Oral History Transcript — Dr. Murray Gell-Mann
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Murray Gell-Mann; July 27, 1982
ABSTRACT: Background of Gell-Mann-Brueckner theory of interacting electron gas.
Hoddeson: Willa Patterson talking to Murray Gell-Mann at the, [Laugh] in Paris on the 27th of July of the History of the Gell-Mann Brueckner work, in the, part of the History of Collective Phenomenon. [Music] Absolutely great.
As I understand it you were at Rand as a consultant?
Right. I went there every week. And...
Hoddeson: When did you start at Rand, about?
Gell-Mann:It was around then. It was around '56.
Hoddeson: Uhm-hmm. What were you working on?
Well, mostly on this problem. That is Dick Latter wanted, and perhaps Albert too, his brother, wanted to know more about the correlation energy of electrons so as to use the electron correlation energy to improve the Fermi-Thomas model, which they were using for various equation-of-state calculations. And, they asked me to look into the problem of the correlation [Car engine revving up]. I looked into it soon and realized that it was being calculated as an expansion in the radius parameter, r(s), which is one over the [???] of the density. And that, at a certain point a logarithmic term in r(s) intervened, which gave rise to logarithmic infinities in the expansion.
Right. Right. This is the term that Bardeen had found in the '30s, wasn’t it, (Gell-Mann: I don't know.) that caused a lot of trouble?
Gell-Mann:But, I, I don't know anything about it.
Hoddeson: You didn't go that far?
But, it was diverged — no. I just looked at new stuff.
Hoddeson: You just looked at the recent stuff?
And it was divergent. And, the question was how to sum up the divergences so as to calculate it as a finite term, which would then be constant times log r(s).
Right. Right. Was it...
Gell-Mann:Then there were various contributions which various people were calculating. David Pines, for example, had done a partial job of calculation, and there was a German, whose name I've forgotten — I think [???].
Hoddeson: [???], Uhm-hmm.
Who had done a partial job of
calculation, and even looking at the infinities I found these various references, eventually.
But I'm still not so (Gell-Mann: Yeah.) I'd like just a little bit more information (Gell-Mann: Yeah.) on why Rand cared about this particular problem? Was it part of some larger (Gell-Mann: Yes.) question (Gell-Mann: They were doing some...) that they...
They were doing some large set of calculations and as part of that they wanted to use. I mean, what were these?) the Fermi-Thomas model.
Hoddeson: Were these large calculations classified?
Hoddeson: Did you know what they were?
Gell-Mann:At the time I must have known what they were, yes.
Hoddeson: But you don't remember what they were?
Gell-Mann:I don't remember. No. I don't remember.
I see. Because one wants to know why this thing started. But it seems...
But, they wanted to apply it to the Fermi-Thomas model and they wanted just to have a reasonable calculation of the correlation energy for high density.
Now, of course, nobody's really interested in very high density for such problems. One is interested in medium density. And, [Vigner] and his colleagues had claimed to calculate with a variational calculation of some sort, medium density.
Hoddeson: This was in the late '30s?
Gell-Mann:Yeah. In the late '30s.
Hoddeson: Thirty-eight. Yeah, '34-'38?
But they had not done a rigorous, there was no way to do a rigorous job of calculating
) in medium densities. (Hoddeson:
Right.) And what we thought was...
Hoddeson: But they didn't even get the log term?
Hoddeson: They missed it? [Laugh]
They didn't necessarily need it at medium density. (Hoddeson: Yeah.) It's not clear what you need at medium densities, because it's nothing but sort of a guess.
(Hoddeson: Right. Right.) And the formula may have been okay at medium densities, but there as no sort of rigor. (Hoddeson: Uhm-hmm. Uhm-hmm.) What we wanted was to get a good calculation for high densities and there was (Hoddeson: Uhm-hmm.) already a good calculation for low densities. (Hoddeson: Uhm-hmm.) And, the idea was then that the medium density calculation could at least be an interpolation between known understood regime. The — anyway, it was sort of a challenge to have something that diverged, (Hoddeson: Sure.) and figure out how it would come out to be direct in the finite log r(s) term.
Hoddeson: Right. Right.
Gell-Mann:I worked on it and I was making some progress and one day Keith Brueckner arrived for a day as a consultant.
