Paul Peter Ewald – Session II

Kuhn:

Before the discovery of X-ray diffraction, what was the status of the wave versus particle debate for X-rays? I know, and you emphasized, that this is very shortly after Bragg has argued very strongly for a particle interpretation. Was this taken very seriously?

Ewald:

Well, I am not quite certain about the historical order. But I would have thought that the center for the photon idea in Germany lay in Berlin, with Einstein. And although we discussed it quite often in Munich, the Munich group was not really very keen on it. Now this may not be quite correct. There may be papers by Sommerfeld, or Debye, or Lenz, Epstein perhaps, who were the main people who would have been interested in it at the time, which followed up the photon concept. And there's no big paper as far as I know I mean it isn't prominent. What Sommerfeld and Debye tried to do for the second Solvay Congress was to interpret the uptake of energy by a resonator and see in what time it could accumulate sufficient energy to eject the electron.

Kuhn:

If I may interrupt a minute, I don't really quite mean to be asking you about photons. I do want to ask you about that a bit later, but that would be out of chronological order. Before you get to the notion of whether X-rays as electromagnetic radiation behave like photons, there's still the question as to whether they are particles or not. And at least in England, as late as 1910 there is very real feeling that they are matter of some sort ... Did that view have any particular effect in Germany?

Ewald:

Yes, I think so. Especially Stark, I think, propagated this idea.

Kuhn:

Now how about the group you were in around Munich, and around Sommerfeld?

Ewald:

Well you see Sommerfeld was working on the diffraction of X-rays ... The discussion of the diffraction effect, as far as I remember, made it necessary for Sommerfeld to rig up an entirely new section in the theory of diffraction. If you have this wedge shaped slit for diffraction, at its thin end it is really not just a slit in a plate but its a deep chasm which does the diffraction. And so this demanded some modifications of the diffraction theory. And as far as I remember Sommerfeld worked on that for quite a while, and in all events the publication of his results on the Koch micro-photometer traces came out only after Laue's discovery. No, I think we were on the whole very strongly impressed by the wave nature.

Kuhn:

Did one then worry about needle radiation, I mean the immense ionizing power of the X-rays?

Ewald:

Yes, one worried about it. I mean there were two non-connected worlds, as it were, for a long time. You had either to consider a thing as a wave or as a particle. And there was no bridge between the two.

Kuhn:

And you think that sharp a recognition of the duality was perhaps already in 1910 and 1911, had reached pretty general awareness?

Ewald:

I think the only person in whom this may have been ready, was Einstein. And I know relatively little of Einstein because I was never in Berlin.

Kuhn:

There is no question that Einstein had this feeling very strongly. And of course 1909 is his famous fluctuation paper. But you don't have residing or remaining particular sense of the way this was in Munich?

Ewald:

No, except it was a time where the theory of fluctuations became very important. I think this probably goes back to Ehrenfest. I always thought it was reining up the horse by the tail — by the tail end, to get statements about thefluctuation and then that led over to entropy concepts and so on. And from there you got the whole story. And this was done a great deal by the people surrounding Sommerfeld. I don't know whether he himself took part in this. But Debye as well as Lenz were very much interested in this aspect.

Kuhn:

Debye did very little with it then, with fluctuations. At least in this period.

Ewald:

Maybe he didn't publish much about it. Yes, but we discussed it a great deal.

Kuhn:

Do you remember in connection with which questions? I take it that Sommerfeld himself was not much given to thermodynamics or statistical operations.

Ewald:

No, it was definitely his weak side ... sorry to say I can't tell you very much about the fluctuation business. It was at a time when I was intensely working on my dissertation, which was entirely apart, because it was pure classical physics without any hint of statistics at all. And, so I just heard these things but never took part very intensely. I might tell you that there are a number of slightly incorrect statements about the origin of Laue's idea. That might interest you. Laue hims has given slightly varying accounts of it. As far as I remember it, I've described it in a book which is to come out. It was so. Sommerfeld had given me as a subject for my thesis the problem of accounting for the double refraction in crystals by assuming that crystals have a regular lattice. According to the usual theory of dispersion one assumed refraction to be due to the presence of dipoles in the interior of the body. Now if these dipoles, which by themselves are isotropic, have different properties in different directions, i.e., if such isotropic dipoles are arranged in an anisotropic way according to a lattice, then would this give rise to double refraction and to ordinary laws of crystalloptics? So I received this thesis subject, which I picked out of about 12 different choices, which Sommerfeld drew out of his drawer. And he rather warned me and said he wouldn't be able to help me, whereas with the other stuff he could help me. But I was more interested in the property of solids than in diffraction of radio waves around the earth and self-induction of coils and other problems which Sommerfeld proposed.

Kuhn:

Do you remember, if I may interrupt, were any of the problems of a more fundamental nature, closer to quantum mechanics?

Ewald:

No, no. None. These were all classical problems of boundary conditions, partial differential equations and boundary conditions. The only one which fell out of that was this last one, of which he said he really couldn't recommend it very much to me because he didn't know himself how to attack it. And so that tempted me very much. And I took off. The summer vacations were coming, and I went for a hiking tour along up the Rhine. And considered this whole thing in a rather dilettante way. Then I came back and began working. It didn't go for a year or a year and a half. And then finally I hit upon the correct idea. The first problem was the summation of spherical wavelets which issue from the dipoles and to find out how they form the optical wave. This I then managed to do, and really when I cane with my' solution to Sommerfeld, Sommerfeld first showed me how to do it. We had done it independently, but' very nearly in the same way. I think I got one step farther. But I know from Frau, Sommerfeld that Sommerfeld at that time sometimes lay in bed at night and said, "It's too awful. It can't be done this way. It should go that way." He was worrying about the problem and how to do it. Well anyway, once this was done I could sum the spherical wavelets issuing from the points, of the lattice. But now for the theory of dispersion you need something more complicated. You have to leave out that resonator or dipole on which the field acts. And you shouldn't add its own contribution to the field exciting the dipole. The dipole doesn't excite itself. This subtraction gave rise to some difficulty. And that again held me up for three quarters of a year or so. And this was solved at a skiing party in (Mittenwald) in the Easter vacations. This was a yearly skiing affair of the physicists. Willy Wien had a beautiful cottage in Mittenwald. And we stayed at the hotel, but we joined forces for going up the hill, and skiing down. And in the evenings in our inn there was one bright lamp, and those who wanted to do work on -paper were privileged to use that lamp. Lenz called it "die (integrieren) Lampe." So we sat down underdie (integrieren) Lampe, Sommerfeld and. Debye and I. And Debye said, "Oh, this is very simple. You just use the method which Riemann used, and you can transform that into theta functions, and then the theta functions are transformed and that is quite simple." Well, Sommerfeld and I were amazed that actually it was that. It was the method which Riemann used in some problem of thermal conductivity and which had been used before by French mathematicians too. And which nowadays really is called. Fourier transform method. And with that I managed to get over these last difficulties of computing the effects, and I found that the optical properties are quite the regular ones. But in the course of this work, where I had been using a very definite, well-defined, model for a solid, it turned out that I had to leave out that part of the usual theory of dispersion which is quite prominent in it. Namely, the incident wave, the so-called incident wave, which plays a big role in the theory of dispersion of Planck and, also of Lorentz. Since I was using an infinite medium, there couldn't be an incident wave. This was not quite clear to me at the time. But I came to the conclusion that by cutting off the crystal and providing a surface, there must be some action of this act of cutting off the crystal which annihilates the incident wave in the interior of the crystal. And this was a general result which seemed to me quite important and rather revolutionary. And I wanted to discuss that with Laue. I didn't go to Sommerfeld for it because Sommerfeld was not a man who was so terribly interested in questions of principle. He was more led on by his mathematical skill. But Laue was a profound thinker and knew this part of optics very well, so I asked him, "Could we discuss it together?" And he said, "Yes, let's go tomorrow and have supper at my home." He was youngly married then. So next day we set out at five or six o'clock from the Institute, and I think while we were still passing through the University, I began explaining to him what my problem was. Laue didn't know what I had been working on. We crossed Ludwigstrasse, and went to the Englische Carton to make a detour through the park. Then after crossing the Ludwigstrasse Laue asked me, "What's the reason for assuming that these dipoles are in a regular array?" I was rather shocked. I said, "Well, this is the general assumption you make of the nature of crystals." This seemed new to Laue, although Laue later on in one of his publications said that of course he had known of this. But, well, he must have forgotten at the time. So I went on explaining what was doing. And Laue interrupted me and asked, "What's the distance of these resonators in the crystal?" And I said, "Well, this distance is very small compared to the wave-length of light, and one doesn't really know. It depends on what you assume the particles of the lattice to be — whether they are single molecules or whether they are groups of molecules, which was the assumption which had been made by Brouvais. Or what they are." We went on. I tried to explain to him the mathematics of the whole problem, and by that time we arrived at his home and had supper. And after supper we began to talk again. Now I was driving for my point, to ask him what his opinion was about this action of the surface. But Laue again asked, "Now what is the distance of these atoms?" And I said I really don't know. The only thing I know is that the distance is very small compared to the light wave-length, and that is sufficient for my purpose. He said, "Well, what would happen if you took very short rays?" And as far as I remember, I answered, "Well, this formula is strict, this conversion of the field from spherical waves to plane waves. It need only be discussed for that case, which can be done very easily. But I haven't the time now. I have to finish the writing of my thesis within the next fort-night. So I just can't spend any time on it. Shall I write down the formula for you?" And I think I did that, and gave him the formula. Of course you never take (to) formulae developed by other people. I don't remember that Laue mentioned the possibility of X-rays passing through the crystals, but he may have. I am, not sure. If he only said "very short wave-lengths", I might even have not recognized that he meant X-rays. Anyway, I finished my thesis. I didn't get any comment from him that evening. I finished my thesis and got my degree. After the degree I retired to the country to my mother's house. I had two offers, to go as assistant either to Hilbert or to Haber in Berlin. Which I considered. I even traveled to Berlin and paid a visit to Haber, who was then sitting in, the cellar of what was to be the Institute of Physical Chemistry. I finally decided to go to Göttingen, which I knew from ray student days, and to Hilbert, whom I revered very much. So over that I forgot entirely this question of Laue.

Kuhn:

What would you have worked on if you had gone to Haber?

Ewald:

Well Haber had asked me a question, or asked Sommerfeld, whether I couldn't do a problem for him. And that was to determine the potential, the inner potential of a crystal. This would have led to the Madelung constant. You see this was again contained in my formulae, and I had to discuss that for the limiting case of extremely long wave-lengths. And this was not quite a nice limit to take. And after Magdelung had done it I did it in a very short time. I just needed to see that it gave sense. Magdelung used an entirely different method from mine. And I developed my method afters the war, I should say in 1919 or '20, and that has become the standard method really for calculating potentials. It's used more than Madelung's. Madelung's is also used, but my method is really a nice method. And nowadays it's very, very easy to explain all these things, because it's just a very simple Fourier transformation. But at that time, I remember I thought it was very good show. You see it all went under the name of theta functions. And these were multiple theta functions. There was one book on theta functions by a man coiled (Trotza), which was written in a rather mathematical style. And I still remember how there was a theory about transformation of theta functions which, the enunciation of which, went over a page and a half of the book. In very abstract terms, it seemed to me. And I took to convert that all into something reasonable. When I had finally done it, it turned out that all these big determinants and other stuff which came in, could be done so elegantly in a few vector symbols, that the whole problem became very simple. So I was very much pleased to see that. I first heard of Laue's discovery when Sommerfeld came to Göttingen to on it ... Laue's discovery was at Easter. Or soon after Easter. And I think that Sommerfeld came to Göttingen probably about 50 days after Easter, in June or so. There I first heard of it. And then I went home and took my old formula — the one I had given to Laue — and discussed it. That gave the reciprocal lattice and the construction with the sphere, which Laue calls sphere of reflection. It gave the whole story very quickly. And I can't remember why this paper was published only nearly a year later in Physikalishe Zeitschrift. It may be that Phys. ZS. didn't publish very quickly at that time ... I think it's early in '14, that it was published. At any rate I am now astonished at the tine delay between this first hearing of it and sitting down — I remember I got that the same day, and next day I went to Sommerfeld and showed him the whole story.

Kuhn:

You say your talk with von Laue was just a couple of weeks before you had to turn in your thesis?

Ewald:

Yes ... As far as I can locate it, it must have been the end of January or February of 1912. I've got it all in the book. I looked it up for the book, so it's not worth mentioning here. You see Laue then discussed the matter with Sommerfeld and Wien, and I don't know whom else. I would love to know who else was at the skiing party in Mittenwald in 1912, Easter 1912, but I haven't been able to trace that down. Usually there was Sommerfeld, me, Wien, and each with their assistants and a group of people. I've only found out that Debye was not there. And they discussed Laue's idea aid came to the conclusion, "Oh, this is quite hopeless. Because the thermal motion, will bring in such irregularities in the crystal that it's all smeared out, all the effect of diffraction cannot happen."

Kuhn:

Who has told you about this, or where does the information about these conversations come from?

Ewald:

It comes from Laue himself and from Friedrich. So Sommerfeld Friedrich, who had just finished his thesis work and taken his exam under Roentgen on the directional emission, I believe, of X-rays. And Sommerfeld wanted Friedrich to investigate the so-called characteristic radiation, the homogeneous X-ray radiation of which we had very little experience. And nobody knew whether it was so thing fundamentally different from the usual spectrum. Well, one didn't know the relation. So sommerfeld wanted Friedrich so far as I remember, to make experiments on the directional emission of characteristic radiation. He was rather unwillng to let Laue have the loan of Friedrich for an experiment which he considered, and others too considered, not to have a very good chance. On the other hand, Friedrich had to set up the X-ray equipment in the little institute of Sommerfeld and had to set up the whole story so that it took very little time to do it. And so finally Laue and Friedrich made it without Sommerfeld's permission in his institute. And Knipping joined in in order to save Friedrich time and preoccupation with this experiment, formally at least. It was good that the result didn't take Ions to come out. It was the second experiment which gave indications of diffraction. But then of course Sommerfeld was quite proud of it. But that was a period when there was quite some friction between Laue and Sommerfeld. Because Laue felt that Sommerfeld had not given him sufficient help.

