Werner Heisenberg - Session XII

Kuhn:

This time, I think,we will stick to electrodynamics. I gather now, through things I've learned since talking with you before, that the last section, both in the Born-Jordan and the Born-Jordan-Heisenberg paper, both came from Jordan. I wondered how you and Born felt about the issue of field quantization as it emerged in those papers.

Heisenberg:

Well, I couldn't say how Born felt about it, but I can definitely say what I thought about it. I felt a bit uneasy about it, not that in principle I had something against it, but I felt that bringing in radiation is bringing in a new thing, that is, the Lorentz group; that I felt was something dangerous, something new. So I was not too happy about it but still I saw he had really some point he could bring out and so I thought that it was all right that it came into the paper. But to begin with, I always had the impression that the bringing in of the Lorentz group, that is, going from non-relativistic to relativistic things, meant such a change that one could not be quite certain that one came to the right result.

Kuhn:

But was the derivation of the Planck formula through the Hohlraum argument in the second of those papers impressive?

Heisenberg:

Yes, I think it was impressive, especially the fluctuation term. I remember that already in the old times Einstein had always made a point of these two terms in the fluctuations and he could always say that the first term was classical theory and the second term was quantum theory. I found it very impressive that these two terms now came out in one formula. So far I was happy about it and therefore I approved that it should be in the paper.

Kuhn:

Well, how much difference did Dirac's '27 paper, the emission and absorption paper make to this feeling about the quantization of the field?

Heisenberg:

Well, first of all it was certainly an interesting application again and in some way I felt that it was a bit elaborate. I felt that perhaps one could do these things slightly more easily. I don't know whether you remember that I wrote a paper then in which I tried to do things still more easily. At the same time I saw that if one really took this problem up seriously, then one should take care of the Lorentz invariance in a rigorous and very general manner. As soon as I thought about this side of the problem, then I realized that I was not satisfied with Dirac's papers because then I felt that the introduction of a Coulomb field, besides the light quanta, was ruining the Lorentz invariance from the beginning and then I felt it was very difficult to get it backwards then from the end. Actually later it turned out that Dirac's treatment was perfectly all right even from the point of view of the Lorentz invariance, but that one couldn't see at that time. But as a practical tool to calculate the probabilities and so on, I was perfectly satisfied. I thought that Dirac would certainly get the right results.

Kuhn:

What about this basic element in his papers of managing to treat the electro-magnetic field as a collection of Bose particles, dropping right out of the wave equation?

Heisenberg:

Yes, well, that was already present, I should say, in the older papers by Einstein and especially also in Jordan's part of the Drei Manner Arbeit, so this didn't impress me as something very new. I was impressed though by the way in which he brought out the result of the old Einstein paper of 1918 — you know, the spontaneous emission, induced emission, and induced absorption and so on. So to get these three terms in such a nice way as a consequence of quantization, that I felt was very nice.

Kuhn:

I'm surprised about what you say about this being present in the Einstein papers and in the Drei Manner Arbeit because although certainly the treatment of photons as particles had been in the Einstein work in particular, this showing the equivalence of the wave equation to the straight electromagnetic treatment is something I think nobody had really gotten at before in nearly that way.

Heisenberg:

Could you say that once more. I couldn't quite get your statement.

Kuhn:

Dirac starts out by setting up what he calls the straightforward problem in which he introduces the field as a perturbation initially.

Heisenberg:

Perturbation between the electromagnetic field. He sets up a Hamiltonian as far as I recall, Hamiltonian consisting of an electric field here and then interaction and then the atom, yes.

Kuhn:

He indicates the route one will take to solve the problem this way. Then he introduces variables which are numbers of photons at various frequencies, treats these strictly as particles, and then shows that if you say that they're Bose particles, you will then get exactly the same result as you get by the straightforward perturbation treatment in which the only way the 'n' gets in is in terms with the amplitudes of the components in an electromagnetic field. This is an elaborate and surprising and I think brand new result except to the extent that, I gather, Jordan had been anticipating bits of it.

Heisenberg:

Well, that's just it. In some way I should say the result itself was, so to say, in the air already. Everybody expected that something of this kind would come out and since the light quanta come out by quantizing the electromagnetic field, the 'n' one understood, "Well, after all, if I set up the interaction between the electromagnetic field and particles, then this whole business will come out." So it was not so surprising. It was surprising to me that he could do it in such a straightforward manner and I think, if I recall correctly, he just wrote down the total energies, the sum of all light quanta energy, n times h nu, and then there was an interaction term which he formed from the electromagnetic field times dipole moment, and that was all there was to it and the rest was just straightforward calculation. That seems to rather simplify the matter but apparently with great success.