Uhm-hmm. Were you working only, constantly or just (Gell-Mann: Well...) now and then?
Every week I would (Hoddeson: Every week you'd go there for...), every week I would, I went there for the day.
Hoddeson: For the day? I see.
Gell-Mann:And, I worked partly on this problem.
Hoddeson: I see. I see.
And, one day Keith Brueckner showed up for a day, (Hoddeson: I see.) and I discussed it with him. I don't remember what advice he gave but he did offer some useful suggestions, (Hoddeson: Uhm-hmm.) which is why I put his name on the paper. And, in fact, it was as a result of talking with him that I felt good about the problem and felt somehow that I could solve it if I tried. (Hoddeson: Uhm-hmm.) Because, the main, the main thing that I remember is that I got a sense of confidence about the problem after talking with him. (Hoddeson: I see.) And, another thing that happened was that I began working on it more at home after that, for the next few months.
Hoddeson: Oh, you really got hooked?
I really got interested (Hoddeson: Yeah. Yeah.) after talking with him.
And, and then I invented the method of — for myself, personally — the method of Feynman diagrams for, for these problems, and noticed that you could do an expansion in Feynman diagrams. And, when you did it, it was clear which were the divergent terms and that they were very easy to add up. Under the integral sine they were just a geometrical series. (Hoddeson: Uhm-hmm. Uhm-hmm.) I never published that Feynman diagram method as a, for itself. I just referred to it in this, in this paper. But, later on (Hoddeson: Do you keep notes?) I gave my student Donald Dubois (Hoddeson: Uhm-hmm.) the problem of calculating the next set of corrections, and he used those diagrams in a very complicated way to do the next correction. It was a very long and difficult problem. He was a very good man. (Hoddeson: Yeah.) You can tell from his subsequent career. (Hoddeson: Right.) He did it. But, at my level it wasn't actually even necessary to use diagrams, because it was a rather low-ordered problem. But, nevertheless (Hoddeson: Uhm-hmm.) that's what I, that's the way I did it.
But this was a period when Feynman methods and other (Gell-Mann: Yeah.) Field Theory methods were just beginning to enter (Gell-Mann: Well...) solid state?
I'm told that the official discovery, which must have been made around the same time, was by Jeffery Goldstone. I've never seen the paper. I've never looked at it [???]. (Hoddeson: Uhm-hmm. I haven't either.) But, I'm told that around the same time he (Hoddeson: It was...) discovered them also and actually published them and treated it as an important matter, and so on. I didn't treat it as an important matter. I just thought it was something incidental to working out this logarithm. Except in so far as I gave it to Dubois ( Hoddeson: Uhm-hmm. Uhm-hmm.) as a problem to do the next corrections, and there he really had to use the diagrams (Hoddeson: Right.) [???].
And what role did Brueckner play other than (Gell-Man: Other than that...) having a conversation?
No, there was none other than that one conversation, but it was a very seminal conversation. (Hoddeson: I see.) I don't remember what he contributed. He made some useful suggestions, and particularly he gave me a sense of confidence that the problem was interesting and soluble, solvable.
Hoddeson: I see. Did he do any of the writing of the article?
Gell-Mann:No, I don't think so.
You just, it was just (Gell-Mann: As I...) simply a conversation?
I must have sent it to him, (Hoddeson: Uhm-hmm.) I think. (Hoddeson: Uhm-hmm. Uhm-hmm.) I must have sent it to him and perhaps he corrected or changed something in the paper. I don't remember that part. (Hoddeson:
Now...) I don't remember what conversation we had about it. (Hoddeson: What, what I'm told...) I know, but I must have sent it to him. I couldn't have submitted it to the journal without submitting it to him for his approval. (Hoddeson: Right.) So, I certainly did (Hoddeson: Sure.) that. But, what I don't remember is what corrections he made, if any, or changes he might (Hoddeson: Uhm-hmm.) have made.
Hoddeson: Uhm-hmm. I see.
But, I would normally not have put my name first, except for the fact that his contribution had been just that one day's conversation. (Hoddeson: I see.) But, I found it sufficiently useful and sufficiently important that I didn't want just to thank him for a conversation. (Hoddeson: Right.) I felt his name should be on the paper.
