I wrote a paper, rather early in this term, on turbulence, and then, later on, from this interest there grew my doctor's thesis on the stability of laminar flaw. You know that this stability of laminar flow has a very funny history? Didn't, I tell you? Well, Sommerfeld had written together with Hopf, a paper on the principles for determining the stability of laminar flow. The idea was, of course, simply that of perturbation theory. One considered small oscillations around the original laminar flow, and then one had to see whether these oscillations or deviations would increase or decrease; if they decreased, then the flow must be stable; if not, it was unstable. Then Sommerfeld had written a paper on (quiet) motion. You know what (quiet) motion is. It is a flow between two parallel planes, when the planes move so that the velocity of the fluid is a linear function of the distance from the wall. That's the simplest kind of motion, and this actually, as one knows, is unstable at a certain limit. But, unfortunately, Sommerfeld found out that treating this problem according to his method, this flow should always be stable. And there was a contradiction. In nature, it is undoubtedly unstable, and here it looks stable. What was the matter? So Sommerfeld suggested that I should try the same thing for the Poiseville flow, that is, that motion where you have two fixed parallel walls and the liquid moves between them so that you have a parabolic profile. I actually found that here you have an instability, and, of course, Sommerfeld liked this very much because it would prove that his method was correct. I actually invented some methods which resembled very much the later methods of Wentzel and Kramers and Brillouin — you know, the asymptotic methods. The result looked quite nice, and I was quite proud of it. I got from Sommerfeld quite a good mark on my doctor's thesis. Then the trouble came about a year later. Fritz Noether applied a much better mathematical scheme to the whole problem. He took the same equation, but used better and more rigorous mathematical methods, more refined methods. He gave a general proof that such a flow never can have any instability, and so my result must be wrong. The methods that he had used were better, so everybody believed Noether was probably right and I must have made some kind of mistake. I was very much worried, and so was Sommerfeld, who said, "What about your doctor's thesis?" It was not a nice situation. But my impression was, "Well, I cannot disprove Noether; his work looks quite good. Still I don't believe a word, of what he says, but I don't know where he is wrong." Then because, for, you see, I had a definite reason to say why the flow should be unstable. I could visualize how the motion actually took place and why there was an enormous difference between a profile of the Poiseville type and that of the quiet type... Noether had not thought about this physical side of it, he just applied the mathematical scheme. Then about four or five years later — that was around 1928 or '29 — Tollmien wrote a paper on the motion of a fluid along a plane — just one plane. There, again, he had the situation which, according to my criteria, should lead to an instability, and actually he did get the instability. There, the objection of Noether did not apply, so I think from that time on people were quite happy to say, "Well, there is at least one case where one knows that one has instability — that's Tollmien's case. The old paper of Heisenberg is probably wrong, but here now we have this case." But again some people said that the methods were not too rigorous and it may be that if one could do it with really rigorous methods like Noether, again, one would find stability. There the situation remained until 1944, when people in the States — I think it was Breit and [???] in Washington — took it up. They did very accurate measurements on the Tollmien problem and they could verify the Tollmien calculations now in every detail. You could find that the instability occurred just at the place and just in the way that Tollmien had calculated. So from that time on there was no doubt that at least Tollmien's calculations were correct. Then (Ling) — a Chinese at NIT — took the problem up. He took up my old problem, and he came to the same conclusion as I came to. My solutions had to be correct according to his opinion, and he found also very similar numerical values. He improved my technique, and so on. So he claimed very strongly that my old solution should be right, in spite of Noether, but again he could not produce any proof against Noether. That was a time when the war was already over and so I was invited to a meeting of the hydrodynamic people and the mathematicians at MIT in 1950. I went in 1950, and I gave a talk on the whole situation as I saw it and gave my general argument that for physical reasons there should be instability in these cases. I, of course, emphasized that there was this proof of Noether, that I did not know what was wrong with it, but I wanted, of course, to hear what the mathematicians would say. And there was some dispute. A pupil of von Neumann took the view of Noether, and said, "Well, there can be no solution." Others said, "Well, something must be wrong." So people decided that the whole problem should be put into one of the big electronic computers, one of the first big ones. The machine did the calculations with an enormous accuracy, and it came out very nearly the same as (Ling) and I had calculated it. So finally the thing was settled, but I think even up to now nobody knows what is wrong in the Noether paper.

