Rudolf Peierls - Session II

Peierls:

One thing I remember since our talk yesterday arises from the translation of the book by de Broglie I mentioned. This was early in ‘29, and this was a book in which he was reconciling himself with the probability interpretation of quantum mechanics. He tries all sorts of more complicated things giving some reality to the waves and works it all through rather carefully and comes to the conclusion it doesn’t work. The conclusion of the whole book is that the standard interpretation is really right. Of course, he later went back on that. What made it interesting is that at that time, when I really had been a student for three and a half years, something like that, it seemed to me perfectly obvious that this was the right thing — that the conclusion he came to was the right one. One realized that de Broglie was isolated, but one was glad that he himself, by whatever clumsy methods or round-about methods worked himself round to that view. I mean, my own feeling in translating the book was, “Well, what would be my reaction today?” On the whole this exercise is rather unnecessary because it’s clear from the start that that must be the answer. But the book is worth having simply because he is a very distinguished man, and it’s interesting to see how a man like that comes to be what he is. You were asking for people’s attitudes to these developments at the time. Well, certainly at that time this was already perfectly clear to me, and I believe obvious to everybody else. I was not terribly original then.

Heilbron:

Among the students, or people who began their college training in ‘25 and afterwards, it’s quite reasonable to expect a ready acceptance.

Peierls:

Yes.

Heilbron:

It seems a little curious that the people who had difficulty accepting it, such as de Broglie and Schrodinger and Einstein, were isolated. Do you recall any others of the older-generation who had difficulty?

Peierls:

Well, there were several people who had difficulty in the sense that they were anxious to convince themselves this thing was really above board and there weren’t any hidden difficulties, such as for example Ehrenfest, whom we mentioned. He certainly was for the new ideas; I mean, he didn’t oppose them in any way, but just wanted to make sure that one really understood them. But be had some difficulty. He had some very interesting questions. I remember in this paper he wrote about posing some questions about quantum mechanics — I don’t recall all the questions now without looking it up. One question was “Why do we have to deal with a complex wave function and how does ‘i’ come into these things suddenly?” I think I was, at that time, inclined to be a conformist. I wasn’t inclined to question basic principles; I came to it very much from the end of applications and the idea of working things out. Therefore I think I was more interested in seeing how things you knew about — experiments or facts — came out of the accepted principles. There is a great joy in suddenly seeing how to solve an equation, or how to describe a situation when you suddenly see that this is the way it is meant to be, the way it comes out. One came to it with the attitude, as you implied, “Well, this is what we are taught is the physics, and we’re not in a position at this moment to question it; that comes later.” That I think was one point I wanted to add. I’ll probably think of other things in the course of it, but will you go on with your points?

Heilbron:

At the end of your measurement paper you make a very interesting statement that one place where you can see the difficulties is in the beta decay. Do you remember that part?

Peierls:

No, I don’t remember.

Heilbron:

Well, it’s quite curious, and the reason it interested me is that this was about the time of the neutrino, was it not?

Peierls:

I think that must be before the neutrino.

Heilbron:

Before, but it’s difficult to fix a date for the neutrino, when the concept was rather more officially proposed. I wonder if you can recollect anything about that — discussions about that with Pauli?

Peierls:

Well, this was a time when I think certainly everybody was aware of the fact that the beta decay was a difficulty. The evidence of course came along gradually. First it was clear that energy didn’t appear to be conserved, and then came later experiments which suggested that the top end of the spectrum was the correct energy for balancing things up; in other words that in the process energy always appeared to be lost. Therefore, people started thinking “Well, is it possible in principle that there might be a one-sided lack of energy conservation?” And I think nobody was particularly happy and enthusiastic about that idea. However, it was seriously discussed in the way, for example, that the possibility of parity violation was first discussed, before it was actually established. Again, people weren’t too happy about it at first, but said, “Well, we must be prepared for anything.” It was in that sort of spirit. Now I don’t recall exactly what we said about this; presumably just mentioned it as one of the places where the theory was in difficulty, and that shows how wrong one can be with such remarks.

