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Oral History Transcript — Sir Rudolf Peierls

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Interview with Sir Rudolf Peierls
By Dr. Lillian Hoddeson and Paul Hoch
In Oxford, England
May 13, 1981

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Rudolf Peierls; May 13, 1981

ABSTRACT: Solid state physics in its early days in Arnold Sommerfeldís and Werner Heisenbergís groups, where Peierls was a student in the late 1920s. Sommerfeldís group compared to Heisenbergí s group; interaction between experimentalists and theoreticians in Germany, in England and in the U.S.; Peierlsís thesis work on heat conductivity in non-metallic crystals (suggested by Wolfgang Pauli), done in Zurich in 1920 and defended at Universitat Leipzig; the application of the Heitler-London approach in other works (especially Felix Bloch, Arnold Sommerfeld); attempt to state the first use of names and concepts: energy bands, theory of solid bodies; the periods of optimism in the history of physics; the ďaccidentalĒ change of fields because of Nazism (Hans Bethe). Significant papers on absorption spectra, diamagnetism, phase changes and statistical foundations, published in the 1930s: reasons for selecting these topics; inspirational contributions in the work; responses; associated circumstances and events. Lev Landau and his work also discussed at length.

Transcript

Session I | Session II

Hoddeson:

Iíd like to start by backtracking a little bit over some of the ground that we covered in Minneapolis four years ago and then go on. First, Iím under the impression that your solid state interests began in (???) where you were between October 26 and Easter, 1928, spurred on by a special topics course by Sommerfeld in 1927-8, devoted to the electron theory of metals, which he was in the process of developing.

Peierls:

Yes.

Hoddeson:

Had you any interest at all in solid state before then?

Peierls:

Well, you must remember that I entered the University of (???) as a first year undergraduate in October, 1935, and until I moved to Munich a year later, in Ď26, I didnít even know much about atomic physics, nothing about quantum mechanics at all, so there was no occasion to develop any specialty. Then I stayed three semesters in Munich with Sommerfeld so that must have been Ď26 to Easter, Ď28, and started to learn about modern physics. Obviously the main interest of Sommerfeld and his group came up in that context. However, I wasnít ready at that point to even think about making any contributions myself. So I canít really say that I developed at that time any special interest in solid state physics. But that came when I moved to Heisenbergís department in Leipzig, where also Felix Bloch was then working on the quantum mechanics off electrons and matrixes. And then Heisenberg suggested a particular topic for me, which was the hole effect.

Hoddeson:

So that is really the beginning. I would like to ask you a few more questions about Sommerfeld and his circle anyway before we Ė- Iím glad we established the beginning of your interest, your relationship to Heisenberg and the problem of the hole effect. Bethe, who was also in that course, recalled that there were actually three courses that Sommerfeld was giving at that time. I Just want to see if that agrees with your memory of that time, to be able to document it at this point. He remembers that there was one large course with about a hundred people, Sommerfeldís regular six part sequence --

Peierls:

Right. Thatís what today we would call an undergraduate course. As I remember, in those days in Germany there was no break between undergraduate and post-graduate. There was no Bachelorís degree. But this was essentially an undergraduate course.

Hoddeson:

Right. Then there was a smaller course with maybe 20 people or so which was again a lecture course, that met about twice a week, the larger ore meeting three times a week, and that was on special topics, and this course on the electron theory of metal was in that category. In addition there was a seminar, which he remembers had almost as many people as the special topics course, which met once a week for somewhat longer, at least an hour and a half.

Peierls:

Yes.

Hoddeson:

Thatís the way you remember it as well?

Peierls:

Yes.

Hoddeson:

Were you part or all three?

Peierls:

Well, I do remember the undergraduate course, of course. I do remember Sommerfeld lecturing on the electron theory of metals, among other things. I didnít recall that this was a regular special topics course, but this may well be so.

Hoddeson:

But it was a lecture course?

Peierls:

It was part of a lecture course. His reports on theory of metals were part of a lecture course. But whether this was a continuing thing or not, I donít know.

Hoch:

Were there any other people that gave lectures on that, on electron theory of metals?

Peierls:

No. Except the seminar of course consisted of members of the department, usually on each occasion one member of the department would give a talk on either his own work or papers in the literature.

Hoddeson:

When you say members of the department, do you inc1ude people who were not yet on the Assistant level?

Peierls:

Oh yes, including graduate students, yes.

Hoddeson:

I see. Perhaps we could also go over -- two questions, first, was the seminar as well devoted to electron theory of metals?

Peierls:

Oh no. No.

Hoddeson:

It was not. OK.

Peierls:

There were occasional talks about the electron theory of metals, though I donít recall any specific ones, but it was simply theoretical physics in general, problems almost exclusively quantum mechanics at this time, but any topic in quantum mechanics. To give you an example, I remember my first assignment for that seminar, which was to report on the papers by Dirac and Pascual Jordan on transformation theory, which Sommerfeld said to me afterwards -- I donít know exactly when it was, but I presume in my second semester in Munich -- he said ďThere are these papers -- none of us are able to understand them really. Would you try and see if you can report to us, explain to us?Ē Now, for a student of three semesters standing at university all together, this was a somewhat tough assignment.

Hoddeson:

Yes! How did you do?

Peierls:

Well, I mean, I learned a lot from this. How much other people got out of it, of course I canít say.

Hoddeson:

You had to learn a whole new formalism in order to read those papers.

Peierls:

Yes. Yes.

Hoddeson:

How much time did you have for it?

Peierls:

I donít remember. A few months.

Hoddeson:

Oh, it was a whole semester?

Peierls:

Well, I donít know. I canít remember. It might have been a couple of months. It might have been a semester.

Hoddeson:

But it wasnít something you had to do in a few days.

Peierls:

No, not in a few days. I remember, I didnít finish in one week and it was continued the following week so I took two seminars with this. I think it was well received except by the experimentalist Willie Wien who didnít like quantum mechanics, period.

Hoddeson:

He was a member of the seminar?

Peierls:

Well, he came to it anyway. This was quite informal. He might have come to some, not to others. There was no formal membership. So he disagreed with what I said, but his heckling was probably good for me.

Hoddeson:

Do you remember any other people who were in the seminar at that time besides Wien and Sommerfeld?

Peierls:

Well, all the people working with Sommerfeld. That is to say, his assistant, who was then I think Fisher, and his graduate students. I mean, there was no clearly defined statue of graduate students but that means, those people who had gone far enough to listen to advanced talks and think about it and such and so; and visitors. There were visitors for varying lengths of time. I canít recall of course how long each one stayed. Now, amongst the students there was of course Bethe. There was also, -- Bethe became an astrophysicist -- I find it hard to remember the names.

Hoddeson:

Eckhart? Houston?

Peierls:

These were visitors, yes.

Hoddeson:

Rabi?

Peierls:

Rabi came for a rather short time.

Hoddeson:

Pauling?

Peierls:

Pauling for a very short visit, when he -Ė

Hoddeson:

I see. Condon?

Peierls:

I donít remember.

Hoddeson:

Iím mentioning the Americans.

Peierls:

The visitors were mostly Americans.

Hoddeson:

Lloyd Smith? Kirkwood?

Peierls:

No, but they may have been there.

Hoddeson:

I donít know who else was there and was not a visitor. That information doesnít seem to be in any of the interviews Iíve seen.

Peierls:

No. Itís -- I mean, my memory isnít as good as it was.

Hoddeson:

But anyway Bethe was there.

Peierls:

Oh, undoubtedly. I think that Bethe was certainly Sommerfeldís assistant. I know, almost all that time did it, and I remember also Unsold was there. Now, there is one way which might Ö the point is, while I was there it was Sommerfeldís 50th birthday. He seemed a rather old man to me then.

Hoddeson:

Whose?

Peierls:

Sommerfeldís. And there was a festschrift, published, which is quite well known. Now, that of course contains articles by lots of people who were not there at that time. But I think or might look at the list of names to see if somebody was actually there at the time. I have it here.

Hoch:

We have a whole group in the Museum.

Hoddeson:

Yes. This is something they might look for.

Peierls:

Thatís right. And also, it might for example be that either Unsold or Bethe, who I think both are still alive, but Ė-

Hoddeson:

It would be worth writing a letter to them. I have another question about the seminar before we move on to Leipzig.

Peierls:

Yes?