Kuhn:

Did you keep up with the hydrodynamic literature all the way through?

Heisenberg:

No, certainly not with the literature. I became interested in hydrodynamics once again in my life and that was in the problem of statistical hydrodynamics. That came through von Weizsacker. Well, but now we make the mistake which you mentioned of coming to a later time.

Kuhn:

I would like, sticking with this question of the hydrodynamics again, for you to tell me a little bit more about how this very first paper of yours came into being.

Heisenberg:

Well, it came about this way. As I told you, Sommerfeld used to talk to the students in his room after the lectures. So once when he had spoken about vortex motion in hydrodynamics and about Helmholtz's law of conservation of vortex motion, he told me that that was such a funny problem. On the one hand you could prove that the amount of vortex motion is always conserved in a liquid without friction. But still, he said, "Isn't it funny that if you move a spoon through a tea-cup or an oar in the water, then when you pull out your oar, you see that there remain two vortices in the water. Now what has happened? That is against the conservation law, and you cannot claim that this is due to the very small amount of friction which is in the water." And so I got interested in this problem. Then he told me about some paper — I don't know who had written it — that suggested the vortex motion was due to the change in the surface when you withdraw the oar. And so I followed this problem further, and I found out that this was actually the case. Not only that, but one could even calculate the amount of vortex motion which we have after taking out the oar...You can calculate the strength of the two vortices, and I gave the solution to Sommerfeld... I don't know how good this paper was, but he was interested to see that one of his students had taken up such a problem so seriously. And from this kind of discussion then later on came this problem of the Karman Wirbelbewegung, which was, I think, rather trivial after one had the Karman vortex motion. But still, I got interested in this possibility of finding a vortex motion in a liquid which has no friction in it.

Kuhn:

Were you deeply involved with these hydrodynamic problems in addition to atomic physics?

Heisenberg:

Well, I found hydrodynamics such a nice subject because one could see what you did in your mathematics. I mean, there was such a nice correspondence between a mathematical calculation which looked rather complicated on the one hand, and the physical picture where you could see what happened in the water on the other hand. So I always loved to play with the water in my teacup or when I went out on the lake for rowing. I thought it was so nice to see the things happening and therefore I liked that kind of mathematics. I would say that it was a kind of sport, you know; I just tried to represent what I saw by a mathematical scheme. This kind of unclean mathematics was the thing which appealed to me very much — not the clean mathematics — that was not my subject. But this way of representing something in nature by means of a nice mathematical scheme and then finding out something which you actually could see, well, that was quite a bit like my nature.

Kuhn:

Was it you who decided to do the thesis on hydrodynamics or was that Professor Sommerfeld's doing?

Heisenberg:

Well, that came about in this way: Sommerfeld thought, "Well, you are always too much interested in atomic physics. It is better that you do some real classical stuff. What about your interest in hydrodynamics?" And I said, "Well, yes, I'm delighted if I can do something useful." Then he told me about these papers on the stability and he suggested the problem. So he definitely suggested the problem in the hopes that at least in this Poiseville motion one could actually find an instability at the right place and thereby get the derivation of the Reynolds numbers.

Kuhn:

That was not something that bothered you. I mean, you didn't have the feeling that this was time taken off from more important work?

Heisenberg:

No, no. I found it an exciting problem; I thought it was a very nice thing, and I was quite amazed to see that such a fundamental problem in hydrodynamics, namely the problem of turbulence, was really not at all solved at that time. You saw turbulent motions wherever you went, and still you could never find solutions and you could not even understand why these solutions were more stable than the others and so on. I found a nice problem, so I learned to treat it. Also, I found it very nice to develop new mathematical methods which, of course, were always taken from physics. It is such a funny procedure in mathematics when you don't really think about whether the approximation is good or not. You just say, "If I find a mathematical approximation which does the same thing as nature does, that is probably quite good." And that was always the point, I felt. For example, this friction in a liquid means that along the walls you have a very steep gradient of the velocity, and therefore the region of the wall is something quite different from the region inside. So I'm entitled to use an entirely different approximation for the solution near the walls and a different approximation for the interior. So in some way I did take the ideas of the (Prandtl Grenzschicht) theory, but that didn't exist at that time... So I never bothered about whether these approximations were justified from a mathematical point of view; I only could see that it happened in nature, and so I was satisfied.