Kuhn:

In one of the places that you talk out the discussions about the effect of thermo-motion, you also raise question as to how generally structure. theory was taken for granted. I know you talked about this in connection with von Laue, and your own impression that he simply had no notion about crystal structure. Who would generally have been expected to know?

Ewald:

Well I can tell you the story there. Sommerfeld, as you know from your own biography of Sommerfeld, began as an assistant to Liebisch in Göttingen, a mineralogists. This was for a very short period, I think half a year or a year. And he had to draw crystal diagrams and this kind, of thing. It was not quite his line of work. But on the other hand, he had a good notion of crystallography. And he was quite aware of some problems of crystal physics which weren't solved, for instance concerning the symmetry of thermo-conduction in crystals. That was one of the unsolved problems. Now this is one thing. Secondly, while in Göttingen, Sommerfeld was in close contact and became a life-long friend of Schoenflies, who was then professor of applied mathematics in Göttingen. They were in the same Mathematische Verein and called one another "du". Which is always a sign of intimacy. Thirdly, in Munich at the Technishe Hochschule, there had, been (Zoldga), professor of physics, who had done a lot on regular arrangements of atoms. In Sommerfeld's institute — I don't know how it came there — but I've a guess — there were little cigar boxes which had a double lid. There were holes drilled through the two covers, and you, could put knitting needles through the two holes and get an array of axes regularly arranged. About these axes, or fastened to the axes, there were little pearls, glass pearls. These were (Zoldga's) models of his 65 different crystal structures. I think that possibly these models came to Sommerfeld's institute and were shown there in a big glass case with other instruments, through the fact that this institute was the successor of a collection of instruments of the Academy, which was under the care of Boltzmann. Sommerfeld of course was the successor of Boltzmann although there had been several years intervening. And so probably that's the origin. Sommerfeld finally gave them to the Deutsche Museum and I think they arc there now. So Laue should have seen these models. Whether he saw them or not I don't know.

Kuhn:

Well you think then it would have been very hard for any student at Munich not to be aware of crystal structure?

Ewald:

Oh, very easy. Not hard at all ... You could stay unawares, because students Generally didn't get into this kind of museum or collection And even so, they wouldn't know by themselves what these models were there for. There were no explanations.

Kuhn:

This was no part of the standard curriculum?

Ewald:

Well, the way students learned about structure theory was in Groth's lecture in crystallography. And Groth was an intimate friend of (Zoldga). He was really sold to (Zoldga's) idea of structure theory, the 65 systems. But being an open-minded person, Groth had also done a lot to get Fedoroff to publish an account of his work in the Zeitschrift fuer Krystallographie. I know that Groth was proud of that, because he told me so himself. 'I got him to write all these papers for the Zeitschrift.' So Groth was fully aware of the different structure theories and, in fact, gave the nearest correct explanation of crystal structure at the time.

Kuhn:

What was the main difference between the Groth and the Fedoroff?

Ewald:

The main difference between it was this. Fedoroff considered space to be divided up into congruent domains. The kinds of things which Schoenflies also introduced under the name of fundamental domain. Fedoroff calls it, I think, stereohedra, but I'm not quite sure. Now, Fedoroff believed these volumes to be physically significant receptables for the ultimate particles, which might be molecules or aggregates of molecules. You see, nobody knew the particles were — that was the important point. Groth was the nearest to say that the crystal is built up of atoms. And each kind of atom forms one of these (Zoldga) or Schoenflies space groups. And they are put one inside the other, and of course they have to fit together. That is to say, they must have a common periodicity, or as the English now say, lattice. There is one great difficulty in this, from the point of view of nomenclature. The English use the word lattice only for the periodic part of the structure, and they use 'structure' for the whole thing, including the various kinds of atoms. Whereas in Germany there is only one expression, "Gitter," which covers both. So the English are always a bit terrified or disgusted when the Germans don't use the correct difference between lattice and structure. For instance diamond is a structure but not a lattice. It contains lattices, but it's a structure. And in Germany it would be "Diamont Gitter." There is no difference between the two. So Groth really was quite close to the proper concept. But I don't believe that Laue had any contact with Groth at the time. Of course afterwards these experiments he had — but not before.

Kuhn:

Did Sommerfeld have much contact with Groth as well as with Fedoroff?

Ewald:

Sommerfeld and Groth had contact, yes. Certainly. I mean they met at the Academy. I think they were in a society of professors and other people, and met quite a bit and visited one another. I don't know whether Roentgen — who worked a lot on crystals — had ever thought about the ultimate nature. But he was very cautious, and, would never have used anything so hypothetical in nature as the structure theory for his own purposes.

Kuhn:

You once told me about an attempt you and Sammerfeld had made to bring Groth and Schönfliess together.

Ewald:

Yes, this was really very dramatic and very interesting. This was after Laue's discovery. It was in fact in August, 1914, or the end of July, 1914, when Schönfliess came to Munich, and Sommerfeld invited Groth and Schönfliess to his office. And the four of us I was of the party, too — sat there and tried to reconcile the nomenclature of these two old gentlemen. Groth at that time was probably over 70, or in his 70's, and Schönfliess well, in his 60's. It was not quite possible to bring them to the same point of view. You see Groth thought much more concrete in a way, and thought of each kind of atom in a crystal forming a lattice by itself, or something more complicated than a lattice, a whole space group arrangement. And these different atoms form space groups which are put one inside the other, which penetrate or penetrate one another. And Schönfliess who was a mathematician, not a physicist really, was very slow at seeing that. He always envisaged in the first instance, the symmetry elements. So he said, "Well, it's up to you what you put in there. It's all the same to me. I have the fundamentale Bereich, and that you can fill as you like. You can put atoms or molecules or groups of molecules into it, whatever you like. I don't care in the least, because the symmetry of the whole thing will be such as corresponds to the whole framework of symmetry in elements." Well, they parted after an hour and a half or two hours' discussion, without having convinced one another very much. And I remember how Sommerfeld and I and Schönfliess went down to Ludwig strasse, and, we came to a corner where there was a big red poster telling of the mobilization of the army. It was just in those days before the war. At that time I did not understand the fright and shock of these two elderly , people at seeing this. And. Schönfliess only one idea. He didn't want to come to the Café where we were heading, but he said, "No, I must go to the station and see that I get a train back to Frankfurt, because the trains will be stopped if I wait and I shall bestranded." Here I think we should pause. [Break] The question of the corpuscle versus wave rays. I think there are two papers which are of interest in that respect. One is the very first paper which Sir William Bragg published after hearing of the discovery. I tried to find out how Sir William Bragg heard of Laue's discovery, and Sir Lawrence Bragg writes to me that he got the reprint from Laue. This is also what Laue said when I asked him the question on his 80th birthday. "How did the knowledge come over to England?" And he answered without hesitation, "Why, by the reprints I sent out." Now this I would not take to be the quite correct answer for the following reason. You see Laue's paper appeared in the Bavarian Academy. One is dated June 8 and the other is June 24 or so. So the papers were not really out, or should not have been out, before the end of June. And in the beginning of July there was a celebration of the 250th birthday of the Royal Society. And, to that of course a lot of delegates converged to London. And among them were Woldemar Voigt from Göttingen who I believe represented the German universities, and Groth from Munich, who represented the Bavarian Academy. I am sure that these people nu have told of Laue's discovery. After all, if you go abroad you like to brag about first-rate pieces of work which have been done in your country, and I don't see why they shouldn't have told the english people. As a result there vas certainly mention of the Laue discovery in the Presidential Address of the British Association Meeting of that year. Bragg, who had been elected to the Royal Society two or three years before that date, may have been at this 250th celebration. I wrote to the Royal Society to find out, but only the foreign delegates were registered and not the Fellows — the normal Fellows — so I couldn't find, out whether he might have heard of it from Groth or Voigt directly. And his son says, "Well, he got the reprint." And that certainly set him work As true experimentalists, they didn't believe the explanation — just as Roentgen wouldn't tie himself down on this explanation of diffraction. And Bragg of course had the particular desire to save his photon theory of X-rays. The first paper he published in Nature was an explanation of the diffraction — a picture of the ZinKblende, the four-fold symmetry picture, by means of photons riding down the avenues between the atoms. This was it seems not his own idea but his son's idea. Actually most of the ideas at that time-came from Lawrence, or Willie as he was called. It happens that in the case of a cubic crystal with this particular direction of incidence along the four-fold axis, you can explain the spots by assuming photons traveling. It wouldn't be true for any other orientation of the crystal or for any other system of crystals, not in general in other words. Well, this is one paper. And the other paper which is worth noting in that respect is one by Johannes Stark in Physikalishe Zeitschrift of 1912 or '13, '13 I suppose. I've got the reference upstairs if you want it. Where he tries to explain it by photons traveling along what he calls pits in the crystal. [Break]

