Eugene Wigner - Session III

Kuhn:

I had asked you yesterday about the question of sympathy for the Schroedinger interpretation. You said that for you and for those you knew, at least best, there was no question from the beginning that it was a probability function of some sort, that it was not to be taken literally as an electron wave and that the packet was not to replace the electron. This is really only the first question in a whole area of questions that we haven’t explored about the new interpretation. For example, there is a particular series of papers: the Born scattering paper; the Dirac and Jordan transformation theory and this more basic probabilistic grounding of quantum mechanics; the Heisenberg uncertainty principle papers; this whole group. I would like it if you would tell me what you can of your own recollections about this area of debate, of puzzle; who was worried about the question of the interpretation of the wave equation, this sort of thing.

Wigner:

I don’t know whether I have a consistent story on that, I remember very clearly that, as I said yesterday, my feeling was always that the Schroedinger equation gives a Fuehrungsfeld in configuration space and as a matter of fact, I thought that that was an interesting and important recognition. It wasn’t the habit in those days to publish papers on semi-philosophical questions, so I sort of knew that and kept it to myself. However, when Heisenberg’s paper came out it was a revelation.

I don’t know why and I can’t really understand why, but suddenly I felt that all those problems which bored at us such as, ‘why does the electron come out right away in the photoelectric effect’, ‘what is the resolution of the old puzzles’, ‘how is the angular momentum transferred to the atomic beam’s constituents’—all those questions immediately solved. Why it so clearly gave me this impression I can’t reproduce. I know that I realized that many of the concrete statements in Heisenberg’s paper did not hold water.

I don’t know, but I also remember that when I read it I felt, “Now isn’t this wonderful!” I picked up the telephone and telephoned Szilard, saying, “Szilard, we can go to sleep,"—these were my words, in German of course—”Heisenberg has solved the problems.” This is a massive statement, and I can’t quite reproduce the motivation for it any more.

Kuhn:

This would indicate that you and Szilard at least had been actively talking about these puzzles. Were there others involved in that?

Wigner:

At that time nobody else to my knowledge was in Berlin; but we were of course in a way in the shadow of Einstein. I never understood why Einstein was so opposed to the statistical interpretation, except possibly you are emotionally opposed to an interpretation it you almost had it and rejected it because you did not find it quite right. I think many people went through such an experience, and this is my interpretation.

In addition, Einstein I think also realized more clearly than I did at that time that there is some fundamental difficulty left because you can’t establish such a decisive epistemological and even ontological picture without going much further. The way I now put this statement is that quantum mechanics only yields statistical correlations between successive observations. Now this is so much a mental statement that it seems somehow unfair to make such a mental statement about part of the human mind without having any knowledge about volition, desires, and so on. It’s no theory of cognition. I think this was at least partially in Einstein’s mind. He always said, “How about the sun? Is that also a probability amplitude?”

Kuhn:

Did he say that in this period when you were still in Berlin?

Wigner:

No, he did not. I did not see him very often at that time. You remember he had a heart disease.

Kuhn:

A heart attack.

Wigner:

He was in bed a long time and during that time, and even afterwards for some time, he did not see many visitors. I was quite taken aback when Pauli once came to Berlin and said, “I am now studying Born’s paper on collisions and I am making it so that the mathematics should become entirely obvious to me because then I will understand the physics.” I am sure that for me, and I am as sure as one can be about any other human’s reaction without having directly asked the question, that for others the physical content of Born’s paper was not a surprise.

Kuhn:

You think this meeting with Pauli in Berlin would be very shortly after Born’s paper came out?

Wigner:

Rather shortly.

Kuhn:

So it would really be before you had gone to Goettingen.

Wigner:

I presume so. It certainly wasn’t in Goettingen and it certainly wasn’t after the Goettingen time. The only reason I hesitate is that I may have gone back for a visit to Berlin, but I don’t think so.

Kuhn:

It’s a little, early because the Born paper, or the first series of papers, is in ‘26 and it is not until ‘27-’28 that you get to Goettingen.

Wigner:

Let me see if I have a list of publications. That will help me with the dates. I was in Goettingen evidently in '27—'28, and when did Born’s paper come out?

Kuhn:

' 26.

Wigner:

Yes. Well then it was in Berlin, unquestionably, because it was not long after Born’s paper.

Kuhn:

But for you, in that paper, on the other hand, the physics was transparent.

Wigner:

Yes. I wasn’t sure about the mathematics; as a matter of fact, I don’t think the mathematics was correct, as Dirac pointed out. I asked Dirac eventually about Heisenberg’s paper which made such a deep impression on me. Dirac is of course much more restrained than I am. He said, “I think it contained a new physical idea.” I asked him, “Paul, this was all contained in your articles.” He said, “I think it contained a new physical idea.” So you see this ambiguity was present not only in my mind but even in Dirac’s mind.

Kuhn:

He didn’t tell me that and it’s a report I’m very much interested in. This is one of the things I wish you would elaborate because it may or may not be all contained in those articles. Dirac’s transformation theory article, which is the statistical basis of quantum mechanics, most of which is transformation theory, and the Jordan article do really contain an awful lot of it. How seriously were you and Szilard and others around you concerned with those papers?