Kuhn:

Can I bring you now back to this list of lecture offerings that we are looking at. You've gotten to the Sommerfeld hydrodynamics.

Heisenberg:

All right. That was in the summer of 1921 — hydrodynamics. I did listen to Herzfeld Mathematishe Einleitung in die Physikalische Chemie. That was about all, I should say. Well, I did attend some mathematical lectures which are not in this list, and I probably also went to Wien's lectures on experimental physics, part two. I tried to attend Seeliger's Theoretische Astronomie but without success. I couldn't follow him. Now let me go on to the winter of '21-'22. Yes, I did attend Sommerfeld-Maxwellsche Theorie und Elektronentheorie. I may have attended Herzfeld's lecture on atomic models — that may be. I'm not sure about it. I don't know of any others here. In the summer of '22 I did attend the optics of Sommerfeld, with exercises, of course, connected. I certainly also did attend the seminar. Herzfeld's Mathematische Einfhhrung in die Physikalische Chemie — it may be that it was only this lecture which I attended and so I can't quite recall whether it was the summer of '22 or '21. Now for summer 1922, your list also gives the mathematical lectures. I think I tried to attend the theory of elliptic functions with Lindemann but without success. Either before this or after this, I did attend Rosenthal's lectures on differential geometry of curves in space, but I did not attend this lecture on plane analytic geometry... Oh yes, now I know. I did attend his second lecture on Ausgewahlte Fragen aus der Theorie der reellen Funktionen. But that I did not like. I had attended, the term before, his lecture on differential geometry in space, but then I also attended this one, Theory of Real Functions, and I didn't like it very much. I thought it was a kind of pathological mathematics.

Kuhn:

It is clean mathematics.

Heisenberg:

It is clean mathematics, yes, that's just the point. Well, when he spoke about the function which was, say, one at every rational point, and zero at every non-rational point, then I felt, "Well, that's the end of it. That's not a function."

Kuhn:

... I'd like to bring you back once more, if I may, to one thing I realize that we left out. You remember we talked a bit about the seminar — now I mean not the group sitting around and talking, but the formal seminar. Did this have a different topic every semester? You speak of having reports on contemporary papers, and I wondered to what extent the subject was determined by what came out in the literature and therefore whether the subject jumped around.

Heisenberg:

I think it jumped around to some extent. I'm not quite sure. I would say there was a general theme, but then there would be exceptions. Sommerfeld would say, "Well, all right, but now an interesting paper has come out, why don't you talk about this." So generally, I would think that he would have a general theme, but still he would make exceptions to it. But I don't recall that very definitely. I cannot imagine that it was a very rigorous, theme which was always kept. No, probably not; probably he would say, "Now there is an interesting paper." He would also do the following: he would come to the seminary and read a letter of Einstein he had just gotten. He would say, "Well, just today I got a letter from Einstein telling this and this and the implications are probably those —." And then he would start discussing the results of this letter with the seminary.

Kuhn:

Do you remember any particular letters that came from Einstein that gave rise to a discussion?

Heisenberg:

I think that it had to do with the precession of mercury's perihelion. I do think that this was one of the topics, but I'm not quite sure. At least I remember that Einstein was extremely happy that some of his predictions had been confirmed.

Kuhn:

Well, I take it from what you say that your own associations, physics associations, were principally with this group at the Institute. And that would have been Wentzel, Pauli —.

Heisenberg:

Lenz, to some extent, while he was still there. That was only the first one or two terms. Yes, they are the three main people. Laporte. Yes, he was at the Institute.