Kuhn:

Then Sommerfeld, when he returned from this trip to America, actually felt pride as a propagator of the Compton effect?

Ewald:

As a propagator of the Campton effect, yes. You see Sommerfeld was a man who was really enthusiastic about some discovery quite irrespective of from whom it came. And so he explained it and took it up and showed the beauty of it, and other people didn't sometimes quite like that. Laue was not very happy about Sommerfeld making the trip to Gottingen and explaining Laue's discovery in Göttingen. He felt that was his prerogative.

Kuhn:

I wondered a little bit about that. We talked a bit with Debye about this also, and, he said he knew nothing at all about what was going on until the announcement of the success. He felt that Laue probably kept this very much to himself until it was successful. Would this have been like Laue?

Ewald:

This certainly was done in a rather clandestine way. You see it would have been quite natural for Laue to inform me of this experiment which was going on, but he never did that. Of course I was in Göttingen at the time, as far as I know, Debye was already away.

Ewald:

Did you have an interview with Debye?

Kuhn:

Yes, yes we did.

Ewald:

Well you see Debye did really a marvelous piece of work — his calculation of the temperature effect. I know that because (Ella) and I in 1913 on , our way to England visited Debye, who had just moved in in Utrecht. And he told me of his work, and I was just aghast at the bravado of attacking this problem where the ordinary diffraction effects were still under discussion. At that time you see there was still a discussion going on between reflection or diffraction, which took a tremendous tiric to get over. The first man who showed the equivalence of reflection and diffraction is the Russian, (Wolfe) in phys. ZS. But this was a rather cumbersome proof, and of course it was very much easier to do that with my construction with the reciprocal lattice. But also there — I don't know. Probably I saw it. I don't remember how long it took me to see that it was equivalent. But the indexing of these diagrams was one of the main preoccupations of the time. This was not quite so easy as it'is' today, because with Laue diagrams you don't have a given scale of wave-lengths, so there are always common factors which can come in. [Break] Oh, you wanted to know about Hilbert.

Kuhn:

You were really the first, were you not, of the physicists appointed his assistant?

Ewald:

Was I the first? Maybe I was. I'm not quite certain. Yes, I think I was.

Kuhn:

Do you know how he happened to pick a person from Munich?

Ewald:

Well because first of all Hilbert and Sommerfeld were very good friends. They were both East Prussians, and, the people from Königsberg stuck together and formed a small community. Besides Frau Sommerfeld and Frau Hilbert, and he, Sommerfeld, and Frau Hilbert were very good friends. Frau Hilbert was a very beautiful person. I mean not beautiful but marvelous person. And he, of course, was, as Laue says, the greatest genius he has ever set eyes upon. And. I think that is the general impression. My first contact with Hilbert was when I came to Göttingen and became his Ausarbeiter. That is to say I had to write out long hand the course which he was giving, for the other students to read up who had missed lectures. And there I was helped very greatly by Hellinger, who was his mathematics assistant. And then after my Munich time I was recommended to Hilbert by Sommerfeld and I decided to go to Hilbert. And Hecke was his mathematics assistant ... Hecke later became professor in Hamburg and is quite famous for theory of numbers.Hilbert was in a period where he said, "Well, now I have reformed mathematics. Now I will reform physics, and then after that chemistry." By reforming he meant that he had axiomatized mathematics. You see his axiomatic geometry was not too long ago, and he wanted to do the same thing for physics, that is find out where the necessary assumptions to rig up a system of physics which was logically in order and complete. For that reason he became interested in physics. Of course it was a good idea to do it for physics first before starting out on chemistry, because chemistry was a great mess. So I was to help him in doing that. Up to then Hecke had helped, and when I came to Göttingen Hilbert was in a stage where he was trying to understand Planck's theory. This was 1912. The quantum theory dated from 1900 of Course had spread. Hilbert knew of it, and he wanted in particular to axiomize the theory of black radiation. So he was very much interested in the papers by Lummer end Pringsheim. I think it was Pringsheim, not Lummer, who had written several papers in Phys. zs. If you look up the Phys. zs. of those years, you'll find several criticisms back and, forth of papers between Hilbert and Pringsheim. And I was put on that. I must confess that I never found very much taste in this hind, of work. I didn't it too well because it was really rather far from the physics background. It was a logical investigation more than anything else.

Kuhn:

Now where the Pringheim papers around 1912 theoretical papers?

Ewald:

They were theoretical papers, yes. You see one of the problems which Hilbert encountered at first was that Planck assumes that there is a pencil of radiation with a certain angular opening. This pencil is being refracted and diffracted so on, and to show that in thermodynamic equilibrium the density of radiation is the same everywhere is one of the fundamental concepts. This is also needed for Kirchhoff's law, that of absorption — of emission is equal to a universal function. Now Hilbert said, "How can you assure that? You know how radiation is propagated. You have the laws for it. So why have you to make assumptions there. And what he aimed at was reducing this whole concept of energy density radiation to the Fermat principle, which contains the laws of propagation of waves. Wow again you see this is a bit away from the physics, because I don't think that the Fermat principle anything about diffraction, so diffraction had, to be left out of the game. I'm not quite mire about this point, but it seemed to me that it was rather restricting, this question to geometrical optics. Before this, Hilbert had tackled the kinetic theory of gases. And there he had found that as everywhere, whatever he touched at that time, he was led, to integral equations. The momentum equation of Boltzmann is such an integral equation. And so he had taken that as the starting point, and from thereon it was pure mathematics. Whereas Boltzmann in his kinetic theory of gases made quite a number of assumptions ad hoc and butted in with physical concepts so on, , Hilbert wanted to eliminate all that and said, "No, this integral equation is the essential equation, and now we have to discuss all its consequences." And he did that in a very marvelous way. **** Well, there he hod carried through this program for the kinetic theory of Eases. He didn't like Maxwell's approach, you know, with the fifth power law, and he wanted to do it in a general way. And, so then at my time it was the black body radiation. And after I left Hilbert actually it was optics, and, he gave a whole semester's course practically on my dissertation. He changed it to a slightly more elegant form — not very much.