Kuhn:

Was there any strangeness about using as variables the total number of photons at a given frequency or in a given state? This transformation to n and theta as variables.

Heisenberg:

Yes, n and theta as variables — that was quite a funny thing to do, yes. That was a bit unexpected to begin with. That was a new type of variable. That's quite true, theta being such a phase variable. Well, how was it in time. Which paper followed the other one? You know, there was this paper of Klein-Jordan-Wigner.

Kuhn:

That's later. That's a full year later.

Heisenberg:

That's one year later, I see.

Kuhn:

In fact, in detail, think it's just over a year later.

Heisenberg:

So that n and theta business was for the first time in Dirac's paper. Yes, I see, ja.

Kuhn:

There's a background to this question which I hoped I might not bring out at first. Jordan remembers a conversation with Born about the Dirac paper in which Born was really quite puzzled and didn't know quite what was going on and thought it very strange. Jordan said to him, "But look, this is just the thing that I have been saying all along we should do, which is to quantize the wave function." Now I think Dirac, when he wrote the paper, did not think he was quantizing wave function. So there is a very strange way in which there is a switch of perspective on this paper which can be read either as a transformation of variable paper or as a quantization of wave function paper.

Heisenberg:

But I think Dirac must have thought of the quantization of waves in the following manner. He must have written down somehow the interaction term between the electromagnetic field and particles. Now this interaction term he can only get from the classical interaction term which is wave potential A times the current. So he must have had some occasion to transcribe the product of potential times current into something like square root of the number of light quanta times current, or something like that. Now this process he must have done.

Kuhn:

When I say he doesn't think of it as quantizing, I don't mean he doesn't think of it as quantizing the electromagnetic field. I mean he doesn't think of it as a process of quantizing a wave function.

Heisenberg:

Oh, I see, a matter wave function. No, no.

Kuhn:

Or even something that is the Schrodinger function for the problem, whereas it can also be regarded as that one. The coefficients which show up could be taken also to be wave functions.

Heisenberg:

No, I agree. He would not have thought of that. Yes, that I also would feel, yes, yes. He only thought of the quantization of the electromagnetic field. And the other story, that is only when Klein-Jordan-Wigner took it up, yes.

Kuhn:

Do you remember from that time any discussions of that paper with Jordan, with Born, with others — this Dirac paper. I think there's a turning point in the development in-between the paper and —. Jordan takes it up first in a little paper in which he does the same sort of treatment for Fermi particles. There's a mistake in the paper, but this whole idea of this transformation of the Dirac approach into a more general quantization of wave approach is in that early Jordan paper.

Heisenberg:

Well, I'm afraid I remember almost no discussions on these things. I'm sure I did discuss it with many people and I was very interested, but I think any statement I would make at all would be wrong. It's no use making statements which I am not rather certain of.

Kuhn:

I'd hoped perhaps this might bring something out in this area, but it certainly doesn't need to.

Heisenberg:

Well, I should perhaps say, this electrodynamic side of the question didn't at that time excite me very much. I thought, "That's all right," and after Jordan's first paper there on the fluctuations, I felt that, that would more or less work that way. But I was somehow excited about the idea of quantizing the Schrodinger waves but that was on account of the problem of interpretation. That was because I was very upset by this idea of Schrodinger that you could come back to a classical wave picture. Then I found it extremely nice and suggestive that one could actually use this three dimensional wave picture of Schrodinger, but one had to quantize it again. So this was the whole point. From that moment on I understood or felt I understood the whole game. Schrodinger is quite right. He may be allowed to draw this kind of wave-mechanical picture as an almost classical picture but at the end he has to quantize his waves. So he has really introduced the h in a very serious way. Therefore, I found these several papers of Klein-Jordan-Wigner extremely satisfactory. Not so much for the formal side of it, this quantization of Fermi statistics — that was a more mathematical point which didn't excite me too much. But the fact that one had to quantize even the Schrodinger matter wave if one took them as being material three dimensional waves, that did please me.

Kuhn:

There's the Jordan-Klein paper first, and then the Jordan-Wigner paper a bit later. I gather from some of the people I've talked with that initially that whole approach was quite distasteful.