Hoddeson: Right. Right. Well, then you wrote another one by yourself?
Well then I added some, (Hoddeson: Yeah.) having done this I was able to add some other things, (Hoddeson: Uhm-hmm.) of which I published one. I published the [Rules] of Magnetic Susceptibility [???].
Hoddeson: Now I don't remember.
Gell-Mann:I think it was that. And, that was a sequel, paper that was a sequel to it.
Hoddeson: That's right.
And, I could have done some other aspect to the problem, to which I had...
Hoddeson: I looked at it some months ago.
Gell-Mann:I had, I had the energy [Laugh] I could have calculated a few other things at the same time.
Did you continue working along this line at all? Or did you...
Gell-Mann:Not particularly. No.
No? Because you were...
But, but an amusing, a series of amusing things happened after this, which (Hoddeson: Oh, one other question.) I was considered. (Hoddeson: Yeah. Yeah.) Yeah?
One other question. Was this classified work while you were doing it? Did you need a clearance before (Gell-Mann: No. Except that...) telling David Pines or others about it?
Except that the Rand Corporation preprint (Hoddeson: Yeah.) must have taken some time to get loose, because that has to be declared declassified, and that may have taken some time. (Hoddeson: I see.) But, there was no question of this work being classified.
I mean, could you just talk about it to anybody who was...
I could talk about it to anybody. But, the preprint itself, the Rand preprint itself probably took some time to get loose, (Hoddeson: Yes.) because it had to be declared declassified. There was nothing classified in it, (Hoddeson: No. No.) but that had to be certified.
But that was, (Gell-Mann: Because...) this is something I got from talking with David Pines. He thought that there was some procedure that had to...
Gell-Mann:Only for the preprint.
Hoddeson: For the preprint? I see.
Not for the material itself, there as no — I mean, nobody could (Hoddeson: I mean, could you, could you send...) conceivably have objected to talking about it.
Hoddeson: No, but, what about sending it, say, to the Physical Review? Was there any declassification procedure?
There may have been some delay in that. I don't know. I don't remember. Rand may have caused some delay in that, (Hoddeson: Uhm-hmm. Uhm-hmm.) because it had to be declared unclassified.
Hoddeson: Okay. Anyway, that's just a fine point.
Gell-Mann:I shouldn't have said "declassified." It had to be declared unclassified. That's all. (Hoddeson: Right. Right.) That's all. But, that may have (Hoddeson: Right.) taken some time.
Right. Great. So, tell me...
Gell-Mann:Oh, now what happened?
Hoddeson: So then what happened? [Laugh]
Well, [???]. (Hoddeson: Okay.) I heard that Brueckner had started working with a Japanese called Sawahata, which means, I suppose, "swamp field," [Laugh] and, and that the two of them together had begun to doubt the results of our calculations and had written a preprint arguing that the results were wrong, (Hoddeson: Was that because they...) and that they (Hoddeson: They couldn't find the...) they couldn't find (Hoddeson: The plasmon?) the plasmon, they couldn't find the plasmon term.
Hoddeson: In order to agree with the Pines-Bohm, Bohm-Pines?
They couldn't find the plasmon term, (Hoddeson: Right. Right.) and they pointed out, quite correctly, that there has to be a plasmon term. At that point I resumed work on it, although I've never published that work. Bill Karzas, K-A-R-Z-A-S, (Hoddeson: I see.) and I at Rand, immediately set out to reanalyze the term that I had calculated with Brueckner, putting it in some new form and using Theory of Analytic Functions, as I remember, (Hoddeson: Uh huh.) in order to exhibit the plasmon term, (Hoddeson: Right. Right.) The continuum in the plasmon term, which we were quickly able to exhibit and we saw that it had exactly the right form and that there was no problem. And in some way or other we communicated this to Brueckner and Sawahata. I don't know whether I wrote them or phoned them, or what I did, but in some way I communicated to Brueckner that he was, shouldn't lose heart. Dick [Farrow] I remember, (Hoddeson: But when was, when was...) visited Rand around this time and he had told people that "This, this Brueckner and Gell-Mann business has its ups and downs." [Laugh] But, for me it didn't have any (Hoddeson: No.) ups and downs. [Laugh] I thought it was right.
