Werner Heisenberg - Session I

Heisenberg:

I could simply start to tell you just quite informally about what I do recollect from my school time and how I got interested in science. That might be of some interest, I think. Actually I may just mention a few dates. I was born in Wrzburg, and my father was a teacher at the school there, at what we call the gymnasium. He was a teacher in Greek and Latin, and, well, he was a philologist. And then in 1909 my father got a call to the University of Munich as professor of Greek — well, (middle-Greek) — history and a bit of Byzantine history. So the family moved to Munich, and I came here and went to the gymnasium, called (Max) Gymnasium. In Wurzburg my father was not only a teacher at the gymnasium, but also Privatdozent for Greek and Latin at the University. So he had the two jobs together. Then he got the call to the University of Munich, and he got what we call Ordinarius (?n) in Munich. That was around 1909 or '10; I think it was '09. Then I got into this Max Gymnasium in 1910. Now, from these early years at the gymnasium I do recollect that both my interests in languages and in mathematics were rather early. I had a school friend with whom I studied Sanskrit, and actually I still have at home a small dictionary of Sanskrit which I had written in Sanskrit writing at that time. It is, of course, very childish, but still it was an interest. Our father used to play all kinds of games with the two boys he had — I have an elder brother. And since he was a good teacher, he found that the games could be used for educating the children. So when my brother had some mathematical problems in his school work — you know, if one pound of apples costs so much then how much are two or three pounds, or whatever. So he tried to use these problems as a kind of game and find out who could do them most quickly, and so on. Somehow I discovered that I could do that kind of mathematics rather quickly, so from that time on I had a special interest in mathematics. And when we got into real mathematics in school, I felt that mathematics was a subject which fascinated me, so I did study differential calculus, I think, when I was about 12 or 13 years of age. I started that kind of thing very early.

Kuhn:

How much older than you was your brother?

Heisenberg:

Two years, or one and a half to put it more accurately. Then I asked my father to bring me from the library of the University some mathematical books. Now my father had no idea about-mathematics and brought just anything he found, you know. So, for instance, again since he was interested as a teacher, he brought mathematical literature which was written in Latin because he felt I should study Latin at the same time. I think it was in 1916 that he brought me a book which turned out to be the doctor's thesis of Kronecher, on the theory of numbers, written in Latin. I think it must have been then because in '15 my father was in the war so in '16 he was wounded and had come back. So I got interested in the theory of numbers, and I got very strongly interested and tried to do something myself. The teachers of the school sometimes gave out papers with small essays on something, and I found an essay on the equation of (Pell) — that's an equation in the theory of numbers. And that again interested me so much that I tried to write another paper giving a consideration of this problem; you know, the extension to some other cases, and that kind of thing. So actually I did write a paper and tried to send it to that periodical, but it was not accepted. It was, of course, very bad, and I (wasn't) very sorry for it; probably it wasn't good at all anyway. So from that time on I had a strong interest in mathematics, and I should say much more in mathematics than in physics. So when I was in the last classes of school — it was when I was 17, or so — I didn't think to become a physicist, but I was strongly interested in mathematics, and I did think of becoming a pure mathematician.

Kuhn:

Had this interest been encouraged in school: Or was the school very heavily classically oriented?

Heisenberg:

Yes. Well, the school was very heavily classically oriented, but fortunately we had a very good teacher of mathematics. His name was (Wolff); he was a very good man who really did teach the people something. He also found that I was perhaps comparatively good in mathematics, so he tried to interest me and give special problems to me. He told me, ""Try to solve that and that." I remember once he had given me a problem about diffraction; he had studied diffraction of light in a vessel of water, you know. I did some calculations which led to elliptic functions, and I did quite a long paper with elliptic functions. But then he told me that unfortunately he couldn't say whether it was right or wrong, as he didn't know anything about elliptic functions. But he was a very nice man, and he did help me a lot.

Kuhn:

Do you remember other books that you read at this time besides the Kronecker?

Heisenberg:

Well, yes. I did then study the books of Bachmann — just all the textbooks on the theory of numbers. I was fascinated by the theory of numbers. Bachmann's was a standard textbook on the theory of numbers. I was very interested in Fermat's theorum, and for some time, of course, I tried to prove Fermat's theorem, as everybody does. Then there was (Goldbach' theorm and all that kind of thing. You know, that is a special kind of mathematics which I feel is still nicer than differential calculus because it's quite clear; everything is so that you can understand it to the bottom. That was during the years 1917 and '18. Then, yes, somebody gave me the book of Weyl on the theory of relativity. And that again interested me a great deal, so I tried to understand the Einstein relation and the Lorentz transformation and so on. Still I didn't think about physics. I mean, I was fascinated by the idea that space and time should be changed; that I felt to be extremely interesting. And I should perhaps also add that I had already at that time quite a lot of interest in philosophy in general. So I did study Plato with great enthusiasm. I remember once a scene which was quite nice. You know in 1918 there was a revolution in Germany. There was a lot of trouble here in Munich; there was quite some fighting. When the troops of the government tried to reconquer Munich, I took part [in the defense] — not really in the fighting, but I belonged to a body of troops. Well, was, you know, a boy of 17, and I considered that a kind of adventure. It was like playing robbery, and so on; it was nothing serious at all, but still I was there. I was in an office opposite to the University; there is a seminary for young priests opposite the University — you can easily find the house. There our troop was concentrated, so I had my duty there. I just had to write things for an officer, and sometimes I had to take the guns somewhere; this was nothing serious at all. I had duty during the night, and it was a nice summer in 1919, so during the morning et 4:00 nothing was happening at the office, of course, and somehow I couldn't sleep, so I went up to the roof of the house into the sunshine; it was nice and warm. I had Plato's Timaeus with me. I studied the Timaeus of Plato partly to keep up with the Greek because I had to know Greek for my examination, but partly also because I was really fascinated by atomic theory. You know that all the atomic theory of Plato was in the Timaeus. So my knowledge of the atomic theory of Plato actually went back to this funny thing that I sat on the roof of a house in the (Ludwigstrasse) in Munich and studied Plato. Then I took my examination, the Abitur, in the summer of 1920. And I came to the University with the intention of studying mathematics, pure mathematics.

Kuhn:

Did you read other philosophy?

Heisenberg:

Yes, I did. There was for instance, the following: in the year 1918 I was for some time not in school. First of all we had absolutely nothing to eat in the family. My father was not very clever in having connections to the farmers, so my mother was quite in despair about how to feed us boys. So we decided that I should simply work as a laborer on a farm. So I went out to a farm in Miesbach — that's about 50 miles south of Munich. And that was a very nice job; I was on this farm from the spring to the autumn of 1918. How on a farm, of course, the scientific interest has not to be very strong anyway, but still I do remember that I had in my drawer Kant's Kritik [der reinen Vernunft], you know. I had the books of Kant to study so that at least shows that I was interested in Kant. I do not think that I did much work on it because I discovered very soon that when you do labor on a farm the whole day, then you just can do nothing whatsoever but sleep in the evening, so that was what I did. But I had a very good time on this farm. I was there with about 6 or 7 other boys of about the same age, and we kept the whole farm going, because there were no men at that time. So we came back in very good health because we had very good food, and so on. So taking it all together, I think, that was one of my most important times, considering my education, because on a farm you really learn to work. You know it's not like in school where you think it's not so important. On the farm we had to rise at half past three in the morning, and if the weather was good you had to cut the grass and do whatever else there was to do, and we sometimes worked until 10:00 at night. So it was really very hard work and very good exercise for a young boy. So the studies of Kant probably didn't come to much during that time, but still I remember that I had the Kant with me. But there was, I would say, a moderate interest in philosophy, but I had a much stronger interest in mathematics.

Kuhn:

Do you suppose you read Ernst Mach in that period?

Heisenberg:

No. I must say that I never have read Ernst Mach quite seriously. I have later on studied it little bit, but that was much later. And in some way I was never much impressed by Mach. I was impressed by Einstein's way of doing things but not by Mach's. And why was that: I would say Mach was always a bit formal for it was too — I would say not too negative, but too modest in what he wanted. It was, perhaps I should say, too little poetical. I mean, Plato is, of course, a poet; that's obvious. Kant is not a poet, but still he has some poetry even in the way he writes, but Mach, I would say, is very little poetical. I mean the positivist is very frequently not poetical with perhaps the exception of Wittgenstein who is in some way also poet.

Kuhn:

And he was, at least, in his later writings also often not a positivist.

Heisenberg:

Yes, that we may also say, yes. So he was, I would say, a much stronger personality than many others of this kind were. But there is not a doubt that Mach has been a great philosopher and has contributed enormously to natural science; there's no doubt about it. Still I was not much attracted by Mach. I was attracted by Kant, and then I liked Plato partly as a poet, and partly as a philosopher. But I was very strongly impressed by the way Einstein had done the theory of relativity; this idea of changing the concept of time, that has worried me a great deal and had appealed to me very much. I felt very strongly that something real was happening there, you know — that one could really turn things around; that was a very essential point.

Kuhn:

Then how much, when you got to the university, both reading by yourself, but also in school, had you read? You had had a lot of number theory; how much other mathematics had you had? How much physics and chemistry did you have?

Heisenberg:

Yes, I had a lot of number theory. Well, I would say I had, practically, a good knowledge of differential calculus. Well, in some way I always succeeded in practicing that sort of thing. You know, that is the kind of subject you have simply to practice; you have to differentiate; you have to solve differential equations, and so on. I got, for instance, the practice in the following way: there was a friend of our parents, a young girl of about 24; she was a chemist, and she was very much in the family. She had to get her doctor's thesis in chemistry, so she wanted to take her examination in chemistry, but she had also to be examined in mathematics as a (main track), you know. Since she wanted to learn differential calculus for that purpose, she asked me to give her advice in it. At that time I was a boy of about 16 or 17. So I gave her regular advice in diferential calculus for, I would say, about three months. And in that time, I don't know whether she had learned it, but I certainly had learned it. And that was a great advantage for me. But, well, she has passed her examination anyhow; I know her still. She is now, of course, an old lady living in Nurnberg and I now just once in a while see her. So that was the way in which I practiced that kind of thing. So I knew differential calculus and integration and that kind of thing comparatively well. I knew the theory of numbers to some extent, but otherwise my mathematical education was very irregular. There were many elementary things of which I had no idea, and other things which I knew comparatively well. So I would say I had a very good chance to get lost in every good examination in mathematics because if I would be asked about elementary things, I would probably be completely lost. Then I came to the University with the definite intention to study mathematics. Since I felt that I already knew something about mathematics, I was very immodest and thought I could already in the first term go into one of the seminars of one of the professors, because I always felt you have to go to hear the man talk and not only go to the lectures. I felt you had to go to the seminar, listen to discussion and so on. But I was not at all lucky in that way. How I must tell complete nonsense, but it's really true in some ways. That is, I went to old Lindemann, the man who had proved the transcendence of pi. He was a bit old at that time and was much engaged in the administration of the University, so he had a room [in the administration department] of the University. In some way he didn't like for a student to come into his office at that time, but my father had asked him whether I could see him to ask him about the seminar, so he couldn't say no. Well, in some way, apparently, he didn't like it too much. Anyway, then he had a funny habit: on his desk he had, beside him a little dog, a pet dog which he liked very much. This pet do: would sit there on the writing desk and would, of course, look at every visitor there, and in some way the dog didn't like me at all. The dog started barking with an enormous noise. So it was quite difficult for the old gentleman to hear what I said; perhaps he was a bit deaf already, and so on. Anyway that was a difficult conversation. Then he heard that I wanted to take part in his seminar in the first term of the university, he was a bit shocked, already. Then he asked me, ""Well, what was the last book on that kind of subject which you have read?" Then I told him that I had read the book of Weyl, Raum, Zeit Materie, with much mathematics in it. Then he said, "Well, now that means that you are apoiled for mathematics forever." So I went out with no success, and I felt, "Well, really the old gentleman didn't like that at all, so I'd better go somewhere else." So I came back to my father, and we talked about where I should go. At that time he was a good friend of Sommerfeld; he saw him quite frequently outside of the university. So he said, "Well, you might just as well see Prof. Sommerfeld, and perhaps you could also go to his seminar." Now, with Sommerfeld it was just the opposite, you know. He was very friendly and said, "All right, you have an interest in mathematics; it may be that you know something; it may be that you know nothing; we will see. All right, you come to the seminar, and we will see what you can do." So I came to Sommerfeld, and already four weeks after I attended his seminar he gave me a problem, which was, of course, very nice. Sommerfeld gave me the experimental values of the anomalous Zeeman effect. He had just published a minor Paper which he told me was not important at all. He said, "Since we suppose from Bohr's work that every frequency is a difference between two energies, one should expect that in these funny numbers" — which one had in the anomalous Zeeman effect for the splitting — "that the denominator should be the product of two denominators belonging to the two states." And that he called the multiplication law of the denominators. Well, of course, it was a minor point, but he said that in this way he would feel that it should be possible to disentangle the line frequencies into statements about the stationary states — initial and final states. And he wanted me to find out what the initial and final states were using selection rules. This, of course, was just the kind of work which I loved to do because I always felt it's nice to do problems oneself.

Kuhn:

And it had elements of number theory.

Heisenberg:

Yes, exactly that. So after a very shorttime, I would say perhaps one or two weeks, I came back to Somerfeld, and I had a complete level scheme. Then I came up with a statement which I almost didn't dare to say, and he was, of course, completely shocked. I said, "Well, the whole thing works only if one uses half quantum numbers." Because at that time nobody ever spoke about half quantum numbers; the quantum number was an entire number, you know, an integral. "Well," he said, "that must be wrong. That is absolutely impossible; the only thing we know about the quantum theory is that we have integral numbers, and not half numbers; that's impossible."

Kuhn:

This was still 1920?

Heisenberg:

That was the autumn of 1920, yes, as I recall. One can never be certain ... It was very shortly after this paper of Sommerfeld. Sommerfeld at once thought that if this multiplication law is correct, it simply means that you can disentangle the levels, and that is, of course, a simple thins to do. Well, in some way, he must have had difficulties because probably he had tried himself: and in some way it didn't work out as he wanted. And I know the reason; he felt that he must do it with integral quantum numbers, and then, of course, it didn't work out. Since I was a complete dilettante and amateur and didn't know anything, I thought, "Well, why not try half quantum numbers?" Then we had a long discussion whether half quantum numbers would be allowed or would not be allowed, but finally it was agreed upon that probably half quantum numbers were correct. Then Sommerfeld had received a letter from Lande telling him that he was interested, and in some way he was closer to the experiment; he had worked with Paschcn and rack in Tubingen. So I think that I have not published on this thing and that only Lande has published on it, which was quite all right because he had started earlier. Anyway I remember this story about the half quantum numbers very well. For quite a long time nobody knew whether that was decent physics or was not. I mean, nobody, of course, thought about the (half integral) representation of the group theoretical side of this problem. That was far away still. So that was at least my entrance into physics at that time. I started at once with the anomalous Zeeman effect; that was practically the very beginning of my study in physics, and, again, it contributed to a very irregular education and training in physics. On the one hand, I learned quantum theory and Bohr's quantum conditions. On the other hand, I had first to learn classical mechanics; well, I had to solve the ordinary training problems, and so on. Still it was great fun; it was much more fun for a student to solve problems than just to study and to hear lectures.

