Oral History Transcript — Dr. John H. Van Vleck
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Interview with Dr. John H. Van Vleck
By Thomas S. Kuhn
At Harvard University
October 2, 1963
John H. Van Vleck; October 2, 1963
ABSTRACT: This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Niels Henrik, David Bohr, Gregory Breit, Percy Williams Bridgman, David Mathias Dennison, Alex Ellet, Paul Darwin Foote, Ralph Fowler, Edward Lee Hill, Edwin Crawford Kemble, Earl H. Kennard, Hendrik Anthony Kramers, Ralph de Laer Kronig, Robert Sanderson Mulliken, J. Robert Oppenheimer, Erwin Schroedinger, John Clarke Slater, Edmund Clifton Stoner, John T. Tate, Webster; Conference on Magnetism (Washington), Harvard University, University of Michigan, University of Michigan Physical Optics Committee, and University of Wisconsin.
Session I | Session II
Kuhn:I will read onto the record that although never an athlete yourself, and therefore reluctant to spell out at length your prowess in this area, you were an avid follower of sports, particularly football, remembered the scores, something youíve demonstrated to me repeatedly, telling me who won Harvard-Princeton games during my time as an undergraduate, and by what margins.
Van Vleck:Remember that time we won by about one point right after the war down at Princeton. I remember I was working with ve Middleton, we had it on the T.V.
Kuhn:Before we come back to the outline itself, Itve remembered over the intervening day following the first interview a few things that you said at one time or another that come into the period we've already talked about and that I wanted to be sure we got Onto the tape. This question about part III of the absorption paper—thereís only one reference to there having been a third part.
Van Vleck:I even started to write it. Might even find a somewhere.
Kuhn:Tell me something about what was to have been in it.
It was just simply to show that there was an asymptotic connection between the radiation by a multiply periodic system and what youíd get out of the Einstein A formulas. No, I guess it wasnít that so much as the fact that the arbitrary multiply periodic system was in thermodynamic equilibrium under the Rayleigh-Jeans law.
As I remember, it was primarily that, but it did have these terms in dJ/dt, where the action variables damped down because of radiation forces. That was what it was about essentially. I had no radiation damping in Parts I and II. I damped down the Jís on that, and then showed that you could get equilibrium under the Rayleigh-Jeans law.
Kuhn:This is the thing then that is responsible for the Rayleigh-Jeans law being in the title of the paper, although in the two parts that were printed there was no reference to it?
Van Vleck:I never even thought of that, but I guess thatís responsible for that being In the title. You're absolutely right.
Kuhn:Well, you do refer to the Rayleigh-Jeans law and say just a little bit about this in the original presentation to the Optical Society. Then the Rayleigh-Jeans is in the title, and there is nothing in the paper about it. What happened to part III, why didnít you ever proceed to round the thing off?
Van Vleck:Very simple: quantum mechanics. Other things broke, and I had to finish up my bulletin on QUANTUM PRINCIPLES AND LINE SPECTRA. That, plus quantum mechanics.
Kuhn:The book is another thing I want you to say a little more about. How long do you suppose you actually spent on that? It looks as though it would have been a consuming occupation at the time.
Van Vleck:It was. As I said, I remember writing on it in. the summer of 1924, and 1925. It certainly engaged a lot of my time in 1924 through the summer of 1925. I forget the deadline of the thingís submission.
Kuhn:It was late in 1925, I think.
Van Vleck:Yes, the proof sheets would be coming about the same time as quantum mechanics so I realized they were obsolete by the time they were off the press.
Kuhn:Yes, you signed the preface in August, 1925.
Van Vleck:I think I was writing some of the first parts of the MS longhand in Switzerland in 1924. when I was traveling and worked on it pretty intensely in the summer of 1925 when father took me to task for my scientific style.
Kuhn:When you work on a project of that sort, do you wait till you sort of have everything in notes and are ready to go, or do you write it a section at a time, and then go read, and compute?
Van Vleck:A section at a time, as I remember. I hoped to whack out five pages a day during the summer when I had nothing else to do. I did almost entirely my own typing: I donít think I had a single stenographer for that thing.
Kuhn:Was it rewarding work?
Van Vleck:I think so. Because I donít think I would have discovered quantum mechanics. I think it served as useful a purpose as, say, another paper or two to flounder around in the old quantum theory. Of course, you can never be sure. In retrospect, of course, I wish Iíd followed up and thought more about my correspondence principle for absorption. That was the nearest I ever came to being on the path of the discovery of the true quantum mechanics. I just never had the imagination to follow that up. I might have later, I canít tell, if other things hadnít broken.
Kuhn:You told me yesterday in the car about a seminar that youíd given at Wisconsin in. which you talked about, I think you said, adiabatic invariance and the correspondence principle?
Van Vleck:Yes, correspondence principle, especially the latter, as the two toeholes that might lead to the discovery of a true quantum mechanics, or perhaps I said true quantum theory, I wouldnít know the exact term I used. I certainly realized, and that must have been in 1924 or possibly 1925, certaitily before the academic year 1925-26 more likely 1924-25 that there was something rotten in the state of Denmark as regards the old classical quantum theory. I remember my father was always very distressed at this idea of suddenly jumping orbits; he said that didn't make sense. He was a pure mathematician, but, of course, he was essentially right in a certain sense.
Kuhn:Did you argue with him about that? Did you think that did make sense, or at least ail the sense that was necessary?
Van Vleck:I felt that it was the best we could do. That was the best theory we had at the time.
Kuhn:Slater clearly was not happy about that aspect of it, and thereís a paper of his that we didnít get to talk about yesterday, but that I hope to get him to talk about more, in which he substitutes for the discontinuity in position, the discontinuity in the operation of atomic forces, so that the electron is actually carried over during a period at least several vibrations long. Did you yourself ever fool with things like that?
Van Vleck:Oh, I think I fooled around with some of those shenanigans where I tried to get quantities out as a properly chosen mean between an initial and the final state, but that still left unanswered the problem of the stationary states and why the things didnít radiate unless there was some fiat of nature.
Kuhn:In general this was not a sort of problem—. You were aware that it worried you but you didnít—.
Van Vleck:I think it worried me, but I donít know as I ever worked actively at it.
Kuhn:You said that when you gave this paper at Wisconsin there was one senior man who took some exception to it, With or without names, could you tell me some more about it?
Van Vleck:He just said he didnĎt believe those two things were going to really help us straighten things out. He just didnít agree with me, thatís all. He was a very good experimentalist. I remember another professor saying about a conference where a quantum theory was going to be discussed, there was no point in going to a meeting where a bunch of ďyapsĒ were going to talk about quantum theory. There were some people who just were not sympathetic with the type of thing that Kemble and Slater and I were trying to do. I guess they felt it was just barking up a wrong tree. There were such people in America.
Kuhn:What would they have advocated instead? Where was the right tree?
Van Vleck:I think it was just agnostics.
Kuhn:And they tended to be the experimentalists?
Van Vleck:Iíd say rather re the theorists. At least this man IĎm thinking of is a theorist.
Kuhn:On this, same score, you took some exception to Slaterís indication of the lack of interest in things that were going on, and spoke of recollections of people pulling you aside at Physical Society meetings and trying to find out about what was going on?
Van Vleck:Yes, there were some physicists, especially in spectroscopy, who didnít really understand all these papers that were coining out, I would say, in the era just before quantum mechanics broke, where there were some interesting papers on the polarization of resonance radiation. We were queried what we made out of those papers. My memory is pretty hazy on particular questions, but I do know that when I did go to Physical Society meetings, I felt there were some of the older physicists who were very avid to have a little better insight into the meaning of these various European papers that were coming out. you remember who some of these people asking these questions were?
Van Vleck:I think [R.C.] Gibbs was one of them, a Cornell spectroscopist. Right after the discovery of quantum mechanics, I can remember one prominent mathematical physicist who claimed all the matrix elements were zero. He had a little of an informal public listening to him in the hall. But he had not taken into account the fact that the square of minus 1 need not have the same sign in two different equations, which I pointed out to him. I think you can say that, by and large, only the younger physicists in this country were ever able to get quantum mechanics in their bones. There were exceptions, but, by and large, I think, this was true.
Kuhn:Did the others try and not succeed, or did they just sort of brush it off as not a thing that they need worry about?
Van Vleck:I think some of them worried. Of course, you know that Arthur Gordon Webster coimnitted suicide. Whether or not his failure to understand all of the new developments was a factor in that, I would have no way of knowing, but Id heard rumors that it was. But Iím in no position to know. He was an older man whom I met only very superficially. But I think some of the older people were worried. There were exceptions, Tolman, I think, kept up with modern theory in quantum mechanics very well.