Kuhn:

Let's see. Nordheim was there.

Heisenberg:

Nordheim — now let me see. I thought I knew Nordheim only from Gottingen, from the Born seminary. I'm not sure whether he was in Munich.

Kuhn:

Fritz London must have been there while you were there?

Heisenberg:

Fritz London in the Sommerfeld Institute? No, I would also put him into the Gottingen period.

Kuhn:

Bechert?

Heisenberg:

Yes, Bechert, he was with Sommerfeld. I remember Karl Bechert, yes. That was a bit later. I would say it was during the sixth term that Bechert was there. That's quite true, yes. Kratzer was the man who was interested in the band spectra. Yes, Kratzer played quite a big role so far as —. You know, he was an expert on band spectra and tried to represent them by quantum formulas. When I had this idea that one had to use half quantum numbers in the Zeeman effect, then he also started using half quantum numbers in the band spectra and found out that this worked very well. So he suddenly discovered that the half quantum was something useful for explaining the experimental effects and so I had many discussions with Kratzer about such things. I think he was privatdozent at the Sommerfeld Institute...

Kuhn:

Was Kossel in Munich at that time?

Heisenberg:

Kossel was, yes. I saw Kossel quite frequently. He was at the Colloquium and he was in close touch with Sommerfeld. He always discussed the Periodic System of Elements and the x-ray pictures. Kossel was very strongly interested in x-rays.

Kuhn:

Can you tell me any more about his relation with Sommerfeld, his role in Sommerfeld's work or what sort of personal relation they had. He's obviously a terribly important figure for certain of the problems we're concerned with and I find it very hard to find out anything about him. What sort of a person was he?

Heisenberg:

How did he look — or what? He was, in his outer behavior, younger but more distinguished than Sommerfeld. By distinguished I mean that he had very quiet manners and was a bit formal. He was still very amiable and a kind fellow, but very cautious, but he had definite opinions. Well, I remember very many discussions, both in Colloquium and in the Institute between Sommerfeld and Kossel. So they would speak together quite frequently and would discuss subjects like the x-ray spectra. You know Sommerfeld was so strongly interested in x-rays because the Periodic System of Elements really came out quite definitely only when you had the x-rays and you could give a definite place to every x-ray line from element to element. And that kind of thing was, of course, Kossel's problem. Sommerfeld would very frequently discuss it with him. They both also must have discovered quite early that the application of Sommerfeld's formula to the x-ray spectrum was really not correct because there were too many lines...

Kuhn:

But how early do you suppose that they recognized that? There's no hint of that I think in the 1923 edition of Atombau.

Heisenberg:

I would say that Pauli always did press this point and Sommerfeld tried to push it away. He did see that there were too many lines, ... what one called "unphysical doublication of levels." So Pauli invented this term and Sommerfeld, of course had to agree that there was a contradiction in his formula, that it didn't fit. On the other hand, of course, the formula did fit so very well in some respects. So there was always a kind of malaise about it. In some way the formula does fit, in some way it doesn't, and there is this doublication of levels. Pauli was very much worried about it since Pauli always had to rationalize things to the utmost. He would always insist on this point. Sommerfeld perhaps would have like simply to forget about it and say, "Well, somehow it will someday come out." And Pauli would say, "No, not somehow, but HOW?" This idea of having a doublication of levels by some not understood scheme; that occurred in these discussions.

Kuhn:

We're now talking about the presence of the irregular doublets as well as of the regular doublets. In the 1923 edition of Atombau, Sommerfeld speaks of a Grund Quantenzahl which will double the levels giving the screening doublets as well as the relativity doublets.

Heisenberg:

Yes. That came into the book by the insistence of Pauli that one had to clear up this point. One should not simply say that Sommerfeld's formula works, one should actually say that in some way it does not work. There's something else to it — and this something else must be a kind of doublication of levels.

Kuhn:

An important part of that story must also be the Hertz measurements in 1922 in which the regularity of these irregular doublets is discovered.