Kuhn:

How much physics had you actually had of this before you got to the University? Had there been any physics, chemistry, or that sort of thing in school?

Heisenberg:

Well, in school we had very little. In school, yes, we had in school the very elements of classical, mechanics; there is a law that mass times acceleration is force. And, of course, then I tried in school to solve the differential equations for the Kepler ellipse. And in that I did succeed; I mean, I could at least do differential calculus to the extent that I could solve the Kepler problem. So that I had done, and so far I knew a bit about classical mechanics. But still the real fundamentals — I mean, the axioms and all that kind, of thing — that I first learned when I was in Sommerfeld's lectures. Sommerfeld was an excellent teacher simply as regards the time which he took for every student. I think almost every morning I was in Sommerfeld's room for at least one hour or two hours, and he would ask me questions and talk to me and so on. He made an enormous effort with his pupils, which is, of course, the first condition of being a good teacher; that is obvious. Well, he had this ability to fascinate people, to induce them to attack the problems by saying, "Well, I can't solve these problems, now you try it." He said that kind of thing. That is, of course, a thing which appeals to the young men; then they will try to use their force. So that was a great time I had from the very beginning. Then, I remember, very shortly after that time of the anomalous Zeeman effect, Sommerfeld gave me the papers of Bohr which had just appeared. And Sommerfeld was so optiristic that he said, "Well, now it seems that Bohr can calculate the whole periodic system of elements because now here he writes about all the different stationary states of the different elements. That must mean that now he has got the key to calculating all the stationary states." Also Pauli, who was also in Sommerfeld's seminar at that time, was quite optimistic. Only later we discovered that this was all guessed by Bohr, but not calculated; and that it was all his enormous intuition. He knew how things were, and there was not any way of calculating it. Well now should we stop, perhaps, at this point, or shall we go on?

Kuhn:

Well, I think perhaps there's not much point in trying to go further forward in time. I [still have some questions about this period]. You went regularly to Sommerfeld's lectures?

Heisenberg:

Yes.

Kuhn:

Did you go to other lectures also?

Heisenberg:

Oh, yes. I tried to get some training. I did go to the lectures of Lindemann and Voss in mathematics. I went to the lectures in astronomy to get some information about astronomy. I did also go to lectures in Physical chemistry; to Herzfeld, for instance. Herzfeld was a good teacher, so I liked his lectures. I got the best mathematical training with Rosenthal. He was a mathematician who later on went to the United States. I have met him still some years ago in the States, but I have been informed that he has died recently. He was a very nice gentleman; he was small, had a tiny figure, and was very lively. And he was, again, an excellent teacher; he could make mathematics so interesting that one tried to solve all the problems. So actually we had exercises with the lecture, and the students had to solve problems. And it turned out that practically all the problems, through the whole term, were only solved by always two students in turn. One was the present Professor (Sauer) at the Technische Hochschule in Munich and the other one was myself. So we always traded it around, and either he would solve the problem or I would; no other one did them. But this made a little game, and we had great fun from it. That was all at this time. At the same time I attended the lectures of on the theory of functions and the proofs of convergency, and so on. And I was terribly bored; I didn't like it at all. I had no success whatsoever with Pringsheim lectures. That kind of exact mathematics, you know, where you prove that it converges within this and this range, and so on, in some way never appealed to me. So I had no success, and I went away again.

Kuhn:

Once you had made the first connection with Sommerfeld, was the decision about physics sort of automatically made? Or did you think again of doing mathematics?

Heisenberg:

I think it was more or less automatically made. That is I did still think of mathematics, but then, again, the fact that I had no success with Pringsheim's lectures, in some way taught me that I was not very well suited for a study of mathematics. I would say I was too "schlampig" for mathematics. ... So it was more or less automatic that I went into physics, and I got interested in relativity. Then I met Pauli among Sommerfeld's students; and he had a very strong influence on me. I mean, Pauli was simply, also, a very strong personality, you know. He would talk to and he was extremely critical. I don't know how frequently he told me, "You are a complete fool," and so on. helped a lot, you know. So we always were very good friends, and we never minded when we criticized each other. So that was very nice.

Kuhn:

You knew Pauli then from the very beginning? Was he in that first seminar you were in?