Kuhn:How old was Tolman?
Van Vleck:Iíd say he was a man about ten years older than I am. By and large, in 1925, there were very few people who understood the theoretical quantum theory of that time, both the physics and the mathematics. There were some mathematicians who understood the formalism of angle and action variables; there were other people who understood the FranckHertz experiment, and things like that. But people who were quantum mathematical physicists or theoretical physicists were quite scarce, and then things changed very suddenly.
Kuhn:Changed suddenly largely through there being a lot of young men coming in?
Van Vleck:Yes, two things: bright young men coming along, plus quantum mechanics breaking.
Kuhn:What is it, do you suppose, that brought so many bright young men into the field about that time?
Van Vleck:Iíve often wondered, Iíve never understood it. These things go in waves.
Kuhn:Just about 1926, you became an associate editor of the Review. What sort of duties did you have as an associate editor?
[John T.] Jack Tate was editor-in-chief. I had the advantage of being right on the spot; he could show me a MS right then and there. At least, I think, I was appointed associate editor only after Tate took over from Fulcher; I may be wrong. I think they wanted to have an associate editor who was conversant with the new quantum theory on the theoretical side. Apropos that, I can say that that had a profound influence on me because in the spring of 1926 there was a paper submitted by David Dennison on calculation of intensities in the symmetrical rotator by means of quantum mechanics.
I wrote to him and, of course, said it was a fine paper and should be inmiediately published. Tate promptly did. I wrote to Dennison for permission to use the results, which I proceeded to do to the calculation of the dielectric constants and showed that the factor one-third got restored in quantum mechanics, whereas in the old quantum theory, it had all kinds of horrible oscillations depending on whether you had weak or strong spatial quantization; you got some wonderful nonsense, whereas it made sense with the new quantum mechanics.
I think that was one of the strong arguments for quantum mechanics. One always thinks of its effect and successes in connection with spectroscopy, but I remember Niels Bohr saying that one of the great arguments for quantum mechanics was its success in these non-spectroscopic things such as magnetic and electric susceptibilities.
Kuhn:How did you happen to be all ready when you read that paper to see the application to susceptibility? Did you worry very much about that before?
I had, of course, written a thesis in magnetism for Bridgman but I really donít know. I may have struggled some with trying to calculate dielectric constants with weak and strong spatial quantization in the old quantum theory. I remember meeting Linus Pauling—we ran into each other on the train in 1926, I think. We were worrying about much the same type of thing. But it all got straightened out by the new quantum mechanics. Apropos that dielectric constants thing, I sent a letter to Nature early in 1926. It was sent back to be condensed.
I must confess that that rather burned me up because I felt it was a quite significant achievement in quantum theory. When I mentioned it to Bohr he said ďyou should have got me to endorse it, it would have gone through quicker.Ē As it was, I think Mensing and Pauli beat me to it on being the first to publish that factor one-third. It was essentially a triple tie, though Kronig had it too, all three of us. Very generally gonig and I seemed to hit upon similar ideas independently.
Kuhn:So far as I know, thereís nothing about magnetism in the Dennison paper.
Van Vleck:Oh no, absolutely nothing about magnetism in there. Itís just a calculation of the matrix elements of a synnetrical rotator. And thatís what we needed. As a matter of fact, you didnít even need that one, you just needed them for the HCL molecule which didnít even have an angular momentum about the axis of the figure, which is a special case of Dennisonís more general formulas. I think Dennison really made two ten strikes when he was over there in Copenhagen: one was this paper, and the other was on the specific heat of hydrogen. This one I immediately saw gave me the formulas I needed for dielectric constants.
Kuhn:Iím concerned to see whether we can pin down more precisely this question of the formulas you needed for dielectric constants, which does argue that you had in fact been worrying about dielectric con- stants in the quantum theory.
Van Vleck:Yes, you almost wonder whether you couldnít have dug that out of some sort of a Sommerfeld-Hoenl-Russell-Koenig formula just stuck in in an ad hoc way; you might almost have been able to do it, as you think about it in retrospect. It gave me a great respect for the matrix mechanics, and I think that Iíd gotten the spirit of that pretty early. Whereas when it came to the Schroedinger things I learned about them at a later date because I had less off-the-record communication with people while they were doing things in advance of publication. you remember when you first saw the Heisenberg paper?
Van Vleck:I remember reading the Heisenberg paper. Then I heard rumors of this new quantum mechanics discovered by Born and Heisenberg; about that time -
Kuhn:How did you react to the Heisenberg paper, which many people look at and canít make anything out of?
Van Vleck:I thought it was good stuff. I liked it, Iím sure of that.
Kuhn:Did you try to do anything with it before the Born-Jordan thing which identifies these as matrices, which sets up the commutation conditions and so on?
Van Vleck:I donít know that I did. You always had a little of the feeling that you were one lap behind compared to what was going on in Europe because those people had an inside track of things compared to what we had. I presume youíre familiar with Bornís MIT lectures. This was the first introduction to the U.S. in English, I would say, of the new matrix mechanics, which I studied very avidly.
Kuhn:But youíd already own and begun working from the original papers, I assume, considerably before that?
Van Vleck:Yes, I remember I sweated over some of those papers in the spring vacation of 1926, I definitely remember that.
Kuhn:How did other people feel? Do you remember having conversations with people about matrix mechanics? You were one of the very rare people who took the matrix approach seriously and rather left the Schroedinger thing slide by for a while.
Van Vleck:Well, the matrix one came out first, donít forget that!
Kuhn:Well, itís interesting to notice that an awful lot of physicists looked at those, decided they couldnít do anything with them, and decided that it was really just another formal approach to the problem and really didnít get into things until the Schroedinger equation came along.
Van Vleck:I got them when the Born and Heisenberg paper came out, was it in the spring of 1926?
Kuhn:All three came out in 1925.
Well, I thought this was it. It was very hard for me to believe that there was another approach that was going to lead to the same thing. At this stage I might recall some of my experiences in June 1926, when I was in Europe. On the way to Europe I had gotten a reprint of the Dirac paper. I reckoned out the mean values of one of r and one of r by the same number method that I later published, a few years afterwards in vol. 143 of the PROCEEDINGS OF THE ROYAL SOCIETY; I saw that that gave the right formula for the fine structure, Sommerfeldís structure, interpreted a la Slater-Uhlenbeck-Goudsmit.
I think I didnít have the cosine law clearly enough visualized quantum mechanically but I used j times j plus I, minus l times l plus 1, minus s times s plus 1 in a kind of ad hoc fashion instead of l dot s . That with the new values of 1/r^2 and l/r^3, and the general idea that the relativity corrections were formally equivalent, in first approximation, to the determination of 1/r^2 , showed me the fine structure came out beautifully in the new quantum theory. I worked on that on the boat, and went promptly down to Copenhagen to Bohrís laboratory and found that Heisenberg had sent in a paper doing just that thing, certainly more elegantly as regards the cosine part. I was rather discouraged by that.
The next day or so I brought around a paper reckoning out the mean value of 1/r^4 by this same Dirac method and found that Waller had just sent in a paper doing that, likewise pointing out that this corrected certain difficulties in the quantum defect of non-penetrating orbits where the main correction was due to polarization which had existed in the old quantum theory. HeĎd used the Schroedinger quadrature method rather than the technique of q numbers- -in some ways the q number method is almost easier for the inverse powers. Anyhow, I was kind of discouraged after those two things plus the retardation of my dielectric constants paper.
The summer of 1926 was, in some ways, a little of a disappointment for me, but, of course, I was very happy that quantum mechanics was finally getting straightened out. When I was in Cambridge, there was a nice young man who was very friendly to me, a you student whose name was J. R. Oppenheimer. He took me
Van Vleck:punting one day. I remember him pointing out that Courant-Hilbert was a book which would be very useful with the new quantum mechanics. That at the time I couldnít possibly understand because Iíd been trained in the matrix mechanics and had not yet, I guess, read Schroedingerís papers. When did they appear?
Kuhn:They appeared during the spring and sumeer of 1926.
I doní t think I had studied them before I took the boat in early June. It had been hard enough getting this dielectric constant business out and understanding the full import of Dennisonís papers and so on. I had other things to keep me busy. When I talked to Bohr and Kramers, and then went to the British association in 1926 where I met Darwin and [R.H.] Fowler, then I realized that the Schroedinger business was, of course, also tremendously important. I went back and studied it.
Iím pretty sure I added it to my lectures in quantum theory in the academic year 1926-27. I remember I gave some lectures down at Iowa and remarked that I thought the pace was a little bit nerve-racking and G. W. Pierce said he got great comfort out of that remark of mine in that lecture. It Ďs funny how you remember a few little fragmentary details some 35 years later. Alex Ellett was then at Iowa. He was a person who in his early days took a good deal of interest in the experimental side of quantum theory, he was sort of R.W. Woodíish if you want. He was the best person in polarization and resonance radiation; he was avid for a good understanding of quantum theory.