Wigner:

Not at all, or hardly. We saw then that you could transform it back and forth, it’s very desirable and very good, but after all, that isn’t the essence.

Kuhn:

But there’s more than that in those papers. Jordan states—-now admittedly it isn’t fully logical—-a few statistical premises about the behavior of probability amplitudes and derives the wave equation.

Wigner:

Yes, well, I don’t know. I don’t think I studied Jordan’s paper, or London’s paper, very carefully.

Kuhn:

And the same would probably be true of the Dirac paper.

Wigner:

Yes. Let me quote one more thing: I quote Johnny von Neumann not as an authority but because he made a very striking remark. I asked him once, not long after Heisenberg’s paper—I called him (“Jancsi”) -“How is it that we are so impressed by this and what did it tell us that we didn’t know? Dirac certainly knew all this. Why didn’t we ask Dirac?” And he said, “Dirac would have said, ‘They do not commute,’ and this would have been the end of it and we would have been left as bright as before.”

I think this was a very true remark. I would have never understood the situation on the basis of the matrix theory. Well, never is a long time. But the Schroedinger theory helped tremendously in understanding it because you could see the propagation of the wave packet. With those matrices one felt, ‘Yes, well, what do they do?’ You see, Heisenberg defined the matrix of p and q as transition probabilities or amplitudes for transition probabilities and not as a motion, and of course it’s very difficult to get a motion out of them. In fact, I don’t think anybody did. Born wrote that paper on the basis of Schroedinger’s picture; I don’t know whether this helps you.

Kuhn:

Yes, it does help. I don’t want to get altogether away from this issue of the interpretation problem, but you constantly speak, and properly, of the matrix approach on the one hand and the Schroedinger approach on the other. What about Dirac‘s approach, the q number approach?

Wigner:

That, as we now know, is a little more symbolic but it is the same as the matrix approach.

Kuhn:

But apart from what we now know; it was not clear at the beginning that it was entirely the same and I wonder whether this made any impression at the time. Did you try to work with q numbers, for instance?

Wigner:

No, never.

Kuhn:

Did anybody you knew try to work with q numbers?

Wigner:

No. We all thought, “Oh, this Dirac is a young genius who knows an awful lot and who is very bright and who also knows things which we don’t know like Poisson brackets and so on,” but we felt that he was a little unusual and it was very difficult to learn. We adopted towards the q numbers the same attitude which most people adopted towards group theory, but without animosity.

Kuhn:

Let me then pose the question in a little bit more general way. At the Como Conference in the fall of 1927 Heisenberg presents a paper. Now simultaneously Bohr reads a paper which is the first and still relatively underdeveloped statement of complementarity in the sense that complementarity really is not in the Heisenberg paper. One of the things that is very obscure to me is how that idea—. People talk about the uncertainty principle and complementarity as if they were one and the same thing, but historically they’re really not; there is this whole idea of duality. The uncertainty principle plus duality of the variables implies complementarity but there is that additional element and I’m not at all clear how seriously people took it, when they began to take it seriously, what sort of discussions it evoked.

Wigner:

Well, as far as I know, very little. I always felt also that this duality is not solved and in this I may have been under Johnny’s influence, who said, “Well, there are many things which do not commute and you can easily find three operators which do not commute.” I also was very much under the influence of the spin where you have three variables which are entirely, so to speak, symmetric within themselves and clearly show that it isn’t two that are complementary; and I still don’t feel that this duality is a terribly significant and striking property of the concepts.

Kuhn:

Excellent. You talked with von Neumann about this?

Wigner:

It’s awfully difficult to know, but I am sure it would not have been new to Neumann that there are three spin operators; whether I mentioned it to him I don’t know.

Kuhn:

With whom else did you talk about this?

Wigner:

I don’t think with anybody, not even with Szilard, because Szilard, so to speak, refused to be interested any more in quantum mechanics. He said his mathematical ability and development were not so strong, that anyway the principal problem was solved, that he was not in terested so much anymore.

Kuhn:

And this he did as early as ‘28?

Wigner:

Essentially, yes. I tried with all my might to get him back. I don’t know why I tried so much; perhaps I felt that it was good to have companionship. Well, I don’t know whether I reasoned, but I was quite unsuccessful. A great deal remained to be discovered, of course, which he did not fully realize.

Kuhn:

But it was true of course that mathematical ability was more and more essential.

Wigner:

Yes, he was entirely right in that. Altogether I think he judges things of this nature quite well.

Kuhn:

What about the measurement problems with which Bohr did so much? Were those ever an issue with you or with people around you? Were they an issue in Goettingen while you were there?

Wigner:

I felt that in this regard Johnny probably was going too far, and I believe it now also. The idea that to a Hermitian operator corresponds a measurement and to a measurement a Hermitian operator is overdoing things, because this would be only reasonable if somebody would tell me how I could make the measuring apparatus with which I would measure a given operator. I felt this very strongly all the time but during Johnny’s lifetime I somehow did not want to write any paper on this. I don’t know why not. As a matter of fact, I did write one, but I felt—well, I don’t know.

Kuhn:

But you concerned yourself with this; you thought about this and from a very early time.