Hoddeson:

Not necessarily about the seminar but about Munich. I understand also from Bethe that quantum mechanics was not included in Sommerfeldís cycle of courses.

Peierls:

Thatís correct. I donít think it was taught anywhere in any undergraduate courses.

Hoddeson:

I see. How did you learn quantum mechanics?

Peierls:

Yes. Thatís a good question. I think, by reading the original papers. You see, there were no books as yet. Though of course, one still had to learn the old quantum theory as a background, and on that there were books, notably Sommerfeldís.

Hoddeson:

Sommerfeldís book on it.

Peierls:

That of course I read. And then, one read the original papers, particularly by Schrodinger, which are so well written and talked with people and so on. But I donít think there were any systematic lectures on it. There were seminar talks about specific aspects of this development.

Hoddeson:

Now, a question about Sommerfeld. He far did he go in his understanding of quantum mechanics?

Peierls:

I think he understood it very well. He preferred the wave mechanics, the wave? PSI? Schrodinger? formulism, partly because he was a great expert in differential equations, and he felt at home. But also with his very concrete approach, he liked the wave function, and I think he was very disappointed also when the probability interpretation became established, which showed that the wave function itself did not have a physical reality. He, Like Schrodinger and many others, wanted the wave function to be something physically real. And now, therefore his particular, his main interest was applications in terms of atomic wave functions and so on, using elegant solutions of differential equations, at which he was a master. For example, he proved theories about the -- he gave the first formula for the photoelectric effect in hydrogen, which involves the hydrogen eiger functions? Very few physicists then knew one end of a [(????) or see an elementary quantum mechanics text for others.] function from another.

Hoddeson:

But he knew.

Peierls:

He knew. But he understood I think also other aspects of quantum mechanics, but his special interest was the very concrete approach to formula problems.

Hoddeson:

The reason I ask you the question is, Iím really interested in whether he was then or later able to grasp the work that you did, that built on the work of Bloch.

Peierls:

Well, I think, my impression is now you see, Iíd left Munich by this time and wasnít in very close contact.

Hoddeson:

Sure. He didnít do any further work in solid state, I gather?

Peierls:

That is right. I think it was getting too complicated for him. Or, he was capable of understanding it, but he wasnít interested in getting involved with it.

Hoddeson:

He just didnít want the work of sitting down and going through that material.

Peierls:

That is my impression.

Hoddeson:

No, getting back to Sommerfeldís theories, the electron theory of metals, did it bother him that his theory failed to account for a certain number of phenomena including the temperature, the temperature dependence of the resistivity and that the magneto resistance that he calculated was several orders too small, and that the mean free path was much too big and that the hole effect, the positive hole effect couldnít be explained? These were problems that must have -- was he aware of them?

Peierls:

Oh, certainly he was aware of them, and he was quite realistic enough to realize that these were important defects. But he was optimistic that in one way or another these problems would get resolved, which turned out to be right. He was, in his presentation in his lectures, he would tend to emphasize the positive side, and think that -- things where you had removed contradictions already -- without trying to hide the other.

Hoddeson:

I see. And of course it was remarkable how many problems were solved.

Peierls:

Thatís right.

Hoddeson:

At that time so he was perfectly justified in being optimistic. But of course the later work depended upon problems that were not solved.

Peierls:

Yes of course.

Hoddeson:

Did he in his lectures, did he try to justify dropping both the electron lattice and the electron electron interactions? And did anyone question him?

Peierls:

I certainly donít remember anybody questioning him. The -- On the electron electron interacting, of course all the older classical physicists left that out, on the grounds that collisions between electrons did not alter the total composite, resultant momentum and therefore did not alter the current, and were therefore irrelevant to the statement, I think which perhaps in classical terms is a good argument. So, being used to the classical treatment, I think he just started with a model where there was no electron electron interaction. But the lattice, well, you see, again, the background was that the old work of Lorentz and Drude, or Bohr had shown that there was such a lot of similarity between the behavior of electrons in a metal and free electrons, which couldnít be understood at the time -- I mean, why could they apparently travel freely? And then we, the distinctions between the fixed lattice and lattice vibrations and so on were not, didnít come up at all. So I think what Sommerfeld was doing was to take over the models that had been tried by other people, and modify them by putting in the Fermi-Dirac statistics, and nothing else. He knew of course that this was not a complete solution to the problem.

Hoddeson:

I gather, Bethe in particular was bothered by this at the time.

Peierls:

Yes. And he may have queried Sommerfeld but I donít remember.

Hoddeson:

Yes. Was Sommerfeld in close touch with the experimental work that was going on in some of the other, especially some of the other centers, such as the work of [Grueneisen?] in Berlin?

Peierls:

Oh yes.

Hoddeson:

Did he keep up with that?

Peierls:

Oh yes.

Hoddeson:

Did he communicate with them?

Peierls:

I think he communicated. He certainly was very well informed about the state of the experimental results, and now, I remember meeting Grueneisen; it must have been at the seminar visit, whether it was at Leipzig or -- no, it wasnít at Leipzig but whether it was at Munich or later in Zurich, I do not remember.

Hoddeson:

Actually anything you could tell us about Grueneisen would be very helpful. We know almost nothing except that his name appears always in the footnotes of these papers.

Peierls:

No, I mean, I didnít know him well.

Hoddeson:

Just anything about his reputation and was he considered one of the outstanding people, maybe second to Pohl or was that putting him?

Peierls:

I couldnít judge that. I wasnít enough involved in talking about the experimentalists. He certainly had a very high reputation, and his experimental results are always quoted. What I know is that he had a tendency to make simplified theories. I mean, there is a Grueneisen formula linking, if I remember correctly. The thermal expansion of a solid with the specific heat which makes some assumptions about -- is certainly oversimplified -- and of course, he did the best measurements about the temperature dependence, something like resistivity of metals.

Hoddeson:

Weíre interested in tracing the theme of the interaction between theorist and experimentalists in the various countries. For some reason, for reasons I could expand upon, but itís not necessary now, there is the feeling that the interactions were rather poor on the whole in Germany in this period, as compared for example to the interactions between the theorists and experimentalists in Great Britain in a somewhat later period and in the US. I donít know if that agrees with your recollections that they were at separate institutes for the most part?

Peierls:

Well, they were at separate institutes, but for example in Sommerfeldís Institute in Munich there were also experiments.

Hoddeson:

I was interested, when you told me that Wien came to the Sommerfeld lecture, I was actually surprised, because I had this impression --

Peierls:

Oh no, they were in contact. One has to remember that at that stage, the development of the theory was not really close to the current state of the experiments. In the electron theory of metals, one was concerned with facts which had been established generations ago, trying to sort these out. I donít even know whether there was anybody doing it in Munich, for example, doing experiments on the electric conduction of metals, anything like that, but the details wouldnít have made contact with the theory as yet, because the theory was trying to explain the very broad features that had been well established.

Hoddeson:

Then, to ask a question thatís out of context -Ė

Peierls:

Yes?

Hoddeson:

-- at what point in the history of solid state physics did the theorists catch up with the experimentalists? At what point did the experimentalists then have to go back and do better experiments perhaps using better materials?

Peierls:

Well, it wasnít a question of better experiments. It was a question of asking different question. I mean, you may remember for example that Mach emphasized in these long meetings how the theory induced Skinner to do experiments on ultraviolet experiments which could test the energy distributions of electrons in metals. Now, these were new experiments, inspired by the state of the theory. Not a question of better experiments, but something that that wouldnít have thought to be interesting before. Now, that of course is a gradual process. Well, I mean, there is the other line about luminosity and semiconductor physics, where the phenomena were only just being sorted out, traced out, at the same time as one was beginning to have a theoretica1 approach. Then therefore, anybody interested in the theory would be in close touch with the latest results of Pohl and so on.

Hoddeson:

So in fact this process happened in a very few years, of the theory reaching the experiments, maybe fiveÖ just a fewÖ maybe five probably? Yes? Very short time scale?

Peierls:

Yes.

Hoddeson:

OK. Then you went to Leipzig, Easter, 1928, to work with Heisenberg. Were there any other possibilities, or was that a completely obvious thing, that you were going to go to Heisenberg?

Peierls:

Well, it was a suggestion made by Sommerfeld when he decided to go away, and it seemed an eminently reasonable suggestion, so I donít think I considered any other course.