He was not a theoretical physicist, but an experimnentalist who wanted to be able to interpret his results quantum-mechanically—aspiring, you might say, to be what people like [Edward M.] Purcell and [Nicholaas] Bloembergen were at later dates, who, shall I say, were able to develop their own theory for their own beautiful experiments.
Kuhn:What happened to him after this?
Van Vleck:Ellett went into industry ultimately. Heís been with Zenith Radio Co. for many many years. He was with Bureau of Standards, I believe, for a while.
Kuhn:Do you know what took him out of his original, more fundamental interests?
Van Vleck:I donít know. May have been financial. I just donít know.
Kuhn:Before getting back closer into the physics, let me ask you about your move in 1928 from Minnesota to Wisconsin.
That was pretty much a nip-and-tuck proposition. I had a great fondness for Minnesota. Wisconsin was my alma mater and where my parents lived, although that was certainly not a major factor. I think at that time the prestige at Wisconsin was a little greater than that of Minnesota, but Minnesota had been wonderful in giving me this opportunity to do solely graduate teaching. I felt a little guilty in some ways in leaving the place. Wisconsin did offer the bait of a visiting lecturer for a term.
At one time there was a plan to get a younger man to be with me in quantum mechanics, but the man we had in mind took another position so that didnít materialize. It was that visiting lectureship that was responsible for bringing Dirac to this country for the first time. I remember father going to some ofí his lectures about the time he (Dirac) developed his general transformation theory and (my father) saying this sounds more like E. H. Moore and his general analysis at the University of Chicago mathematics department than it ever did like what he conceived of physics as being.
Kuhn:The transformation theory papers are actually 1927.
Well, . . . I went to Wisconsin in the fall of 1928, and Dirac came there in February 1929, and he was lecturing on that at that time. The transformation theory undoubtedly came out earlier, but that was when he was lecturing on it. We also had R.H. Fowler over as a visiting lecturer in 1931. Wentzel was my replacement the semester I was away as a Guggenheim fellow.
I didnít meet Wentzel as a consequence for many many years because we were always exchanging places. It was only many years after that I had the pleasure of meeting him for the first time. Wisconsin had a great many visiting lecturers at one time or another, a rather imposing lot.
It had Debye, a brief visit from Max Born, Schroedinger for a substantial period, Schroedinger was there, I think, in the fall of 1926. He wrote a paper for the PHYSICAL REVIEW, essentially a digest of his problems, that should spot it.
Kuhn:Would you ever go to Wisconsin and hear him?
More than that. There are two things, and I canít remember which one came first. They had a colloquium on problems in the new quantum theory at the University of Wisconsin—more of a little syiosium—and they had Schroedinger and me on the same program, which kind of scared me naturally, but I did raise some questions on Schroedingerís ultra-hydrodynamical interpretations ofí quantum theory. I said how in the world could you get rid of the fact that the initial and final concentrations appeared symmetrically if you took the extreme hydrodynamical viewpoint. I think that is a very real proof that the naive idea that the atom is some sort of an oscillating charged jelly, which I might say is an almost right theory of atomic structure but isnít really.
Just like somebody said there's no such thing as a moderately good egg, I think that fills just that same criterion. I remember I raised that question and Schroedinger was never able to answer that particular one. I brought that difficulty up in a paper I gave at some meeting of the Physical Society a year or two later and Kennard took violent exception to that and said that either Klein or Pauli had that all straightened out. Since Kennard was a senior man, I felt a little squelched, but I remember Herzfeld, I think it was, coming up and saying, Ďwell, after all, didnít they just plain suppress in an ad hoc way that Boltzmann concentration factor,í and, of course, the answer is that they did.
If you look at the early editions of Pauli Ďs quantum theory, I think youíll see that that is essentially thrown out the window. Of course if itís done correctly ŗ la Dirac, thereís no trouble. But it is an argument against the extreme hydrodynical model. which, I think, Schroedinger was very reluctant to give up. I think I even remember him saying to me, or somebody saying he said to them, that he wished he had never invented his atom if it was just to be interpreted statistically. Have you beard that from other sources, or is that just my own—?
Kuhn:No. If itís an apocryphal story, which it may be, itís a widespread one. It probably isnít. There certainly is no question about Schroedinger having believed it and felt that it was one of the great advantages of his whole theory. I think ití a a good deal of what appeals to him in the de Broglie theory; here was a way of preserving many of the classical continuities.
Yes, he really wanted to have a classical model. I think his motivation was quite different from Bornís. In connection with Max Born, I think, it should be emphasized that he kept impressing what as a Harvard person Iíd like to say was the Bridgman operational point of view, on his students at Goettingen. That concepts have meaning only so far as they can be observed. . . . I do remember coming down and bearing a lecture by Max Born at Madison.
That was the same year he was over lecturing at MIT, certainly the academic year 1925-26. He made a statement that profoundly impressed Warren Weaver who repeated it to me: Ďwithin the atom there is no geometryĒ—itís a classic gem. That is perhaps the ultimate extreme of the matrix point of view; the other, which we might say is more accurate, is within the atom there is only statistics, in a certain sense.
Kuhn:In one of your papers on quantum mechanics you also make this remark about Bornís having impressed people with the observational point of view. This may very well be right, yet Iím not clear about it. Iíve talked to a number of people and tried to find out more about it. Itís very clear from Bornís writings that he does say clearly part of whatís the matter with the new quantum mechanics when it comes will make no reference to certain classical quantities which are not observable. He particularly emphasizes here the position in the orbit. To what extent there was a general positive position and a generalized operational philosophy current in Goettingen in this period Iím not clear.
Van Vleck:Well, I think the people who were there are much better qualified to talk than I am. This is just my impression 3000 miles away. I'm in no position to really—
Kuhn:I wondered where youíd gotten that. You said undoubtedly the people who were there are better qualified to talk about it, and yet Iíve had great trouble getting answers from them.
Van Vleck:I may have got that impression from Bornís lecture in Wisconsin. I donít Imow.
Kuhn:Whatí s certainly true is that everybody talks about that Heisenberg paper as being the paper which said: ďlet us only use observable quantities.Ē Something very like that, is also to be found in Bornís book Atommechanik. But the question of where it comes from, how general the discussion was, and what the attitudes were: Iíve asked Born, Iíve asked Heisenberg, Iíve asked Hund, all of whom were very much there at that time Iíve asked Jordan. There are still things I donít know about that that I would be very glad to know.
Van Vleck:I donít know. I had the idea that Born sort of set the tone of the place as Bohr did in Copenhagen, but it may have been indirectly Heisenberg, I donít know.
Kuhn:I think thereís no question that this is explicit in Bornís writing at least earlier than itís explicit in Heisenbergís, but itís not clear to me how generally and widely believed, how much a part of the Goettingen program that was. Another thing that happens in this period that causes a considerable fuss in Europe is, of course, electron spin. Do you remember how you first heard about it and what sort of an impression it made on you, or any discussion with other people about it?
Van Vleck:I remember I was rather shocked at the boldness of SlaterĎs paper. Then when Ublenbeck and Goudsinit came along it was perfectly clear, I should say. Exactly how many months separated those two papers I wouldnít know without going back.
Kuhn:It is in any case a matter only of months. By Slaterís paper here you mean the paper in which he says hydrogen should be handled in analogy to the alkalies?
Van Vleck:Yes, exactly. So that instead of having a ďkĒ, or whatever you wish to call the azimuthal quantum number, you have j plus 1/2 coming in there, two degenerate levels of the same j. It seemed to me a very bold suggestion. I had a little of a hard time swallowing it, but now wait a minute, I was going to say I had certainly swallowed it pretty well by the time I was on the boat going to Europe in June 1926.
Kuhn:By then thereís time to have swallowed it: spin is out by then. As I remember it, the Slater paper was published early in 1925, possibly even late in l924. The spin papers come out in 1925, so that by the spring of 1926 it wouldnít be true that everybodyís caught on to that, but it would at least be true that the material is there.
Van Vleck:I wonder if I even mentioned electron spin in my BULLETIN ON QUANTUM PRINCIPLES AND LINE SPECTRA which closed in late 1925. [Looks it up in the Bulletin] Oh here it is. Naturwissenschaften late 1925. ZEITSCHRIFT FEUR PHYSIK AND NATURE in 1926, so it was about Christmas that that broke.
Kuhn:How did you feel about the suggestion itself? If you had had the Slater paper on your mind, this would have possibly made things come more quickly.