Heisenberg:

Well, I don't know. Well, not to me. I didn't mind. I found it was quite nice.

Kuhn:

Pretty much from the start, you think.

Heisenberg:

Well, yes. You know, after Schrodinger's proof of the equivalence of wave mechanics with quantum mechanics, I felt, "Well, this mathematical formalism is in so far rather different from earlier formalisms in science, that it seems to be extremely flexible and may take on very different shapes." Therefore, I was not too surprised that it should also be put into this new shape which Klein-Jordan-Wigner had given to it. So I didn't find it distasteful. But I think you' quite right that some other people didn't like it. But I did like it.

Kuhn:

Do you remember talking about it or arguing about it with people? Pauli in particular or others.

Heisenberg:

Well, certainly I have spoken about this with many people. I know I had many arguments when people spoke about second quantization and I always tried to emphasize that there is not a second quantization. That is first quantization. There are different pictures which you may quantize, but you have to introduce the letter h just once and that is where you introduce this whole notion of probability and Hilbert space and so on. That you have to do, either in particle picture or in wave picture.

Kuhn:

In what sense do you only introduce it once? You've got it in the Schrodinger equation in the first place and then you introduce it again with a commutator.

Heisenberg:

No, I wouldn't agree to that. I would say that if you have a three dimensional Schrodinger equation and you just speak about matter waves — let's speak about history now for a moment. Let us assume that nobody had ever seen an electron as a point charge, but actually, just by some luck, people would first have had the radiation from a cathode and would have seen the interference pattern. Then, of course, they would perhaps have been able to discover the Schrodinger equation but then they would have introduced the letter h squared over m as a new constant, characteristic of this thing. So h squared over m is a characteristic of this wave. But not h and m separately. In that sense I would say that you haven't introduced a real discrete nature of the thing. The real discreteness comes about when you introduce h and m separately.

Kuhn:

When did arguments of this sort go on? Clearly this sort of question is one you must have spoken to very nearly at the time.

Heisenberg:

Oh, yes. Certainly, but I certainly have spoken about this with Pauli and also in my seminary and so on. But I don't recall any special discussion about it. I only remember that I got angry whenever I heard the word 'second quantization' and I always protested against it.

Kuhn:

Do you know where the word comes from? It probably comes from Jordan, but I don't know where. It isn't introduced in any paper that I've yet read.

Heisenberg:

Is it never used in papers or does it occur —.

Kuhn:

I haven't read enough of the quantum electrodynamics papers to be sure. It is not in the early papers. It is not in the Klein-Jordan-Wigner paper.

Heilbron:

What did Bohr think of that argument? I'm thinking in particular of his later argument against the Peierls and Landau where he says m has got nothing to do with quantum mechanics. So I wondered, this argument now sort of depending on some relationship between h and m, what Bohr would have thought about that.

Heisenberg:

I don't really know. It's so long ago. Of course, we talked forth and back about these things. I know that to begin with I made some effort to explain to Bohr that these papers of Klein-Jordan-Wigner were just a very good illustration of what he wanted with the complementarity because then there was a complete symmetry between waves and particles which had been up till that paper because only then you could really say, "Here we have waves, namely three dimensional waves, and here we have particles, three dimensional particles, and we have to quantize both and then they are the same thing." So the symmetry was complete only after these papers. Well, Bohr perhaps in the first moment did not feel exactly that way, but I think later on he saw quite well that this was an illustration that he wanted.

Kuhn:

Right about this time one gets the Dirac equation, and the hole problem. I just wondered whether there were any conversations about that or reactions of your own about the Dirac equation?

Heisenberg:

I remember when I heard it for the first time that it caused a great excitement among all those who were present and also in me but in some way I felt a bit uneasy. First of all, I felt it was a kind of magic, just by taking the square root, to get the spin and everything out of it, and then at the same time I was very much afraid of the Lorentz group. I felt that this is now —. Well, I would put it this way. Up till that time I had, had the impression that in quantum theory we had come back into the harbor, into the port. Dirac's paper threw us out into the open sea again. Everything got loose again and we got into new difficulties. Of course, at the same time, I saw that we had to go that way. There was just no escape from it because relativity was true. But I had the strong feeling that this introduction of the Lorentz group introduced very new features.

Kuhn:

Well, now you say you got into new difficulties and new problems and the whole thing loosened up. What problems were clear at the start and then —.

