Ralph Kronig (original) (raw)

Heilbron:

May we begin at the very beginning and see if you can give us some idea of how you became so knowledgeable in physics at so young an age.

Kronig:

Well, you ask how I started — what interested me in science. To begin very early, I was interested in mechanical toys. I had a (mechanum) when I was about 10 years old. I even went about using this (mechanum) to try to construct a perpetuum mobile at one period. When I was about 12 years old, I came across a chemistry school book which interested me very much. I was presented with a set of chemical equipment also at about that age. And then we carried out chemical experiments at home. We had at school a sort of pupils club, or society, for natural sciences. There lectures were held by older pupils; some teachers were interested, and we met perhaps once a month, or once a fortnight. There were lectures on biology, and there were lectures on chemistry and physics. I remember giving my first lecture at this club; I may have been about 14, and the subject was radioactivity. I learned a very important thing from that lecture — that you must not try to tell too much in one lecture. I got into difficulties with the time. I also learned that an experiment, or demonstration, should be tried beforehand; none of the demonstrations worked.

Heilbron:

What had you studied, do you remember, to get up that lecture?

Kronig:

Oh, I had read some popular or semi-popular books. As you know I went to the Gymnasium in Dresden. There was a German collection, (Aus Natur- und Geisteswelt), a collection of small books on different scientific topics mostly written by a man of good scientific reputation. I had used, among others, this book. I still have it in my bookcase; if you are interested, I can show you. It’s, of course, now quite out of date. Also, in my class we had a club of 4 boys who got together more intimately and did all manner of scientific work. We dissected animals; I made meteorological observations and chemical demonstrations. There was another boy interested in geology, and we had meetings at our respective homes once in a fortnight, or once in a week, and we had discussions, and so on. We even gave out a scientific journal, if I may call it, in a rather primitive form. I still have the first number in my possession; it is from 1918. You’ll find a contribution on the forces of cohesion which I have made.

Heilbron:

Was your family interested in science?

Kronig:

No, not at all. My grandfathers were manufacturers and merchants. Further back, too, there may be some lawyers among my ancestors. My father was an artist, a painter, so there’s a certain artistic element perhaps, but there is no scientist, as far as I know, among my ancestors. There was a good deal of stimulus among each other, and when I was about 14, my interest shifted more and/more to physics. Of course, chemistry is more picturesque and less abstract, but as I got older, my interest in the mathematical side began to grow. The book I paid attention to was a book by Grimsehl, Lehrbuch der Physik, I think it was called; you may know it. It was used a good deal in America later too. And I soon discovered that my mathematical equipment was not very adequate for doing all I wanted, so I had some private lessons with one of our mathematics teachers from the school. He introduced me to the elements of the calculus, and I also studied some of these books, Aus Natur- und Geisteswelt, on calculus. And one of the first books I read which, however, it took some time before I could follow, was this book by Lorentz, Einstein, Minkowski on relativity. I think I bought it when I was about 15, but I found it too heavy to start with.

Heilbron:

I’m glad to hear that.

Kronig:

Well, that I think would give you an impression of how I got interested in science. It was a natural interest which had favorable soil to grow upon in view of the contacts I had with other pupils who took an interest in it.

Heilbron:

But this was a very unusual thing wasn’t it, in the Gymnasia in Europe?

Kronig:

Well, I don’t know. It is difficult to sit in one class; you don’t know what happens in other classes. I know that Pauli sat in a class in Vienna, and that class was called the class of geniuses. There came from this class two Nobel Prize winners, and about three more university professors, and a few famous actors, and, I think, a (musicologist), and a few men of industry. So you may have such density fluctuations like that.

Heilbron:

What determined you to pursue your education in the United States?

Kronig:

Well, my family moved. My father was an American citizen; I was born in Europe as the son of an American citizen. And conditions in Europe around 1918 being not very pleasant, my family went to the United States, and so I came to study in America. As I say, I was 15; I had to do what my parents wanted; I could not decide what I wanted at that time. I found it was very interesting to see something of the world.

Heilbron:

Had you been taught English at home?

Kronig:

We spoke English at home. We were raised on a bi-lingual basis, I would say.

Heilbron:

Well, when you did begin at Columbia, was your background considerably more advanced in the sciences and mathematics than that of your fellow students?