Heisenberg:

I remember one talk in the Colloquium here, which was a bigger group. That was a general Colloquium where also Wien and these others would take part. Somebody explained the present situation of the x-rays and it must have been these measurements, or at least something belonging to them. At that time one had solved these many levels and one could follow them through the whole Periodic System and there was some excitement about it. It was just that there is a simple formula, which is not the Sommerfeld formula, but something slightly more complicated. Now, of course, everybody said, "Well, it's the spin." But at that time, of course, it was very funny and made some excitement. That I do remember definitely. But there was no explanation for it, just the experimental effect.

Kuhn:

It's terribly interesting, in reading in the third edition of Atombau, to notice the triumph really, with which Sommerfeld presents these two different doublet patterns. But Sommerfeld doesn't even point out the fact that physically he has no notion why this should be. The sense in which, from one point of view, this must be nonsense, for all the fact that it works, is just never hinted at. Was that like Sommerfeld? Would he not have been uncomfortable about a point of that sort?

Heisenberg:

Well, I would say that this is one of those points where one could clearly see that Sommerfeld's instincts in physics were stronger than his brain. I mean, of course, in his brain, rationally, he could see that there was a contradiction — that here was something which one could not understand. At the same time, he felt, "Well, here is an empirical regularity, which in itself looks very nicely and very convincingly, and still my old formula does work to some extent because these levels are close to the old formula. So this is so nice, so somehow we will understand it later on." So he would just say, "Well, never mind; we will understand it later on, but isn't it nice that we have these simple laws?" This was an attitude which he had quite frequently. For instance, also in this formula — I think we discussed it last time — about the Voigt formula for the anomalous Zeeman effect.

Kuhn:

Well, you told me that story and I didn't know the formula at that point. I have seen it frequently since, because I've read more papers. I'd be very much interested in knowing how Sommerfeld felt. Because that's another perfect example of his bringing in a formula that, in terms of everything else that's been said in the book, is just nonsense physically, and expressing really very considerable satisfaction. Did he talk to you about this or how did Pauli feel about it? It's a very strange situation.

Heisenberg:

Well, if I tried to rationalize it, I would say this: a man like Sommerfeld had very strong feelings about the mathematical description of nature, and these feelings could be pleased, even if the rationalization had not succeeded completely. Even if the whole thing still contained definite contradictions, he would still feel, "Well, this looks right." Now, of course, one should analyze what you mean when you say, "It looks right." That is a very difficult thing to do. But when he had seen these old Voigt formulas and he had tried — well, actually he and I together had tried — to put them into the language of the quantum theory, that is, a line should be the difference between two energies, then we found out that that can actually be done. You can give the shift of the level as functions of the magnetic field, in a rather complicated formula, and still everything works out now quite well and you do get the correct line. Then Sommerfeld just felt, "Well, this looks right, and therefore it must be right. I don't understand a thing here." — He agreed about that. "We can expect that the mathematical scheme must contain contradictions because from classical mechanics we never can understand such a thing. But never mind, it looks right." And he would publish it only if he was sure that it looked right. And that was his attitude also in the x-ray case. He would say, "These formulas with the two kinds of doublets, that looks as if it is correct physics. We don't understand it anyway, but these formulas which we must stick to — they are good." I would say that this is an attitude towards physics which should actually be practiced even in our times — more than it is practiced. I discussed this matter with Feynman once, who is perhaps that physicist in the United States who most understands this side of physics. He has this kind of attitude to see whether the thing is right. But we discussed this and he said, "Well, among the younger generation nowadays there are very few people who would dare to publish a thing which contained contradictions." Practically nobody would, because he would say, "Then I will very soon be criticized by the other fellows who would say, 'There is your contradiction, you must be wrong.'" But then to say, "Well, I know that I must be wrong; certainly there is a contradiction, but damn it, I can see that it's right." Now, of course, you can again say that that is a very funny attitude. How can you know it? You cannot prove it; it contains contradictions. What are the criteria which then distinguishes a good thing from pure nonsense? And these criteria, of course, have been at stake ever since Sommerfeld. And even at that time Sommerfeld, as I told you, was criticized very strongly by the other physicists, such as Wien, for talking pure nonsense. Wien said, "Well, it contains contradictions; what does all his enthusiasm mean if the thing can't be correct?" But history then has shown how actually Sommerfeld was right. The trouble is that actually there are no criteria — I wouldn't know how to describe the criteria. Still, I was very strongly impressed by Sommerfeld's way of talking about things, and when he had that kind of enthusiasm I could also definitely feel, "Well, he must be right, there. In some way, that looks right."