Wigner:

Oh, yes. As a matter of fact, there is a remark here which I never published and which I told Neumann very very early; namely, that one can show that the operators which can be measurable can only be Hermitian. This I eventually did publish in ‘45 or so. I could look it up. Do you want it or not?

Kuhn:

No, this is all right.

Wigner:

Maybe ‘52 even. It doesn’t matter, but anyway I published it eventually in a footnote. But he carefully avoided mentioning this in his book even though he knew it from me. He felt that he should leave it to me to publish. You know, he was very careful and very conscientious in all these matters. I did think very much about it and I presented many puzzles to Johnny which are still not solved and which still bother me on the theory of measurement and interpretation.

Kuhn:

What sort of problems?

Wigner:

Why is it that we always see positions macroscopically? Position operator is just an operator like every other operator. What is it that makes our minds principally think in terms of position operators? Why are there macroscopic bodies? Why do they have definite positions rather than having another, arbitrary, wave function, or another, arbitrary, operator measured? I may be completely wrong, but I do feel that there is some mystery here not completely cleared up. Several times I’ve had ideas on this but nothing really convincing. I’ve discussed that with Johnny also.

Kuhn:

Again from very early.

Wigner:

Very early.

Kuhn:

Can you tell me other things of this sort that bothered you?

Wigner:

These two are the problems of a specific nature that bothered me. There is a difference between feeling that the solution is in a certain direction and feeling that the solution as mathematically presented is perfect. The two are not the same; every recognition leaves problems. The two problems are, firstly, that Neumann ‘s measurement theory seemed to me too schematic; the fact that there is for every Hermitian operator a measurement. Of this I was not convinced.

The question is, if somebody gives me a Hermitian operator, how do I measure it? This is of course an unsolved problem and this was one thing that bothered me. The other thing which now perturbs me did not bother me so much at that time, namely, that we make an entirely—or largely—idealistic epistemology and it is not fair to do that without knowing much more about the mind. This did not bother me much at that time; what did bother me was the behavior of the macroscopic bodies, that it is always a concentrated wave packet with the position operator "sharp". .

Kuhn:

That’s very good. I’d ask you a very different sort of question though I’ve got some more concrete ones to come back to. In general, when you went to Goettingen from Berlin you went really to a very different sort of scientific community, a smaller, more concentrated one, one which had been much more deeply involved with quantum mechanics. There you were not alone in the sense that you had been very nearly alone in Berlin, What sort of differences did you feel in this situation? Was Goettingen an eye opener to you? Did you feel very differently?

Wigner:

No, This is a new point which has never occurred to me and I did not feel that, The only person with whom I had much contact, as far as I can remember, was Heitler, and that contact was not as fruitful for me as the contact with Szilard and von Neumann because mathematically Heitler certainly was not as much above me as Johnny von Neumann and philosophically he was not as penetrating a thinker as Szilard. I saw relatively little of Jordan. I had and continue to have a great admiration for Jordan, very great; he has imagination much greater than most others whom we have mentioned.

Kuhn:

This brings me then to a question I do also want to explore with you. This is the paper of which you say, and I think you are very likely right in this case, you had so little to do with, which is the field theory paper, the Fermi-Dirac particles. Tell me how you got involved with this at all.

Wigner:

Well, Jordan told me one day that it would be nice to derive the commutation relations for Fermi particles.

Kuhn:

Do you think he really did put it that way? He had done this earlier paper end he had a pretty clear idea already that they were to anti commute.

Wigner:

I don’t remember, but I thought be just came to me with that. Did. you discuss it with him?

Kuhn:

Yes. I hesitate to say too much about what I have already been told in advance, but he says that in the first paper there was a mathematical mistake which he didn’t notice until after it was published and that he asked you to help him straighten out the mathematics of it.

Wigner:

I’ve forgotten.

Kuhn:

You have no particular recollections about this?

Wigner:

No, I am sorry. I remember that there is one mathematical trick in it which I contributed and which I used again later on, also, interestingly enough, in connection with Jordan, in an article which Jordan, Johnny von Neumann and I published. It is how to solve a certain set of matrix equations, and that I contributed to it.

Kuhn:

Which trick is that?

Wigner:

That you make those matrix equations be group equations and if it is a group equation, then it is a representation of the group which will solve it. In all these cases it turned out that the group has only one faithful, irreducible, representation, so that is the solution. I remember also that there are some parts of that paper with which I was not in complete agreement. I said to Jordan at the end when the article was written, “Now look, Jordan, we could. eliminate the whole first part and start with the second part and it would be much shorter and much more concise.”

He said, “Yes, that is true, but I don’t want to do that because everybody knows that the second part is written by you whereas the first part is written by me, and if we eliminate the first part it will appear that it is your contribution, wh-wh-which a-a-as y-y-you kn-kn-know—.” And of course he was right. As soon as he said that I said, “Well, you know that I am essentially honest.”

Kuhn:

When you say there were parts of it with which you disagreed, you don’t mean this lack of conciseness though.

Wigner:

No. I don’t know whether I have a reprint of it. I think it is an anticipation of some of quantum electrodynamics which at that time neither of us understood. There are equations in it which neither he nor I understood, but he guessed rightly that these equations would be part of a later theory.

Kuhn:

Do you suppose you do have a reprint, because I would be interested to have you tell me which equations you mean.