Kronig:

I did not finish the Gymnasium in Dresden because the usual age is about 18; I had nearly 3 more years if I had wanted to get the Abitur — the final degree. And when I came to the United States I went into Columbia College, and I got some advanced standing because my knowledge of the modern languages was rather better than what most of the American young people had, and my mathematical training was quite far advanced due to the interest. On the classical languages they were not too rigorous, so I think I then came into the second year when I arrived in America. And my commencement at which I got the AB degree was in June, 1922. I came in 1919, so I did the AB degree in three years.

Heilbron:

And you decided on physics at the time you entered?

Kronig:

Yes, my interest was so strong. Of course, I had to take some English literature and some of these subjects which are obligatory in college. I must say, it was very good for me to get more acquainted with English literature than I had, of course, in Germany. But then the rest of the courses were mathematics, physics, and chemistry.

Heilbron:

You said in your article in the Pauli volume that you were taught nothing but the classical physics.

Kronig:

Yes. I would say there was very little at that time, at least as far as theoretical physics was concerned, at Columbia University. I think it was more general, while experimental physics was in a very good way and always had been — I think we all knew people like Michelson and Compton and Millikan and R.W. Wood — the theoretical physics was not quite up to scratch. I must say I got a very good foundation in classical physics and mechanics; in electromagnetic theory and those things. But the more modern things, the atomic theory, actually I got in an auto-didactic manner.

Heilbron:

The publications were available though?

Kronig:

Oh, there was a very good library in Columbia University, and there were, of course, books I wanted. I found the books I felt I needed, if I may put it that way. Well, a book like Sommerfeld’s Atombau was read among the younger people; it attracted attention. But, I mean that there were no courses; that you could not follow these subjects by way of lectures. Of course, this all was very much in a way of development and it is always somewhat difficult to teach a thing which is still so undecided, and so on.

Heilbron:

What did you finally take your thesis on?

Kronig:

Oh, my thesis was mainly an experimental thesis, and it was devoted to a study, you might say, of semi-conductors which was at that time not —. It was an investigation of the change which selenium undergoes when bombarded with electrons. It was, of course, well-known that illumination of selenium changes the resistance, and photo-cells were based on that. But my interest was to see if when you shot electrons onto the selenium, then you could get a change of the resistance. And I had actually an arrangement of a selenium cell with two electrodes to send the currents through the selenium, and then from a third electrode, by means of an applied potential, electrons were made to fall into the selenium. And, indeed, resistance changes could be noticed. You might say it’s a very funny sort of transistor because the third electrode of the transistor, such as you have now, was replaced by a cathode.

Heilbron:

And you did nothing more in that line?

Kronig:

No. Because selenium is a nasty stuff to work with, and germanium, which has the same make up, was not available in a pure form. You see the method for purifying these substances was quite unknown. You ask me here in this note you sent ahead of your arrival what sort of books I used. I don’t know if you are interested, but I may mention some titles. There were, of course, the books which were suggested in the lecture courses, and then the books which I read on my own. I had some calculus and differential equations, and there was a book by (Loeb), Calculus, which I have still here in my library, the book of (Cohan) Differential Equations, the book by (Coffin) on vector analysis. Those were several books which were used in the courses. I learned my calculus really from the book by Serret in the German translation which I got hold of; there are three big volumes. Bocher Algebra. Whittaker and Watson, of course, I started using. The book by Fraenkel on Mengenlehre. The book by Courant on function theory I think belonged to one of the courses given. So those were the mathematics books. In physics there was some college textbook, and I have forgotten now what the name of the author was. I read a good deal on physics on my own. Thermodynamics I learned from Planck’s Thermodynamik; theoretical physics from Schaefer Theoretische Physik; then electromagnetic theory from Abraham; relativity theory I learned from Laue’s book. Sommerfeld’s books then called Atombau und Spectrallinien, were the place I learned something about the atomic physics of that time. Also there were Planck’s Theory of Heat Radiation, Jeans’, Kinetic Theory of Gases, Wood’s Physical Optics, Millikan’s The Electron, to mention some of the books I had at that time. And I found most of these books were present in the library; that’s how I came to touch them. You also asked who were the most influential teachers. I think at Columbia the man who was most stimulating as a physicist was a professor who wasn’t very young anymore called Davis — Professor Davis — Bergen Davis; he was an X-ray physicist. And he has done very beautiful research on the diffraction of X-rays — at that time a difficult method. When I was a student, he must have been about 55, but he gave nice demonstrations and lecture courses, and so on.