Heisenberg:

Well, clear was only that by means of quantization of waves you could get particles. That seemed to be clear, I mean. In so far it was reasonable that one could quantize electromagnetic waves and one would get the light quanta. That was all right. But then there was already some difficulty with the Lorentz condition ..., so the relativistic formulation of electrodynamics was not too easy. It was easier in classical physics than it was in quantum physics. Well, in later years one learned that this difficulty was already quite serious. Well the best way nowadays to describe the mathematics is to use the indefinite metric, I mean, this Bleuler-Gupta business. At that time, of course, nobody would have dared to introduce an indefinite metric because it would upset the whole scheme of probabilities and so on. Therefore, in some way, you felt that you came into troubles somewhere. Already there it was a bit artificial to do the Lorentz condition without introducing the indefinite metric. Well, finally Pauli and I succeeded in replacing it by some symmetry argument, but again it was a bit funny. You could not say that the fourth Maxwell equation is not a rigorous operator equation, it's only a supplementary condition to the —." Well, you know. It came into the region of the "Ausrede."

Kuhn:

But that's moving an awful long way ahead. The negative energy problem in the Dirac equation need not initially have seemed particularly bad because after all it existed in the classical case also. And it existed in the Klein-Gordon equation. The question as to how that built up as a difficulty and in what other sense one felt cut loose and in trouble with the Dirac electron —.

Heisenberg:

Well, there I believe that I remember only vaguely a discussion with Dirac when Dirac tried to explain to me that this difficultly was really much worse than the classical theory. In the classical theory it was no difficulty because you could just forget about the negative energies and in quantum theory, he explained to me that, since one has quantum jumps, you may jump over from the positive to the negative energy. And this made some impression on me but my reaction would always be, "Yes, you see how dreadful it is when you introduce the Lorentz group." Still one couldn't help it.

Heilbron:

Perhaps this Klein paradox made a big —.

Heisenberg:

Yes, the Klein paradox was a most interesting illustration of this situation and one could really see that one could jump over —.

Heilbron:

It would seem that, that was a-point —.

Heisenberg:

Well, that was already some years later. Then, of course, we tried to work with the Klein paradox and see what actually happened. But that was when we had the hole theory.

Kuhn:

Dirac's own version of the hole theory where there are protons no, that one we have talked about. Let me ask you then what you could tell me about the origin of the Heisenberg-Pauli paper. This is your first deep involvement with this set of problems and I wondered how you had come back to them, how you had worked with Pauli.

Heisenberg:

Well, I remember that it came like this that I had, of course, discussed this matter frequently with Pauli and I had tried to explain to him, or he to me — that I don't know — that quantization of the waves is a difficult thing in many aspects. First of all, you get the Lorentz group, which is disagreeable. But then also you have to quantize continuous variables of space and time which is something very different from quantizing the discrete things. And we felt that we had not a good mathematical formalism by which to deal with the thing. We felt that the Fourier analysis business was a bit artificial and not very satisfactory. Then I remember quite clearly that one day I got a letter from Pauli, who apparently at that time had been in Italy. He wrote to me, apparently I have just had a discussion with some Italian mathematicians and they had explained to me that there has been an Italian mathematician, Volterra," whether he was alive or not at that time, I don't quite recall, "and Volterra had invented a new formalism called functional formalism, that is, the function of a function." Then he said, "Now I think we could do the quantization in a much more rigorous manner because by using these functionals one can really get some good mathematical tools for doing it." So he asked me to participate in this study of the Volterra mathematics. Then I wrote back to him that Volterra's papers were a terrible difficulty and I wondered whether I would ever understand it, but still I had grasped from his letters the general idea. So I played around with it and wrote to Pauli some results, what I thought would probably come out of the formalism, and then it turned out that this was actually what happened and we agreed on it. So gradually we came to the idea, why shouldn't we write a paper together. But then we got into difficulties with this Lorentz condition and we had to make all kinds of funny efforts, limiting processes, first introducing — I don't know what we did. But we both felt that it was very much a kind of "faule Ausrede", but we couldn't do it any better. Then I think we had a discussion with Fermi, who had written a paper where he did the whole thing very much simpler than we, and then we also felt that even if we do it in our own way and follow our first paper, then we can improve the whole situation considerably by speaking about in variants for the gauge group. And so we wrote I think the second paper which was better than the first, which was the origin of conservation laws in such a field theory. We introduced the condition divergence of E is equal to 4 rho as a consequence of a gauge group. After the second paper we felt that, that is at least formally all right. Formally, it seemed to be as it ought to be. We had not yet realized that by the local interaction you introduce all the kind of trouble which later came out by Weisskopf's paper, and which was decisive then. So in that time I would describe my own attitude in this way. I thought that formally this problem of wave quantization in quantum electrodynamics is now solved. But still, this doesn't look too good in many places. So I didn't feel too easy about it. I felt that it was artificial some places and I wondered whether this would really work. So I doubted it but still I felt it was consistent; you had to do it that way, but I wondered what would come out if you really applied it. So I was not at all surprised when just a short time later Weisskopf discovered that the self energy of the electron just went wrong.