Hoddeson:

I see. I wonder if you could comment on the difference in environment in the two centers. In a way, at that point, the center of research in quantum theory of metals switched at that point to -- well, most of it in the beginning divided between Leipzig and Zurich, but I guess more of it was at Leipzig.

Peierls:

Yes. Well, thatís just accidental. You see, one was not then thinking of theoretical, of solid state physics or atomic physics or anything like that. There was quantum theory, quantum mechanics, and different people applied it to different problems and the same people at different times to different areas. I mean, in Leipzig the emphasis on solid state physics in Leipzig I think originated from the fact that Heisenberg realized there was a problem, he wasnít working on himself, and suggested to Bloch to look at the questions of electrons in matter.

Hoddeson:

When he was doing ferromagnetism himself using this --

Peierls:

Yes. But that I think didnít start with being interested in magnetism, but started by his having noticed the exchange interaction in problems of atomic spectroscopy Ė

Hoddeson:

-- his famous resonance paper Ė-

Peierls:

-- and then realizing that this could be an explanation for ferromagnetism, getting to work on that. So I mean in a way itís one of the cases where you start with the solution and then find the problem it fits into.

Hoddeson:

Unlike Sommerfeld who was really interested in solids, Heisenberg was really interested in quantum mechanics.

Peierls:

Yes. Well, Sommerfeld was also interested, not only -- this is just one line -Ė

Hoddeson:

Yes, he was interested in both, thatís right. All right, then, you were there while Bloch was working on his -Ė

Peierls:

-- thesis Ė-

Hoddeson:

-- his thesis. By the way, who thought of trying the tight binding Heitler-London [two separate physicists, Walter Heitler and fritz London] approach, which I think is first in the Bloch paper?

Peierls:

Well, one has to distinguish -Ė

Hoddeson:

I mean it was done by Frederich Hund and London in another context.

Peierls:

I think the Heitler-London paper came out first, and then, it was, everybody realized that there were two kinds of problems. One was the hydrogen molecule ion, the two protons and one electron, where the problem arises from having two centers. The other was to have the hydrogen molecule, as in the London paper, which has two electrons. Now, you could generalize both to a solid. That is to say, Bloch really used the (????) one electron problem. He just solves the problem with one electron in the lattice, and then possibly puts the interaction of electrons in as a correction or not. Now, one could alternatively start from the complete Heitler-London approach of neutral atoms, and in fact, Heisenberg suggested to me that I should try that.

Hoddeson:

In connection with the hole effect?

Peierls:

No, no, in connection with conductivity Ė-

Hoddeson:

(crosstalk) Ö with conductivity in general, I see.

Peierls:

And I struggled very hard, but couldnít get away from the conclusion that as long as this model was any sort of an approximation at all, you would have no conductivity. So then Heisenberg accepted that and we dropped the approach. It was not appropriate for metals. Thatís right. I mean, the point is that, if you have a metal, the probability of some atoms having excess electrons and others having a default of electrons must be appreciable, therefore this Heitler-London approximation which neglects that possibility, or itís small, canít be used.

Hoddeson:

How closely did you work with Heisenberg? Did you see him every day, once a week, or was it random?

Peierls:

Random. Iíd see him on the average probably once or twice a week, but more if there was a problem. I mean, you could always -- he was very approachable and you could always go to him if you had any question.

Hoddeson:

My impression of Sommerfeld is, the Germanic professor who was much harder to talk to than some of the younger people -Ė

Peierls:

Yes -- that was only a manner. He was really very approachable. But he was a busy man, and of course one didnít call on him quite as easily as on Heisenberg. I think, youíre asking about the difference in the atmosphere Ė-

Hoddeson:

The atmosphere, and also including the personal aspect.

Peierls:

Well, I think it was governed by the fact that Heisenberg was just about half Sommerfeldís age, and certainly, very informal, very modest in his manner. I think Iíd describe it, it was that the -- one used to play ping pong in --

Hoddeson:

With Heisenberg?

Peierls:

With Heisenberg or without, but Heisenberg was very keen and very good, and his ambition to excel in table tennis was more obvious than his ambition to be a very great physicist.

Hoddeson:

I understand he was also a very good piano player.

Peierls:

Yes. Yes. In fact, he as a young man, people tried to persuade him not to go into science but to music. I wrote a biography of Heisenberg.

Hoddeson:

Oh, I actually have that book; I just remembered (crosstalk)Ö I think you sent me a copy of that one. How far had you gotten on your work when you visited Cambridge in the summer of 1928? Were you already in the middle of your hole effect work?

Peierls:

No, I think I hadnít started that yet, or at least hadnít got very far. That was a period when I had just about abandoned the attempt to do things with the Heitler-London approach, and in fact, it was funny, when I mentioned that to Fowler in Cambridge, he said, ďI guess my student McCrae is just trying to do that, and I got in touch with McCrae, and my impression was that he had been doing the same thing. I wrote to McCrae to confirm this, and it turned out that what he was doing was something quite different. Either Iíd misunderstood at the time or my recollection was wrong.

Hoddeson:

I see. I was going to ask you a question about that because you did mention it in your article [Peierls wrote a review in Notgemeinschaft der Exact Wissurschaften (I think) might be a reference to this] in the Mach volume.

Peierls:

Yes.

Hoddeson:

It suggested that there were people in other countries also thinking about these issues.

Peierls:

Yes.

Hoddeson:

But I guess thatís not been -Ė

Peierls:

Well, McCrae was interested in conductivity.

Hoddeson:

Oh, he was interested in the electron theory of metals?

Peierls:

Yes, but he had a much more primitive approach, which didnít work. He published a paper, I think -- now, did I quote this in here? I have it here, I think. Yes, number 4. Footnote 4 on page 37.

Peierls:

No, I donít remember now what it was, but it didnít get very far.

Hoddeson:

It didnít get very far.

Peierls:

I mean, I think many people realized that the electrons in metal were one proving ground for quantum mechanics, and one should try to make some progress Ö

Hoddeson:

The question I had was whether this Ė- this otherwise suggested that there were perhaps individuals working a whole -Ė

Peierls:

Possibly -Ė

Hoddeson:

-- number of universities perhaps.

Peierls:

Yes, but you see, (???) at that time hadnít yet seen Wattís paper.

Hoddeson:

But they had seen Sommerfeldís work and that probably was what stimu1ated the -- I think what weíre trying to get a feeling for is (crosstalk)

Peierls:

-- yes, but itís not easy to reconstruct the, what people will do, think about one thing or another.

Hoddeson:

Well, one can look at the McCrae paper and look at the footnotes of course.

Peierls:

Yes, he might not, he might for example have been inspired by the Sommerfeld paper and he might not want to mention it because he wasnít making a direct application.

Hoch:

Did you have any interaction on this with Walter Heitler or Fritz London?

Peierls:

No, I donít think so. They visited various places, gave seminar talks on their papers, and I certainly heard them talk, one or the other talk about it, I canít remember where or when. But there was no close interaction.

Hoch:

This question of applying it to this situation was never really discussed with them?

Peierls:

I may have mentioned it to them.

Hoddeson:

What impressed you when you were in Cambridge? Did you for example hear about Diracís quantum electrodynamics which was then I suppose a hot subject. Or were there other things that impressed you at that time? Iím particularly interested in --

Peierls:

Well, the occasion for my being in Cambridge was really a summer holiday in Eng1and. I just, while I was in England I decided to visit Cambridge and to exploit my rather casual acquaintance with Dirac. Heíd been in Zurich visiting.

Hoddeson:

Did he tell you about his work?

Peierls:

No. Dirac is not a great talker, you realize. He likes to answer questions if you ask him. But I wasnít good enough, experienced enough to ask him any questions.

Hoddeson:

When -- I was wondering, when the hole in quantum electrodynamics came up, itís somewhat analogous concept to the hole in semiconductors. I guess he first published his paper with the physical interpretation of that in 1931, but it must have started earlier.

Peierls:

I certainly -- Dirac will never talk about unfinished things. I mean, his standard reaction, if you ask him a question, if he knows what heĎs talking about and knows the answer heíll say yes or no. If he hasnít, he will say I donít know. And therefore, you canít -- you can never engage him in arguments about speculative questions. So, certainly, no I think I probably talked very little physics with him then.