Kuhn:

You say he was strongly criticized by a number of people, including Wien. Who else stood in that position?

Heisenberg:

Well, let me see. Who else? Well, I remember that Niels Bohr criticized Sommerfeld to quite an extent. He said, "Well, he's too much enthusiastic for things which are not clear yet." So he was not too happy about Sommerfeld's book and said, "Well, this book certainly must contain a number of errors and mistakes, and it's too bad to write big textbooks for students and to get them enthusiastic for a thing which cannot be correct in this way." So that was one criticism. There was one of the mathematicians who liked Sommerfeld's way and who defended him against others. The Greek mathematician who was in Munich. He was a close friend with the Greek minister of foreign affairs, (Mr. Venigelos.) Caratheodory. That was it. I sometimes heard discussions between Caratheodory and other mathematicians, and Caratheodory always emphasized that, "Sommerfeld is alright. He sees that there are still some contradictions and things don't fit but he goes into physics in the same way as a good mathematician goes into mathematics. He first knows the solution and then later tries to prove it. For a good mathematician, it is never the other way around — that you first find the proof." And he would say, "No, that's not the way to do it. You first must know what you have to prove, and then only much later you find the proof." That is also the attitude which I have heard expressed by the mathematician Hardy in Cambridge. You know there was a rather strange relation between Hardy and the young Indian mathematician Ramanujan. Ramanujan was just that kind of a fellow who always invented mathematical laws which, in most cases, were absolutely correct and still he couldn't prove anything of it. And Hardy spent a large part of his life proving the theorems of Mr. Ramanujan. So Hardy saw this side of the game more clearly than many others. I think that I have still a book written by Snow in which I found a statement by Hardy. The statement more or less means this: Those things in science which you can do by rational arguments are really not worthwhile doing. I must find the statement. I have the book at home in my library. I will find it quite soon because I was so glad to see it that I made a pencil mark beside this statement...

Kuhn:

I'm surprised to find the mathematicians involved in this controversy about Sommerfeld. Carathéodory at least knew what was going on in physics. Did the other mathematicians also know?

Heisenberg:

Probably not, no. Well, Sommerfeld was on quite good terms with many of the mathematicians, so this was not the trouble. But I don't think that they were especially interested. I would say mostly the pupils of Wien and also the privatdozents of the experimental institute would criticize Sommerfeld. Well, Wien actually demanded that before I should get an examination — a doctor's thesis — I should have to work in this institute — actually in the practicum. He gave me a problem which I actually couldn't solve at all. It was to measure the hyperfine structure of lines in the Zeeman effect. My experimental skill was very far from being sufficient for that kind of problem, and so I actually did very little at the experimental institute. However, I spent quite a lot of time in the institute, but I spent most of it discussing with the experimental physicists and assistants the general situation in atomic physics. There I always felt that these experimental physicists thought that this Sommerfeld was just too bad. "The old man just gets too enthusiastic about this thing." They always spoke about Sommerfeld's Atom-mystic. It may be that among the professors it was mostly Wien who criticized him. The mathematicians did not criticize him too much; they would say, "Well, all right. He knows that the things are wrong. If then he still believes them, he be quite right."

Kuhn:

Was there then a pretty complete separation between the people at Wien's institute and the people at Sommerfeld's?

Heisenberg:

Yes, I think there was a pretty strong separation. Of course, we would come together at the Colloquium. There we would have discussions. But otherwise there was a slightly unfriendly attitude between the two institutes. The two institutes would criticize each other in the sense that Pauli would say, "Well, experimental physics is 90 percent extremely annoying." That kind, of thing. But I don't know how seriously one should take this criticism because, of course, it was student talk. Students are always eager to criticize.