Heilbron:

We would be quite interested in learning of your reactions to these rather remarkable events that took place during your college study.

Kronig:

Here in this list you have mentioned some. The Stern-Gerlach experiment I think I read in Sommerfeld; my first contact with it was from Sommerfeld’s book. The Compton effect was during my period in Columbia University and attracted a good deal of attention, particularly as it was in the X-ray field that this Professor Davis was very much interested in. He immediately tried to do the experiments over.

Heilbron:

Was he successful?

Kronig:

Yes. He regretted that he hadn’t found it himself, I might say. So the Compton effect was much in the foreground. You have mentioned here de Broglie’s thesis. That only came in 1925; then I was away already. The Bohr-Kramers-Slater theory I read about myself in the articles in the Zs. f. Phys., I don’t think it was ever discussed in any way with people I came into contact with.

Heilbron:

What did you think about it? Do you remember?

Kronig:

Well, I thought it was an interesting problem. It went of course in the direction of not keeping the conservation of energy to the very end, of having it only statistical. But, well, I think everybody had the feeling that’s a matter which must be decided experimentally. And it was about a year later, when I was in Copenhagen, that Geiger and Bothe demonstrated that it was rigorously conserved and not statistically. But that was a matter of discussion, I think.

Heilbron:

But it wasn’t an uncomfortable idea?

Kronig:

Well, nobody liked the idea of having energy only statistically conserved. Even in Copenhagen the sentiments were not very strong. One thought that the possibility was worthwhile deciding. And when the experiments came along, of course, the idea was immediately dropped.

Heilbron:

They were relieved at the results of the experiments?

Kronig:

Yes, perhaps, yes. The dispersion theory, too, came along when I was in Copenhagen. I was there at the time when Kramers and Heisenberg published. They had just written the paper when I arrived in Copenhagen, so it was one of the first things I came in contact with when I arrived in Copenhagen. And about this Burger-Dorgelo sum rule, which you mention; I had spent a good deal of time before I left America in 1924 studying this theory of the anomalous Zeeman effect and the whole spectroscopy. And I think I was one of the people who had the rules of spectroscopy, which were mostly empirical at the time, more or less at the tips of my fingers. And I knew about the Burger-Dorgelo sum rules before I came to Holland. I was well-equipped when I came to Holland in the end of 1924 to understand what people wanted and what they were doing.

Heilbron:

What got you interested at the beginning in the anomalous Zeeman effect?

Kronig:

Oh, well, you had the feeling there was something very mysterious about these too many states which there were. And Pauli had, of course, published a number of papers on the anomalous Zeeman effect, and it was a clear-cut situation. The measurements were exact; you could study these levels and so on. It was a very quantitative thing, not vague. Of course, intensities were not so quantitative; they had large errors or the possibility of large errors. But otherwise, as regards the position of the Zeeman components, the pictures of the Zeeman effect were very, beautiful — the twenty components separated. Of course, it’s not so sensational now any more, but at that time it seemed very fascinating and mysterious, I might say. So one had the feeling or intuition here is a corner where something will come out.

Heilbron:

Was that the reason you decided to come to Holland to begin with?

Kronig:

Well, there was a traveling fellowship at Columbia University, (Behr-Cutting) Traveling Fellowship, and that was, I think, available every year or once in two years. The professors — Davis, and I think, the professor of theoretical physics, Wills — thought it might be good for me to see something else and suggested my applying for this traveling fellowship. I received the traveling fellowship, and then I came to Europe. I knew where atomic physics happened so that was the reason I wrote to Bohr and various other people to see if I could work there. I had met Ehrenfest. Ehrenfest had been in the United States in the spring of 1924, and he stopped at the same house where I was living. I had, a room in a sort of family hotel where you could have a room and breakfast, and Ehrenfest had stopped at this same house. It belonged, I think, to the University in some way. And so I came in quite close contact with Ehrenfest. Ehrenfest, too, had said to me I should once come to Europe.

Heilbron:

The fellowship allowed you to do whatever you wanted?