Heisenberg:

Yes; he was already at Sommerfeld's when I came there, so I met him. Well I don't recall what our first conversation was. Yes, I do even recall our first conversation. I had seen him sitting there at a desk in the seminar but never spoke a word with him, and at that time somehow I got interested in general relativity. Sommerfeld had talked about a letter he had gotten from Einstein about general relativity — whether there vas a red shift or was no red shift, and so on. And I had studied this book of Weyl's again, and I had not understood the special formula about — well, there was a formula I couldn't understand. So I thought "Well, there is this Pauli." And Pauli had written on general relativity; that I knew of. And he was writing a book on it. So I asked him, and he then explained the thing to me. He always knew everything, and so i think that was definitely our first conversation. So then I was impressed that a man of my age already knew all about general relativity, and so I was at once interested in this fellow student who sat there and knew so much. And from that time on, we started again and again discussing things. Then when the Bohr paper came, Pauli was interested. Then I asked him, ""What do you think about this new paper of Bohr's? How did he calculate it, and so on?" So that was a very early connection.

Kuhn:

You say you had, not had success with Pringsheim in the mathematics; what sort of problems had you been doing for Rosenthal?

Heisenberg:

That was differential geometry. You know, theory of curves and surfaces and that kind of thing — things which you can nicely visualize. And that appealed to me, so that I liked.

Kuhn:

I think that is often the difference between the sort of mathematics that appeals and that which does not.

Heisenberg:

Yes, that's quite interesting. I would say, I had never much fun in mathematics where you have to prove something. But I had much fun in mathematics where you have to find out how things are. I don't know whether that says anything, but I think it's that way. This proving of such and such I found to be almost like cheating. You start somewhere, and then you go into a dark tunnel and then you come out some other place. You find you have proved what you wanted to prove, but in the tunnel you don't see anything. So I never liked that very much.

Kuhn:

In this period what sort of a future was there for somebody who would mathematics, or who would pick physics?

Heisenberg:

Yes. Well, at that time that was, of course, a question which I was asked several times by my father. My father wanted to know, ""Well, how will you earn your money later on?" Well, we discussed the possibility that at least if one studies physics, one could perhaps go into industry, and so on. But on the other hand, my interest was a theoretical interest, so after a while it was clear that the only chance was to get into a university later on.

Kuhn:

Was there much industrial physics in Germany then? There was, of course, lots of industrial chemistry.

Heisenberg:

I would say, yes, there was a lot of industrial chemistry, and industrial physics did start to some extent. I would say that an experimental physicist had a good chance, or, at least, a finer chance to set a job at the Siemens factory or at the A.E.G. — at the electric factories, or in optics, or so. But a theoretical physicist had not much chance, so that was a question. Only later when there was a definite hope that I could enter at the University, then my father was somewhat —. Well, he felt that it was all right. But I remember that still —. You know, I was very little successful with my doctor's thesis; I almost didn't make the examination in the doctor's degree. Then my father was so worried that he wrote a long letter to Max Born asking him for his serious advice about whether his boy was on the right track. Because after such a poor examination on the doctor's thesis it seemed quite doubtful to my father whether I would have a chance to enter into science. But Born was quite optimistic about it, so that was all right.

Kuhn:

Would, your father have had the same sorts of worries about a career if you had been in mathematics? Were there school jobs in mathematics that there were not in physics?

Heisenberg:

Well, perhaps he would have thought that mathematics was a more firmly established subject than theoretical physics. My father knew about some troubles within the University between experimental physics and theoretical physics. Here in Munich, there was really a rather difficult situation between Willy Wien, who was an experimental physicist, and Sommerfeld. Now, this difference between the two men was perhaps, partly, a political difference. I would say Willy Wien was very much on the right side of politics, and Sommerfeld on the left side, if these terms left and right mean anything. Besides that Willy Wien considered experimental physics as the center of physics, and in some way he disliked theoretical physics. He still, of course, had been a theoretical physicist himself — you know Wien's law. But certainly one would say that he disliked every Physics which was not as clear as classical Physics, so quantum conditions and that sort of thing, that he considered as a kind of weak talk which meant almost nothing. And I do remember that Willy Wien gave, when he was rector of the University, a speech about atomic physics and never mentioned the name of Sommerfeld. Everyone felt that that is a thing that one can't do because Sommerfeld after all was a very famous and certainly a very good physicist. So there was lots of trouble between the two, and my father was worried because he saw this trouble and saw that men like Wien just disliked theoretical physics as a kind of subject. So he felt, "Should my son go into a line which is still so much under suspicion among the physicists at the universities."

Kuhn:

To what extent was it Wien's resistance to the non-classical nature of theoretical physics in 1920 and to what extent was it being against theoretical Physics?