Kuhn:

This is hard for me to understand. The Weisskopf paper is '34, The first of the Heisenberg-Pauli papers is '29 and the second is '30 or '31. Oh, they're both '29. Now you do get at least the two infinities in that paper already. You get an infinite self energy term and you get an infinite zero point.

Heisenberg:

Yes, but the self energy term — that was not decided yet whether that was infinite. I don't know. How was it with respect to the hole theory of Dirac?

Kuhn:

There's no hole theory used in that —. No hole theory available. It comes a year later and I think when it comes you don't believe it, in the absence of the positron. So the question as to how you felt about these initial infinities —.

Heisenberg:

Well, certainly the way that something is still wrong, but of course at that time you could imagine that you get rid of the infinities by introducing a finite radius of the electron like in classical theory. Certainly, one wasn't so far advanced that one had to worry too much about these things. Still, one felt that it's not as good as the quantum mechanics had been. It's not as finished, but still it seemed consistent. Well, yes, there was the riddle with the negative energy states which had not been discussed properly yet. Then when the Dirac paper came about the holes, we certainly did not believe about the proton. The proton was too odd to be believed. And the positron didn't exist. But if one should believe in the holes, then that they should have the same mass as the electron — that I should say was almost clear at the beginning. I remember a discussion in our Leipzig seminar about such problems, but we always felt a bit uneasy about these things. It's very difficult to describe that state because it was psychologically so different from the state in 1923 or '24. In '23 and '24, one knew that there were difficulties and one also had the feeling that we were quite close to the final solution of these difficulties. Just one step and we will be in the new field. It was as if we were just before entering the harbor, while in this later period we were just going out into the sea again, that is, all kinds of difficulties coming up and really one didn't know where it would lead to and even if new and good ideas came up, these ideas would work a short way and then again one had new difficulties. It was clearly seen that this was now an entirely new story. So nobody expected quick results at that time.

Heilbron:

May I ask a bit about the history of your paper with Pauli. For instance, when did you decide to use a Lagrangian approach and so forth?

Heisenberg:

Well, that I think would come very natural because classical mechanics was always set up by means of Lagrangians and then we had learned how to quantize as soon as we started from this classical scheme. I mean we had learned in quantum mechanics to quantize a theory which was set up neatly according to the textbooks on classical mechanics. And the textbooks say first you write down your Lagrangian, then you form your p and q and then you have your Hamiltonian and so on. So our intention was, can we not repeat just the same game. And we felt that if we do that, then we are on the safe side and then everything will come out all right. So our first attention was bring electrodynamics into a form which was practically identical with classical mechanics. That could be done by means of this Volterra formalism. Therefore we were so fond of the Volterra formalism.

Heilbron:

You carried out this by correspondence, did you?

Heisenberg:

Yes, largely. I think we met occasionally, once in a while, and then would discuss it, but I think it was mainly by correspondence. I definitely remember a letter from Pauli when he explained the Volterra formalism and he knew that he would vary the wave function by a delta function and he drew nice pictures there. So I know that I learned from him the Volterra formalism which looked very natural as soon as one had grasped it almost familiar, as a most natural extension.

Heilbron:

Did you find that other people grasped it so simply? Did people have trouble with that part of the paper?

Heisenberg:

Well, that may be. Functionals are more disagreeable. Yes, well it was more difficult than ordinary differential equations, of course, yes. I don't think that was so disagreeable, no. And our definite intention was to say that we must make wave quantization as similar as possible to quantum mechanics because in quantum mechanics we really know what to do. That's a clear scheme and that must work. Therefore, if we do just the same thing in wave mechanics, then we will get the right wave quantization and it will also work. That was our optimism. This optimism was not justified, as we know later on, but at that time it was a natural thing to try.