Kronig:

I was quite free to travel as I liked; I got an amount of money which I used sparingly so as to spin out the fellowship as long as possible. I started in Cambridge; I spent a couple of weeks in Cambridge. I saw the Cavendish Laboratory there; I met some of the younger people, but I looked around more to imbibe the atmosphere of Cambridge. Then I went to Leiden. There I knew Ehrenfest, and I simply dropped in. And at that time Goudsmit was there. He was working partly in Leiden and partly in Amsterdam. He was, I think, assistant of Professor 279 Zeeman and did some work with Zeeman, and the rest of the time be spent in Leiden. And there was a physicist, Dieke, who is now at Johns Hopkins University who was interested in band spectra. Then there was Fermi; he was stopping in Leiden for some time on some Italian fellowship. And then there was a young man, Tinbergen, who was doubting whether he should go into physics or into economics; he finally decided to go into economics, and he is now our economical expert of our government here in Holland. So they all made good. That’s where I first met Fermi; we stayed at the same pension. There was room at the pension where Fermi was staying, so I stopped there too, and we got rather well-acquainted then. Fermi, of course, was quite unknown; he was 23 or so – 22 — and he had not yet done important things.

Heilbron:

He had not yet become Fermi. Well, if we can retrace our steps just a bit back to Cambridge — what particularly struck you at Cambridge? You said it was very much different; you soaked in the atmosphere, and so forth. Were there great differences?

Kronig:

Well, of course, I listened to Rutherford speaking. I went into this Cavendish Laboratory where there was a very good research atmosphere, and people in the afternoon discussed their things together at tea. I had the impression of a good deal of contact. Of course, in theoretical physics there wasn’t so much in Cambridge at that time.

Heilbron:

But was there a feeling even there that there was about to be a large —?

Kronig:

Yes, well of course, the work of Rutherford which was at that time the central activity of the Cavendish Laboratory was a very fascinating and pioneering work. I think the majority of the people worked themselves with nuclear experiments. Then there was Aston doing work on isotopes. I think they were the two most prominent experimenters at the Cavendish’ Laboratory at that time.

Heilbron:

Did you meet Fowler at that time?

Kronig:

Fowler, yes. The son-in-law of Rutherford. I met him not in Cambridge, but I met him in Copenhagen. He spent some time in Copenhagen in 1925, and there I got to know him quite well. And I think Fowler made efforts to get atomic theory introduced in a larger measure in Cambridge. Rutherford was, of course, a typical experimenter. Ehrenfest, I think, is the best didactic person that I have met. He was really the born teacher, and he had the knack of interesting young people and guiding them, and stimulating them in a way that I don’t think I have ever met since. Perhaps Sommerfeld in Munich. He, too, was a man who made a school and knew how to get young people interested and critical toward their own work. I would say these two people at that time were really the people whom all the —. Born, perhaps, in a certain measure in Gottingen. There were only these three schools in theoretical physics at that time.

Heilbron:

What was Ehrenfest’s particular method?

Kronig:

Well, I would say a sort of Socratic method. He made people question the essentials. He had a very wonderful way of putting the finger on the essential things in a physical problem and pushing all paper work — as I might call it — to the side and seeing what the fundamental point of the problem was. And he had a way of making people ask themselves questions. Often, I think, he knew the answer, but he acted as if he didn’t know it because he wanted the young man to give the answer. And he had a lively temperament. He spoke no language quite free from mistakes, but you could understand him in any language he spoke.

Heilbron:

Then you began to work with Goudsmit. How long did it take you to turn out that little paper?

Kronig:

Oh, I don’t know. I was in Leiden a few weeks. He also was interested in this intensity problem, and we discussed it. And, of course, the point was one knew from the Correspondence Principle approximate expressions for these intensities, and there were a number of empirical indications of what had to be. There were sum rules which had been discovered experimentally by Ornstein and his school — Burger and Dorgelo, and so on, which one wanted to satisfy. And then by systematic elimination we arrived at these precise intensity formulae. Of course there was no quantum mechanics, one could not derive them from fundamental principles; it was an attempt on grounds of partly intuitive insight to find, a more precise form than the Correspondence Principle would give. (It was really the first step of having a result which went further from a semi-quantitative to a quantitative formulation.)

Heilbron:

And from there you went on to Tubingen?

Kronig:

Yes. Lande had been in Leiden for a lecture. I got acquainted with Lande there and he suggested that if I came on into the area of Tubingen that I should visit him. And in Tubingen was not only Lande, but also Back, the man who was the expert in measuring Zeeman effects. So I came to Tubingen, and when I arrived in Tubingen, Lande said to me, “Oh, you are coming at a good moment, tomorrow Pauli will be here.” I did not know Pauli personally yet. Lande had received a letter from Pauli in which a number of questions were asked on the matter of spectra which Pauli wanted to have verified with a view for confirming his exclusion principle.