Heisenberg:

Yes. I would say it was the first thing; he was against the non-classical nature. It was this thing which people criticized as Sommerfeld's mysticism. I mean, you know he was enthusiastic for having integral numbers and that hind of thing. He knew, of course, quite well that quantum theory was not consistent. I mean, as he did classical physics he was a very good physicist and has written a number of excellent papers which wore comletely clear. On the other hand, he had an enormous instinct, or intuition for how physics really is. Therefore, he didn't mind contradictions when he knew, "Well, finally this must be so." So I was always greatly impressed by this ability of Sommerfeld's to see quite early what are the important problems and how they will finally be solved. I remember that later on, when I had to write about Sommerfeld, I studied his papers. I found a talk which he had given in the year 1910 or '11, at the Physical Society in Germany. At that time, of course, everybody spoke about the success of relativity and so on, but quantum theory was completely unclear. There was only the Planck paper and Einstein's paper on the light quanta which nobody believed. And Sommerfeld said, "Well relativity is now such a nice subject, and many people think that is an interesting success, and, of course, it is most interesting. "But," he says, ""relativity is in some ways finished now — special relativity. It has been solved by Einstein, and that was a great achievement. But the most interesting part of physics at the present is quantum theory; that is the key to all the problems of chemistry. That is the key to—," and then he had a long list of what quantum theory would once be the key. And I was greatly impressed by this possibility of Sommerfeld to see so early what the point was. That was his force. So when Bohr's paper had appeared in 1918 and 1920, and so on, he knew that Bohr was right about the system of the elements, in spite of the fact that nothing came out from mathematics. I mean, it was all intuition from Bohr, but Sommerfeld at once could see, "Well, that is the right way to go." And Wien disliked this tremendously because he felt, "Well, only people who have that kind of intuition can take part in the game. And the people who haven't, well, they just can't help it, that's it." I would say that was one of the reasons — that you could not use the standard methods of doing things, you could not use your classical way of calculating things. It was such a funny situation; you always had to work in a kind of fog of uncertain knowledge, and so on. And Sommerfeld liked it; he felt, "Now I see how things are connected, and that's enough." Well, the two personalities, Wien and Sommerfeld, were very different in this way, and therefore, it was quite natural that they wouldn't understand each other. I remember that this difference between the two came sometimes to very hard fights, and the worst of all was later. After quantum mechanics had been pubblished — the papers of Born and Jordan and myself — and the Schrödinger papers had appeared, then Willy Wien was enthusiastic about Schrodinger's way of doing things. He hoped that now everything would come back to classical physics. So he never wanted to hear anything about quantum mechanics and he just disliked it. But he was interested in wave mechanics, so he had invited Schrodinger to give a talk about wave mechanics at the University here. This invitation was sent out simultaneously by Sommerfeld and Wien, and the lecture actually took place in Sommerfeld's lecture room. So Schrodinger gave a talk. At that time had the idea that really the stationary states were not energy states, but just frequencies, that the whole thing comes down to classical physics. You have to have a continuous wave around the atomic nucleus and that has a frequency and so on; you know the kind of philosophy. Now, Sommerfeld, of course, you kmow, he was not so certain in this kind of thing. He was not quite certain whether he should criticize Schrodinger or not. In some way he felt, "Well, this is very beautiful, what Schrodinger does," and it certainly was. "And so," he thought, "It may be true, and quantum theory may not be true," and so on. So I started at that time — but I was a very young man — to argue with Schrodinger. And Willy Wien was simply furious. I criticized Schrodinger; I said, "Well, that cannot be true because when you make these assumptions, you cannot even explain Planck's law." That was simple thermodynamics; I mean, that was clear from Einstein's paper of 1918, and so on. But Willy Wien got up and almost threw me out of the lecture room. He said, "Young man you still have to learn physics, and it will be better if you sit down!" or something like that, you know. So he was so angry. And then he said, "Well, there may be still some difficulties with Planck's law; we have no doubt that Mr. Schrodinger will solve these difficulties. We need not worry about this at all." Well, that was the hind of situation it was.

Kuhn:

Willy Wien could say this to you in '26?

Heisenberg:

Oh yes, yes. I mean, I don't exactly know the wording, and perhaps I shouldn't exaggerate it now, but it made a very deep impression on me because in some way I had felt that I knew something about quantum theory at least, at that time. But Wien certainly didn't take what I said seriously at all. He just didn't believe a word; he felt, "Well, after all when Schrodinger has now solved all these problems what worry is there about quantum conditions?"

Kuhn:

You say that these people called Sommerfeld a mystic?

Heisenberg:

Yes.

Kuhn:

There are very few people who, when you read their writings today, seem to strike one as less of a mystic. How widely was this felt?

Heisenberg:

Well, I remember, for instance, a case between Pauli and myself. There was an advertisement on the streets at that time, a slogan from some optical firms, saying, ""If you have trouble with your eyes, go to Mr. Runke." Then Pauli used to say, "If they're integral numbers, go to Sommerfeld." So there was this love of Sommerfeld for integral numbers. He would always find integral numbers in some relations; the ratio of the intensities of the two sodium lines was two to one — that hind of thing. So this was a kind of almost mystical enthusiasm for integral numbers. Of course, Willy Wien hated that kind of thing, but still Sommerfeld was right after all. But, I would say, this mysticism was perhaps more a different word for his enthusiasm. You know, he was enthusiastic for the new and unclear things; he felt, "There's something real. That's a real connection which we have not understood yet, and I'll think about it." You know, he loved it when things were not understood yet. And in some way, in spite of his clarity in classical physics, he knew that it's much greater fun to do things than have them solved by somebody else already. So he was enthusiastic about these situations in which one saw already vaguely in the haze how things would probably be, but still you couldn't formulate them exactly, and that the problem which one should solve. And that's why Sommerfeld had this enormous success with the young people because that is the kind of thing which the young people, of course, liked; they want to see the problems.