Van Vleck:Well, it was fine. Of course Bichowsky-Urey had some business in there that almost got it, didnít they? Iíve never been quite clear on that....
Kuhn:You were pretty well imbued yourself with the operational point of view—werenít you at all bothered by this notion of the attribution of such a property like spin?
Van Vleck:No. Itís just as operational as anything else is; it would be the way Iíd say that. Heavens, if youíre going to take that point of view, you can throw everything in the atom out the window. I donít see how spin is worse than anything else.
Kuhn:Do you think you felt that way at the time?
Van Vleck:Yes. Well, I felt very happy after I saw the thing came out right on the boat. No worries I had in 1925-26. One was in connection with the quantum mechanics would it crack the hydrogen atom? Now when did Pauliís paper on that come out? I think Born said heíd heard from Pauli that it came out all right. I donít think Bornís MIT lectures had that in them.
Kuhn:The paper actually came out, or at least was submitted, before the Born Jordan paper came out, I think. The work was done very, very quickly.
Van Vleck:Of course, Bornís MIT lectures were almost more Born and—which is the first of the two—Born and Heisenberg?
Kuhn:No, itís Heisenbergís little paper, then Born and Jordan, then Born-Heisenberg-Jordan, all inthe fall of 1925. Now just where in that sequence the Pauli paper comes Iíll have to look to see. What about the factor of two with the spin and the fine structure—the thing that Thomas takes care of when he does the relativistic theory, which bothered Heisenberg so much. Were you conscious of that?
Van Vleck:I was conscious of that. I think in this ill-fated MS I referred to the fact—when did Thomasí s paper come out?
Kuhn:January 1926 was the Pauli paper on the hydrogen spectrum. Thomasí is in the April 1926 issue of NATURE.
Van Vleck:I may have seen that at the time I wrote this on the boat, and I may not have, because diffusion time on those papers was rather slow. I do not recall whether I took it in an ad hoc fashion or took it from Thomas. I remember Bohr saying, ďwhat rather strange mental processes Thomas had used in straightening out that factor.Ē I remember Bohr expressing himself on that. Of course, it was a brilhiaat piece of work.
Kuhn:How did you happen to go to Europe that summer?
Van Vleck:My father and mother and aunt were going.
Kuhn:Did they go to Copenhagen with you?
Van Vleck:No, I diverged from them for a while. We played a lot of duplicate bridge when the four of us were together, but I traveled quite a bit independently. I was with them on the boat, but I worked quite a bit on the boat. I was so excited about these tbings-we were on a Norwegian-American line boat, Stavangerfjord—I took the very first train from Oslo to Copenhagen in preference to traveling in (Delakala) I do remember that. I spent two or three weeks in Copenhagen: that was my second visit to Copenhagen. I then met my family in (Trondhjem) and then toured the beautiful fjords of Norway, and then went back to Copenhagen a second time, then took the boat to England and went to the British Association for the Advancement of Science which was in Oxford. The Prince of Wales, later Edward VIII, was there.
Kuhn:Did you by any chance at that meeting run into any of the conversations which, I take it, went on? I take it Davisson was there. There must have been some conversations there that lead into the electron diffraction experiments.
Van Vleck:I don't remember anything of that. I remember Hartree was plugging along in trying to figure out something analogous to his ways of calculating spectral terms in the old quantum theory. I remember talking to Hartree. I remember being entertained by the—I forget whether it was Lady Darwinís or Sir Darwinís father who was the Warden of one of the Colleges. My memories of that meeting are rather vicarious. I donít remember any particularly exciting physics at that meeting.
Kuhn:Do you remember any general air of excitement about that meeting?
Van Vleck:I think mostly people were excited that the Prince of Wales was there. I remember Rutherford giving a paper, and everybody standing and a very bored young man walking in and sitting down; after he stood it for about 20 minutes or so he got up and walked out, and everybody else stood up, and that was Edward VIII. Thatí s the type of thing I remember at that meeting, Iím afraid, more than any particular things in physics. I do remember that I went over to Cambridge a little later where I ran across Oppenheimer. I also called on Dirac in his room. He showed me one of his manuscripts—it might have been the MS where he first got things interpreted in terms of the antisymmetric determinants. Could that have been antisymmetric wave functions? I didnít understand the thing too well as is sometimes the case when people show you MSS.
Kuhn:IĎd have to check. It seems to me it could very well have been.
Van Vleck:Or it might have been his paper on the elimination of nodes in quantum mechanics. It was one of—.
Kuhn:No, that would have been well out by then. I think very likely that it may have been the paper that, among other things, includes a bit on the antisymaetric wave functions.
Van Vleck:Iím sure it was. I got as excited about that as I did when I first saw the issue of the PROCEEDINGS OF THE ROYAL SOCIETY with the quantum theory of the electron. Of course, that was a much later date.
Kuhn:Not so darn much later. Itís amazing how quickly those things—. It must have come out more or less while you were moving.
Van Vleck:I moved in 1928, and I think I had been there a while before it came out.
Kuhn:It came out in 1928. What about the transformation theory papers-the Jordan and the Dirac transformation theory papers?
Van Vleck:I approved of them, but I think practically all my whole lifeís work has been in the Heisenberg system of representation. I think thatís the answer to that.
Kuhn:Those papers— and this is the reason Iím pointing to them particularly here—on the one hand are transformation theory papers but even more they are papers pointing basically into the statistical interpretation.
Van Vleck:Sure. I always believed that. Iíve got some correspondence that I had with Slater to show that he and I both thoroughly subscribe to the statistical interpretation of quantum theory.
Kuhn:Was there much sympathy in this country for the Schroedinger attempt to keep the thing continuous and causal?
Van Vleck:Well, this may be another apocryphal story: Einsteinís remark "God doesnít throw dice.Ē
Kuhn:I think thatís not apocryphal. But how about feeling among American physicists? Was there much support for the attempt to avoid this sort of fundamentally statistical approach?
Van Vleck:I donít recall. In those early days there were a relatively small number of people versed in quantum mechanics and the contact between them was somewhat limited. I went to meetings once or twice a year, but I canít recall people being especially worried over that. At least among the ones I esteem most highly, people like Slater and Breit. I donít think Kemble was worried over it, was he?
Kuhn:Not that I know of.
Van Vleck:Well, they are the people whose opinion I esteemed.
Kuhn:How about the Heisenberg paper, the uncertainty principle paper, which follows pretty inmediately on the transformation theory papers?
Van Vleck:That seemed to be very interesting. I was always interested in it, but I think Bridgmanís article in HARPER'S MAGAZINE really stirred me up most emotionally about it. I always appreciated its significance, but that was, so to speak, a very dramatic presentation of it, which I always quoted to my classes, as you doubtless remember.
Kuhn:What about the whole set of issues regarding radiation and the quantization of the field, second quantization and so on? Were you much involved with those?
Van Vleck:No. I never, at least until recently, got thoroughly imbued with the spirit of second quantization. I remember [R.H.] Fowler saying to me one time, he hated it. Iím afraid I had more or less the same emotional reaction. I realize that for certain purposes itís very useful; on the other hand, I think there are certain problems which it tends to obscure rather than elucidate. For instance, I like to think of radiation as a bunch of ethereal oscillators each with a Planck distribution formula rather than Einstein-Bose particles. Thatís a matter of taste and semantics, of course.
Kuhn:Did you feel that way from the beginning? Did you follow those papers closely?—the Dirac paper?
Van Vleck:Yes, the Dirac paper I liked.
Kuhn:How about the Jordan? Thereís the Heisenberg, the Jordan-Pauli—
Van Vleck:That one I never studied too hard.
Kuhn:And I guess particularly for the anti-symmetric commutator, thereís a Jordan-Wigner paper thatís very important.
Van Vleck:I never went all out on those papers the way I did on some of these other things. Perhaps itís just as well because there were certain aspects of the applications of quantum mechanics that seem to be untouched for a remarkable long time, when you figure that the rules of the game broke completely by the end of 1926.
Kuhn:In this same area, what about the Dirac equation, the electron theory?
Van Vleck:Well, I think it was fine, one of the great intellectual achievements of all time, I think.
Kuhn:When did the problems about it begin to bother people? The negative energy solutions, for example?
Van Vleck:Well, I was never a high-energy physicist particularly, I was perfectly willing to just throw them out the window, I guess, and forget it.
Kuhn:How did you feel about the hole theory?
Van Vleck:Well, there was always the difficulty of the mass of the proton not being equal to the mass of the electron. That was an obvious flaw in the thing. But donít forget that Iíd been through this period of the old quantum theory in its dying gasps and realized that out of that true things came out, and the best you could do was to live with what you had, and I guess that was the attitude I took in that one.