Hoddeson:

Back in Leipzig, Heisenberg then suggested that you look at the hole effect to see particularly if the positive hole effect could be explained, and that resulted in your first paper, which was published in [Zeitschrift fur Physik] in 1929, and then another more detailed oneÖ

Peierls:

YesÖ yesÖ yes, (crosstalk) Ö the one in was essentially the summary of a talk to the meeting.

Hoddeson:

Do you remember which meeting?

Peierls:

It was the German Physical Society, but where, on what occasion, I donít recall.

Hoddeson:

But was it really a regular Physical Society?

Peierls:

Yes. I, probably in fact, the mentions the -Ė

Hoddeson:

-- oh, not here, but maybe somewhere else.

Peierls:

Maybe at the heading, papers at the meeting.

Hoddeson:

Iíll have to go back and look.

Peierls:

But that Iím not sure.

Hoddeson:

Yes.

Hoch:

Maybe he remembers that large meeting on ferromagnetism that Bethe talked about?

Hoddeson:

That was in Ď33, so Ė-

Hoch:

Weíll come to it.

Hoddeson:

We should certainly get to it because thatís important. Ok your acknowledgement in this paper suggests that you talked to Bloch a lot about it. Itís the longer one.

Peierls:

Yes. Well, mainly that Ė-

Hoddeson:

You thank Heisenberg and Bloch.

Peierls:

Well, Bloch I think essentially made his thesis available to me, which I donít know whether it was published at the time I did the work.

Hoddeson:

It came out, well, it doesnít have the date. It was submitted in August, Ď28, and it appeared in Ď28.

Peierls:

Yes.

Hoddeson:

I donít know which month.

Peierls:

Well, I moved to Leipzig at Easter, Ď28. So it was probably started -- well, thatís right, it was submitted August Ď28. Those papers were published quickly but it must have been October, November, so obviously I must have seen Blochís copy of it, and he no doubt talked some about it. I donít think he specially helped with the specific problems. Ach, I remember, there are in that paper questions about the current of electrons (the Bloch electron)? The current of the Bloch electron, also the acceleration of the Bloch electron in a magnetic field, and I remember discussing that with him. We had some arguments, whether what was good proof and so on.

Hoddeson:

Youíre talking about his paper or your paper?

Peierls:

My paper.

Hoddeson:

Your paper. I donít think he turned on the magnetic field in his paper.

Peierls:

No.

Hoddeson:

All right. Well, letís turn to the hole effect work. You used BlochĎs approach, which is based on Heitler-London but slightly different, not exactly the same.

Peierls:

Well, we donít usually call it the Heitler-London because that takes the electron electron interaction into Ė- Now, he may have Ė-

Hoddeson:

He called it the ď(???)Ē and then the only reference he gives is Heitler-London.

Peierls:

Yes. But that I think is misleading. Itís probably a correction. Ah, he says, well, he uses perturbation theory in the spirit of HeitleróLondon, but he immediately says, ďOh no, they deal with the two electron problem, we restrict ourselves to the one electronĒ -Ė

Hoddeson:

-- the one electron problem.

Peierls:

So he merely uses their ideas, that he used perturbation theory.

Hoddeson:

Ok. Ok. Now, Heisenberg, he was using a somewhat different approach.

Peierls:

Ah, he was using the Heitler-London model for his ferromagnetism work.

Hoddeson:

Right, he was using the whole Heitler-London machinery.

Peierls:

Thatís right. And therefore his model of ferromagnetism is really not very good for a metal. But it is a good model for a molecular insulator. A source.

Hoddeson:

How did Heisenberg respond to your discovery that electron near the band edge, an electric field, would cause a decrease rather than an increase of velocity? That essentially was a solution of the problem. Do you remember when you brought this to him?

Peierls:

I think he was pleased by it because he saw that that was the answer. Now, there is an uncertainty, which I think I may mentioned, I think at the interview in Minnesota I probably told you that Heisenberg put the problem to me with the idea that the answer was probably analogous to the spectroscopic experience, that the atom was a complete shell minus one or two electrons, which has a similar structure to the (???) of the electrons. Now, I thought at the time that Heisenberg had seen that from the beginning, and told me to look for it, for this. But I then got out (???) and it may also be that he made that remark only when I went to him with the solution of the problem and he said, ďAh yes, of course, thatís just like the -- ďSo I donít know which is right.

Hoddeson:

Do you remember when you solved the problem? The occasion or is that something that doesnít come out in your memory?

Peierls:

Well, it came gradually, you see, because first of all (crosstalk) it is not a sudden thing, because Ö (off tape) So, first you had to see that the solution was this way. Then you got worried, of course, that this might mean that the conductivity would be negative, which would be nonsense. So you had to think of statistics, of a lot of electrons, to see what this would do to the conductivity. And then, having seen that the conductivity wasnít changed, then you thought, well, maybe that would also not change the hole effect either. So then you had to put the magnetic field in and work through it, and so there were many steps before or could really see that this was the answer.

Hoddeson:

How long did it take you to do this problem?

Peierls:

I couldnít say. Not very long. Things happened very quickly in those days.

Hoddeson:

The question about holes. The question is, where was the hole invented? It seems to be here in the second paper already, or am I distorting things? The passages that are underlined on page 262 of the lengthier paper on the hole effect Ė-

Peierls:

-- yes Ė-

Hoddeson:

-- not completely here yet -Ė

Peierls:

It is there, but it certainly is not emphasized. You see, this of course is a fantastic thing, that it seems that it took a very long time for people to realize that an insulator could be a system with a full band.

Hoddeson:

Which is already here, too, in these two papers.

Peierls:

Yes, but apparently nobody else paid attention to this. Itís not surprising, because theyíre long papers and not very well written, because Wilson reports and Bloch confirms that when Wilson made that statement to Bloch some time later, Bloch disagreed with it and wouldnít accept it as such.

Hoddeson:

Right. I guess we talked about that in our earlier interview.

Peierls:

Yes.

Hoddeson:

And itís come up before.

Peierls:

Yes.

Hoddeson:

But itís here already. Were you aware of it?

Peierls:

I must have been, on this. I must -- Iíve not said anywhere explicitly ďthis is an insulator.Ē

Hoddeson:

And Bloch must have read your paper on the hole effect?

Peierls:

It seems so, but not necessarily to think about every sentence in it.

Hoddeson:

Because this argument about the filled bands is -- and that substantially is -- the question, of course, is for us to face in writing this history, is, when did the idea of bands begin? When did the idea of holes begin? Was it understood that if you have a filled band, you have an insulator? It seems to me that itís already all here in the papers.

Peierls:

Yes. Well, the point is that, if you, if itís a question of priority, who made the statement first, then probably this might be relevant. If it is a question of, when was it generally realized? Thatís a different matter, because it doesnít seem that anybody noticed this.

Hoddeson:

Thatís true. Do you know when the concept of the hole in the context of solid state physics did become, first, clarified? I found it, I didnít look thoroughly through the literature, but I found it very clearly described in a paper by Heisenberg in 1931 on the Pauli principle. I donít have it with me, unfortunately where he was using that as just one example to explain the Pauli principle.

Peierls:

Yes.

Hoddeson:

And there one gets a very good description of the hole acting as a Ė-

Peierls:

-- yes, well, (crosstalk)

Hoddeson:

Ö infinite sea of, not infinite, but Ė-

Peierls:

Well, that is, yes, yes Ė-

Hoddeson:

-- filled sea of electrons --

Peierls:

-- yes, well, that doesnít surprise me, because I had the conversation with Heisenberg which I mentioned, either when I started on this work on the hole effect, or when I finished it, I donít know which, but certainly one or the other, where he saw very clearly the analogy between this situation and an atom with an almost complete shell.

Hoddeson:

Right -- Right.

Peierls:

And there certainly this concept is clear.

Hoddeson:

Now, I was Interested when I looked at Diracís paper, which I looked at for another reason -Ė

Peierls:

-- what is the date on that?

Hoddeson:

The Dirac paper was 1931. I donít remember when in 1931. And the Heisenberg paper was 1931. And in both papers, they make the same analogy to many electron atoms.

Peierls:

Yes.

Hoddeson:

But I was curious then because nowadays in courses people make the analogy between the two different poles, and I was wondering whether that analogy was made around 1931 as well, and I see no evidence for it in the published work, but you were there at the time and probably the best person to comment on this.