Heilbron:

You would say that when you had completed the paper, your main dissatisfaction were things like introducing epsilon and the delta —.

Heisenberg:

Yes, epsilon and the infinities and all that kind of stuff, yes. Well, the negative energies were of course in our mind. We knew that from Dirac, so we felt that this whole thing is preliminary but still it's a natural step to take.

Kuhn:

You speak of the '34 paper of Weisskopf as being sort of crucial in this development. It doesn't surprise me that at this point it should be cited as the one that finally established the point, but one suspects that there was perhaps more intervening discouragement that this one seemed to cap, and probably also people who thought that this still wasn't necessarily the final answer.

Heisenberg:

I should perhaps add that when Weisskopf wrote the paper —. To begin with we thought that probably one would have to introduce a radius of the electron anyway and then we get into all the old trouble of classical theory. Then we saw Weisskopf almost had succeeded to get the final answer because a logarithmic divergency is almost no divergency. So it was a bit funny that he got very near to the goal but just had to stop half a meter from the goal. That was a bit funny, but still it was infinite and one couldn't doubt it and one didn't know what to do about it. Definitely one saw that this local interaction is something very, very disagreeable. Then, of course, Pauli and I had seen from the very beginning that such a local interaction in a wave theory is something very much more disagreeable than the non-local interaction in quantum mechanics.

Kuhn:

There is a previous paper by Waller, I think, that also gets an infinity.

Heilbron:

Then, of course, Landau and Peierls in their listing of grievances against the current theory are particularly hard on infinities and that was '31.

Heisenberg:

'31, I see, yes. Well Landau and Peierls had a quite interesting way of doing it. Still it was a very mathematically ugly paper. There were very clumsy formulas and not nice to work with.

Heilbron:

I'm thinking of — what is it called — 'on a new uncertainty in the electrodynamics.' No, I don't mean the one where he uses Maxwell's equations to get a wave function for the proton.

Heisenberg:

No, that other one I simply don't recall. No.

Heilbron:

That was the one that was supposed to have inspired Bohr and Rosenfeld. Oh, I see, yes, yes. Well, the Bohr and Rosenfeld paper I felt was a very natural consequence of all these mathematical connections. That appealed to me as being a natural way of interpretation, also perhaps a bit too complicated and too elaborate.

Kuhn:

It is your sense of the situation that, that Weisskopf paper was the one that sort of finally put the cap on this?

Heisenberg:

Well, I would say that it sticks in my memory as the one which was final in that respect. Whether that is stressed or not I am not quite clear. But for instance also here in my lecture I did quote it as a decisive paper.

Heilbron:

Do you at all recall this paper by Wentzel in '31 or '32 where he tries to eliminate the infinite self energy in the classical theory by some vague way of taking limits, and at least Wentzel had the hope that one could operate similarly on quantum theory?

Heisenberg:

Well, I don't recall the paper. No, it didn't make much impression. Well, there are so many attempts published, I think, in any stage of physics where people try to get rid of the difficulty by "faule Ausrede" and certainly also Pauli and I did that scheme. It's unavoidable, but still, when one reads other papers and one has a definite feeling that that is "faule Ausrede," then one doesn't like to go into it. That kind of thing where Pauli would say, "Das ist nicht einmal Falsch."

Kuhn:

Turn now from the infinities and the quantum electrodynamics problem. At what point did you really begin to involve yourself with the nuclear problem. That is, I think your first real paper in this area is again '32. But that comes so quickly after the neutron — you must have been thinking and worrying to some extent about these problems earlier?

Heisenberg:

Well, the main reason was that I was worried about the existence of electrons in the nucleus. I didn't like the electrons in the nucleus. It's difficult to say why. I think it's mainly the Uncertainty Relation. When you have an electron in the nucleus, then this electron must have a pretty high momentum and somehow I felt that there was no force which could keep the electrons in the nuclei. Yes, it was something like the Klein paradox again. If I would invent a force which was so strong as to bind an electron in the nucleus, then this force would really just produce pairs of electrons and positrons all the time and would not keep constant. So I felt it was something very odd to fix electrons in nuclei. On the other hand, one could see the electrons coming out of the nuclei so everybody was convinced that the nucleus consisted of protons and electrons. But when the neutron had come, then I saw that the neutron may be something which is really not a proton plus electron but which is something of its own, and is more related to the proton. So the neutron exactly fitted with my hopes. So I said, "Well, then it's obvious that all nuclei must only consist of protons and neutrons. Then we have pushed the problem of the electron just back to the neutrons. Then, of coarse, we have to understand why a neutron can be something small as a proton is and why it can emit electrons and so on." But I remember that I had some heated discussions with my assistant, Guido Beck, or former assistant, not my assistant at that time. He was in Leipzig at that time. But Guido had written a paper on the nuclei and he had engaged himself in the idea that there are electrons in the nucleus. So when I stated that electrons are not in the nucleus, there are only protons and neutrons, he was quite angry about this and he told me, "Well, you rain the young generation by telling them that there are no electrons in the nucleus and after all, the electrons are there and you can see them coming out." So we had once a very heated argument about it. Well, I had hoped that something of this kind would come out and of course then it was also necessary to make the neutron something of a brother to the proton. Not to say the neutron is a system consisting of protons and electrons. I would rather say the neutron is just a proton without charge. So I came to this isotopic spin business at that time.

Kuhn:

Prior to the neutron, had you felt reasonably clear that there was going to be a way through the problem of the electron, that would still satisfy quantum mechanics, or did it seem more to you that one might have to have here a whole new formalism?

Heisenberg:

Oh, you mean that one should come through the nucleus with quantum mechanics if one could forget about the electrons or have I not understood your question?

Kuhn:

There was I think current here and there at least, I think Bohr had it, the notion that the problem of the electron in the nucleus was itself a problem so fundamental that one would need a theory perhaps as different from quantum mechanics as quantum mechanics had been from classical.

Heisenberg:

Yes, I think there was something in it. As I said before, to keep an electron in the nucleus would be a dreadful affair from the ordinary point of view of quantum theory. Therefore, if actually there were electrons in the nucleus, then probably you would have to change everything again. So I was extremely happy to see that this was not necessary. And as soon as one could avoid the electrons in the nucleus, then one could see that at least one could get quite a long way by using only quantum mechanics. Because a quantum mechanics of neutrons and protons, that would work all right. At least one could hope that it would work all right. Then the real trouble with the Uncertainty Relations was avoided.

Kuhn:

What about the problem of the continuous beta spectrum? I think Bohr in particular said that this was a violation of conservation of energy.

Heisenberg:

Well, of course, that I only watched at a distance. Pauli told me about his views. Pauli was always very skeptical of Bohr's attempts to violate the law of conservation of energy. So when we spoke about it, Pauli always made critical jokes. Well, of course, he could not object to Bohr's arguments because there you have the continuous spectrum but one could see that he would prefer to do it some other way. I don't recall exactly at what time he told me about this neutrino, but when this idea appeared, it was clear that this was at least a very definite possibility which one should take seriously. Was the neutrino paper of Pauli in 1932?

Kuhn:

It's almost impossible to date that one. It had been talked about for at least a year and a half before it ever appeared in print. I've got a very elaborate chronology of people remembering Pauli's talking about it at a variety of meetings, I think the first of them at Cal Tech. It doesn't get into the published literature —.

Heisenberg:

Was Pauli at the meeting in Rome in 1931?

Kuhn:

I'm not sure.

Heisenberg:

Well, that would be an interesting thing to decide because it may be that Pauli had told me about his ideas already at that meeting. But I'm not sure about it.

Kuhn:

I certainly think that the idea had been discussed among physicists before 1931.

Heilbron:

When was it clear that the maximum energy of the decay particle was equal to the difference of the nuclear energies? There was some experimental —.

Heisenberg:

Yes, yes. Yes, that was a very interesting experimental indication of the situation.

Kuhn:

I've looked at the Mott and Ellis paper, but I can't think now where in the devil it is. But I'm particularly interested in things that may have been said about —. Bohr recurs so often to this notion that energy may not be conserved, one almost gets the sense finally that he hopes that it isn't. This hints at a more fundamental reason than experimental difficulties. Do you have any ideas what that was about?

Heisenberg:

No, I don't. No, I don't know. That's a very interesting question concerning Bohr. But I really don't know. I remember his first discussion in connection with the Bohr-Kramers-Slater paper and there he had a real argument in it. Because at that time one really could not understand the dualism so he had really a strong argument.

Kuhn:

I've looked at only bits of the correspondence, but there's some correspondence quite early with Dirac about electrodynamic problems before 1930 in which again Bohr thinks that we're going to have to get along without conservation of energy and Dirac says no, we've got some problems that we haven't learned how to set up yet.