Kuhn:

Now when you actually worked with him, what sort of things did you do for him?

Ewald:

Well, frankly I don't remember. I got engaged, and, the only thing I remember was that we were stuck by the Cauchy relations. Born and Kármán had done their work on lattice theory — vibrations in lattices — in 1912 I guess, and so the way for an understanding of the solid body seemed to open up, but there was the formidable obstacle of the Cauchy relations. These were the consequence of assumptions which Cauchy and NaVier and other people had made, and which led to the restriction in the number of coefficients of elasticity, which was not found by experiment, or was disproved by experiment. So I remember that Hilbert asked me to look up the old papers and sec whether I could find fault with them. I sat in the library in Göttingen over these rather stuffy volumes of the French Academy and read them with much interest. But I couldn't find fault. As no one else had been able to, until Born came about a year and a half cater. And Born saw the light because he introduced the concept of the structure in contrast to the lattice.How we can use these two expressions. The lattice is just the Periodic array, and. the structure is the whole atomic structure where there can be deformations inside each cell. And these internal deformations cancelled the restrictions which were valid in the case of a lattice, where every single atom is the center of symmetry. So Born cot rid of these restrictions which everybody had found because they all used the simple Brovais idea of a lattice.

Kuhn:

When people used the Brovais lattice in this period, did they have notions, or think they had notions about what it was that went at lattice points? Well, the notions I think developed from Haüy's concept that the ultimate particles of a crystal resembled those particles which you can obtain by ever finer cleavage of crystals. This was taken from the notion of calcite, where you can cleave always smaller polyhedra and the angle will remain the same. And so that (Häuy) finally supposed that one such little block must be the ultimate particle, of which the crystal is the ultimate brick. And Cauchy and Navier certainly assumed atoms as far as they spoke of it. And they assumed particles which exert central forces on one another. Now in your own work, you're again making assumptions of this sort.

Ewald:

For the optics, yes. Although I did not assume any forces between the particles I've really isolated particles which are in a geometrical order, and that's all.

Kuhn:

And which are polarizable?

Ewald:

And which are polarizable, yes. And for my own work I also assumed the simple lattice. Hilbert of course was a remarkable man, and. I have a number of beautiful stories about him. It is incredible. We have always hoped somebody would collect them, but it's very difficult because part of the fun comes from the very outspoken East Prussian accent which Hilbert had. But he was quite a queer chap. He had a nice house on the Wilhelm-Weber Strasse, with a big garden in back of it, and he was very fond of cultivating fruit trees, pears and apples, and wall trees, on the spalier. On one of the, walls of his Garden he had a long blackboard with a small roof on top of it so that even in rainy weather he could walk up and down, up and down, and just jot down things on the blackboard and think.

Kuhn:

How did he feel about black-body radiation? How did you' feel about it at this stage of the game? Planck's discovery of the law of radiation and his introduction of the energy quanta, Of course this was something which aroused general interest. I only knew it from the lecture courses and was not terribly excited about it. I was terribly specialized.

Kuhn:

Did Hilbert concern himself about the conflict between this and classical electro-magnetic theory or classical mmechanics?

Ewald:

Hilbert was deeply impressed by the necessity of having quanta of energy. You see Hilbert and Nernst were close friends, and of course in Nernst's work; this comes in too, in the determination of the chemical constant. Hilbert also did quite a lot of thermodynamics at the time and was worrying about the chemical constant. There were papers by Sachur and Tetrode on that, which posed some problems of calculation. I don't quite remember what the situation was.

Kuhn:

Was this going on during your year there?

Ewald:

I think it was. And Nernst's third theory of course was important. I think during the period I was his assistant Hilbert may have lectured on thermodynamics. Usually thermodynamics and black-body radiation went together in a lecture course. I remember however having very, very long discussions about what the Nernst theory really meant with respect to specific heats — whether they had to go, in what power they had to go to zero, and so on. This kind of thing. Hilbert's interests lay always in the question, what is mathematically proved? What is the consequence of what? And reduce the assumptions to as few as possible.

Kuhn:

How did Hilbert and Nernst keep in touch? Did they write frequently? Because they were not geographically together.

Ewald:

No, Nernst was in Berlin. Nernst had been in Göttingen, as you may know, for a long time ... And Nernst was the first owner of an automobile in Göttingen and a very early one in Germany, anyway. But I remember seeing him with Nernst's daughter, whom I visited in London. She had a beautiful photograph of Nernst in a terribly old-fashioned car with his bowler hat on and driving the car. And the whole family sitting on the back seats.

Kuhn:

How did the physicists take to Hilbert's involvement? Were they impatient with it, or did they welcome it?

Ewald:

We'll, I'll tell you ... In Göttingen there was a strict division between physics and mathematics. The physicists had very little contact with the mathematicians and vice versa. Officially of course they met quite often. But I don't remember any physicists coming to a mathematics colloquim or seminar or the mathematicians going — the younger people were, of course, doing both. Born and Kármán for instance. But a man like Hecke, who up to then had done the physical part for Hilbert — I don't think that he ever went to the physics colloquia. And on the other hand, I don't think that a man like Madelung, who was Voigt's assistant, would have been seen in the mathematics group. They were separated by the entire town, which is a very small distance after all. But it was going through the Weber Strasse over the Market and into another region where the physics institutes were at the time.

Kuhn:

I reacted strongly, because people talking of a slightly later period than the time you were there, speak of how very close they were.

Ewald:

Yes, there was a — And I don't think there was much mixing even at the usual dinner places where people had their lunch. The mathematicians were a large group, Hellinger, Hecke, (Berens), Toeplitz — a number more were there. So they stuck together. And the physicists stuck together probably. I belonged more to the mathematics group at the time. So I don't think that the physicists thought too much too highly about Hilbert's attempts, which after all were not terribly productive.

Kuhn:

I guess actually it was Landé who talked about how close the relations had been at a time not very much after the period in which you were there.

Ewald:

Well Landé was my successor, so it was not very much later ... Well I'm, quite aware that other people might give you a different view on this.

Kuhn:

No, as a matter of fact this sort of conflict on testimony is particularly useful to us. I just was wondering whether there was anything particular to be made of it.

Ewald:

You see I was very close with Born and and Föppl . Born, Kármán, (Boyoslovski), Renner and Bolza kept house together. And I and Föppl came in every day for our meals. So this was a very close group. But as it often happens in these small universities, there was a certain rivalry between the groups. We would invite Hermann Weyl and Hecke and madelung on certain occasions, but in between there was not much contact. They had their other contacts, other groups ...

Kuhn:

You identified yourself with the physicists.