Kuhn:Tell me the set of developments that were obviously of more direct concern to you. What about the coming of group theory?
Van Vleck:Oh, I had to work that up myself and it was hard going.
Kuhn:Did you start with it from the beginning, practically from the time of Wigner's first paper, or at what point did you get convinced that you were going to have to work that out? There were some people, and Hund is one of them, who tried for a very long time, relatively successfully, simply to get along without group theory. Dirac almost tried to reinvent group theory in a more physical form, and was relatively successful.
Yes, that I thought was wonderful. I must have learned group theory by the year that [R.] Schlapp was at Wisconsin, because I remember him saying he liked my lectures on group theory because they were so physical. Probably around 1930, I would say, was when I dug in. I remember Abigail saying that whenever I got a particularly distracted look on my face, what was the matter, I was trying to understand group theory. Iím afraid I got a blind spot.
I was a long time in seizing the idea that you had to simultaneously reduce all the elements of a group by one and the same equivalence transformation rather than different ones. When you read a thing in a foreign language especially you sometimes are apt to lose just the vital step. Itís dangerous to rely too much on formalism. Heisenberg has a paper where he thought heíd reckoned out the second approximation in the theory of ferro-magnetism for spin greater than a half by means of group theory. I could never plug it out by the Dirac vector model and I finally discovered that Heisenberg had made a mistake.
Kuhn:When was that? The ferro-magnetism papers I never had a chance to go through.
Van Vleck:Thatís mentioned in my book. Heisenbergís paper was in some kind of a Festschrift that was in honor of—
Kuhn:From now on I want to talk about what in these general areas—One of the things more in Slaterís area than in yours, and one in which he's an active contributor—In the period immediately after the group theory, where it gets on the one hand, the Heitler-London approach to valences, on the other hand, Hund, Mulliken, and others doing the chemical structure. There was a good deal of conflict between these two approaches. This is what, in the 1930ís, in the paper, for example, that Slater pulled out yesterday and said we had left off the bibliography, was directed to wards healing those wounds, trying to show that the two approaches were two approaches to the same thing.
[A.] Sherman and I went into that in considerable detail in a paper [ďThe Quantum Theory of Valence,Ē REV. MOD. PHYS., 7 (1935), 167-228] which we wrote in the REVIEWS OF MODERN PHYSICS which has been translated incidentally, I am told, into Russian. The truthís in between the two. You can start with any system of representation you want in solving the Schroedinger equations. The only question is, which is a better engineering approximation with a smaller correction. and it looks oftentimes as if one is just half-way between the two.
If they both give the same result qualitatively then you can feel happy. I wrote a number of papers on the quantum theory of the chemical bonds— such things as CH4 and so on—giving some more or less skeletal calculations, but I pulled out of the field because it seemed to me that you could make the thing quantitative only with very dinosauric calculations. Itís been a revelation to me how seriously chemists in later years took these very skeletonized approximations because actually youíve got an enormously complicated eigenvalue problem.
Kuhn:Do you remember anything that went on in the opposition between these two views? You speak of that paper of yours as being again an attempt to show that there was truth on both sides, that these were simply different approximations, different representations, solutions applied to the Schroedinger equation. I gather that in Europe there was actually a certain amount of real anxiety and some hostility evoked.
Van Vleck:Well, that persisted many years in the theory of magnetism. I can remember some quite heated arguments in the Conference on gnetism in Washington, I believe, in the summer of 1950.
Kuhn:Still basically resting on issues of this sort?
Van Vleck:Somewhat on issues of that sort. And Stoner stuck to his collective electron ferro-magnetism. I remember our committee feeling thereíd be a pretty good cat fight if we had people that each adhered to certain viewpoints.
Kuhn:Do you remember arguments, fights, group feeling over this in earlier periods?
Van Vleck:Mainly by the magnetism people—Stoner and his school. Well, thatís a little different. Thatís not quite the Mulliken controversy, because there it's Hund-Mulliken to the extreme of free electrons versus bound electrons. Well, I suppose the moment you bind things pretty closely you get over the Bloch approach or something equivalent to the Heitler-London approach.
Kuhn:Tell me about some of the controversies over magnetism.
I canít think of any real controversy, but I meant that there was Stoner who had his very beautiful collective electron ferro-magnetism where he had applied a Weiss molecular field on top of the Fermi-Dirac statistics. Itís a very clean-cut model and involved a good deal of numerical work. I remember [R.H.] Fowler remarking that it was a beautiful job with a very succinct model, and it is. But whether that model is ultimate physical reality any more than the Heisenberg model with the minus 2Jsi * Sj When youíve got conduction youíve really got something pretty complicated. I donít think even today thereís a unity of feeling on this.
I donít think there was any bad feeling, each person simply had his own brand of religion, so to speak. Although they probably all had the same basic fate in quantum mechanics. It isnít the same thing, as say, the argument between the statistical and the non-statistical interpretation of quantum mechanics. Thatís something fundamental. The other was purely computational differences of opinion.
Yes, but it can also very often be a total failure to see what the other man is working on. Hund told me a very interesting story in this respect, nothing of great consequence. Born asked him to come to talk to the Goettingen colloquium or perhaps to Bornís seminar. He talked about what he had been doing, and the Born group was taking the opposite approach and at the end of this, Hund told me that Born said to him, ďI see Iíve been misunderstanding what you were doing.
Now I understand what youíre doing. It isnít the same thing weíre doing at all.Ē What had previously looked like a conflict between two solutions to the same problem Born now suddenly after this exposition saw to be in some sense due to really a difference in interest, in what the two were trying to find out. This sort of thing, I think, is of interest when there are communication failures of this sort, and how theyíre straightened out. This sort of story, even if not central to the development, is a part of the ironing out and standardizing of the applications of quantum theory, and it for this sort of thing that I am fishing at the moment.
Van Vleck:I doní t remember too much of that particular thing. What I do know is that the people who were too versed in these orthogonal functions were not quite quick enough on the trigger to realize that for low values of j, when youíve got conserved total angular momentum, youíve got a nice quadratic formula or something of that kind. People at Harvard werenít realizing that the problem of the decoupling of electron spins was a purely algebraic problem of degree which increased progressively with the amount of spin. If you only had a spin of a half, it was just a simple quadratic equation. This is rather interesting that [E .L.] Hill and I obtained—Hill was a PH.D. student of mine—the right matrix elements by reading Dirac. We didnĎt use Schroedinger theory. I remember Hill quoting me as saying if you read Dirac enough you can find pretty near anything in it. Well, we found just the matrix elements in it we wanted.
Kuhn:This was DiracĎs quantum mechanics book, was it?
No, I donít think his book on quantum mechanics had come out. This was late in 1927. The way I had my students reckon out a matrix element even as late as some of my Wisconsin period when [A.T.] Goble was working on the 4-vector problem, we did it out of Dirac and the correspondence principle, whereas nowadays people use Racah coefficients. But we got the answers. Then another one was the asymmetrical top. Witmer had written a paper on it in the ZEITSCHRIFT FUER PHYSIK, Warren came to Wisconsin with me as a post-doctoral fellow, and had some beautiful functions that were going to do this thing. I realize that it was a purely algebraic problem. You only got 2J plus 1 states coupled together as long as you had no applied magnetic field and you could furthermore factor the equations . . . by means of what I call a Wang transformation—I still refer to a Wang determinant.
People picked that up, and this was as late as 1928-29. Of course, the asymmetrical top is now almost an attribute of the chemical laboratory. Itís rather interesting how that thing could have kicked around for a couple of years without anybody ever realizing that you get a nice simple secular determinant. Itís rather amazing the time lag from the appearance of the first Dennison paper to the time when the asymnetrical top had been set up and formulated. Of course Oscar Klein got a very elegant way of doing it but I donít know whether his paper preceded or followed Wangís but be didnít set up the explicit algebraic problem in any case.
Kuhn:Would you feel that the algebraic approach had increasingly died out, that there was more and more reliance on Schroedinger functions?
Van Vleck:Yes, at that time, I think, there was a little too much reliance on that and not enough on understanding matrix algebra, coupled with the correspondence principle.
Kuhn:Was anybody else in this country working along with you utilizing more often the matrix technique?
Not that IĎm aware of. I think I pushed it perhaps a little harder than almost anybody. Other people were interested in electron impact problems or were using a little more emphasis on the Schroedinger equation. I think that the matrix approach enabled me to give my general derivation of the Langevin-Debye formula. During that period of 1928-29 the person I found most stimulating to talk to was Mulliken because he had the sixth sense of interpreting these band spectra qualitatively and then it was always a job to really put the thing on a firm quantum mechanical basis.