Wigner:

I may have it. Let me see first which year it is.

Kuhn:

I’m sure I’ve looked at it more recently than you have, but I have not looked at it as carefully as I should have. There are too many papers to read.

Wigner:

Of course it’s impossible. Here is the br You know, I would have sworn that they are called a’s.

Kuhn:

Well, you deal with both a’s and b’s in there.

Wigner:

I see. I don’t remember that,

Kuhn:

In fact, part of the difference between this paper and the previous one is using a’s in places where the previous one has used b’s.

Wigner:

Here is a typical Jordan notation: capital psi, beta q, alpha p. This whole part is entirely correct, but it’s not necessary in the long run. Let me see whether I can find that, [Pause as Wigner looks through the paper.] That would be a scandal if I couldn’t find it. This is that trick which I mentioned.

Kuhn:

Pages 650, 651.

Wigner:

‘51, yes, but I didn’t find the equation which I—. [Tape stopped while they look for the passage.]

Kuhn:

Just for the continuity, if you get a chance to look over this and write me a note or something of the sort as to what it was about this that concerned you, that you felt was an equation that was not really understood, I would be very grateful.

Wigner:

I think it probably is this Θr in Equation 11—what the significance of that is and the introduction of these k’s in equation 15 of which the purpose was unclear to me.

Kuhn:

In 15, right, and earlier.

Wigner:

I think that was it. That’s the best I can do right now. [In a letter of 27 May 64 Wigner writes, “I checked the question and, on the whole, confirmed the tentative answer which I gave at that time. The introduction of Θ appears unnecessary and equation 27 is, of course, incorrect.”]

Kuhn:

This is already very helpful. Jordan says, and I think this is probably true and he does not get sufficient credit for it, that he had in fact had this whole notion of field quantization from very early and that in fact it goes right back with him to his contribution to the ‘Dreimaennerarbeit’ which the others were not very happy about.

Wigner:

I think he is right, I think he is right. However, I remember a conversation with Jordan in which he felt that since Heisenberg and Pauli started on the problem of field quantization for electromagnetism he left it alone because he could not compete with them. In other words, he felt that they were very powerful thinkers and also good mathematicians so that he turned to other subjects rather than to compete with them. I don’t know what Jordan said about this article, whether he told you that it is practically his work, but if he did he was right.

Kuhn:

He didn’t put it that way, but he did say that your role in it bad been principally to help him with the mathematics.

Wigner:

Well, you can put it that way. I think that is entirely fair, which of course I can express in the slightly different way that his role was a much more significant one.

Kuhn:

How did you feel about this whole rather strange idea of generating particles out of fields?

Wigner:

I think I understood transformation theory a little better as a result of this paper. After this I formulated matters this way: We must know somehow a priori the set of values which one complete set of commuting observables can assume. Then we introduce a wave function the definition domain of which is that set. These wave functions form the Hilbert space of all possible states. I don’t think I understood this point as well before this paper as I did as a result of this paper.

As a matter of fact, this is the essential idea of the paper: the wave function depends on a variable which can have only two values, zero and one. This was not clear to me before to the same degree. I am sure you are familiar with the fact that whether one knows something or not is not clearly defined. I know many things which I have never articulated, but I think this goes a little beyond that, at least a little. I got this knowledge: the wave function, the manifold of states, can be defined if we know one set of commuting observables, or rather, their characteristic values; and then we have to define probability amplitudes for these values.

Kuhn:

This is not at all to contradict your sense of what you had gotten from this, but it falls into an area which particularly interests me because my sense here is that this paper, and particularly the Jordan—Klein paper which appeared just a little bit before this are very like Dirac’s paper, which is still just a little bit earlier. Yet Dirac’s paper is, I think, an almost pure transformation theory paper.

Wigner:

Dirac was a captive and is now a captive of the Hamiltonian formalism and he thinks extremely strongly in terms of the Harniltonian formalism. This is one of the mistakes I never made because I was a chemist and Hamiltonian formalism meant very little to me. But the fact that Dirac did not establish the commutation relations for particles obeying the exclusion principle, which always irks him a little, is a direct result of the fact that he always thought in terms of the Hamiltonian formalism, and canonical commutation relations.

Kuhn:

I wonder whether there is not just one step more to it than that and I’m not sure now that I can even still phrase this clearly because it’s now too long since I’ve read the papers. I had the feeling as I read Dirac’s radiation theory paper, which one can now read and say, “Here is the field theory for Einstein—Bose particles,” that in fact it isn’t yet, in the way that he is thinking about it, a field theory; that is, that this is a straight transformation to other coordinates and that there is no thought of something like a quantized wave function.

Wigner:

That’s very difficult to answer. The method of modern theoretical physics is essentially to give a new form to the equations by a not entirely sound mathematical procedure and then see that this new form is more meaningful than the one from which one started. This is how I interpreted Dirac’s radiation paper. It was a question on which I also worked but not suecessfully, and I don’t think Dirac’s paper came out very much before the paper of Jordan and myself. But when I understood our own paper really, which of course was during the course of working it out—I didn’t have to read it again in the journal to understand it—I understood Dirac’s paper at once in that way; namely, he says that in this case the possible states can be given by giving the occupation numbers of the different black-body modes and the occupation numbers can be from zero to infinity—this is the Hubert space.