Kuhn:

You say that Sommerfeld, of course, saw that the quantum theory was inconsistent.

Heisenberg:

Yes.

Kuhn:

And I suppose, in one sense, he must have; but it is striking as one reads the 3rd edition of Atombau, Sommerfeld will raise the question, "Should we really say that there's a contradiction here or not," when he talks about the circumstances under which you use the wave theory for light. One has the feeling that really there is an approach here and an evaluation basically different from Bohr's, and that he thinks that maybe physics is like this. Maybe this is not really to be called inconsistency.

Heisenberg:

Yes, I think you are quite right. In some way, Sommerfeld still hoped that perhapss it was consistent. I think, he was most strongly impressed by this very strange fact that one could get out all these details in the Stark effect from a simple calculation with quantum conditions. I mean, in some way that was a complete miracle, that things should come out quantitatively that way. That must have made such an impression that he always hoped, "Well, somehow the inconsistencies may disappear." Of course, he saw the inconsistencies, for instance, in calculating the intensities. The way calculating the intensities just by means of the correspondence principle was, of course, not really satisfactory. Still, as you say, he was loss worried by the difficulties than Bohr was.

Kuhn:

When I said inconsistency I was not thinking so much of the places where the theory will not yet work, as I was how can light be both a photon and a wave. In 1922 he seems to be sayng, "We could perfectly well get used to this. It is not inconsistent if you know where to say it's one and where to say it is the other." He seems to be saying that there is not really here that sort of inconsistency with Maxwell's equations.

Heisenberg:

Yes. I would perhaps say that Sommerfeld was not a man like Bohr to urge always for complete clarity. I mean, in some way he felt, "Well, that's difficult, and you don't know how, and perhaps somehow it will go together," and that kind of thing. And Bohr would never be that way; he would always say, "Well, we have not understood it." So he would be absolutely merciless in such discussions. I once again heard a discussion with Schrodinger which was exactly about the question which came up in the lecture Schrodinger at the invitation of Willy Wien. It took place about one or two months later in Copenhagen. Schrodinger was invited to Copenhagen, and Bohr wanted now really to discuss that with Schrodinger. It was almost a pity to see; I mean, Schrodinger had given this talk, and then he was criticized by Bohr. Of course, now Bohr did all the talking, not me. In some way, Schrodinger was so worried; he got ill there; he got a bad cold. He was put in bed and Mrs. Bohr brought him tea, and so on. And Bohr would sit at Schrodinger's bed, and would say, "Now, Schrodinger, you must see; you must see," you know. I mean, he wouldn't let him go for a single minute in the whole day; he wanted all this push, push, push, you know. So that's Bohr; Bohr wanted complete clarity to the end. Sommerfeld, perhaps, was not that way; he would say, "Well there's a difficulty; we must hope for the future." So he was not so deeply worried about the dualism between waves and Particles as Bohr was. Sommerfeld would, perhaps, just at this point escape in a kind of mysticism, and say, "Well, somewhere perhaps the two things go together." And, after all, he has been right; somewhere they do go together, but he was not by his nature forced always to go deeper and deeper and deeper until he finally got to the bottom. I should perhaps mention the following because it belongs to that. Shortly afterwards Bohr was invited to Gottingen to give talks on his theory; I think it was in the summer of '22. I must say that I always thought it was the summer of '21, and I had a discussion with van der Waerden about this. But now van der Waerden has convinced me that it was '22. There I had this very exciting experience; Bohr had given a talk on the quadratic Stark effect of hydrogen. That was a paper of Kramers' which Kramers had just written, and then Bohr at the end of the paper said, "Well, we know that the quantum theory still contains many contradictions; we can't calculate the intensities and so on, but still I feel since we have had so much success in the linear Stark effect of hydrogen with the quantum conditions, there can be no doubt that also the quadratic Stark effect, as calculated by Kramers, must be correct." Now, this I didn't believe because at that time I had thought a bit about dispersion, and I had realized that in the calculations this quadratic Stark effect is just mathematically almost the same thing as the dispersion for an infinitely low frequency. You know when you have an infra-red wave falling on an atom, then it's almost the same as having a constant field on an atom. Therefore, you can simply say, you take your dispersion formula, go to the limit of low frequency, then you have your quadratic Stark effect. Now, this was a rather trivial remark, but still, at the same time, I felt that we know that the dispersion doesn't come out from quantum theory because it gets a resonance at the wrong frequencies; that's obvious. You always get a resonance at the orbital frequency. Now, on the other hand, there cannot be the slightest doubt that the real dispersion, the real resonance, is at the real frequencies. So I criticized Bohr's remark, and I said that this I couldn't believe for the reason I just gave. Now, I saw at once upon making this remark that Bohr was rather shocked by it, and he felt that there were some faults in the remark. He said something then about, well, (it's a problem where the finite widths of the lines come in and the radiation pressure, and there was the reaction of the radiation). But he also elt tha s this was more a kind of excuse than a real argument. So after the lecture he came to me and asked me, "Couldn't we go for a walk in the (Hineberg) and have a nice time together, we must really come to the bottom of this problem." And then we had a talk of, I would say, about three hours on a long walk at the (Hineberg). It was my first conversation with Bohr, and I was at once impressed by the difference in his way of seeing quantum theory from Sommerfeld's way. For the first time I saw that one of the founders of quantum theory was deeply worried by its difficulties. Sommerfeld was not as deeply worried; he did not know how to solve then, but he just said, "Well the problem is there." But Bohr had always to go to the bottom, and he saw that there was a serious difficulty. So, of course, that remained unsolved. Then later on he talked to Kramers, and then, well, the papers which Kramers and I wrote together were practically finally a consequence of this first discussion. But the strongest impression on me at that time was that Bohr thought so differently on these problems from Sommerfeld. He never looked on the problems from the mathematical point of view, but from the physics point of view. I should say that I have learned more from Bohr than from anybody else that new type of theoretical physics which was almost more experimental than mathematics. That is, you have to cover the experimental situation by means of concepts which fit. Later on you have to put the concepts into mathematical forms, but that is then more or less a trivial process which has to be solved. But the primary thing is here that you must find the words and the concepts to describe a funny situation in physics which is very difficult to understand. And I felt that here there was a real philosopher who tried just to get concepts by which you can handle things, you know. It's easy enough to talk about the experiments; you see a spectral line here, you see this intensity, but you must find connections — how is the intensity connected with the line, and how is the dispersion relation connected with the position of the line, and so on. So this new way of theoretical physics did actually occur to me for the first time in just this very conversation with Bohr. Later on, of course, I have tried to learn that way of thinking from him, so that was a very exciting experience — that discussion on the (Hineberg). But the anomalous Zeeman effect that was, of course a minor problem. Still it has played quite a hip role in this first period. It's funny though that such a snail point plays such a big role. Well, with respect to physics nowadays, I love to tell the story about old Woldemar Voigt in this respect. Nowadays people are so fond of dispersion relations, and they certainly have lots of successes with dispersion relations. Now, it's quite funny to see that even in the old time dispersion theory it was in this way a very fashionable and successful subject. First there were the old papers Drude and so on. But then, at that time, whenever people had the spectral line of an atom, they were, of course, forced to explain it by assuming an harmonic oscillator which just sent out this line. That is very much like nowadays that people always must assume a new elementary particle whenever a new resonance state is found. Then the followinc thing happened. The first experiments on the anomalous Zeeman effect were published, and there was the old Professor Woldemar Voigt in Gottingen, and that was in the year 1913; that is even before the Bohr theory was known. But he thought, "Well, couldn't we understand this anomalous Zeeman effect in the sodium just by means of dispersion relations; that is by puttinc in harmonic oscillators and making coupling between oscillators in such a way that one Lets them out." So, what he did was this: he assumed two oscillators for the two sodium lines, D₁and D₂, and then he invented a good kind of coupling — some kind of linear interaction — so that when he now introduced the macnetic field, he would get the anomalous Zeeman effect. Not only that, but he also succeeded to such an extent that at very hich fields he would :et the Paschen-Bach effect. ... So he had published a paper, and of course, that paper had been completely forgotten. Then in '20 or '21, perhaps it was '22, Sommerfeld again asked me, "Well, there is this old paper of Voigt, who gets such very complicated formulas for the transition from small magnetic fields to big magnetic fields. Would it not be possible to put these formulas into formulas for levels?" So for some time we worked together on the problem, but then Sommerfeld continued alone, so he published a small paper just translating Voigt's old paper into the language of the level scheme, and actually it did work. So for this problem now one had, on a purely phonomenological basis, a level scheme with very complicated dependence on magnetic fields — you know, long square roots of h², coupling squared, and so on, and also very complicated formulas for the intensities. Then in 1926, when the quantum mechanics was there, I wrote a paper with Jordan, and we said, "Well, now we two have to solve the problem." We took just ordinary quantum mechanics, and you know what came out? We got exactly the formulas of old Voigt, you know, with every square root and every detail both for intensities and for the levels and everything else. Now, you say, well, that's a miracle. What has happened? But it's quite simple, the point is, what does a man do when he writes coupled oscillators? He writes down a set of linear equations — several linear equations with several unknowns. What do you do when you write down a secular determinant in quantum theory? You write down a set of linear equations — well, that's all. That's just all, and so if you make it right on both ends, you just can't avoid making it right also in the middle. So it was quite obvious. But also even in the intensities, everything comes out exactly as old Voigt had calculated it by means of dispersion theory. So this is, on the one side, an enormous argument in favor of successes of dispersion theory; on the other hand, of course, it also shows the limits of dispersion theory because old Voigt would not have been able to find Bohr's theory in such a way of doing it. That was a very exciting thing in the old times.