Kuhn:

What it does speak to is the amount of communication between the two institutes.

Heisenberg:

Yes. That is quite true. There was not too much communication. I would say that there was probably not quite sufficient communication between the two sides.

Kuhn:

It is interesting that you, yourself, were put on a problem of measuring hyperfine structure. I didn't know this was going on in Wien's laboratories. But nevertheless, apparently all such data that Sommerfeld got and used came from Tubingen.

Heisenberg:

That came from Tubingen. Yes... Because of this gap between the two institutes. Yes, that's quite true.

Kuhn:

Would you people in general just not see very much of each other?

Heisenberg:

Possibly yes. Well, of course, we were only 100 yards apart. Also I must say that Sommerfeld had this habit of going to the Cafe at the [???] before or after the Colloquium, and. I quite frequently joined him there. I had frequently found mathematicians going there and discussing problems with him, but I have never found an experimental physicist with him. Except Kossel. Kossel was an experimental physicist, or would you call him a theoretician? ... There was a definitely close connection between Kossel and Sommerfeld, and not only Kossel, but also Grimm. Grimm was a funny figure there. I don't know much about him. I think he must, later on, have been lost in industry. He hasn't played a great role in science. But Sommerfeld, Kossel, and Grimm would sit together and discuss problems of x-rays and atomic spectra. I will tell you the story about the integral at the marble table in the cafeteria. That is a nice story. There were small tables in the Hofgarten — tables made of marble, without tablecloth — and there you took your coffee. So we used, simply, to write formulas sometimes on these tables or figure something out. Once Sommerfeld explained to one of the mathematicians that there was an integral which he didn't know how to solve, and he wrote it down on the table. Then we had to leave the place to go to the Colloquium. A few days later, it just so happened that we came back to the same table and there we found the solution of the integral written out. Some other mathematician must have been there since and solved the integral. That's quite a fine story.

Kuhn:

How often did the Colloquium meet?

Heisenberg:

The Colloquium met, I think, every week. That was the normal physikalische Colloquium. Now let me see. Perhaps it was not announced in these things.

Kuhn:

I think it may not have been. Who organized the Colloquium?

Heisenberg:

I would say officially Sommerfeld and Wien together. I would have thought that in the Vorlesungsverzeichnis it would read, "Algemeines physikalisches Colloquium, Wien und Sommmerfeld."...

Kuhn:

In practice, do you suppose that Sommerfeld and Wien agreed to do it every other week or something of the sort?

Heisenberg:

Yes, I would say that they would discuss how frequently it would be held not quite sure that it was held every week, but it was pretty frequent — either every second week or every week.

Kuhn:

Who generally spoke? To what extent were the people who were in Munich invited to speak and to what extent were people from other places invited to speak at the Colloquium?

Heisenberg:

I would say that mostly people from Munich, mostly assistants to the professors, were invited to speak. Only in rare cases would Wien or Sommerfeld speak. The speakers would be mostly people like Herzfeld or Wentzel, or Pauli, or the experimental people like (Glaser). They would be the main contributors to the Colloquium. Then there would be a rather lengthy discussion about what we should think about some new paper. Mostly the Colloquium was about new papers not from Munich, new papers which appeared in literature or about which one had heard something.

Kuhn:

Did the split between the experimentalists and theoretical people become particularly clear at the Colloquium?

Heisenberg:

No, I would say that there it looked as if there was very good agreement. People tried not to show it too much. Well everybody, of course, in his brain, recognized that one can do physics only by the exchange between the experimental and theoretical physicists. This was clear enough. Still, there was some feeling on both sides... You asked me who else did criticize Sommerfeld. There was, of course, this group composed of, say, Stark and Lenard — these radical anti-Einstein and anti-theoretical physicists. Stark was in Munich and he wouldn't take Sommerfeld seriously. He just thought it was all complete nonsense. So this was a great difficulty. Now Wien wasn't as bad as all that in his criticisms of Sommerfeld. Wien was much more reasonable. But still, of course, this view expressed by Stark and Lenard spread among the students. The students would repeat what these men had said about Sommerfeld... I could imagine that this difference, or this gap, between experimental and theoretical physics had a political component already at that time. Experimental physics, after the first world war, was in a very difficult situation in Germany, just for economic reasons. They had no equipment. So they had rather little success, while the theoretical physicists like Sommerfeld had very big success. Also, Einstein was now very famous for what he had done and the experimental physicists were not so well known. So it was this feeling of frustration from economic reasons and other reasons which made them uneasy and in some way they started hating the theoreticians who had a so much easier life. This is one of the components which certainly had contributed to the difficulty to some extent. Of course, this affected the good people only to a little extent, and affected the poor people to a large extent.

Kuhn:

Stark had, in the very early days, been a tower of strength for physics. Then just before the beginning of the war he turns his back on all this. Do you have any idea what that was about? Did people talk about it? Stark is one of the first people to use the quantum; he gets some quite interesting and important results using the quantum...

Heisenberg:

Yes, that's strange. Pauli always told me, even at that early time, "Well, this man Stark has gone crazy. He has given up quantum theory just in the very moment when it became convincing." We never understood why. There must have been some break in Stark's life. I don't know whether it was purely personal. I don't know — that can happen in every life. Something must have happened in Stark's life. That I cannot doubt. All of a sudden he felt that he had to change all his views, and actually he gave up, his good physics and started to do very poor physics. From this moment on he became a very disagreeable fellow for the others; he criticized extremely strongly and without any real justification. So, from that moment on, instead of becoming a good physicist, he became a funny figure. Pauli never took him seriously. He always spoke of him as "Mr. Fortissimo." I have seen him in Colloquium sometimes, but then he never did say anything which one could take seriously. It was very strange.

Kuhn:

Did others take him seriously?

Heisenberg:

Well, I remember one fellow. That was Dopel. Dopel belonged to Wien's institute and in his political views he would be very much on the side of Wien. Not as radical as Stark, but still he would be a typical Deutsch-Nationaler — not an antisemite, but Deutsch-Nationale. He was strongly against Sommerfeld and the "clique," as he would say. It just so happened that he was in Leipzig when I was in Leipzig before the last war, and we had to work together on the uranium problem. We had a very nice collaboration. I found that he was quite agreeable if one kept him on the right track, that is, to just avoid rather foolish discussions of political things which didn't exist. Then it was quite nice... He told me about his experience with Stark. When Stark had gone out of the University, he had a private laboratory, not very far from here in [???]. Dopel became Stark's assistant. Stark lived from some industrial money and could give quite a good salary to Dopel so Dopel had taken that job. That led to complete disaster. Dopel's views on experimental physics benefitted a great deal from this experience which he had with Stark. Stark would tell him "Now, I believe that there is a dissymetry in intensity in the Stark effect of hydrogen. You measure this dissymetry in intensity." What happened then to poor Dopel was this: he took very good pictures; he took about 500 pictures. Then he looked through the pictures and found that he couldn't see any real dissymetry in intensity. On one plate a line on the right looked stronger and on another plate a line on the left looked stronger. Then he gave the whole material to his chief, Mr. Stark. Stark said, "Well, yes, your plates. are not all equally good. There are rather poor ones among them, so we will first try to get out the good ones." Stark took out all those plates where the intensity was strong on the right-hand side and threw away all those where the intensity was stronger on the left-hand side. Then he told Dopel that now he should publish the paper with this material. Of course Dopel refused and said, "That was not experimental physics." Then he got into a big quarrel with Stark, and Dopel left. That was Stark! That's very unusual for an experimental physicist who had done excellent work to do that kind of thing. What's the idea of it? You can't cheat nature anyway. Even if he had published the paper, nobody would have believed it because somebody would have tried later on and would have seen that it was not right. I would say that it is a thing which happens more frequently than we believe that people get some psychological trouble when they get to a more advanced age. They have had some human experience which was very disagreeable; someway they get off the track and they can't find their way back again. Well, you know about Stark's later history, about becoming a rather disagreeable Nazi.