Heilbron:

It seems that Bohr was willing to abandon the conservation of energy without great qualms.

Peierls:

Well, that was a little earlier in the Bohr-Kramers-Slater paper.

Heilbron:

But again, at the end of the twenties and into the thirties he was willing, almost anxious, one would say, to abandon energy conservation. But at Zurich I imagine that wouldn’t be the case.

Peierls:

Well, I think one was always prepared to admit that possibility, but one certainly was not very fond of —. JIH: Where did Landau obtain his great familiarity with all the current problems of physics? He had studied only in Leningrad, hadn’t he?

Peierls:

Yes. Well, he’s of course a remarkable man who can pick ideas up extremely quickly, and most of those ideas, I imagine, came straight from books and journals. Frenkel was one of the teachers there, who was a very intelligent man and no doubt helped Landau quite a bit. And there was Fock; there were some good people there. And there he no doubt got his basic training. Then he started reading himself, and he is one of the people who will never read a paper in detail. He’ll glance at it to see what the man is trying to do and then will sit down and reproduce the results in his own way.

Heilbron:

Fermi would, I understand, work that way too.

Peierls:

Yes.

Heilbron:

But he had a certain amount of iconoclasm that must have been somewhat different from the German school approach.

Peierls:

Oh yes. Particularly in those days when he was young, he was given to very extreme views about everything; not only physics. I think one of my favorite recollections is the occasion when, in a discussion, some name came up that Landau hadn’t heard before, some physicist. So he said, “Well, who is this, and where is he, and how old is he?” Somebody said, “Oh, he’s 28, or something.” And Landau said, “What, so young and already so unknown?” You were asking in your notes about Rome and Fermi. Well, I don’t think I actually worked with Fermi very directly, except in a minor way because at that time most of the people in Rome were working on certain features of atom spectra. There were some things that hadn’t been sorted out yet, and that was the time to get those clear. And everybody was working out numerical solutions of Schrodinger’s equation for an outer electron of an atom using the Thomas-Fermi potential or something. It seemed to me that it would be useful once you were in such a place to take part in what was going on, and I asked if I could do a job like that as well. As a result I sat down at a little desk calculating machine solving the equation for some particular case, which I have now forgotten. But it was quite valuable experience because I had no practice in numerical solutions of differential equations and it showed me how easy this was.

Of course it’s true I think everywhere in one’s formal training that numerical methods get neglected; people can solve differential equations by series expansions and by contour integrals and by elegant transformations, but they don’t realize how easy it is on the back of an envelope just to run off a numerical solution. Very often in doing that you see something about its structure which then leads you to some analytical or approximate solution. Of course now people are are conscious of numerical methods through computers, but, again, I think the common attitude is that either you can solve an equation in closed form or you put it on an electronic computer. And very often it’s quicker to work it out by hand — if you want one solution for one case — than to get hold of a computer and write a program; this also tends to be forgotten. Certainly, nevertheless, one profited enormously from Fermi because of the simplicity of his attitude and the way he could in almost all cases get a simple quantitative answer to a problem without any highbrow methods. In fact he had a series of books that no doubt you’ve heard about, where he had written down all his thoughts and all the arguments. Generally when a problem came up he pulled out a book and turned to some particular page and there it was; on one page was the argument written out. Very interesting.

Heilbron:

You were just describing some of the peculiarities of the Rome school.

Peierls:

Oh yes. I certainly got a lot of useful ideas of clarification from Fermi and from the other people, including Wick, and Majorana, who died shortly after that. Rasetti —. There was quite a good bunch there.

Heilbron:

Majorana was a very clever fellow, was he not?

Peierls:

Yes. He was somewhat strange and retiring; he was a Sicilian, and he later was lost from a ferry boat crossing over to Sicily. It was never clear whether this was accident or suicide.

Heilbron:

But he didn’t publish a great deal?