Kuhn:

In Jordan’s mind, you see, there is another thing playing a role here and this is that just as we get photons by quantizing the electromagnetic fields, so we should be able to get material particles by quantizing the Schroedinger field.

Wigner:

Perhaps this is also the thing that neither of us completely understood at that time and which is contained in this article, at least in words. Neither of us completely understood it at that time. The div E = 4πp is the equation which I don’t think we completely understood at that time.

Kuhn:

I will put just one more point to you in this connection and then we will drop this topic. Jordan said to me that when Dirac’s paper came out, Born showed it to him or he showed it to Born and Born said, “This is nice but it isn’t about anything,” or something. And Jordan said “No, this is just what I told you we could do and have been telling you ever since the Dreimaennerarbeit; this is the quantization of waves.” Born said, “Yes, you know, that’s right; I see what you mean now.” My feeling is that this is a very plausible story, but that it isn’t the way that Dirac meant that paper.

Wigner:

That is also possible. Dirac’s mind works differently. It’s very difficult to know. [Short interruption]

Kuhn:

You told me just now that you had also been working, but not successfully, on radiation theory, and also on a relativistic wave equation. I wish you would tell me about these two things.

Wigner:

I was working on the radiation theory just because I did not, at that time, understand this point which I mentioned—that in order to obtain the Hilbert space you have to know one set of commuting operators and their possible values. This is the variability domain of the wave functions. Because I did not know this I did not get anything even approximating Dirac’s radiation theory. When Jordan and I wrote our paper, this became clear to me. I also understood then clearly, possibly, as you imply, more clearly than Dirac himself, his paper on radiation; but if the problem was largely solved I would essentially forget about it.

I turned to the relativistic wave equation with spin because I realized that without electromagnetic potentials this is a group problem. I did have a set of equations which were equivalent to Dirac equations without field, Jordan knew this, and when Dirac’s paper came out he wrote a letter to me. First of all he told me that Dirac’s paper came out; I learned from him not of the paper but of Dirac’s solution of the problem. He gave me that famous letter: “Well, somebody else solved it. It’s too bad.” Jordan said, “At first it annoyed me a great deal, but it really is so beautiful that we should be happy With it,” and I concurred with him.

Kuhn:

When you say you had a form like Dirac’s without the field for a relativistic equation with spin were you yourself trying, in the first place, to take, say, the Pauli equation with spin and put it into a relativistically invariant form?

Wigner:

Yes.

Kuhn:

So that you had the spin terms in it from the start?

Wigner:

Surely.

Kuhn:

Now in this sense your approach was very unlike the one Dirac shows in his paper.

Wigner:

Right. This is of course what Jordan said, so to speak: “You did it by hard work and group theory by which you can do it, but Dirac did it by a beautifully clever trick." This is what Jordan told me. Jordan later on wrote a letter to me saying that he had seen an article by two Russians who also explained that they did something similar to Dirac. He wrote to me and said, ‘Well, since they published their attempts at a pre-Dirac treatment you should publish yours too,” but I didn’t feel that anybody would learn anything from such a ‘pre-Dirac’ thing, so I did not do that. I don’t think it would have had any value,

Kuhn:

I’d ask you about a puzzle that you may know nothing about, but it’s a puzzle to me and you may, from your knowledge of Dirac himself, have an answer to it. As one reads the Dirac electron paper, it looks as though he wants a relativistic wave equation. It must be linear and the spin comes out without its having ever been put in. It looks as though this were an accident, as though he were not looking for spin at all when he sets this up. On the other hand, there is a story which neither of the participants can confirm, but which I have on relatively good authority, that Heisenberg and Pauli made a bet in Copenhagen in ‘26 that within a year they would understand what spin was about. This would make it likely that Dirac had been looking for spin from the beginning, which is not what the paper itself looks like.

Wigner:

I cannot help you on this. I can tell you something else: Heisenberg and Pauli told me that the hundred thirty-seven will come out of quantum electrodynamics as a magnitude of charge for which the equations will assume a particularly simple form; which of course did not materialize. So not every surmise, not even of Heisenberg and Pauli, was justified, and of course it would be terrible if it were.

Kuhn:

How did you yourself feel when you saw the Dirac paper? You’ve told me how Jordan felt.

Wigner:

I felt the same way. I was not even as much annoyed as Jordan; I said, “Well, he solved it in a different way,” and I realized that it was a more beautiful way.

Kuhn:

It was a beautiful way.

Wigner:

I realized also that to describe the interaction with the electromagnetic field would require a new idea from the point of view of my approach. I did not have any way to tell how to formulate that, so that my program was not even going as far as to get in the electromagnetic field. I did not know how to do it.

Kuhn:

Your formulation wouldn’t have enabled you simply to substitute the p-A for p terms.

Wigner:

I thought that that was a special trick which Oskar Klein and Gordon used for the Klein-Gordon equation, but I didn’t think that, had much significance. I did not know of a physical basis for that. Now I could more easily think of one. So that trick would not have occurred to me, and that in itself sort of relieved my mind. “Now they have solved even this.”