Peierls:

Well, let me, certainly, when Diracís paper on the hole field came out, it was obvious to me, of course, if there was an analogy with the electrons in metals and other places -- now, when was Wilsonís paper on the semiconductors?

Hoddeson:

That was also 1931, though I donít remember when. He doesnít mention holes at all though.

Peierls:

No, no, that was obvious.

Hoddeson:

What do you mean?

Peierls:

I mean, the fact that, if you get a few electrons, if you have an insulator and you transfer a few electrons, either through a conduction band or through an impurity, that whatís left behind are holes I think is obvious.

Hoddeson:

Yes, but he doesnít mention that in his paper.

Peierls:

He doesnít mention the word.

Hoddeson:

No.

Peierls:

No, no but Ė-

Hoddeson:

But the idea.

Peierls:

On a slightly facetious note, I donít know whether I told you one of my favorite Dirac stories.

Hoddeson:

I donít think so.

Peierls:

Once Dirac was walking in Cambridge together with Hume who was a physicist also, and Hume had something in his pocket which rattled. He said, ďIím sorry about the t noise, but I have a bottle of aspirins in my pocket and I took some because I have a cold, so itís no longer full and it rattles.Ē A pause, after which Dirac said, ďI suppose it makes the maximum noise when itís just half full.Ē

Hoddeson:

Thatís a very nice story.

Peierls:

I knew that story but I donít know the date, and I thought it would have been very nice if that had been just before the hole paper, but I checked later with Hume and it wasnít. It was after.

Hoddeson:

Itís still a wonderful story. OK, around, letís see, weíve already commented on this Wilson-Bloch business, where Bloch was surprised when Wilson pointed out that a metal is a case with a partly filled band.

Peierls:

Yes.

Hoddeson:

In Wilsonís papers, here -- more than two years after your paper Ė-

Peierls:

Yes.

Hoddeson:

I wanted to ask a question about group theory. 1928ó29 Bethe began to study the group theory as written by Wigner and von Neumann at Frankfurt. Did you also study it?

Peierls:

Everybody did.

Hoddeson:

Everybody didÖ

Peierls:

Yes. The reason was that at that time it was believed that you could do calculations about many electron atoms or many electron systems only by using the representations of the permutation group, and you had to know group theory to do that, because according to the value of the spin, the orbital wave functions could be -- would be partly symmetric and partly unsymmetrical, would be mixed symmetry. It was only when Slaterís paper came out, who showed that by carrying the spin variables, you could always work with wave functions which are completely unsymmetrical and you could forget about group theory. All the -- Or the permutation group theory. At that time we happily started to forget all the group theory we had learned. But there was a period when -Ė

Hoddeson:

When everybody learned it.

Peierls:

Yes.

Hoddeson:

I guess Heisenberg must have learned it very well.

Peierls:

Yes. I think youíll see that in his ferromagnetism paper, he used the group -- (crosstalk)

Hoddeson:

-- he uses it; I havenít looked at that in a long time so I have to go back. But certainly Bloch uses it.

Peierls:

Oh yes. Oh, Bloch uses essentially translation group -- thatís a very simple -- you donít need much group theory for that.

Hoddeson:

All right. In the spring, actually, did you apply any of your papers, I donít remember seeing that Ė

Peierls:

I wrote a very minor little remark, I think it was my third paper published, on ionization energies.

Hoddeson:

Oh yes, I did look at that paper. Yes, thatís right, in 1929.

Peierls:

And there, this was where somebody made an analysis of the ionization energies and concluded from that that you shou1d break the L shell in the middle into two shells, pieces, into two groups, which was not a good conclusion, and I wrote a paper showing that without any such assumption you could get that behavior. I used the group factors for that because I didnít know any better.

Hoddeson:

In the spring of Ď29 you moved over to Pauli.

Peierls:

Yes. Hoddeson I seem to remember, some years ago when I was looking at the Pauli letters, that there was some bargaining going on between Heisenberg and Pauli over who would get Peierls. They felt they needed you around to help them with their problems. I donít know whether you were aware of it?

Peierls:

Iím not aware. It surprised me, because I moved to Zurich when Heisenberg went off on a sabbatical.

Hoddeson:

I donít remember the date and I would have to go back there Ė

Peierls:

Certainly on that occasion there was no question. In fact Heisenberg himself said, ďIím going away so youíd better go somewhere else and I suggest you go to Pauli.Ē

Hoddeson:

It may have been somewhat after that.

Peierls:

Maybe after that?

Hoddeson:

But you didnít leave Pauli at all, you stayed with him for --

Peierls:

-- thatís right, and if there was any desire on Heisenbergís part to get me back, I wasnít aware of it.

Hoddeson:

I may be remembering it wrong Ö perhaps you could also then comment on the difference between Leipzig and Munich now, having commented on the difference between Ė-

Hoch:

-- Zurich Ė-

Hoddeson:

Leipzig and Zurich, excuse me.

Peierls:

Well, in general Pauliís group was much smaller.

Hoddeson:

Who else was there?

Peierls:

Except for -- I mean, just at the time when I came there -- because most of the people who would have been, would have stayed in Leipzig moved over there. Just as a lot of people had come to Leipzig from Sommerfeld, you remember.

Hoddeson:

Right.

Peierls:

Now, who else was in Zurich? Now, who was Pauliís assistant at the time? I think it was Bloch the first semester I was there.

Hoddeson:

I see. Did you both move over at the same time or Ė-

Peierls:

He might have got a semester earlier. Itís hazy. And itís hard to remember because his home was in Zurich, and therefore even when he was working in Leipzig, he turned up in Zurich frequently. But I think he was there the first year, first semester I was there as Pauliís assistant. Now, who else? There was the university, which is not the same department, but there was close contact -- there was Menzel -- the professor. Iíd have to think very hard to recall names in that period.

Hoddeson:

To go to this separation between the university and Pauliís department, perhaps you could explain that a little bit. Weíre not familiar with the institution.

Peierls:

Letís see. Pauli was at the E.T.H. [Eigennossische Technische Hochschule] which was the Federal College of Technology, and this is federal, whereas the university belonged to the (???) of Zurich.

Hoddeson:

I see. And physically how close were they?

Peierls:

Physically they were, oh, ten minutes walk from one to the other. Wetzel, I think would come to most of the seminar meetings at Pauliís place. And I think probably he didnít have a -- ah, no, there must have been some physics meeting, some physics colloquium, because there were experientialists but there werenít enough theoreticians at the university to have a theoretical seminar. Thatís what I remember. I donít know whether Wetzel had at that time any students. He hadnít been there long. So, officially there was no connection whatever between the two, but in fact there was a good deal.

Hoddeson:

Intellectually.

Peierls:

Intellectually there was close contact.

Hoch:

Do you remember what Wetzel was working on at that time?

Peierls:

Pardon?

Hoch:

It wasnít electron theory of metals?

Peierls:

It wasnít metals, no. And Ė-

Hoddeson:

We can look it up, I suppose. Anyway Pauli then starts you on a problem involving heat conductivity in non-metallic crystals. That was the first problem?

Peierls:

Yes.

Hoddeson:

And I gather that, although he wasnít interested in solid state physics, although he started it in a way, he was interested in this problem possibly because it was a model for field theory, as you mentioned in the interview two years ago, or is this speculation?

Peierls:

Thatís just a speculation. Well, he was intrigued by the problem generally of non-lineal effects in these, in crystals, or he had himself started some work on the absorption of sound waves by crystals, which is essentially due to the same cause, or in fact had reported on that to a meeting of the German Physical Society, or he gave -- where he gave the wrong answer Ė-

Hoddeson:

You mentioned that.

Peierls:

So obviously I think he wasnít satisfied with the situation, and thatís why Ė-

Hoddeson:

-- he gave this to you.

Peierls:

Yes.

Hoddeson:

I see. This was then your thesis.

Peierls:

Yes.

Hoddeson:

In your interview with John Heilbron in 1963, on the quantum physics project, you reflected that in this problem, if you make any of the plausible and obvious approximations, something goes wrong and you get complete nonsense.

Peierls:

Yes.

Hoddeson:

You discussed for example Debyeís abortive attempt to picture the phenomenon in terms of density fluctuations.

Peierls:

Yes.

Hoddeson:

Looking at the problem more carefully and considering momentum, the momentum conserved in the collision of the phonons then led you to the idea of phonon drift in this paper.