Peierls:

No, no. Well, nevertheless, he made his reputation on two important things. One, the exchange nature of the nuclear forces, where essentially he corrected an oversight in Heisenberg’s ideas and then the other was the neutrino theory.

Heilbron:

This was about the time at which the Rome group was going over to nuclear physics?

Peierls:

Yes. They were then making plans for getting hold of equipment and so on. It may be that they already had some small experiments going on, but Fermi wasn’t as personally involved in those as he was later.

Heilbron:

Would you say that there was a general sort of feeling, elsewhere too, that one had reached the limits of any of the older problems, and it was essential to cultivate some new territory? Was there a general change of fields —?

Peierls:

No. No, there was still plenty to be done, but, of course there was a new field opening up which was exciting. This of course was just the time when the artificial radioactivity had been discovered, and when there were the experiments beginning to come out which led to the discovery of the neutron. Fermi always had a slightly peculiar attitude to that. I think he felt that the Paris group, the Joliots, should really have seen the existence of the neutron from their experiments which were later pointed out by Chadwick. I had the impression that he knew what the experiments meant, but hadn’t got round to publishing it, or felt he must leave it to the experimenters. I don’t know this is only a hunch. But this brings me to another amusing recollection. There was one of the regular conferences in Copenhagen — I think it was just before the discovery of the neutron; it may have been the conference of ‘32 or ‘31, I don’t know. The interesting point was that there was a general feeling among some people there, not everybody, that physics was almost finished. This looks ridiculous looking back, but if you look at it from the point of view of the time, practically all the mysteries had now resolved themselves, nearly all. Everything that had bothered one about the atom and molecules and solids, and so on, had suddenly fallen into place just as a result of developing quantum mechanics.

I mean, there were some complicated things like, for example superconductivity, which were completely unintelligible; but one understood, I think rightly, that this was in principle contained in the known equations but was just too complicated to see through. The real exceptions were the relativistic problems because one had trouble with the Dirac equation over the negative energy states, which weren’t completely understood. One had trouble with electrodynamics, and then one couldn’t say anything about nuclei; in particular the nuclei then still consisted of protons and electrons and one had no idea how the electrons could manage to stay inside the nucleus. In addition there were then only two dimensionless constants in nature: the fine structure constant and the proton and electron mass ratio. They were not so very far from each other; one knew about Eddington’s equation that linked them, although nobody believed in his argument. Still whatever you thought of the argument there was a quadratic equation which linked the fine structure constant to the mass ratio, which might be right— or something like it might be right. Then it was natural to think, first of all, that there was one step missing which would resolve the difficulties of electromagnetic theory, or all the relativistic electron theories — these two seemed to be connected. And it was plausible that this would be possible only for one particular value of the fine structure constant and that when you’d understood this.

Then you would also understand the mass of the proton and you would also understand how electrons got to be in nuclei because that evidently was a relativistic problem. Now I’m not saying that this was the common view; I don’t think I shared it really; I don’t think Niels Bohr for example would ever have had any such illusions. I don’t recall this statement being expressed in his presence, but there were sort of over lunch or sometime quite serious discussions about what we would do when physics was finished. By finished was meant the basic structure; of course, there are all the applications. The majority of people said that that would be the time to turn to biology. Only one person really took that seriously and did turn to biology, and that was Max Delbruck, who certainly was present at these discussions.

Heilbron:

So the outstanding difficulties were thought to have imminent solutions, or were likely to be set aside soon?

Peierls:

Up to that point things had moved so quickly that it seemed hard to believe that if you have solved all but one of the problems that the last one would take very long. Now it was very naive of course because it was hard to believe that one single step should immediately resolve all the problems about nuclei. But then there weren’t any problems about nuclei basically because so little was known; I mean, there wasn’t any quantitative evidence to explain.

Heilbron:

Excessive particles!

Peierls:

Certainly not that, but I mean nuclear levels and anything like that was —. Oh, there was some fine structure of alpha rays where you had to take different nuclear levels, but otherwise nuclear spectroscopy didn’t exist.