Kuhn:

I continue to skip around. We talked a little bit yesterday about the manner you did with Witmer on molecular spectra. There’s very little about that paper in particular that I want to ask you, but there is I know, without knowing very much about it, a very real polarization of the people concerned with molecular spectroscopy, between Heitler and london and perhaps Born on the one hand, Hund at least, and perhaps Mulliken with him, on the other, between two approaches which perhaps come together with Slater in the early ‘30’s or perhaps don’t even come together then.

There was apparently a good deal of argument back and forth and there is at least one place in the paper where you refer to london’s saying that you get a lot of terms which may be in the continuous spectrum—this sort of thing. Can you tell me something about those arguments or about your own feelings about them? What happened then?

Wigner:

The objective of the paper by Witmer and myself was very different from the objective of the Heitler-london paper. Heitler and London wanted to explain the chemical bond which, if I translate it into terms useful for this, is the electronic structure of the lowest state. We were interested in the spectroscopy, which essentially says, “Let us assume that we know the electronic states. What then will be the structure of the spectrum?” London’s papers impressed me with their skill.

Perhaps later on I became a little more critical when I recognized, for instance, that oxygen is paramagnetic so it is a crass contradiction to london’s ideas, and I veered over to the Hund—Mulliken type of considerations. The weakness of that, which I recognized, and I am afraid still recognize, is that it doesn’t speak about the bond, but rather it has molecular orbitals which extend over the whole molecule. This is too far away from the very useful and very fruitful chemical concepts, and so I felt, “Oh, this is difficult .“ And we must admit, as I think everybody does, that the quantum mechanics of chemistry is not a resounding success. The Heitler-London paper is very beautiful, but much of what came afterwards is only “all right.”

Kuhn:

I want to try to push this a little further. You say, and there is no question that you’re right, that your objectives in the paper with Witmer and Hund’s objectives, by and large, are quite different from those of Heitler-London. Yet that’s something that is apparently now clear to people.

Wigner:

Oh, but it was clear to me at that time.

Kuhn:

I think it’s fair to say it wasn’t clear to everybody at that time. For example Hund tells the story of coming to Goettingen: Born had a seminar, a little later than this, on molecules, and Hund came from Leipzig to give a lecture. Born said at the end of the lecture, now I suddenly see what you’re trying to do. You’re not trying to do the same thing at all that we’re trying to do. What you’re doing is all right, but I’m not interested.” But up to that point, these had looked like opposed ways of doing of problems that appeared identical; at least one felt an opposition between these two, and that was apparently widely felt.

Wigner:

Not by me.

Kuhn:

You never ran into this?

Wigner:

No. This was completely clear to me. I often teased Heitler, I must admit, because Heitler sort of felt that he had explained the whole of chemistry, and I was a little skeptical of that. I asked him, “Well now, what chemical compounds would you predict between nitrogen and hydrogen?" And of course since he didn’t know any chemistry he couldn’t tell me. These problems are not solved even now. I just see that I did even publish an article in a Hungarian journal on the modern theory of chemical bond in which I am sure I explained how far Heitler and London had gone and what the purpose is, and I am sure I did not confuse it with the paper of Witmer and myself.

Kuhn:

You did a pair of papers with Weisskopf.

Wigner:

Yes. [Papers No. 20 and 21]

Kuhn:

He’s talked to us a bit about those, and again I would start out by not telling you what he said. I’d be interested to hear from you about it.

Wigner:

That’s more embarrassing than to tell about the Jordan paper.

Kuhn:

Let me say, I am prepared for that response because of what he has said about them.

Wigner:

One thing that he did on that, and a very important thing, was to bring the problem to me, and that in itself is a major contribution. Probably the mathematics was more nearly due to me than to Weisskopf. But, you see, this is not deep, so I don’t think it matters really. However, I think I learned a great deal out of it and I must say I enjoyed working on the line-widths paper. Afterwards I read Pauli’s article on line-widths on the basis of the old theory, and I greatly admired the sharpness of mind and the clarity of the analysis; the point which he could not possibly have guessed was that the problem is fundamentally different if two successive lines do have the same frequency and if they don’t have the same frequency.

As a result Pauli could not abstractly solve the problem with pre-quantum mechanics quantum theory. This was very interesting to me, because without that it would have looked like a new principle or the possibility of a reformulation of quantum mechanics. Just because the reformulation does not work if you have two successive transitions of equal energy. Because what the standard mechanism says is evidently correct, while the extrapolation of the simple rules in the other cases is not. I became convinced that there is no reformulation here of quantum mechanics. I am not sure but what I have spoken too elliptically.

Kuhn:

I have not understood that entirely.

Wigner:

The result of the paper was that the line width is the sum of the level width of original state and final state. This is a very general principle, and I thought for a while that maybe we should reformulate quantum mechanics altogether, in such a way that the characteristic values are not sharp but have a certain width—that that is part of the picture. I got away from that because in the case of the oscillator the result which you obtain on this picture for two successive transitions with equal frequency is incorrect because we knew that in the case of the oscillator the width is not the sum of the widths of the levels but very much smaller. So I got away from this, but it was a very interesting experience for me.

Kuhn:

Weisskopf says that he thinks back to this pair of papers and thinks they represent the first time that the attempt to solve a concrete problem ran into a ‘not—eliminateable’ infinity. But this, however, does not appear in the papers.