Peierls:

Yes. I donít think I called it phonon drift, but --

Hoddeson:

-- itís there, another beginning, in this paper.

Peierls:

Yes.

Hoddeson:

Which later came to be understood as significant on the bearing of temperature. The main result of the work, I suppose, is the concept of the CronKlapp processes, and the prediction of the exponential rise of the conductivity, which was then verified in Ď50. When it was also realized that isotopic purity was -Ė

Peierls:

-- important Ė-

Hoddeson:

Important in order to see this experiment exponentially, rise. I guess we donít have to go over that, because this you commented on pretty Ė-

Peierls:

-- I think so Ė-

Hoddeson:

-- pretty well in the earlier interview.

Peierls:

Yes.

Hoddeson:

Now, your degree came right after this thesis was then submitted in 1929?

Peierls:

Yes.

Hoddeson:

Do you remember who evaluated this work?

Peierls:

Yes. It was Hund who was the second professor at Leipzig. Heisenberg was still away, so, also Hund conducted my oral examination in physics, where he asked me -- I was expecting of course to be asked very intricate questions about quantum mechanics and atoms and possible solids, instead of which most of the questions were about the classical theory of three dimensional rotation, all the angles and what not, which I remembered to some extent. And when the interview was over, he said, Hund said, ďI only asked you these questions so you shouldnít think that you know everything.Ē

Hoddeson:

Did he go through this in detail, this work?

Peierls:

He must have done.

Hoddeson:

He did.

Peierls:

I donít remember whether he asked me any questions about it. He may have done but I donít remember. The time scale is funny, because I moved to Zurich in April, Ď29. I spent all my spare time in the first few weeks translating a book by de Broglie into German in a hurry. And then I got things organized in the department, was given this problem by Pauli, solved it, wrote a thesis, typed it myself, submitted it to Leipzig because I didnít have the residency and got my degree, took the final at least at the final oral examination. I canít remember whether this was the 23rd of July or the 23rd of August.

Hoddeson:

But it was in Leipzig.

Peierls:

Yes.

Hoddeson:

Thatís where Hund was then based.

Peierls:

Yes.

Hoddeson:

There must be some document some place.

Peierls:

Yes. I think I still have my doctorís diploma somewhere.

Hoddeson:

Letís see. Oh yea, I put a box around the first line in this paper, because it refers to the kinetic theory of solid bodies.

Peierls:

Yes?

Hoddeson:

And another theme that will be going through our book is the emergence of solid state, the study of solids, which eventually became called solid state physics, as a central theme.

Peierls:

Yes. Right.

Hoddeson:

And one wonders when words like this first began to be used. Now, was this a very common, to refer to the theory of solid bodies? The earlier work refereed to electrons, electron theory. Does this mark a transition?

Peierls:

Well, there are no electrons involved here.

Hoddeson:

Right.

Peierls:

I couldnít call it --

Hoddeson:

You couldnít call it electron theory. But were people beginning to think of the study of solids?

Peierls:

Well, I think, you see, all, the work, well, starting maybe with Einsteinís first paper on vibrations of crystals, then Debye, von Karman and so on, I think one realized that they were talking about solid bodies, and the experimental work also on measuring specific heats, thermal conductivities and so on, I think you may find that certainly in Germany the tradition goes back quite a long way. For example, it will be interesting to look up, I donít recall it, there was in the thirties or -- the first edition of the Handbuch der Physik had many volumes -- I wouldnít be surprised if one of those volumes is called physics of Solids or perhaps Crystal Physics but Iím not sure.

Hoddeson:

Well, we can certainly check that. I wonder -- One wonders when all the isolated subfields, some of which go way back, even thousands of years perhaps if you consider the metallurgists, but most of them just a century at most, but they were separate areas which then came together some time in the twenties and thirties and were put under a common umbrella of solid state physics, and one wonders when this coalescing began to take place, in the minds of people who were working at that time. So thatís just something that I hope in our work we will be able to answer. Well, now, you, I wonder, was Pauli, after this you went, you picked up the electron theory again, studying electric and thermal conductivity.

Peierls:

Yes.

Hoddeson:

How did Pauli feel about that? I gather from Bethe and some other people that he wasnít really too happy with solid state physics.

Peierls:

I think he didnít mind that. In fact, at one time, when he realized that these UmKlapp processes would also arise in metals, not only in insulators, in certain circumstances, and therefore that in some circumstances you might get a very high conductivity at low temperatures, and then, obviously like with any new idea, you ask yourself, could this help to understand superconductivity? I remember discussing that with Pauli, and Pauli getting quite enthusiastic and saying, ďWell, if you can justify that, if that really can explain superconductivity, then it would be very nice.Ē But the context was that I was anxious then to get the habilitation -- as you know, permission to lecture, for which you submit a special thesis -- probably with the FC or something like that -- so when this came up, Pauli said, ďWell, if this can explain superconductivity, then you can certainly have your habilitation.Ē

Hoch:

Thatís very generous of him.

Peierls:

Which of course it didnít. I got the habilitation with some other paper.

Hoddeson:

Itís superconductivity he was interested in?

Peierls:

Oh yes.

Hoddeson:

If not the other problems.

Peierls:

He knew that that was an important principle. You see, he was not so keen on work on details, with approximations and quantities questions and so on. Principles, he was interested in. Thereís another thing about his attitude, perhaps I could mention, another bit of history there. I wrote a paper on diamagnetism, which he didnít like because it was complicated and made approximations and so on, and in fact, I remember some very uncomplimentary remarks he made about that paper. But then, extending that to low temperatures and thinking about it, it became clear that the other thing was the explanation of the de Has-van Alphen effect, which is a very interesting oscillation of the diamagnetism, and in that Pauli was very interested. In fact, when I wrote my book about electron theory of solids, I sent a copy to Pauli, and, of the first printing, and then I got after some time a very rude letter from Pauli, because it turns out he had given some graduate lectures in which he wanted to present the theory of the de Has-van Alphen effect, and had used the equations from book, and unfortunately there was a misprint In one of the equations, so Ė-

Hoddeson:

He blamed that on you.

Peierls:

Yes, he was very cross about that. Well, whether it was a misprint or due to the printer or, in which case I failed to correct it, or whether it was a copying error of mine, I donít know. Anyway, as far as I know it was the only mistake in the book, but that it should happen just in the one thing that Pauli wanted to pick up -- but obviously here was again something in solid state physics that interested him.

Hoddeson:

I was just curious because itís well known that he didnít like solid state physics, and here you were working for him for a number of years on solid state problems and he seemed Ė-

Peierls:

Well, not only. I was interested in other things as well. Not all of it was published, that I was trying to do.

Hoddeson:

I wonder if you could comment on the way in which Pauliís thinking influenced you, in contrast perhaps to the way Heisenberg inf1uenced you, or is that something that is not -Ė

Peierls:

One isnít always so aware of this. I think Heisenberg had -- his main characteristic was an enormously powerful physical intuition. In fact, I have described his lectures; described his way of working, that he intuitively knew the answer to a formula, and then set out to find a mathematical technique, a mathematical method which would give that answer. Which is alright if you have as good an intuition as Heisenbergís, but otherwise youíd better not try that? But I mean, his way of looking for the simple physics in the situation, before you sit down to do the calculation. That I think I got from him, to some extent. Pauli -- well, I suppose I learned more, first of all, to see the connections between different things, and also his very critical approach of not being satisfied with a sloppy argument, but really wanted to get down to, to get things right. That is bound to have an effect. I am not saying it very clearly, but Ė-

Hoddeson:

I get the idea. The next -Ė

Peierls:

We should break.

Hoddeson:

Should we break soon? Weíre getting to the end of this, -- Ok, well, letís, if youíd like to break now (Crosstalk)

Peierls:

Well, or we can go on for a littleÖ, see a ÖstopÖ

Hoddeson:

Why donít we stop here?

Hoddeson:

Weíre now continuing after lunch, and we were up to the very important paper that you wrote on the theory of electrical and thermal conductivity in the 1930ís and this is the paper where I think you first described the band gaps.

Peierls:

Yes.

Hoddeson:

As I gather, this is where the discovery is made.

Peierls:

That band gaps arise even in the weak bonding.

Hoddeson:

Right. Right. Actually you discuss the concerns which led to this in your interview with me and Gordon earlier.