Heilbron:

When would you say that that attitude was changed? When was it recognized that one was a long way from any solution? Just restricting the conversation to the quantum electrodynamics, when would you say people were convinced that there were fundamental problems that weren’t going to be solved very quickly or easily?

Peierls:

Well, the idea that quantum electrodynamics was very hard I think grew gradually just as time went on and all efforts to get round the difficulties failed; that made one realize it was really a tough problem. But more generally, of course the discovery of the neutron which followed shortly after this time immediately made it obvious that physics was richer than we had seen prior to that. Then of course shortly after that came both the work about the interactions of neutrons with nuclei and resonance levels and so on and also the artificial disintegration which immediately started showing up nuclear levels. A new field opened up where it then became obvious that there was a lot to be done and to be understood. For one thing, as soon as you know of the neutron, it was quite clear that you must have new kinds of forces holding nuclei together. I think probably people who had thought seriously about it, always realized this, but not very quantitatively. I think then one just forgot about this idea of physics being finished.

Heilbron:

Were there any difficulties in accepting the neutron itself?

Peierls:

No.

Heilbron:

You regarded the evidence immediately as convincing and there were no other difficulties?

Peierls:

Well, I mean with any piece of experimental discovery there is a period of discussion about whether the experiments are really conclusive and so on. But there was certainly no theoretical difficulty; there was no reason why there shouldn’t be a neutron.

Heilbron:

No, except that one hadn’t found them before; that’s always a partial reason.

Peierls:

No, but with the neutrons I think it was immediately understood that by the then conventional techniques they were very hard to detect. Therefore it was much less surprising that the neutron had escaped discovery than that the positron had. In fact about the positron there is a nice point. There was one physicist then I think in Cambridge, Champion, who was investigating beta decays with a cloud chamber. He took thousands of photographs of beta ray tracks in a cloud chamber, sometimes with and sometimes without a magnetic field. He used various sources, some of which give positrons and some of which don’t. He had no actual positron emitters, but sometimes you have a mixed decay, or sometimes you have a secondary positron through a pair creation by gamma rays, and so on. And it so happened that he never had a magnetic field on with any sources which contained positrons. I mean, many of his tracks must in fact be positrons. Almost any source gives you, if the energy is high enough, some positrons, but of course if you see one or two tracks of the wrong curvature, then you think there are secondary particles going the other way. He must have felt rather bad after the discovery of the positron because if he’d just happened to have a magnetic field on, on the right occasion, he would have seen lots of them, well before they were discovered.

Heilbron:

Was that work done in the early thirties, do you recall?

Peierls:

It must have been.

Heilbron:

So that work was going on just when you arrived in Cambridge — those were nearly the final experiments.

Peierls:

Yes, I didn’t see much of the experimental side then, but I knew Blackett whom I had met before, and of course he was just right in this work.

Heilbron:

Was the situation at Cambridge much different than it had been in Borne, or in Germany; was it more casual perhaps?

Peierls:

Much more casual and, well, also it was summer and there was not very much organized activity going on, though there was some at the beginning. Theoretical work in Cambridge has always been, until quite recently, hampered by the fact that there was no department in the physical sense; there was no place where the theoreticians could normally be found. They usually worked in the colleges. Well, you could always go and see someone in a college if you really wanted to see him, but that takes some motivation, particularly as you weren’t sure you’d find him there. It’s very different from having a lot of people in adjacent rooms and running into them five times a day. I remember my first experience coming to the Cavendish. I had arrived there and wanted to call on Fowler, who was my official contact. I knew roughly the wing of the building and the floor he’d be on, and I found myself in a corridor with lots of doors without any labels and nobody around. So I wandered up and down the corridor trying to pluck up courage to knock at one of those doors. I found one door which seemed to be somewhat less conspicuous, or less important than the others, and I thought I might find sour kind of secretary or something in there to give advice. So I knocked at the door and went in, and it happened to be Rutherford’s office; Rutherford wasn’t there; I would have felt bad otherwise. Then eventually I went to somebody to tell me where Fowler could be found.