Wigner:

Oh, I think it does.

Kuhn:

Let me put it this way. There is a week justification for discarding it. Weisskopf says that he was relatively satisfied with this; he did not know when these papers came out that this was real trouble.

Wigner:

Oh, I think he should have; I think he did.

Kuhn:

In any case you did.

Wigner:

Oh, yes. There is a footnote on it; again I don’t know whether I have it.

Kuhn:

They’re both 1930; I think the first is Volume 63 and the next is 65.

Wigner:

[Wigner finds the articles] There is a footnote on this, and I think everybody knew this. I hope I’ll find that footnote; I wasn’t very good at finding the Jordan footnote. Here it is.

Kuhn:

This is the footnote on pages 61-65.

Wigner:

No, that doesn’t say that it is infinite; it does not. But I knew that, excuse me for insisting.

Kuhn:

Well, my impression is that the point at which the infinity itself emerges is pointed to, but it is then gotten around in a way that is not really possible, finally, to maintain. Victor’s indication is that he was really not very much bothered by this, but that he thought you were discontent.

Wigner:

I surely realized that there is a very real difficulty here and that one again begins to calculate in these cases as one did with the old quantum theory when one navigated between difficulties and got a result which looked correct but which did not follow from the equations with which one started—and which one does even now in a sense.This article introduces the Tamm—Dancoff method....

Kuhn:

Yes, I hadn’t thought of that.

Wigner:

It does say that, it does say that [i.e., that infinities occur]. I would have to read it in order to be sure what it says explicitly. Let me say one more thing—-forgive me on this. Breit read this extremely carefully and he realized that we realized the infinities; he told me so. Altogether, you know, Breit may have a very good memory in many things; I have also otherwise an extremely high regard for Breit.

Kuhn:

I hope very much to talk with him. When I have written asking him whether I could come he said, “I will try to write answers; I don’t want to try to talk with the recorder.”

Wigner:

Yes, he’s terribly careful.

Kuhn:

I will send him a list like the one we sent you just as soon as I can after I get back. and I will see what happens.

Wigner:

I do believe that he will bear this out; I really can’t believe that Vicky did not realize that there are infinities in the theory.

Kuhn:

That may well be the answer. You did not go on much with field theory after this, did you? I must say that my knowledge of your bibliography stops at just about this time.

Wigner:

Well, I was a little afraid that the problems of field theory were not ripe for solution. Perhaps I was not so wrong. As I look at my papers, I see that I went into a number of other problems which have to do with chemical physics in which I still had a very lively interest; not into the chemical bond which I felt was terribly difficult and where I could not conceive an idea. It’s very difficult to work on something unless you see an idea or a picture, and I did not have one. I see that not much later I started out on the solid state. That, of course, kept me busy for a long time; there I had a picture of what the solid state looked like and how the binding was established.

Kuhn:

When you went back to Berlin after the year in Goettingen, you were there just two more years, weren‘t you? And then you were back and forth.

Wigner:

Yes.

Kuhn:

What sort of duties did you have there?

Wigner:

I was a Privatdozent and I gave a class on quantum mechanics. I had a good number of students.

Kuhn:

Nobody had really been giving that before, had they?

Wigner:

Nobody had really been giving that before as far as I know, but at that time I was a very poor lecturer and I remember that Becker once came to my class and was flabbergasted at how poorly I lectured. I was quite taken aback. It happened that I explained the spin, which of course I understood very well, and I wrote down the amplitude for up spin and the amplitude for down spin below it, and Becker thought that the two had to be added.

He said, “Well, now you have exactly zero;” I was of course terribly embarrassed and I explained the equations, but I realized how poorly I explained it before. I did not make clear that the first line and the second line are not to be added but that these were the amplitude of up spin and the amplitude of down spin. I don’t think that you are really interested in this.

Kuhn:

You say you had a number of students and you were giving the first class, probably, in quantum mechanics as such, except for certain special topics that had been given. Was there now suddenly much more interest in Berlin than there had been before? You say you had been relatively alone before in your concern with these.

Wigner:

Yes. By this time Schroedinger was in Berlin, London was in Berlin. There was a lively quantum mechanics colloquium—Moeglieh and Szilard usually came—

Kuhn:

This was in addition to the regular Wednesday colloquium?

Wigner:

Right. I think it met on Thursday. After the colloquium we always went to a coffee house—I don’t know if this is a concept to you? In the coffee house we discussed matters further; those were very good years for me, I learned an awful lot, I worked very hard, and I was very happy.

Kuhn:

What seemed, at these discussions, to be the main problem? This was after all late ‘28 already when you get back.

Wigner:

Well, I think specialized problems and not field theory.

Kuhn:

Do you remember any of the problems?

Wigner:

Chemical bond on the part of London, chemical physics which I worked on, more abstract problems—. Do you mind if I go on looking through the reprints? It may remind me of something. . .

Kuhn:

Yes, you’re quite right; I missed some papers.

Wigner:

Here there are two papers with Johnny von Neumann [Papers No. 11 and 12]. I didn’t mention that he was in Berlin, but that was terribly important.