Hund came out with his general theory of lambda type doubling, Kronig applied it to a case of molecules without any spin, but actually the most interesting molecules were those that had the spin in them, so I wrote my paper putting that in. I wrote some of my conclusions to Mulliken and I remember him writing me an answer that they fit the experiments like a glove, or something like that. I was rather pleased at that naturally. Thatís a problem in straight application. Iíve been by and large an ďapplicationsĒ man.
Kuhn:When would you say that the trend away from quantum mechanical applications decidedly toward doing work on the nucleus had taken place in this country?
Van Vleck:I can answer that in part. I lectured at Michigan in the summer of 1933. Fermi and I were the two visiting lecturers. I lectured in magnetism, Fermi lectured in nuclear physics. Even discounting the fact that I may not have been as good a lecturer as Fermi, you can see that the interest of the students was more in problems of the nucleus than it was in a subject like the quantum theory of magnetism, although there was a great deal that needed to be explained in understanding the basic magnetic phenomena. It was something that had just broken at that time, within a year or so, but people didnít seem very interested in it.
Kuhn:Would you say the trend had gone on in that direction ever since?
Van Vleck:Well, I donít know. In a certain sense that was a rather low ebb in the period of magnetism. Microwave spectroscopy and molecular beam and the Maser and various other things have tended to keep it fairly much in the forefront of applications. I donít claim that thereís been the same widespread interest as in nuclear physics, but itís been an important branch of solid state physics right along.
Kuhn:I now want to go back and talk about your own papers in the period from the coming of the new wave mechanics on. I want to start out by asking about the paper that you half-wish hadnít been on this list at all, the one you decided that you—
Van Vleck:I would raise the fraction from a half to a larger fraction, not wished—
Kuhn:I'm interested in that paper for a variety of reasons. It clearly must have been a tremendous effort. Weíre talking about the paper on the specific heat of hydrogen in the light of the new mechanics. [ďThe Dielectric Constant and Diamagnetism of Hydrogen and Helium in the New Quantum MechanicsĒ Nat. Acad. Sci. Proc. 12 (1926), 662-670]
I had worked on it in the winter of 1925-26. I had an investment in the way of time in it. Now why I didnít throw the paper in the wastebasket you can ask me and Iíll say I donít know, but at any rate, I felt Iíd put in a lot of effort and wanted to publish a paper. Thatís about it. Iíve never been proud of that paper, as you can see. Well, quantum mechanics came along and made it obsolete.
I remember Heisenberg saying to me sometime that maybe the Fermi-Dirac statistics answered the specific heat of hydrogen problem, but I didnít understand well enongh what he had in mind to follow it up. Of course, itís perfectly clear that if you weigh the states 3 in 1, why, in retrospect, everything comes out beautifully. I quite agree with a conmaent in Goudsmitís paper that that is a very fundamental paper of Dennison. Was it known at that time that the spin of the proton was a half or was that the first evidence for it?
Kuhn:I'm not sure, they come very close together. I havenít read Dennisonís paper. One of the things that strikes me about this paper comes out right in the beginning of the new quantum mechanics. It uses the new quantum mechanics and the results are a great deal worse than they were with the old.
Van Vleck:Well, itís because it was incorrectly used, thatís the answer.
Kuhn:I realize that now. But how did you feel about that at the time? Did it shake your conviction in the new quantum mechanics at all?
Van Vleck:No. It shook my convictions in my own work, I should say, and that particular approach. I felt Iíd spent a lot of time on it, and it was worth recording, but—
Kuhn:But it didnít raise any fundamental questions in your mind as to whether the new quantum mechanics was on the right track?
Van Vleck:No, I don't think I ever thought of that paper as being any argument against the validity of quantum mechanics, because about that time we began to do some things that really worked beautifully, like those calculations on the boat I referred to. Hill was working with me on band spectra.
Kuhn:A very minor question comes up, but one that rather interests me. At several places in your early work with the new quantum mechanics you speak of it as ďquantum dynamics." Almost everywhere in the European literature the term is ďmechanicsĒ rather than ďdynamicsĒ except for a very interesting transition in Dirac when, in connection with the transformation theory, he begins to use the term ďquantum dynamicsĒ. Up to that point it had been ďquantum mechanicsĒ. Do you have any notion of what accounts for that vocabulary difference?
Van Vleck:No. There was Whittakerís ANALYTIC DYNAMICS that was all. Mechanics is what you teach to juniors and seniors, and when it becomes graduate stuff it becomes dynamics. I think thatís about all I can say in that connection. I donít think thereís anything recondite in that at all.
Kuhn:Iíd really like you to talk about now the whole development of your work on susceptibilities. We talked a little bit about the beginning of it. Iím still not happy in the sense that you look at Dennisonís paper, and you say ďah ha-it gives the factor 1/3 I need for susceptibilities! ď
Van Vleck:Well, it took me a little while to do that because all the contribution comes from—. Letís take the simple diatomic case in the state j equals 0. For a day or so I was getting zero. Then I woke up one morning and realized, heavens, youíve got to put in j equals zero does contribute and thatís a beautiful analog of the fact that in classical theory all the contribution to susceptibility comes only from molecules that arenít able to turn over, (that have rotational energies less than kT). Thatís quite nice. I think that was one of the nice achievements of the quantum mechanics, that it cleaned that up.
Kuhn:You took that stuff and you went right out and tried to do susceptibilities with it. Thereís nothing I know of in your earlier work thatís concerned with it except perhaps this Bridgman paper that you speak of a good deal earlier. Yet you were all prime to go at this. Had you been concerned with magnetism in the interim?
Van Vleck:I wonder if Iíd fooled around some with strong and weak quantization and that type of thing in connection with my book. I donít know. There was a paper of Paulingís that I donít think I agreed quite with the way he applied his quantum conditions in the old quantum theory, or maybe different fields gave different results. Iím hazy on the thing. That was the period when everything was in a bad way. I was worried over variations of field strength—I think I had that worry. I mentioned plenty of worries that I didnít have, but I think that probably I was worried about the effect of different quaritizations on the susceptibility. I think I had worried over that.
Kuhn:From the way the paperís written, it looks as if you had. worried about it. But thereís nothing that I know of in your previous work that indicates your concern with that set of problems.
Perhaps so. I never thought of that. I think I had had that worry at least in the back of my head; whether it was in the front of my head I wouldnít know. Why I happened to turn so promptly to dielectric constants is a question I really canít answer. And I can go on with the chain of research that that started. I told you how I wrote a paper on that, and Mensing and Pauli came out with it. Then I tried to generalize it, and applied it not merely to the diatomic molecule but the polyatomic molecule where the three quantum numbers symmetrical top, j, k—I think it was called k in those days the thing thatís the angular momentum about the figure axis—and m, and I still got one third, and Kronig came out with the same thing.
Kronig and I always seem to come out with somewhat similar things. Then I began to think about 02 and NO as the only common polyatomic molecules. I made the usual naive calculation where I calculated out the susceptibility of NO and say that the only contribution to the magnetic moment comes from the magnetic moment parallel to the diatomic axis and was getting the wrong answer. Then one evening I suddenly recalled there are those non-diagonal matrix elements, and that the second order Zeeman effect contributes as well as the first because the first contributes only in the second order because it averages out only in so far as you can carry the field strength in the exponential as well as in front of the Boltzmann factor.
Then the thing seemed to give the right answer. I wrote it to Mulliken. He read the paper for me at the meeting of the American Physical Society in 1927. I didnít know whether to believe it or not, it worked too nice. It made me realize the more general formalism where you can express the susceptibility as a linear term in 1/T plus a constant, as long as the multiplets or the fine structures are either very small or very large compared to kT. I worked out that general formalism. I think Born and Jordan were probably about ready to go into that in connection with their ATOM MECHANIK vol.II when my papers came along and they realized they didnít need to follow that particular line of thought.
That was general formalism. This reminds me that I had terrible arguments with the physicists convincing them I needed to put in the second as well as the first order Zeeman effect. If I wrote down a formula 4S times S plus 1, plus L times L plus 1 as a Square of the effective moment, they said that that meant that you had the Paschen-Back effect and that the spin and the orbit were separately quantized. In space; all thatís required is that coupling energy be small compared to kT. I had some great arguments, particularly with laporte on that particular thing. I got Miss [Amelia] Frank to do the numerical work and that straightened out samarium and europium which had not fitted into the original Hund thing. I was invited to stay over for the Solvay Congress in 1930 when I was there on my Guggenheim, which started in February 1930.