Hoddeson: But it did for Brueckner?
Gell-Mann:When I heard it was challenged I, Bill and I found this plasmon term in order to show that it was okay. We, I don't think we ever wrote that up but we might have in an internal Rand report, or perhaps not at all. I don't remember.
Hoddeson: Now, where was Sawahata working?
Gell-Mann:I don't know. I don't know anything about Sawahata. I'm not sure I've ever met him.
I see. But somehow he and...
But Keith, Keith and I were friends and I must have communicated to Keith somehow that I thought that our work had been right and it was not necessary to correct it. And, in the final version that was published of their work I'm told that they didn't make the claim that it was wrong. I don't think there is anywhere in the literature a claim that, by them, that (Hoddeson: That it was wrong? I see.) our paper was wrong. I don't think. Maybe there is, but I don't think so. I think it got, (Hoddeson: I don't think so.) it got caught before it reached the public stage of print.
Hoddeson: I see.
Gell-Mann:But that was really [Laugh] very exciting.
Hoddeson: I see.
Because, for a while Keith was (Hoddeson: Were there...) at war with himself over this, (Hoddeson: Were there...) [Laugh] over this matter.
Hoddeson: Were there other responses? I mean, this paper is terribly seminal now. I mean, you're not working in solid state now, so you probably (Gell-Mann: No. I never have, except for that.) don't know how people (Gell-Mann: And I never — no.) talk about it. (Gell-Mann: No, I never paid much attention.) But everybody always (Gell-Mann: I see. Really?) — yeah. It's one of the (Gell-Mann: Well, that's good.) important papers because it offered a way to do the, you know, see how good the approximations were rather rigorous.
Gell-Mann:For me, it represented something very bad, which was that I wasn't working on weak interactions at a very crucial time in weak interactions, and I should have been. That was all it meant to me. [Laugh] I had very little interest in this domain. It made a nice dissertation for Dubois, I guess, doing the Feynman diagrams and the next correction.
Gell-Mann:I haven't paid much attention to it. So.
Hoddeson: Well, anyway, it's, it played a role in this larger story that I'm writing about. The story really is the story of a change in the point of view of solid-state theorists, you know, about their subject and taking the interactions into account, basically, which then enabled them to solve a lot of the problems that were lying around for a long time.
The connection with solids is, of course, one of the most, requires a great idealization of solids to connect this electron gas. But, the electron gas is an interesting mathematical...
Hoddeson: Well, this was one of the arenas?
Electron gas with a constant background of, (Hoddeson: Yeah.) of opposite charge (Hoddeson: Yeah.) is a, is an amusing mathematical entity. It requires a lot of idealization to connect physics with it.
Hoddeson: But nevertheless it was one of three or four important arenas out of which, which resulted in the new collective point of view. One was the whole discussion about superconductivity. Another was helium, and a third was — well, the third was this electron gas problem. And . . .
Gell-Mann:But I think it was generally understood, except for the value of this number, the coefficient of the log and the finite term left over, both which we computed.
I think apart from that it was generally known what the situation was, about the correlation energy but they, people just didn't know how to (Hoddeson: They didn't know how to calculate it?) calculate, didn't know how to calculate these two numbers, (Hoddeson: Yeah. Yeah.) the coefficient of the log and the finite remainder.
Hoddeson: But just in doing this calculation they had to bring in the, the new machinery that ultimately became part of the standard machinery for solid-state physicists. Another area that was important was critical phenomenon, though not as important as the other three, I think, so far as I've looked at them. [Laughter] I'm just getting — well, not just getting started. But [???].
But the other, this conductivity thing, although it's again not very much directly connected with real superconductivity and real materials, but the solution, in principal, of how that, that kind of thing could arise, that involved some really interesting, a couple of two very interesting physical ideas, the Cooper Pairs, and then the Collective Phenomenon resulted from the instability resulting from the two Cooper Pairs. Both of those were very, very nice in physical results. And here I wasn't aware that we had any [???] physical results. I guess that's why I didn't make more fuss about it. [Laugh] I regarded it mainly as an improvement (Hoddeson: I see.) in that part of the machinery.
Hoddeson: Uhm-hmm. Okay. Well thanks. [Laugh]
Gell-Mann:You're very welcome.