Heilbron:

Here on Page 2 of the outline we prepared we have divided this up in a rather arbitrary way beginning with the general work. We wonder about reactions to the great papers of 1925. There is that very interesting letter you quote in “The Turning Point” by Heisenberg; Heisenberg had written you. What did you make of that?

Kronig:

Well, the situation was — and I have mentioned in a still earlier paper that the success which one had arrived at with these intensities of multiplets and Zeeman components led to the question of whether or not one could sharpen or make precise the Correspondence Principle in other cases, too. And one of the problems where the Correspondence Principle had been studied semi-quantitatively was the Stark effect of the atomic hydrogen spectrum. I spent quite a little time on trying to get rigorous expressions from some point of view for these Stark components. And I have an earlier letter from Heisenberg in which Heisenberg makes a suggestion. The functions which describe the Stark effect components are Bessel functions, not trigonometric functions as in the case of the multiplets. And the question was, could one make these intensity expressions, in some way, more rigorous, too? It was, of course, a natural question to make the Correspondence Principle precise. The multiplet formulae were one example, the dispersion theory of Heisenberg and Kramers was another example of a rigorous form. And now the point arose to try to get the more general theory, and that is what Heisenberg had said lay in the A of the problem. But it was the question of finding some point of view by which you could translate from the classical physics into a quantum physics which would conform to the Correspondence Principle. It contains the Correspondence Principle as a semi-quantitative approximation if I may put it that way. And that was what Heisenberg tried to do in that letter, and the letter appealed to me very much. In the letter the thing isn’t quite worked out, but it is at the stage where things are nearly coming around. Heisenberg wrote the letter to me, I think, from Heligoland; he spent a few weeks there to be in privacy, or in retreat as a hermit, to gather his thoughts. And, I think, the final ideas which led to his quantum mechanics evolved there. Then Heisenberg read this reproduction, he was much interested; he said this letter was probably the earliest formulation of the quantum mechanics which was available. It must have been in quite an early stage, when it just began to take shape with him.

Heilbron:

How did you interpret to yourself the coefficients and the rules in there? Did you make any effort to do that?

Kronig:

It was known that the frequencies combined. The frequencies lm mn were added together to give a frequency ln. And Heisenberg’s idea was to make the multiplication of the coefficients, too, in such a way as to conform to the additivity of the frequencies. Later Born recognized that as the rules of matrix multiplication. Heisenberg did not know that; that is a contribution which came entirely from Born. But it sounded reasonable; it appealed I would say.

Heilbron:

Were you with Fermi then again, later, in ‘25?

Kronig:

I was not with Fermi this year in the winter. We went mountain climbing. That was in July or August, 1925, I think.

Heilbron:

Did you discuss this, do you recall, with him?

Kronig:

We didn’t talk very much about this quantum mechanics. Fermi was interested at that time in quite different things. He was interested in resonance radiation and that sort of matter, and was not at that time very well versed in spectroscopic questions. [Kronig locates Fermi’s letter from that period and looks through it.] He was calculating –- that’s quite interesting — he was working on the space quantization in a rotating magnetic field, such as one has later used in electronic spin resonance or nuclear resonance. It goes in this direction. This is from January, 1925. [Quotes from the paper briefly in German.] But Fermi was, at that time, more an experimental physicist than a theoretical physicist; at least he experimented a good deal. Well, he has always done that later on in nuclear physics, too.

Heilbron:

Later, after the work of Born on the subject —.

Kronig:

Of course, I might say that at Gottingen the Heisenberg paper had attracted a great deal of attention. I was in Gottingen, I think, in July of ‘25, before I went to Fermi. And there everybody talked about this matrix method, and so on. So Gottingen was full of these developments. … Every day they had a new result; that was very exciting.

Heilbron:

What ideas had they on the interpretation of their manipulations; had anybody so early —?