During which time I wrote a good deal of my book, especially the 40 days I spent in Zurich when Pauli and everybody else was away and there was nothing to do but work. This has its advantages sometimes. I think both Sommerfeld and Pauli both mentioned to me that Iíd certainly be invited to the Solvay Congress if I happened to be in Europe, and Iíd had a cable from Mendenhall saying that I had permission to stay for the Solvay. Congress if invited. So I had to change my steamship passage and went to the Solvay Congress in 1930. The number of Americans who had attended Solvay Congresses at that date was relatively small. There was a completely different atmosphere than the Solvay Congress in 1954 where a very appreciable fraction of the attendees were Americans, probably flown over on this contract or that.
There I read a paper on straightening out samarium and europium. The iron group was still an enigma. It had this so-called ďspin onlyĒ formula. During my whole stay on the Guggenheim fellowship there was no question but where I learned the most. That was about 3 or 4 days with Kramers in Holland, just stopping over more or less en route to Leipzig, which is more or less the Mecca for Americans at that time, with Heisenberg and Debye there. Kramers called my attention to Betheís papers which I read. It was that which probably impressed on me that I had just got to learn group theory. I remember meeting Bethe very pleasantly in Munich during that trip. I did quite a bit of traveling, spoke at a number of colloquia. Mulliken and I were at Leipzig at the same time. Hund was there. There was an active seminar of Hundís on molecular spectra. Of course, Mulliken was one of the leading lights.
I contributed to a certain extent. Then I was invited to give a few colloquia at various places. I got coached in German, practically memorized my MS and people would say afterwards they had no idea I knew so much German, and I got the grammar much better than Mulliken. They said I didn't do very well when it came around to the questions. Well, I had just been tutored in this, whereas Mulliken had good enough German that he could really speak extemporaneously. That was the subject I always talked about, the samarium and europium. Even 30 years later I find Iím still working with those molecules because theyíre rather exceptional among the rare earths and require a rather peculiar form of theory which people usually donít include, just as (???)ís thesis in 1958 or so, didnít attempt a theory for europium. Then I wrote my book; all my books in a way are a little unfortunate in their timing.
At the time I wrote that book, whereas I did have the general idea that multiplets are small and large compared to kT, and I did suggest qualitatively that electric fields might account for the ďspin onlyĒ formula in iron group—I should say that Pauling independently had that idea. It was when [W.G.] Penney and [R.] Schlapp were with me at Wisconsin that I feel that I really straightened out what was going on in metals of the transition group of dominantly cubic coordination. It looked at first hand as if we had to use a different sign of the crystalline potential for cobalt, which is very an-isotropic, and nickel, which was nearly isotropic.
But then I showed by arguments somewhat similar to that with which Goudsmit established the inversion of multiplets, that there was this curious quarter multiplicity, repetition with a quarter rather than a half period, or inversion with a quarter rather than a whole period, as regards the crystalline Stark patterns being up or down. That, I think, is the clue to whatĎs been established by the chemists under the name Ligand field theory. I had no idea the chemists had annexed so much of this until I was invited to a conference of the Faraday Society in Dublin in 1958 and found chemists talking about such quantities as (10d^q), quantities that Schlapp and Penney had used for their parameters for the cubic splitting and so on.
But I think especially that paper by Schlapp—it was called Schlapp and Penney but actually Penney did the rare earths paper and Schlapp the iron paper. For sentimental reasons—they were both at the University Club-they wanted to collaborate, and so they wrote one paper Penney and Schlapp, the other Schlapp and Penney. Iíd unearthed this fact that it was legitimate, so to speak, to turn Schlappís calculations upside down going from nickel to cobalt. That was my own paper I wrote in the Review in 1932 which I always regarded as my favorite paper. After I was at Harvard, during a summerís vacation at Madison, I wrote a paper which was the first, I think, to distinguish between what chemists call the strong and weak field cases.
Not a very happy terminology, because Iíd call ordinary iron electric Stark fields pretty strong. What they call strong I would call superstrong, theyíre able to break down the Hund rule and make the ground state one not of the maximum multiplicity because it has lower Stark energy. A few years after Penney was with me at Wisconsin, he showed that the extra stabilization due to the Stark splittings making certain ions have extra lowering of energy as compared to others, manganese in the middle—manganese double plus has none because the level isnít split—accounts for the irregularities in the heat of formation of these various elements of the transition group—something that had been more or less an enigma to chemists.
That whole thing was rediscovered by [L.E.] Orgel in Cambridge in the 1950ís without apparently any cognizance of Penneyís paper, and that is what, I think, led to a great deal of Orgelís reputation, but Penney had that idea in TRANSACTIONS OF THE FARADAY SOCIETY around 1940. But that was after I left Wisconsin. I think that I got him interested in that type of thing. That was a follow-up on the work. That was a period in which I had some of my most able students. Iíve already referred to one, Schlapp and Penney; there was also Bob Serber who was at work on the Faraday effect. Itís still quoted, but after heíd taken his Ph.D. with me, I felt he had learned all he could from me. I sent him to work with Oppenheimer, and Iím afraid after that he was lost to the cause of solid state physics, and has been in nuclear physics ever since.
Kuhn:At what point did you decide to do a book, on susceptibilities? Was it your decision, or—?
Van Vleck:When [R. H.]Fowler wrote me a letter asking me to write a book in the Oxford series, that was very simple, and that seemed the thing I was best qualified to write on.
Kuhn:Did you pick the subject or did he ask you to write on susceptibilities?
Van Vleck:I think he gave me some leeway, but indicated that susceptibilities would be welcome. I may have a letter on that.
Kuhn:Was that again a very long job?
Van Vleck:Oh yes, thatís why I donít get around to doing the second edition quicker.
Kuhn:Youíre working on that now?
Van Vleck:Yes, when Iím not engaged in teaching and vicarious speaking engagements which usually require a MS and consequently seem to take a great deal of my time. I started on that more or less the day I finished my paper on lambda doubling which must have been the spring of 1929. I finished it, I would say, in the late summer of 1931.
Kuhn:To what extent, in doing a book of that sort, did you have things pretty much under control, to what extent did you have to do research continually as you went along?
Van Vleck:For the first chapter I had to more or less recreate my own way of looking at the passage between the miscroscopic and macroscopic field equations. I remember I slugged that through. Of course, it had been done other ways by Lorentz and so on, but I had a particular way I wanted to do that. That I remember I had to do. I thought I had a somewhat independent way of proving Miss [H.A.] van Leeuwen theorem on the absence of magnetism in classical statistics. Iíve got two proofs in my book. But Bohr tells me thatís the way he did it in his Ph.D. thesis. Iíve never been able to find it, but Iíve no doubt itís true. Somebody said it wasnít his Ph.D. thesis but some other dissertation of his at an early date.
Kuhn:It probably was his Ph.D. thesis. . . . As you went on from there, did you also have to work out—?
Well, I remember talking to Pauli, and I said I was writing a book, and Pauli said ďI would not write my papers up just over again into a bookĒ or something like that, but I really think that thereís considerably more in my book than there is in my two or three papers in the Review that were a sequence that came out in 1927. For one thing, the formulation of the ferro-magnetism in terms of the Dirac vector model. Of course, Dirac had done a good deal of that himself. He hadnít reckoned out the second moment as I remember it; maybe he did, but at any rate, I did it over again and popularized it a little. So Iíd say thereís a good deal of steam.
Certain chapters were old hat, you might say—the NO and 02. In the interim, of course, there had been a development. I didnít think they could go to the lower temperatures and check the formula, but as soon as my paper came out, three different laboratories went to work on it at progressively lower temperatures— Zuerich and Bitter and Leiden. I remember at the Solvay Congress somebody reported, I guess, on the work from Holland. I remember Scherrer saying, Ďthat man of mine hasnít yet got his results. I was always tough on him, now I Ďm going to murder him.Ē I remember some such remark by Scherrer at the time of the 1930 Congress. I think Iíve already sized my debt to Mulliken and to Kramers; they were very stimulating people.
I didnít have the same degree of contact with Slater as I did in the early days, and I donít know as any papers of mine were triggered off by contact with Slater. I said my one on the correspondence principle for absorbtion was triggered off by a misunderstanding of one of Breitís remarks. Dennisonís paper, I have mentioned. Kronig found an incorrect statement in one of my early papers that led me to look into it further and establish the importance of the second order terms. Susceptibility was sometimes called the Van Vieck paramagnetism.
Kuhn:Did Kronig make a printed reference to the mistake, or was it something he said?
Van Vleck:He wrote me; that was just a brief job in the National Academy. When I wrote it up in the Review I Ďm sure that I acknowledged it. I feel I benefited by contact with Kronig. Usually the people I' ve benefited most by collaboration with seem to always to have been at some other institution. I donít know why it has always worked that way.
Kuhn:Isnít that partly because institutions tend not to pile up people in the same field, or at least didnít use to?