Peierls:

And I think also in the --

Hoddeson:

Right, so actually I guess we donít have to go over that. You showed that the gaps would arise no matter how weak the periodic potential, so letís move on. One of the important aspects of this paper is that then, as you say, it led Brillouin to his theory of Brillouin zones in three dimensions, and thatís discussed in his 1931 paper in the classic book: Did you have any interactions with Brillouin over this?

Peierls:

No. I met him on some occasions at conferences. We had polite conversations. Thatís all.

Hoddeson:

Right. Was there a big effort started then in France, or was he working essentially in a vacuum at that time? We havenít really had a chance to go into that.

Peierls:

I donít know that, because at that time I wasnít in close touch with the people in France, so I donít know.

Hoddeson:

Because here suddenly someone from another country is making a major contribution to this area which, up until now, was almost entirely confined to -Ė

Peierls:

-- well, he was in touch with -- I mean, he read the papers, he knew what was going on in physics elsewhere. But how many other people? Iím not aware of any other theoretician in France that was interestedē There may have been. There was experimental work, but not on these topics, I think. I canít recall.

Hoddeson:

Now, the idea of energy bands, as we discussed before, comes up first in your hole work, but at this time -- now, Iím not trying to ask about Ė-

Peierls:

Itís in Blochís paper already.

Hoddeson:

Itís in there, yes.

Peierls:

I mean, whether he used the word ďbandĒ, thereís no, I donít know whether I used it in my hole effect paper. But the concept is there and the concept is in Blochís paper.

Hoddeson:

Now, the next question is, when did the concept become accepted? Certainly it was well accepted by the time you wrote your review in the (???) because you used the word there.

Peierls:

Yes.

Hoddeson:

So then, the question is, when does it gradually become accepted, as a way of describing solid, metal in particular?

Peierls:

Thatís hard to pin down.

Hoddeson:

Yes, but thatís what we will have to try to do. The work of (???) maybe.

Peierls:

But I mean, you have to be clear about how you define being generally accepted, because clearly the number of people who understand and use the concept will grow continuously. There is no sharp line, when it is accepted.

Hoddeson:

Thatís true. Well, one thing to look for is, when the term began to be used.

Peierls:

Yes.

Hoddeson:

I havenít found that out yet. I know it certainly is (isnít?) in the Ď32 papers but I havenít gone through the (???) work yet.

Peierls:

I donít remember.

Hoddeson:

I mean, here I donít think you use it in this paper, so, -- Ok then you have this brief paper, remarks on the theory of conductivity, where you try to deal with the phonon problem and you get a T4 log but you donít really -Ė

Peierls:

-- yes, which was a mistake.

Hoddeson:

-- come to grips with this until a later paper, in 1932. You say in the (???) volume that the T fifth law worried you a lot, and the fact that the exponential rise couldnít be observed.

Peierls:

Yes.

Hoddeson:

Actually we discussed this, yes. Another question from the volume article, you referred to a conversation with Landau on estimating the contributions at various factors to the resistivity by dimensional reasoning.

Peierls:

Yes.

Hoddeson:

In which he showed that the electron-electron collision was negligible at certain temperatures. And essentially the argument deals with electrons at the Fermi surface being the only ones important --

Peierls:

Yes.

Hoddeson:

And you dropped provocative statement that this was really the basis of the Fermi liquid Ė-

Peierls:

-- well, the beginnings Ė-

Hoddeson:

-- theory. That, I was wondering whether you could tell me a little more about this, because thatís something that weíll probably be looking into.

Peierls:

Well, I mean, it was only hindsight, when I saw Landauís work on the Fermi liquid theory, that I saw the analogy; that this sort of thing must have been in his mind there. You see, the essence of Landauís remark is that if you are at low temperatures, the only interactions that can take place are between electrons near the, in the narrow range near the Fermi surface, and their number, therefore, the importance of such collisions goes down with the temperature. Therefore, although the interaction matrix elements may be quite strong, nevertheless the electrons behave as if they are in a definite state, and well, that means, in the early conversation what came out of that is that therefore the electron-electron interactions do not interfere much with the conductivity, and the Fermi liquid paper then, the Fermi liquid theory, it means that you can really describe the whole situation as, the state of excitation, in terms of quasi-particles moving independently. You see, thatís the same thought carried a little bit further. Does that explain it?

Hoddeson:

Yes. Thatís very good. Itís very helpful. Letís just focus for a few minutes on the magneto resistance, which is a longstanding problem in the electron theory, because the experiments were very good quite early.

Peierls:

Yes.

Hoddeson:

I guess. And you worked on this problem in 1930 and 1931. OK, you explain, you give some explanation of this in the volumes, no need to go over what you say there. The question I have that wasnít asked is was Bethe working on this also in the same period. And I was wondering whether you had any interaction with him on this?

Peierls:

I donít remember. There may have been correspondence. We werenít in the same place then but there may have been letters.

Hoddeson:

I didnít have a chance to ask him about that.

Hoch:

I think we have some of those letters.

Hoddeson:

Oh, do we?

Peierls:

Donít I say something here about it?

Hoddeson:

I think you mention some contribution that Bethe made to the problem, but I donít know if you related it toÖ basically in this Mach volume, you explained that there were really two problems, that simple theories like Sommerfeldís gave a negligible effect, but Kapitzaís experiments gave a linear H dependence, while the theories gave a (???) dependence. And then you talked about a -- you gave a talk about this in Leipzig in 1930, arguing about the breakdown in terms of the usual expansion.

Peierls:

Yes.

Hoddeson:

Under circumstances, where the lambda? Period is shorter than the collision time. But then that gave zero, negative resistance.

Peierls:

Yes. Yes.

Hoddeson:

And you talked about your embarrassment about that.

Peierls:

Well, you see, here, this has also been found by Bethe, and I donít remember clearly how far my ideas have been inspired by his paper. I didnít remember it then and so I donít remember it today.

Hoddeson:

Yes. Well, I was wondering whether you two, because you had known each other so well Ė-

Peierls:

Yes, well, I mean, if there was a letter on that subject, I donít recall it. It might exist.

Hoch:

I can check that.

Hoddeson:

Well, we can try to check that. We donít need to go over your argument with Wilson about the cyclic? boundary because thatís in the other interview. The only part that was left out of the interview is whether or not Wilson ever came around to see the light?

Peierls:

Well, I think he must have done. He has written a book on theory of metals, which doesnít say much about conductivity but I think by implication he certainly accepts it now. So, I donít remember his ever stating in so many words that he agreed with me, but I think he must.

Hoddeson:

OK. Let me just change tapes.

Hoddeson:

Letís see, this small paper on the Fermi-Thomas model of positive ion, I guess thatís not really solid state?

Peierls:

No.

Hoddeson:

Weíll skip that one. As far as the -- yes, the diamagnetism, I would like to talk about, next time, so weíll skip that now. Why donĎt we comment, however, on this meeting in Leipzig in early 1933; arranged jointly by Sommerfeld and Debye on magnetism before you attended.

Peierls:

Well, I think that is the one where I had the embarrassing situation with my talk on magneto resistance.

Hoddeson:

I see. Do you have any other recollections of this?

Peierls:

No, that was my main recollection, you see.

Hoddeson:

Do you remember who else was there?

Peierls:

No.

Hoddeson:

We might get a copy of the Proceedings.

Peierls:

Well, the Proceedings are published both in German and in English.

Hoddeson:

I see.

Peierls:

Because I remember being asked to read proofs of the English translation of my talk. And the German version was published in a little booklet by Hitser, the publisher I think in (???) I cannot recall who published the English one.

Hoddeson:

We can trace that one down, as long as we know it exists.

Peierls:

Yes. Of course one doesnít quite know the title, of the English version. I think it was Macmillanís. It may have been Macmillanís.

Hoddeson:

There were papers in there by Heisenberg, Kramers, and Bethe. You donít remember?

Peierls:

I donít remember.

Hoch:

Your paper, this one, became your doctorís in

Peierls:

Yes.

Hoddeson:

OK, well, I gather the main subject was ferromagnetism.

Peierls:

No, I think just magnetism.

Hoddeson:

It was generally magnetism.

Peierls:

Just magnetism. Maybe some or the papers were ferromagnetism.

Hoddeson:

I see, well, Iíll go back and sort that out. All right, now in 1932, Ď33; you had a Rockefeller Fellowship to Rome and Cambridge.