Heilbron:

Finally I thought if you would, it would be quite interesting if you could perhaps make some remarks in connection with your own work on theory of metals and solid state, at least into the early thirties. I have a partial bibliography which may be of some assistance.

Peierls:

Well, we have already mentioned the Hall effect and the small things. Then, the one paper on the thermal conductance of crystals which was my thesis. I found that extremely amusing because it’s a field which is remarkable in that if you make any of the plausible and obvious approximations, something goes wrong and you get complete nonsense. I mean you really must, to get any approximate idea of what goes on, include a large number of facts which at first sight seem unimportant. Therefore all the previous treatments which had tried to idealize the problem, in some way or other, went wrong. Starting with the theory of Debye for example, who in his usual, nice, way of approaching a subject, had said, “Well, the finite conductivity of a crystal is due to the fact that you don’t have linear equations; you have un-harmonic effects, and therefore waves interfere with and influence each other. Now we can picture this as simply due to the density fluctuations. If a wave travels through a medium where the density is not the normal one, that is, has a different refractive index, we can observe the dependence of the compressibility, of the sound velocity, on density. Therefore if you can work out the density fluctuations you get the right answer.” He did that, and he got a finite answer for the thermal conductivity, although one knows from other arguments that in the continuum model he uses the thermal conductivity should still be infinite.

The reason for that is that he put in formulae for static refractive index, whereas, of course, the density fluctuations caused by the lattice vibrations are in the form of waves which run with the same velocity, or approximately the same velocity, as the wave they’re trying to scatter. Therefore a static description is of course complete nonsense. And so it goes. This you see had nothing to do with the fundamental problems of the time, except in so far as it was important to check that the theory was now ready to account for the things that could not previously be handled. I learned in particular from this work the importance of what one might call momentum conservation in the collisions of the phonons with each other, so that you may get a kind of drift set up in a phonon system which would tend to persist in spite of collisions. I realized that this could or would be of importance also in electric conductivity of metals, and proceeded to look into that. This had not been taken account of in the work of Bloch. I thought at the time that this was a dominant effect probably under all circumstances; later one learned that it was important only at rather low temperatures. It has recently become of interest in connection with the so-called phonon drift in very peculiar experiments on thermoelectric effects at low temperatures, where one sees that this phenomenon really exists and is important, but not as generally important as I at first assumed. Also, similarly, the main point of the thermal conductivity in crystals, my Ph.D. thesis, was to predict that in a pure crystal at low temperatures the thermal conductivity should rise exponentially as the temperature goes down. This is true, but it was discovered only in the 50’s.

Heilbron:

Were there any attempts to discover it before?

Peierls:

No, I don’t think so. Well, first of all this was experimentally a difficult problem. That’s one reason; another reason was I think my paper wasn’t very easy to read and nobody believed it. Also, I probably overestimated the temperature at which this should start. I mean, I had the impression that if you just went down to liquid air or something you should see the beginning of this — actually you have to go to liquid helium temperatures. There was one other thing; I’ve mentioned that everybody previously got the treatment of this problem wrong. Well, I still made some quite serious omissions, a most important one being that I was talking about a pure crystal, not realizing that pure for this purpose meant also consisting of a pure isotope. If you have an isotopic mixture, then of course the random difference in the masses of the atoms, which is important for the lattice vibrations, of course, causes an irregularity which is quite enough to give you thermal resistance. This was of course something one shouldn’t have overlooked. It was pointed out by Pomeranchuk that this was an effect, but again it wasn’t noticed, and it was only when the Oxford people did experiments and noticed that some substances gave the exponential rise and others didn’t that it dawned on them that the substances which did were those which consisted of practically only one isotope. Then it was clear what was going on.

Heilbron:

Those were the experiments in the 50’s?

Peierls:

Yes.

Heilbron:

That’s most interesting.