Kuhn:

Those two papers with von Neumann puzzled me a bit because they seemed to be side remarks out of a continuing discussion which is never given, What was the continuing discussion?

Wigner:

We played around. We know a great deal of classical mechanics: I know that if I throw a rock against a board, what happens is that the board gets a push, will give a noise, and will get into vibrations; the rock will fall down, the board will be damaged. One has a number of such feelings and experiences where one knows what happens; one has it at one’s fingertips. I think we tried to get quantum mechanics to our fingertips, to understand what all this was. These were two such things.

Kuhn:

That’s very good.

Wigner:

Then Szilard persuaded me to write a book on group theory because he felt it would be good to have a book on our theory and also he felt it would support what he called my priority claims, Of course it did, and I felt that it would be good for me.

Kuhn:

When you wrote the book, did you have to learn additional things or was it all writing out what you knew plus the pedagogy problem?

Wigner:

It was very much the pedagogy problem. I learned, I think, hardly anything out of books at that time; in fact, I think virtually nothing. But I did rephrase my own material, reformulate it, and also put many things down on paper for the first time which I had known for a long time and had not published.

Kuhn:

How long did it take you? Do you remember?

Wigner:

Infinitely long. About two years. I was not articulate and the material is large.

Kuhn:

Yes, there’s an immense amount in that little book.

Wigner:

Thank you very much, but it was not difficult to write it except in the sense that I wanted everything to be exactly right; and there are few mistakes in it. In fact, Born once sent a list of errors to me and what bothered me most was that most of them were Born’s errors which means that the pedagogy was very weak. I probably have that letter at home; I put it into one of the copies. You know, one other thing we could do now is to look at my files.

Kuhn:

I’d like to ask you just one more question and then we’ll take a peek and see. Of course, whatever is to be done about the files we’re not going to do now, not because I wouldn’t like to but because it would take more time than you have. Let me ask you just one more thing which is about your transition to this country. How did that come about?

Wigner:

I received a telegram one morning: ‘Princeton University offers you a lectureship of ' —I forget although I should be able to remember— ' $4,000 dollars. Please cable reply.’

Kuhn:

Just like that—no preparation?

Wigner:

No preparation. Johnny by that time had had a telegram somewhat earlier offering him a similar thing, (about $5,000). but $4,000 was an inconceivable sum for me, I never thought it existed. If you translated $4,000 in those days into Marks, it was 16,800 Marks; I still don’t believe there is so much money in Marks! Sixteen thousand dollars means much less to me than 16,000 Marks because I never saw that. I went to Becker and to Haber and told them about it dutifully and they said, “Well, of course you have to accept it,” and Haber called up the Minister für Kunst, Wissenschaft und Volksbildung in my presence and told him, “Well, it is too bad that the Americans have to tell us whom we should promote.” Evidently the minister did not like this statement.

Kuhn:

Did you think of this at the time as a temporary move?

Wigner:

Yes. I thought that this was for one term——that they wanted to hear me. I didn’t know why. There was somebody from Princeton in Berlin at that time, who is here even now, Dr. Alyea. I asked him, “How does Princeton look? Where is it? How do I get there? Are there any stores there? Where do I live?” America was not something that I thought really existed, but something that you can read about. It didn’t play a real role; it wasn’t one of the objects the existence of which you had to count, but something like the Middle Ages, which also, perhaps, existed.

Kuhn:

At what point did it begin to become clear that you would stay?

Wigner:

Very much later. That I would stay permanently I think dawned on me slowly.

Kuhn:

Was it really after Hitler already that this occurred?

Wigner:

Well, the situation in Europe deteriorated more and more. I did hope against hope. First of all I did not want to abandon a sinking ship. Johnny was much more realistic, but I felt I should not abandon a sinking ship. At one stage, a conversation had a tremendous effect on me when I realized that the Germans did not consider me part of the complement of the ship, that I was a foreigner. That helped; that made it much easier for me to abandon the sinking ship.

Kuhn:

That was when, do you suppose?

Wigner:

Two years after I first came to Princeton.

Kuhn:

How did you feel about physics here when you Came?

Wigner:

It was very rudimentary and very, very elementary. I felt that a great deal had to be done and often I felt that I engaged in baby talk. However, after a couple of years I realized that their interest was sincere, that they didn’t want baby talk, that they wanted to learn or at least wanted me to teach the young people, and of course that made a great impression on me. I did not realize that at first, I first thought it was sort of an extravagance of the Americans that they wanted two people here from Berlin and perhaps it had no significance. But after a couple of years I realized that what they wanted was a transformation of the theoretical physics school into a modern, progressive, powerful school, and that of course had a great effect on me.

Kuhn:

Who here was really most behind that?

Wigner:

Oswald Veblen. Veblen was a great man.

Kuhn:

Were there people more strictly in physics who were also very much convinced that this needed to be done?

Wigner:

The end of the first half year that Johnny and I were here K. T. Compton, who was here until that time, left to become president of M.I.T. Evidently he had been spending a great deal of his time negotiating his move to M.I.T. because he could not even tell us apart. Johnny wanted to leave a few days earlier and Compton did not know which one it was who had come to see him, so he gave us both leave to leave earlier! The mathematics department was much more progressive principally because of Veblen.