Kronig:

Well, at that time, of course, you could calculate energy levels, you could calculate frequencies for transitions and you could calculate intensities. One thing one had not calculated — and that was felt to be a very urgent task — was the hydrogen atom. But that was very difficult with matrix mechanics. Pauli later has done so, but, I think that was only in 1926 that he published his paper on the hydrogen atom. But that was a difficult matter. Of course, one felt this matrix mechanics was not very suitable to deal with collision problems. There were really two groups of problems in which one was interested: one was problems of spectroscopy to which this matrix mechanics, in principle, gave an answer; and there were the problems of what happens when atoms collide with electrons or electrons are scattered by atoms. There was no quantitative approach visible at that time even from matrix mechanics on how one should deal with collision problems. And only after the idea of the wave function came along in Schrodinger’s theory with the probability amplitude did it become possible to deal with collision problems in a reasonable way.

Heilbron:

There is an interesting question about collision problems in that by 1925 they’re still fairly recent. I mean, people haven’t been interested in them for very long, I think. The older spectroscopic material and the Zeeman effect and so on has been known for some time.

Kronig:

Well, of course there was Frank who has made collision experiments — he was one of the first, Frank and Hertz. Frank, too, was in Gottingen, so in Gottingen one was aware that there were problems which one should be able, from a theoretical viewpoint, to give an answer to, but one was, in 1925, not in a position to do so on the basis of matrix mechanics.

Heilbron:

And that complex of questions about the collision problems were particularly of interest in Gottingen?

Kronig:

Yes. It was, of course, of interest because here the experiments were made, so people didn’t forget about it. I think in other places the spectroscopy prevailed, and there was so much interest in that, so that one didn’t think very much about collision problems.

Heilbron:

Well, I’ve also suggested the same sort of question about the exclusion principle.

Kronig:

Well, the exclusion principle: I think everybody felt relieved when it came along. It summarized or brought under one denominator all manner of partial results; this work of Stoner with these new quantum numbers, the sub-shells in the periodic systems, the periodic system as a whole, the answer to what spectroscopic terms an atom could have when the electrons were bound in certain orbits. That really was the question which Pauli came to Tubingen to have verified; he came to see if the terms which the theory predicted were actually found in the spectrum of lead. I think it was. When people comprehended the exclusion principle, it was immediately felt as a great advance.

Heilbron:

Now I have gone on in this outline to some of your own work. You have explained how you became interested in the Zeeman effect.

Kronig:

I was interested in the Zeeman effect in general, and part of this work was, of course, intensity work. These intensity rules of Ornstein and Burger were rather fascinating; they were simple, rational proportions between spectral lines. And looking at the Zeeman effect, in general, one wanted, of course, to know something about the intensities. And Goudsmit, too, had already been thinking about it, and so that fitted in quite well, and immediately we could talk the same language. Besides, Goudsmit had worked at Zeeman’s laboratory in Amsterdam and had had close contact with Zeeman in this post with the new material — very beautiful photographs of the complicated Zeeman effect. Then you ask, “What did you think of the extension of the sum rules by Ornstein and Burger in which they claim that there is a ‘Nichtubereinstimmung’ between experiment and theory, that is, the requirements of the Correspondence Principle.” I was in Copenhagen then, and if somebody said, “It is not in harmony with the Correspondence Principle,” then the reaction was, “Well, then it must be wrong.” [Kronig goes to look up his “Uber die Intensitat der Mehrfachlinien und ihrer Zeemankomponenten”, received by Zs. f. Phys. on 18 Feb. ’25.] Evidently Ornstein had sent me his paper in its manuscript. I must have seen it in proof, or I must have seen it in manuscript. [Locates footnote on page 885 and, quotes it.] I suppose that Bohr, who was always very diplomatic, said to me, “You must mention it, but you must not say that they are wrong.” And so this note was put in. I think we were all taught by Bohr, and everyone in Copenhagen was inclined to imitate the Big Bohr style. And Bohr was always very careful and was very friendly his criticism of us.

Heilbron:

Well, how would that have been regarded elsewhere, though. It seems so extraordinary that in 1925 one would publish such a statement about the apparent —

Kronig:

I think everybody in Copenhagen would have said, “If it’s not in harmony with the Correspondence Principle, it cannot be right.” How strong the belief in the Correspondence Principle was in other places is a little difficult for me to say.

Heilbron:

It evidently wasn’t very strong in Utrecht.

Kronig:

Perhaps not, yes.