Heisenberg:

Have you asked this question to other physicists? I think it's a very interesting question, but I do not know any good answer. I wonder if any of Bohr's other good friends would know an answer. Why did he so frequently come back to the idea that energy might not be conserved? That's a very interesting point. After all, energy is not any better or worse than momentum or angular momentum and he never doubted any of these other conservation laws so far as I know. So it's quite funny that he would always come back to that. Did that come from his interest in thermodynamics where energy plays such a predominant role?

Kuhn:

It may.

Heisenberg:

You know he loved Gibbs, as I mentioned today, yes.

Kuhn:

Incidentally, I'd be very glad to have this on this record also because this statement about his strong preference for Gibbs — I take it that he felt that Gibbs had seen what this was all about in some sense in which Boltzmann had totally missed the point.

Heisenberg:

Yes, that was Bohr's definite meaning. Well, he asked me, "Have you studied thermodynamics?" And that was very early, I think in one of the first weeks I came here and I said, "Well, I have studied my lectures with Sommerfeld." And it turned out that he had followed more or less Boltzmann's line. Then he said, "Well, you know that is all really not understood. That's not the real point. You read Gibbs and there are these chapters in Gibbs' book and that is really everything that can be said about thermodynamics." And this view was very different from the view I had learned in Gottingen or in Munich. Because all these other physicists always felt that the canonical ensemble was something dreadful, I mean an ensemble of things which didn't exist, of which one example existed and all the rest was just imagination. That was, for most physicists of that time, something which was extremely disagreeable, but I have in the course of time very well understood why Bohr had such an emphasis on this point. As I say today, Bohr emphasized the complementarity between temperature and energy to the extreme. He said, "As soon as I know the temperature, then the concept of energy has no meaning. I mean this is just one example of a canonical ensemble which means that I do not know the energy. So either I can know the energy or I can know the temperature, but I can never know the energy and the temperature. So that temperature came in some way to be a concept concerning our knowledge of the thing, because a canonical ensemble defines our knowledge. And the great paradox both for Bohr and for all of us in this discussion was always how can a concept, which in some way means our knowledge of something, be an objective property of the thing. So we say this thing here is of a temperature of say 20 degrees centigrade. This seems to be an objective statement. It definitely defines what this thing does. On the other hand, it defines, according to. Bohr or according to Gibbs just a statement about our knowledge of the thing because it is just one piece of a canonical ensemble and we don't know more of this thing than just this one property. That is really a very deep paradox, and I'm sure that if Bohr had listened to our discussions with Delbruck he would also have said this introduction of a new concept is something very fundamental and it cannot be over-emphasized. While most physicists have the tendency to play it down and say, "Well, it's not so important, we may use this or that concept," and so on. So one can really not understand Bohr unless one really understands this deep liking for Gibbs.

Kuhn:

Well, clearly in the earliest discussions that you had with him of this, there was no notion of complementarity in anything like its later form. Can you remember at all the sort of thing he would have said before he had?

Heisenberg:

That's very difficult. That's more or less imagination what I say, but still, when he spoke about Gibbs, he felt that it was such a reasonable step to take to introduce some paradox to the very beginning. Simply to say, "Let us, to begin with, not start with statistical averaging in time or such things but let's say we start from pure imagination, that this thing here is only one piece of an infinite number of similar things. Then let us study how this thing will behave if we stick to that notion and say we define a modulus of canonical distribution. Then, of course there comes these famous arguments of Gibbs about what happens if I have two such objects and they touched each other." That Bohr always liked to say was real physics, that one finds out that if one once had started with this concept of the canonical distribution, then everything comes out as it should be or as it experimentally does. Never in physics can you do anything else but that. He would say that it's like old Newton, that Newton would write down just as a kind of trial, mass times acceleration is equal to force and then how far can we get with it and then actually we can get everything out of it. But we have to put it down on paper once and introduce concepts which we either fetch from empirical facts or we fetch them from nowhere, but still we must state something which to begin with is new or paradoxical or unexpected or whatever you may say. Only when we have made such a step, only then we can go on and explain. Therefore, I'm sure that he would have said in this discussion today, "This introduction of the concept of information is something essential in biology. And one should not try to play that down, and say, 'Well, that's all right, information (is in the computers and so on)'. It is decisive that we are false when we want to describe life, we are false to introduce such entirely new concepts." So I was quite happy about the discussion today.