Peierls:

Yes.

Hoddeson:

I was wondering if there was any overlap with Bethe in Rome. No?

Peierls:

No. He was a year earlier or two years, I donít know, I think a year earlier. I improved on his arrangement, because he arranged to spend the winter in Cambridge and the summer in Rome. I reversed the order.

Hoddeson:

Good thinking. When did you write your review article in the (???)?

Peierls:

I think it must have been in Zurich.

Hoddeson:

It must have been. It came out in Ď32.

Peierls:

Well, then it was definitely in Zurich because I didnít leave Zurich until the autumn of Ď32.

Hoddeson:

Right. And how did you come to write it?

Peierls:

I suppose the publisher asked me.

Hoddeson:

They simply asked. This was a period when there was a cluster of review articles. The most massive being the Sommerfeld-Bethe.

Peierls:

Yes.

Hoddeson:

Which was written mostly by Bethe?

Peierls:

Yes.

Hoddeson:

Here again, were you in correspondence with the other people who were writing similar articles, people like Bloch and Bethe and other? Did you know about it?

Peierls:

I must have done. I canít remember the sequence. I think my article was published before theirs.

Hoddeson:

Yours was first, yes.

Peierls:

Yes. Therefore I didnít know. I donít think I had any advance copy of Betheís article. I mean, presumably I knew he was writing this article or he knew I was writing mine, but I donít think there was any detailed exchange of information.

Hoddeson:

This looks as though it was written for a different audience than the Sommerfeld-Bethe.

Peierls:

It was much shorter and therefore not as mathematical.

Hoddeson:

Itís much less mathematical.

Peierls:

Yes. Yes.

Hoddeson:

Was there a specific -- is this written to inform graduate students who were entering the field?

Peierls:

I donít think --

Hoddeson:

-- or was there -Ė (crosstalk)

Peierls:

-- I donít think I thought about that part of it, but in formulating the general 1ine of that series, it was meant for people who were not necessarily specialists. Not only for theoreticians.

Hoddeson:

Well, the fact that an article on this subject enters that series says something about the state of acceptance of this in the larger subject of physics. 1932-33 seems to be a sort of a turning point, do you agree, in this? In fact, you say something like that at the end of the article, in a passage which I actually cut out because I was thinking of using it for something. But you perhaps remember that passage at the end, which is a very optimistic passage in which you say that this is the time when all the problems with the exception of superconductivity and a few other little details are solved now.

Peierls:

Solved. Yes.

Hoddeson:

It seems to be one of these, periodically in the history of physics there are these periods of optimism.

Peierls:

Yes.

Hoddeson:

Which usua1ly are just the beginnings of a reversal, when the subject goes into a different direction.

Peierls:

Yes.

Hoddeson:

There was certainly one like that in the thirties in quantum electrodynamics, after the Dirac period, when they discovered all the infinities. It looks to me like it was a definite turning point intellectually, but also for the field in general institutionally because of the coincidence of certain political factors, such as the rise of the Nazis and Fascism in general, the -Ė

Peierls:

-- migrations Ė-

Hoddeson:

Thatís right. It was a -- it was a also a time when, I donít know if this agrees with your recollection of that period, in one of Slaterís review articles about solid state he says that this was a time when the experiments began to be limited because the samples werenít pure enough, and that started to cut down on progress in solid state theory. It required better samples which were developed during World War II. Do you agree with that?

Peierls:

On certain aspects, yes. I mean, there are certainly, I mean, one distinguishes structure sensitive and structure insensitive properties of solids, yes. On all the structure sensitive things of course that applies.

Hoddeson:

Was there a feeling, a definite feeling that now solid state physics was really beginning, a field in its own right, as a sub-field of theoretical physics? This was a time when all these problems were coming together. Was it something that was widely felt? Iím getting it mainly from your paper, and one or two others. Iím wondering if that was something that was widely felt.

Peierls:

Well, I donít think we asked ourselves the question that way, and therefore, itís not clear, what would have been our answer at the time.

Hoddeson:

Well, looking back on it now, do you feel that that was a turning point? There was certain a restaffing at that time. People like you and others who had contributed in the period before that were picking up other problems. Nuclear physics and quantum mechanics espec1ally. And it was just at a time when people like Neville Mott were entering. I mean, in the US Wigner was trying his first group of graduate students, and then stayed in solid state, and similarly Slaterís group was beginning to become very specialized in the solid state area.

Peierls:

Yes. (crosstalk)Ö

Hoddeson:

And then it was also the time when the Wigner-Seitz per came out.

Peierls:

Yes.

Hoddeson:

There seems to have been a new emphasis suddenly, change from ideal solids to reel solids.

Peierls:

Yes. And also, you see, as we discussed before, I really felt that the problem of doing quantitative calculations predicting the binding energy or any other specific properties of a particular metal was too difficult, to do that, that the theory ought to consist of setting up general relationships and understanding these qualitatively, and then, I suspect Bethe would have said, Bloch might have said, the same thing at the time, Iím not sure. But then people came in who were willing to face the problem of making quantitative calculations, and really getting numbers from those principles, and that was certainly a change in the nature of the problem, since not only different people but also different formulas.

Hoddeson:

Well, Bethe would have fitted into the new approach, donít you think?

Peierls:

Except he never (crosstalkÖ) didnít apply it to solid state physics. He probably would have.

Hoddeson:

He made the comment that he would have done more with solid state physics, had he not had to leave Germany at the time he did in April, Ď33, because of the Nazis. But I believe I asked you that question earlier, whether the Nazis had something to do with your leaving the field, and in your case I gather it was different. It had more to do with the subject matter.

Peierls:

I think so. Well, I mean, indirectly. For example, I might not have gone into nuclear physics or, without (a) being in Cambridge and seeing a lot of people in nuclear, and (b) being together with Bethe and discussing some of these problems with him. To that extent, the location and therefore the Nazi period had something to do with it. But I think itís more accidental.

Hoddeson:

Paul is going to ask you more questions in his next session with you, about the feeling in Cambridge, being a refugee.

Hoddeson:

I have just one question. Iíll ask you now because it follows a theme of questions Iíve been following, and this goes back to this relationship between experiment and theory. Bethe commented that, when he was in Germany, he certainly didnít interact very much with the experimentalists, but the minute he got to Eng1and he began to interact closely with the experimentalists and this was true of severa1 of the refugees, including you and I guess Heitler, and the question is why. Bethe speculated that, well, there werenít that many theoreticians around and the ones there came out of a different tradition. They were people like Dirac, who were not used to communicating with the experimentalists, but the British experimentalists were very anxious to have this communication. And therefore the refugees by entering at this time filled a need that was really felt in Great Britain at this time.

Peierls:

Yes.

Hoddeson:

Do you feel this is a valid?

Peierls:

I think that is valid. That is true.

Hoddeson:

It applies also to the U.S., which was the next place Bethe went.

Peierls:

Yes.

Hoddeson:

And then he continued to interact closely with experiments lists.

Peierls:

Yes. Well, there is a difference, because in England, you see, the funny thing is that in England traditionally theoretical physics was called applied mathematics and was done in the mathematics department usually, particularly at Cambridge, by students who would never see the inside of a laboratory. And that is partly responsible for this a situation you describe. Now, that was not true in the United States.

Hoddeson:

Right. The United States has a long tradition of experiment.

Peierls:

Of course. But, of course generally there werenít enough. I mean, until the thirties, there werenít enough theoreticians in the United States.

Hoddeson:

In that sense the refugees filled a gap there too.

Peierls:

Yes, just because there werenít enough.

Hoddeson:

There werenít enough people who were highly trained.

Peierls:

Yes.

Hoddeson:

Just one last question, two, Iím sorry, before we stop this. What was your response to the Wigner-Seitz paper? Did that strike you as something very important when it came in or was that Ė-

Peierls:

-- oh yes.

Hoddeson:

Did you get it by reading the PHYSICAL REVIEW?

Peierls:

I presume so. Because they had no preprints in those days. And I mean, you found out in advance sometimes from a letter or by somebody coming into your seminar, or I imagine, I read this, -- I mean, I was very impressed by the various ways he had to get logical estimates on things that I wouldnít have thought were easy to get.

Hoddeson:

OK. I think Iím going to hold off on my last question, because weíre running out of time.

Session I | Session II