Heilbron:

But at Gottingen presumably —

Kronig:

Well, there was a man like Heisenberg there. Of course, the number of physicists who made physics at that time was quite a limited number who mostly knew each other and transmitted their results by correspondence. That was one of your questions: “How did people work at that time?” A great deal of physics happened by letter. People didn’t travel so much; there wasn’t so much money to travel, and traveling was more difficult than nowadays, but physicists wrote letters to each other and were kept informed in advance. What now is done by reprints was done by letters mostly written by hand because people didn’t have secretaries to type them. This is in some ways a pity because of a good many of these letters one may not have copies available. I have the letters I received from Pauli, but I have no copies of the letters which I wrote to Pauli. So if at the other end things got lost, one can’t establish a complete correspondence today. This would be better now when everyone has a secretary and has a dossier where he keeps a copy of his own letters.

Heilbron:

That reminds me, I wanted to ask you when we were speaking about Heisenberg, when did you first come in contact with Heisenberg?

Kronig:

Well, when I came to Copenhagen in 1925 — in January, 1925 — then Heisenberg was in Copenhagen. He had made the theory of dispersion together with Kramers, and he was at that time in Copenhagen.

Heilbron:

And then one just corresponded?

Kronig:

Then he left again for Gottingen. He stayed some time in Copenhagen, and from that period when he was in Gottingen, I have letters. Here this letter was written which I quoted in “The Turning Point,” or somewhere, from his vacation. When we were together, of course, there was no written record, but when we were separated there were letters. Some people kept their letters and others threw them away, and I’m quite glad that I kept them. I have rather a complete collection of the letters which I received.

Heilbron:

I have something you might be interested in here. I can tell you exactly what you thought of the Burger-Dorgelo paper. [Heilbron gives Kronig a copy of his own letter to Lande on this subject.]

Kronig:

This is more like what we thought. Bohr looked to it that nothing came from his institute which might cause too much —. That’s quite amusing. The criticism of young people is often ruthless. Now you have here some questions as to the model. I think that in this whole intensity discussion how the quantum numbers were to be interpreted — as long as they were considered as moments of momenta – didn’t matter. For the question of the intensities these moments of momenta could be assigned to a spin or to a Rumpf, or whatever it was. In the case of the ordinary spectra of the orbital electron of the alkalis, for example, the moment of momentum of the orbital motion and the other moment of momentum which later was recognized as the spin precessed around each other. The model was just a geometrical question of the precession of these two vectors, from which the correspondence theory formulae for the relative intensities were derived. So it was indifferent whether one said —. For this question it didn’t matter if one said the quantum number, as it is called in my papers, is due to a moment of momentum of the Rumpf or whether one said it is the moment of momentum due to spin, in the sense that we use that word nowadays.

Heilbron:

But if now you ionize the atom —.

Kronig:

But for this question, for a given multiplet, it was indifferent what the interpretation was as long as you bad the picture of the two precessing momenta coupled to each other according to a cosine law and rotating about the total moment of momenta, you see.

Heilbron:

In this second model of Heisenberg’s that came out in between the two papers you published — there is this model in which the kernel of the noble gases is given an angular momentum, the non-mechanical angular momentum. Then there is an angular momentum due to the electrons, exclusive of the radiating electrons, and those two are coupled together.

Kronig:

Yes, I have looked into the older papers because I have forgotten a little bit. Let me write here on this paper, otherwise I go too far from your instrument. For the ordinary alkalis you had two quantum numbers, called k and r in my paper, precessing around their common resultant j. There was still this undecidedness of normalization — there were various systems different by 1/2 which really didn’t matter in the end. But then there was the problem if you had two electrons, for example, outside of a closed shell; today we would say with k different from zero, not “s” electrons, k1 and k2. And then the idea of Heisenberg was that these two are coupled to each other [he is illustrating this on paper] and give, I think, a resultant k, and this k then with the r is coupled to a resultant j giving rise to the multiplet structure. And in the second paper the question was raised: what are the relative intensities of the various systems which arise from the different orientations of k1 with respect to k2? Here the question was what is the relative intensity of the multiplet components of one multiplet; here the question was, in the second paper, what is the relative intensity of different multiplets with respect to each other. So this coupling to r gave the fine structure of the multiplet which one was not interested in — here one was only interested in how strong is one multiplet corresponding to, for example, k1, and k2 being parallel and another multiplet where k1 and k2 made an angle with each other. And as this precession here is a very much faster precession than the precession of k and r about j, one really is not concerned with this fine structure problem. One might consider all the lines in each multiplet coinciding, forget about this fine structure, and ask what is the total intensity of the one multiplet with respect to the other. Here, too, one had only to deal with the two k’s — the k1 and k2.