Ewald:

Yes, well, Born and Kármán were physicists, and Föppl was assistant to Prandtl, so he was mechanics. And (Boyoslovski) was a physicist, who was working on dielectric constants.

Kuhn:

Do you have strong impressions of Born from that period?

Ewald:

Born? Yes, surely. The nicest thing I have or probably I have not even got it, but Born I know had it, is a play ... We gave a big invitation in this house where they all lived together, and we made up a play where everybody, was to be condemned to hell. Hell was downstairs where you got your food. And the play was given upstairs, so everybody had to go down to hell. And there they were all characterized in a very neat way. And this play was done in beautiful verse by Born — who was very good at poetry — and Kármán together. We all contributed. Born was the main man who wrote the thing down. We others went through the room, and as soon as anybody had, a good verse he gave it to Born. It vas a very beautiful play. [Break]

Kuhn:

With Pauli I think I'd be very grateful for any stories that you've got that illuminate the sort of person he was and how he got to be that sort of person.

Ewald:

I don't know whether I can say very much. He was in Munich as a very young person, 18 or 19. I know exactly when it was — it was Christmas 1919. And it was his very first Christmas away from home. And so we told him wouldn't he like to come for the Christmas Eve to our house, where there were two children already running about, and one just born. And, he came and was very happy. I had to retire soon after the meal because my youngest child was only four weeks old. I had still to rest, and my mother was there, who always looked after me. In a while she came to my room and bent over the bed of my little daughter who was then four weeks old and said, "Linda, should I tell you the story that Pauli just told." It was the story of the man who offers sausages in the station and always cries his own You know the story? He always said, "Heisse Wurst." Now this is a story which every single being in Germany grows up with, but Pauli told that to all these grown-up people there. That shows a hind of innocence. He was at that stage still. Just to illuminate that. And my mother thought it was good to tell it to the baby now. What was interesting is what he told about his childhood, but you may have heard that from other people ... We asked him when he really started to have this interest in theoretical physics. He said that when he was 13 he read a book of Weyl under the table during the Greek lesson. The teacher passed him and said, "Again, this awful mathematics." But I think he didn't mean any harm any more. His parents just indulged, him. In Vienna at that time the young genius was just adored and helped in every way. And so during the holidays he did nothing but mathematics . He said when he was a boy he was always glad when school started again because it was so much less strenuous than having holidays and working at home on mathematics . As far as I remember, if I am not mixing it up, he didn't say much during the first term, but just sat in Sommerfeld 's lectures. And I don't know whether he was admitted to the seminar already. But after the first term, he care and brought something to Sommerfeld. Whereupon Sommerfeld said he would have to call Epstein because it was too difficult for him without Epstin's help.

Kuhn:

Do you know what that was about?

Ewald:

Probably relativity. I don't know. I thought that he had given such a Good seminar paper ... At any rate Pauli sat there. First I think he had to sit in the same room with Lenz, and when Lenz went away Pauli got Lenz' desk and sat there, working out his article on relativity, which Sommerfeld had entrusted to this young man, who was 18 or 19 ... I don't think he was 20 yet. It was for the Encyclopedie der Mathematischen Naturwissenschaften, which was one of the most difficult articles to write because the whole theory of relativity was in a very controversial stage. And there were these various types of development of the general theory, which had to be discussed and brought into unison somehow. And Pauli sat there all the time swaying back and fro with his body, writing this article. And when the manuscript was finally submitted to Einstein for a look — or the proofs maybe — Einstein just declared this was a masterpiece of work.

Kuhn:

Even then Pauli swayed back and forth?

Ewald:

Even then. Much more so then than later ... You see Pauli came from a Viennese family. His father was a very well known colloid chemist. And Pauli was brought up in a tradition not to know his own background at all. I remember that Pauli made some remarks which showed that he had not the slightest idea that he was Jewish. So I thought it would be worthwhile just letting him know that there was no doubt about it. And I told him that surely you are Jewish. And he said, "I? No. Nobody has ever told me that and. I don't believe I am." And I said — in fact I think I took him before a big looking glass and said, "Look at yourself. You can't deny that you are a proper Jewish type." And so he said, "Well, nobody has ever told, me that and I've not the slightest idea." And then he went back for vacations home, and I think then they told him. But he had, been brought up in entirely outside any religious connection. Probably he went to the Catholic lessons they cave at school. And in many ways he had to be educated. Lenz took that upon himself very much and definitely too ... I don't know what Pauli's dissertation is on, it played no role really.

Mrs. Ewald:

I'll tell you, when Paul [Ewald] got his professorship and Kossel got his first professorship ... that was in '21. It was the same moment. Sommerfeld gave a lovely dinner for the occasion, and Pauli was there too. Sommerfeld gave a nice talk, and he said, "And soon I hope there will come the time when Pauli has been long enough with us that we can put the doctor hat on his curly head." At the same time I remember that Sommerfeld said after the meal to Pauli, "I have a message for you from Klein. He says, ''When will you send the article?'" So it was long before his doctorate ...

Ewald:

I don't know whether Ella said that already, that Pauli at school had worked physics, and found the vacations the easier part of life. During school he had to go to bed at 12 o'clock, whereas in the vacations he was allowed to stay up as long as he liked and so he worked through all night. Then he told us how he went to a classics school, and they had the verbs on ('mi') in Greek. Now that won't tell you anything, but this is a certain stage of teaching Greek where some of the irregular verbs begin, and it's quite an incision. Pauli read Weyl's Baum Zeit und Materie. And the teacher came to him and said, "Why do you always read this stupid stuff?"

Mrs. Ewald:

But at that time you wouldn't have guessed that he would become on the human side such a wonderful personality. You would think he might develop in a very one-sided scientist. But you see when in '49 we met him there, we told him that we would go to America. We were just finishing in Belfast. And, he said in his frank way, "I don't like that. I don't like the idea that at this age you still change from one country to another one." And I wouldn't have expected it from him. I thought it was very nice that he said it so warm-heartedly and unafraid.

Ewald:

Yes, this was in Florence at the conference which had been arranged by the Union of Pure and Applied Physics on statistical methods. It was a very nice conference. We enjoyed it very much. I came there really because there was, a meeting of the executive committee of the Union on Physics. But I took part in the scientific activities also. And Born gave the talk on the theory of liquids, which he had just developed with Green ... Pauli didn't approve at all and always said to Born that he didn't like the influence green had on paper. Probably Born said, "Well, Green said it is so." And Pauli several times said, "Born, der Green ist lhr Unglück." Which was 797 one characteristic saying of his, with this frankness and the very sharp wit which he had from his early days in Munich. He had already a sharp wit and a sharp tongue, but it was usually justified. And besides, there was a great kindness behind it.

Kuhn:

It's a propos of this episode that Born said, "Pauli says it's wrong. There is no point in going on."

Ewald:

Yes; that was the same —

Kuhn:

Did Born in fact stop, or did he go on?

Ewald:

Well he was nearing the end of his talk anyway, so —

Kuhn:

But later he persuaded Pauli?

Mrs. Ewald:

Later privately he persuaded him. He sat down with him and persuaded him.

Kuhn:

And was particularly proud to have been able to do it.