Van Vleck:Perhaps so. I think itís more than anything the importance of thinking. Research is a matter more of time than environment.
Kuhn:You made a few references to the chemists taking over certain of these problems. I wanted to ask you about the attitude of chemists toward quantum theory and its increasing penetration into chemistry. A good place to start that might be that paper of yours in the Chemical Reviews. [ďThe New Quantum MechanicsĒ Chem. Rev., 5 (1928), 467-506]
Van Vleck:Yes, I was invited to give that paper down at St. Louis in the spring of 1928, when I was still in Minnesota. Chemists were beginning to be interested in these things at that time. Of course, one of the very first to be interested was Pauling.
Kuhn:I have some impression that there was some resistance among chemists to this penetration: it was so unlike chemistry.
I wasn't close enough to chemical laboratories to be in a position to talk about that. I would say mainly the trouble was that they werenít sufficiently analytically-trained to be able to follow these developments. But certainly by the late 1930s I was getting students in chemical physics here at Harvard writing their Ph.D. theses with me.
It was a far cry from, letís say, 1921 or 1922 when there was a question whether a thesis in theoretical physics was acceptable to people in the chemistry department coming over and writing purely theoretical theses with me on magnetism—I suppose chemists call it Ligand field theory. But a great deal of that whole subject has been taken over by the chemists.
Kuhn:What sort of responses did you get to this paper in St. Louis?
Van Vleck:I got some nice fan mail, I think. I think I got some compliments on my presentation. In fact, I felt that was a worthwhile endeavor of mine.
Kuhn:You didnít find people there who were saying ďNot for Chemists.Ē
Van Vleck:No, I didnít. I think that had pretty much gone out by that time. I think they were beginning to get a guilty conscience so theyíd better learn something about this stuff. That had come over to them by that time. It was some 20 years later that every chemistry department has, what I would call, a theoretical physicist or two in it. At least what theyíre doing now would certainly have been classed as theoretical physics in the late 1920ís. Thatís the type of thing that people like Wang and Penney and Schlapp were doing, and has more and more been taken over by the chemists. As far as these splittings get over into the microwave area and have repercussions on a maser why then the engineers begin to get interested. My papers on relaxation in 1940 are clearly too late to be of any relevance, I think, to your survey.
Kuhn:I think for this moment, yes. Clearly if somebody wants to go on from the dates that weíre being more or less forced to quit at, this becomes very relevant again. But for us, about the time that the ways of going about the basic applications are established and it becomes pretty clear that the problems are going to work out—
Van Vleck:Gorterís first paper on parasmagnetic relaxation I guess was about 1936.
Kuhn:Iím out of questions but Iím not sure Iíve got all the information you can give me.
Well, let me look over the questions. Well [I .A.] I didnít mention that my grandfather as well as my father was a professor of astronomy. [I .B.] 'Had you much interest in literature or philosophy or sports?í I donít think I ever had much interest in philosophy. I took a number of courses in literature.
I was a conscientious attender of football games. [II. A. 3, a.]ĎThe ďspiritĒ of physics—was there a sense of excitement in physics when you began your studies?í I think physicists were very small in number so that you felt that they were a very minor part of any educational institution, as I remember it. Most of the mathematics and physics concentrators at Wisconsin were girls. Men all went into engineering. That was the era when physics was sort of considered by a substantial part of the population as an esoteric subject, I would almost say.
Kuhn:In this general area of these headings under #3, you mentioned that you felt that Slater had given me in certain respects a rather different impression from the one you had given me and I think thatís probably— Iíd have to listen to those tapes again—but thatís probably true. Did you have any reactions to the sorts of things he said?
Van Vleck:Well, I said I felt that he and I talked over some of the current developments in physics.
Kuhn:Certainly there you gave more emphasis to talks between you than he did. He felt clearer that everybody had, studied the literature very systematically.
Van Vleck:The statement I would challenge the most was where he said that there were a lot of physicists in America who knew quantum theory. That, I think, is open to question. I mean, there were men like Adams at Princeton who perhaps knew some of the formalism, but the spirit that was pervading Bohrís laboratory, or people like Darwin and. [R .H.] Fowler at Cambridge and so on, I think, this was by and large absent from most of our American institutions. There were experimentalists who did nice work in the photoelectric effect—Mendenhall, for instance, at Wisconsin. But when you come to straight theory, there was comparatively little going on. I donít know about [Victor Fritz] Lenzen in Berkeley-Wasnít he interested in it at an early date?
Kuhn:I donít really know. So far as I know, he may have been interested in it, but I think not creatively.
Van Vleck:I think the answer to that is how many people made creative contributions to the literature of quantum theory. Of course, there was Kennard who had some ideas about the spinning electron. Of course, the Uhlenbeck-Goudsmit immigration to the United States was a major factor in the development of physics in this country.
Kuhn:Tell me more about that. Thatís an interesting remark. Was it particularly through the summer school?
Van Vleck:No, I think that Randall just wanted to get some bright boys from Europe. Ehrenfest sold them Uhlenbeck & Goudsmit—thatís my understanding. The employment opportunities in the Netherlands were limited. I think those two people coming to Ann Arbor certainly strengthened immensely the American team in theoretical physics at that period. Just how and when Laporte came over I donít know. He tended to shift into hydrodynamics and other interests, sort of an inverse Burgers after heíd been there a while. Of course, Uhlenbeck went into nuclear physics.
Kuhn:But you speak of their influence on American physics in raising its level of tone. I wondered what the vehicle for doing that was?
Van Vleck:Well, both Uhlenbeck and Goudsmit were both exceedingly good classroom teachers. I remember Schlapp remarked on what fine lectures on quantum mechanics Goudsmit gave at one of the University of Michigan summer schools. And then they were the nucleus around which the Ann Arbor summer schools were formed. That was, of course, the great Mecca of theoretical physicists during essentially the depression years, I should say.
Kuhn:How large a group went there, and how regularly did people go to the Ann Arbor sumner school?
Van Vleck:I would say perhaps fifty attended my lectures, forty or fifty. There were some bangers-on at the more elementary level, but by modern standards, they were small. By standards of those eras, they were big.
Kuhn:These were presumably graduate students from all over the country who came?
Van Vleck:Yes. When I first taught at the University of Minnesota there were exactly thirteen graduate students in physics. That gives you an idea of the size of the physics departments, even, though it was a university of, I suppose, 5–6000 students at that time.
Kuhn:How many graduate students were there at Harvard by the time you got here?
Van Vleck:Probably around forty. There again itís a little hard to do your bookkeeping because itís a question of whether or not you count Cruft [Laboratory]. By the time I went to Wisconsin, I think Wisconsin had rather more graduate students than Minnesota. Maybe physics had expanded. There were about 30.
Kuhn:How many do you suppose there had been at Harvard when you were a student?
Van Vleck:I doní t know. The attendance at Bridgmanís courses was certainly about a dozen in his electricity course. In his elasticity course there were three taking it for credit, and I remember his calling a class off because only two showed or something of the kind. Iíd been delayed in getting there, I got there about ten minutes late so the course had to be called off. But that shows that the graduate students were not large in numbers. There seemed to be a rather larger and more flourishing group in mathematics, I should say. At least, there was an active graduate and undergraduate mathematics club.
Kuhn:Do you want to continue turning pages to see if they suggest anything? [ĎVan Vieck is looking through the questionnaire]
Van Vleck:I might comment a little bit on paper #17. That was a little outgrowth of a discussion with Oppenheimer. I said what in the world is the connection of this with the classical percentage of time—the correspondence between the square of the modulus of the Schroedinger wave equation and the time that an electron spends in a particular place. I remember Oppenheimer saying that he thought it came out in the second approximation. That, I think, I proved generally in this paper #17 which, incidentally, has been greatly extended recently by [R.] Schiller to include spin and other things that I did not include. I might mention that conversely I stirred up one of Oppenheimerís papers that I just referred to in vol. 43 of the ZEITSCHRIFT FUER PHYSIK in which I asked a question, if an electron is a plane wave, how come Rutherford ever got his formula for scattering? To what extent can you identify scattering at a definite angle with a certain distance of approach? That Oppy investigated in his paper in vol. 43 that I just referred to.
Kuhn:Both of these papers that are not far from the same time indicate some sort of concern about the statistical interpretation and its relationship to the older causal trajectory interpretation. How live was that issue? To what extent were these problems that had to be solved giving you confidence in what was going on?
I wouldnít say so much confidence as understanding, because I was feeling that this was it. I was, I guess, a pretty devout convert to quantum mechanics, but there were a lot of things I just didnít understand. As often happens when you donít understand a thing too well and try to educate yourself on it, you find very often that other people havenít understood it too well either, and thereís the genesis of a paper.
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