Peierls:

Then this paper about metals [Paper No. 6] where I try to follow similar ideas. There I made the mistake of writing too many things into the same paper, because it really contains a lot of quite disconnected things, or independent things. I had always been bothered by the fact that for the whole picture one had, at the time, of the band structure — I think the word band structure wasn’t used yet — it was important that you should have energy levels which were separated by gaps, and in which, at the top, again, the velocity went to zero as it does at the bottom. Now this came out very easily from the Bloch picture of tightly bound electrons, where you just make the approximation that the state of the system is almost that of separated atoms which just interact slightly. But it was not clear now that would come out on the opposite limits starting from free electrons. Then I suddenly saw, and that was a great pleasure, that if you took free electrons and you put in a periodic potential, allowing, in the ordinary way, for the scattering of the electrons by that potential, these gaps would arise no matter how weak the potential. Only if the potential was weak the gap would be small, but the fact that it was there and that the velocity then at the highest level in the band was a standing wave, comes out.

Now that’s today a very elementary argument, but I think I was the first to point that out, and it was then picked up by Brillouin, and that satisfied me that I could see what was going on. And Brillouin then discussed the three dimensional case and came out with the Brillouin zones. But this was hidden away and Brillouin had noticed it. I believe today I would write that as a separate paper and not hide it away in. a paper on transport problems. Paper No. 7 we have discussed; No. 8 was essentially I think some corrections to paper No. 6 where I had noticed —. No. 9 was a lecture at a conference and a discussion really about what one could say about magneto-resistance, which then also was a problem, because what Sommerfeld had got out of his simple theory was wrong in order of magnitude. This was rather embarrassing because I thought I had an explanation and therefore gave a lecture at the conference. By the time the conference started I had realized that in the model I was then trying everything again canceled out and was in effect as small as Sommerfeld had it. But still I had announced the lecture, and well, I gave just a general review of the situation, and then in the paper No. 11 I had really seen what was going on. Paper No. 10 we have discussed. 12 was just a little point.

Eugene Guth was then in Zurich and was interested in solving the Fermi-Thomas model for a positive and negative ion. You can’t do it for a negative ion — that’s of course wrong — but certainly for a positive ion. There is then a question of what boundary conditions you have to assume and what happens there. This is one of the typical things I got annoyed with; there were some errors I saw him make, and so we started on this. And we thought we got it right. No. 13 is probably that famous paper where I had an argument with A. H. Wilson. He had come out with a paper saying the whole Bloch theory was nonsense and my papers too. Then I got interested in. optical properties of solids, and No. 15 was essentially my Habilitations schrift. Here the concept of excitons I think comes up for the first time. I didn’t use the word excitons; that was used by Frenkel.

Heilbron:

I noticed that you contributed to the first volume of the ‘Phys. Zeits.’ of the Soviet Union, and I was curious as to how that journal got started. Did they ask for contributions to their early volumes? Do you remember how that came about?

Peierls:

I don’t remember. I think that — now let’s see — that was in ‘32. I think that must have been during a visit there. Let’s see, ray recollection is that’s it’s probably quite a short paper and might have been just the basis of a talk given at a conference. Maybe it’s part of a talk. I was then visiting the Soviet Union several times. The first time in 1930 when I went to a conference there in Odessa — I think I went largely on the invitation of Frenkel who had been interested in my work on the Hall effect. Then I was invited the next year — that was presumably in ‘31 — to spend two months in Leningrad giving lectures on the theory of solids as it then was, and that’s when I got married also. Now this was published in ‘32, so it probably was written during one of those visits. I think it’s essentially a summary of the results of the paper No. 15. Well, I don’t know how far we should go on with that. Then come two papers on diamagnetism which are really extensions of Landau’s idea of electron diamagnetism in which I was very interested. Particularly the second one shows how one gets the de Haas-van Alphen effect out, which has now become a very interesting tool for studying metals. It seemed a complete mystery at that time.

Heilbron:

Was there much interest in this work of yours at Rome?

Peierls:

No. There was a polite interest, but I essentially worked on this by myself. I don’t know whether you would like for me to go over the rest. It’s really getting away from the fundamental period.