Ewald:

Yes, he was very happy. Not at all offended, just happy.

Ewald:

Well, I can tell you of this. You see I had become Privatdozent in 1919, I suppose, ... I guess it was Pauli's first year or second year in Munich ... I gave a lecture on crystal dynamics. And I followed Born of course — read Born's book very closely. And it defined what you understand by elastic stresses. This is a bit ticklish in the first edition of Born's book, which was then the only one. And maybe I didn't quite understand it myself. At any rate, Pauli at the beginning of the next lecture said, "Could I make a remark?" And I said, "Of course, please." Then he gave an entirely different definition of stress, leading to the same result, but deriving it in a different way from that of Born. Born then adopted this from Pauli for his second edition ...

Ewald:

No, that was even before that Christmas. It was the very beginning. It must have been the first term of Pauli in Munich.

Ewald:

Well, I don't think I can say very much more about Pauli, but if you'd like to have it, I could say a few words about Fues, about Fritz London, and, maybe Bethe. Hermann is of less interest to you, but the others might be interesting. In Stuttgart I had an assistant. I had not gotten an assistant when I was called there in '21. But then in '22, I suppose, I got a call to the University of Muenster, and not accepting that brought in an assistant. This was always the bartering method for young professors to achieve something. That was Fues. Fues was a native from Stuttgart, and had taken his doctorate from Sommerfeld. He suffered a shot in his lung during the first war, and one side of the lung had to be collapsed. Still the wound was not properly healed. It gave him a lot of trouble in the years after that. He had to have several operations made by (???) to become a man who could live without constant surgery on him. He is a very cautious and very — oh, what should I say? — delicate physicist. Yes, gentle and precise and very modest too. There are several things which are much to his credit. One is that in '21 he obtained a Rockefeller Foundation Fellowship, I think it was. At the time it was called International Foundation Fellowship. This was in 1925 or '26 ... With that he went to Zurich to do work with Schrödinger. Remember that Schrödinger's wave mechanics comes from 1926. And so Fues was there from the very start. He did some very interesting and, at the time very difficult work by taking care of the continuous spectra. I don't know exactly in what problem. But there was a difficulty in taking into account the continuous spectrum — a difficulty of convergence. At the time I think Weyl was professor in Zurich. And of course Weyl and Schrödinger and Fues — and these people were in close contact. I believe that Weyl had developed the idea of considering the parts of the continuous spectrum to form a unit, and to substitute that in place of the discrete levels. And Fues carried out this work which was really a model for later work to be performed on that. After that Fues went to Copenhagen and worried with Bohr for a while. Fues' further Career was that he became Privatdozent at Stuttgart and later professor in the Technische Hochschule in Hanover. And after a few years he was called to the chair in Breslau. Meanwhile war had broken out, and during the war he became professor in Vienna. At the end of the 'war he returned to Stuttgart where he is still. He is now retired ... And he has had a great number of pupils.and they have produced very good work. Well, that was Fues. Then as the second assistant I had Fritz London. He was the son of a mathematician who had been in Breslau and had been the teacher of Born and Toeplitz and this whole Group of Göttingen mathematicians who came from Breslau. It was quite a large group. Breslau was a famous school of mathematics. London's father later had become professor of mathematics in Bonn. London himself had studied philosophy and I think had written a philosophical thesis. And then turned to physics ... He worked with Sommerfeld, and then I got him as an assistant. And he was an awfully nice chap. We really loved Fritz London very tenderly, from the personal point of view and also a very gifted physicist. At the time, he came weeping to me several times. He was a very tender soul, or had a very tender soul. The first time he came weeping was when I had asked, him to draw up a big placcard with the periodic system. Now London, you see, had, a philosophical mind. He had learned Greek and Latin and maybe Hebrew at school, but he had never learned English. And he had never learned to handle a drafting pen ... On the other hand I had to give a general lecture on the introduction to atomic theory to the chemists, and I wanted a large atomic table. So I asked him could he do it. And we laid it out together, and he had to ink it in. And of course he spilt. He was the kind of person who always spilled an ink pot. And when it was nearly ready he came in weeping really because he had spilled it. And he always ridiculed me later on whenever we met by saying how hard a master I had been, that I had made him draw this periodic system. The other occasion was a more serious one. That was when matrix mechanics came out, and the various operations of matrix mechanics — for instance the exponential of a matrix and, so on — were introduced. London did that by himself, but every time he had, a paper ready to send away, the next number of ZS für Physik would bring exactly the stuff he had done. And this happened three or four times, until he was really at the front and could join in. But this was very bad luck and he felt it very hard. In Stuttgart, of course, he was relatively isolated in contrast to the people in Berlin, where there was this whole smart group of (Breit), Wigner and Neumann and other people, who were doing this kind of thing. We spent one very nice vacation hiking together, Files and London and I, on the Italian Riviera, and went down to Florence —

Kuhn:

Do you remember talking with him when the matrix mechanics first came out?

Ewald:

I don't know any of the contents any more. No. Of course he tried to teach me what it was about. But, no, I only remember his disappointment. Well, London again got a fellowship from the International Education Board ... I think London went to Rome, I'm not quite sure ...

Mrs. Ewald:

Later he was assistant to Schrödinger and Privatdozent in Berlin — He went to Schrödinger after Ries had gone back to you. London went to Schrödinger in Zurich and then went with him to Berlin.

Ewald:

Oh yes, of course he did. Because the London-Heitler paper on the bond in hydrogen, the first Lovalent bond ever 'explained arose in Zurich ... Then as an interim assistant I had Hans Bethe, who was really Sommerfeld's assistant. When Sommerfeld went for half a year to America I got Bethe on loan. And that was a very stimulating and exciting time. Bethe did a very beautiful paper which was stimulated by me and which has been translated quite recently into English. Although it is a paper of — when was it — 1928? ... You see I had asked him, "What is a Stark effect like in a crystal?" The splitting of the atomic emission by an electrical field must be quite different because the electrical field is not homogeneous. In a crystal 881 you have a field of different directions surrounding the atom. So we discussed that a bit, and then Bethe sat down and did it with group theory — which — I could have never done — in a very profound and beautiful way. It is still a model nowadays. Of course Bethe's theory of electron diffraction is directly modelled from my theory of X-ray diffraction. I remember that I was once skiing in (Arosa) with Sommerfeld, and Sommerfeld had just started on the theory of electrons in metals. We spoke about that. It must have been shortly after the discovery of electron diffraction. As we went up the hill in (Arosa) — I could still show you the spot — I suggested to Sommerfeld that the electron moving in a crystal must be diffracted in a very similar way as the X-ray passing through a crystal. Sommerfeld must have taken that on to Bethe, and he modelled his theory of electron diffraction on it. Bethe was there only for a short while.

Mrs. Ewald:

Just a few months.

Ewald:

But it was very nice, especially since this was a kind of family affair. Because Bethe's father had been the assistant of my uncle in Strassbourg — no — or they had both been assistants to the professor —

Kuhn:

And you kept it a family affair.

Ewald:

Yes, we kept it a family affair.

Mrs. Ewald:

That is only very much later.

Ewald:

Yes. Well, then who else was there? Then the next assistant I had, was Hönl. Hönl was a very cultivated person. He is professor at Freiburg now. And his work on the atomic factor, dispersion of X-rays and similar work, is often quoted. Even the paper, we wrote together on the electronic structure of diamond, seems to be very much better than I at least thought at the time. I thought it was a horrid paper, very bad, but it turns out that it comes fairly near to the truth. And all the modern methods which have been tried on this same subject haven't given very different results. Hönl also came from philosophy, although I think he — look, I think I'd better say nothing, because I don't know.

Kuhn:

Could we go briefly back to where we left off, on the subject of the mathematicians and the physicists ...

Ewald:

Well, I can only give my very personal impression. Maybe I should not have said physicists and mathematicians at all, but should have said gangs of scientists, or groups of scientists. There was this group to which Born and Kármán and a number of other people belonged, who were, if you like to put it that way, applied mathematicians. They were in very close touch with other. pure mathematicians. I think it may have had just local origin. You see Born comes from Breslau, and Courant comes from Breslau, Toeplitz came from Breslau, Hellinger came from Breslau, and probably still more of them. So they had a common background. They formed one group, which was very close to one another. And they saw one another frequently and they discussed problems with one another. And Born, for instance, got a lot of help from Toeplitz. Toeplitz was a specialist on cyclic systems in mathematics, (Zyklanten) they were called. These are cyclic matrixes or determinants, or whatever. So we got a lot of help from Toeplitz on our crystal problems, where these play an important part. On the other hand the real experimental physicists were at the other end of the town, as I said, and kept largely to themselves. Now and then there were common meetings, but not too frequently, and there was not this free daily exchange of small items — "I've got stuck there, how can you do that?" — and then your friend would tell you, "Oh well, this is a situation where you can try that." That was restricted to these various groups, and rather not too much intergroup communication, as far as I could judge.

Kuhn:

But Born would then have had much more communication you think with the mathematicians on the whole than he would have had, with the physicists?

Ewald:

I would say on the whole, yes. The prevalent idea in Göttingen was that Born was more of a mathematician than a physicist. You see Born had taken up the work of Minkowski, and had edited Minkowski's papersr and his work on relativity. Minkowski of course was also considered a pure mathematician, which indeed I think he himself would have stated. Hilbert was also of course a pure mathematician, but he took interest in physics problems. Klein of course was the great Zeus overriding everything and wanting all the disciplines to come under the mathematical aspect and be united in that science, but going even farther, because he wanted engineering also to come in. However, there was no real engineering training in Göttingen, as nowhere in German universities. Prandtl's Institute on fluid dynamics came closest to it ... This was, I think, in the old Physics Institute. Physics had moved to the other end of the town. This' was the Institute where Gauss and Weber had constructed the first telegraph, and so it was Weber's old Physics Institute on (Prinzen) strasse. A very dilapidated building, but it had space. Prandtl and Runge shared these premises. Runge, of course, was the perfect example of the combination of mathematics and physics, with his very long and useful work on spectroscopy. In Göttingen he was professor of applied mathematics, which according to German usage means that it is really the application of mathematics. It is not theoretical physics which is meant. It means numerical methods, graphical methods in mathematics, and similar things.

Kuhn:

And he and Prandtl would tend then to meet with the mathematics group rather than with the physicists?

Ewald:

No, they would meet with both probably.

Kuhn:

Would a man in Born's position look forward to an appointment as a mathematician or as a physicist or an applied mathematician?

Ewald:

I think as a theoretical physicist, and there were not too many at once ... Not every university had a chair, but if there wasn't a chair there was usually a special Lehrauftrag for theoretical physics. And this man would then have been within the physics department, mit Lehrauftrag für Theore- tische Physik. One of the most interesting experiences concerning the action of surroundings on a man's proficiency is the example of Born. Born was professor at Frankfurt. I think he succeeded Laue after the war — probably from 1919 to about 1926 or 1927. I don't know the dates. For a great number of years lots of students flocked to the German universities, after the war — all the pent-up young people. Landé was his assistant. I think he had two or three Doctorands, in all that time. Then he came to Göttingen. And within a year he had 12 or more Doctorands so that he said, "I don't know where to get problems for them. They're just overcrowding me."

Kuhn:

What accounts for that difference? Is it that Göttingen could draw because it was the center and Frankfurt was not?

Ewald:

Göttingen had a tradition. Frankfurt was a new university which had been founded just before the war ... (Schönfliess) was the first. After leaving Göttingen he had gone to Könisgsberg and then he had been called to the Frankfurt Academie — I think it was called — which was to be converted to a university ... I have a short biography of (Schönfliess) in a book. In Munich the difficulty between mathematics, mathematicians, and physicists was over mechanics. Mechanics is traditionally a subject which the mathematicians claim and the physicists too. And I think the way it is dealt with is different according to who teaches it. The physicist is likely to stress the physical aspects more than the mathematician. In fact in Munich there was Voss, a famous professor in that field. His course on analytical mechanics was really a course on the calculus of variations and nothing more. Whereas in Sommerfeld's course the physical aspects are stressed, and I have found that in many places ...

Kuhn:

Was there more or less relation between the mathematicians and the theoretical physicists at Munich, as compared to Göttingen?

Ewald:

I think there was none in Munich.

Kuhn:

So that here the theoretical physicists and the experimental physicists were closer, and the mathematicians further apart?

Ewald:

Yes. For instance in Munich, the experimental physicists and the theoretical physicists had a common colloquium. And now and then a mathematician came to it. Rosenthal, for instance, who died in Purdue some two or three years ago, was one of the mathematicians who always came to the colloquium, and also to our Cafe (Loetz) table in the Hofgarten. But of course he also worked on theory of sets, and, was interested in problems of the Zermelo type, which arose there.

Kuhn:

Now how was the colloquium at Göttingen? Because you're right, that's a very good index.

Ewald:

In Göttingen there was no colloquium, as far as I know. There was a much more formal Physikalische Gesellschaft and Mathematische Gesellschaft ... They met, as I said, on opposite places of the town, and there was not so much mixing between them.

Kuhn:

People like Born and von Carman would go back and forth?

Ewald:

They might go to both, according to the subjects.

Kuhn:

[Narration after above.] There are really two things that came up during tea that are not on the tape in very full form. One of them was, that in discussing the clustering of the mathematicians and the theoretical physicists at Göttingen, Prof. Ewald suggested that this might have something to do with anti-Semitism, that there were a good many Jews in the theoretical physics group and among the mathematicians, and not many among the experimental physicists. And there was, here and there, some feeling on this score. The other thing that needs to be added is something I don't really have down in any detail. It appears that when Ewald was in Göttingen for that year, though he lived by himself he ate regularly with a group that came together at a house owned or perhaps only rented by Born and Kármán and a third man, (Buchau) or something of that sort. The third man had a good deal of money — he had a wealthy father. These three had decided to get together. They were not satisfied with living in rooming houses. They'd hired a retired nurse, and they ran the house themselves. Ewald didn't live with them, though Mrs. Ewald had taken a room there. In fact the Ewalds met .at this house. Other members of the group I'm less certain of, but there would appear to have been perhaps eight all told who came together regularly. Von Kármán Born, Ewald himself, I think Toeplitz, I guess that's as far as I can go.