Heilbron:

Had you worked this out in the language of the spinning electron? You do get rid of the problem of having an r for the noble gases, which I should have thought would have been a disadvantage.

Kronig:

Well, of course this r was, in this case of a triplet spectrum, the r of the two electrons —- the spin of the two electrons. But here again with these intensity questions it was of no importance how these moments of momenta were interpreted as long as one considered this vector model and asked what the relative intensities were. It was a problem of two things precessing, so for the intensity problems, it didn’t matter if one thought of the r as arising in one way or the other, as long as the r was there. Of course, from the fundamental point of view the question was: what must the r be? And the r now is seen as the spin.

Heilbron:

There are advantages to be gained by the spin interpretation, in getting rid of this r.

Kronig:

Yes. To begin with the alkalis, of course, the idea that was stated by Pauli was that you have two quantum numbers assigned to one electron — the orbital quantum number and the spin one-half. Only Pauli desisted carefully from saying what this other quantum number was. And I’ve always thought that was a rather fine intuition. Pauli, after all, had a fine nose because later on, as things became clarified, the model interpretation of the spin one-half of the electron as due to a sort of rotation of the electron about an axis was, by a theory of Dirac, discredited entirely. For this thing is not visualizable in such a way. Now I haven’t looked into Pauli’s mind, but I think one of the things which Pauli felt intuitively was that if you take such a charge — at that time one thought of the electron as a surface distribution with the radius 10-13 cm — and if you want to make a magnetic moment of one Bohr magneton, then you have to rotate the charged sphere so fast that the energy which you have to put in would give this electron a mass of the order, I think, of the hydrogen atom. And somehow this feeling must have been present with Pauli that it was not acceptable to think in such simple terms. He never expressed that to me in that way, but I think he felt that.

Heilbron:

I think so, too. This stricture of Pauli’s that all the quantum numbers have to refer to the electron did not appear to have any repercussions, in the literature, on the models.

Kronig:

Oh, the models. Only the basic interpretation of the quantum numbers changed, but the vector models precessed just as they did before.

Heilbron:

But they were recognized as unsatisfactory in any case?

Kronig:

Well, they were recognized in their limitations, namely as giving, from the correspondence point of view, certain qualitative indications as to what intensities should be as in these multiplet formulae. But as soon as one wanted to get precise expressions, of course, the model could not be applied quantitatively any more. Of course, as quantum mechanics came along and one recognized that orbits might not be spoken of except in a rather vague way, then it became quite clear why these models had their limitations.

Heilbron:

There is another question that occurred to me just recently when I was looking over those papers — in the first paper where you derived the intensity relationships for the multiplet levels you write down expressions involving unknown constants. [They locate the paper.]

Kronig:

Yes, here I see what you mean; you mean these things here. There were those a’s and b’s and so on one was inclined to say from the Correspondence Principle that the expressions for the intensities must be quadratic forms, linear quadratic expressions in j and in and certain unknown constants. And these constants were then adjusted so as to take care — begins here to illustrate his point. Let’s take the Zeeman effect. I’ll put down the levels of the upper state and the levels of the lower state; for example, this is the state with a given j, and this is the state with one quantum number higher. The magnetic quantum number is then -1, +1, +2, and so on. Then you have the transitions where in jumps by 1, and then we have the transitions where it does not change. Here you have certain transitions where in changes where there is no lower level, and here, too [see figure]. And then, of course, you came to the idea that one should take care that the formula was such that these things which do not lead anywhere because there is nothing, i.e. the transition, should have the intensity 0. And from this you can get the determination of the constants just algebraically, just by seeing that when +m is equal to j then this transition, for example, should not be present any more. And that, I think, was the guiding idea. [figure in transcript]

Heilbron:

The one that interested me, you see, was this case where you’re not talking about, the Zeeman effect, but you’re talking about just the intensities of the multiplet levels. Then you say that you can get enough equations to solve this, but the equations are non-linear, and you’re not going to bother. So you write down the answer, and I was just wondering what the motivation of that was?

Kronig:

I must first recall it. You first say it must be formulae of this type. And then we have these conditions, that the sum rules shall bold. For the Zeeman effect we would have to have a number of multiplet levels — 1,2,3,4,5 - 1,2,3 — and then we have here the various transitions. Now I don’t immediately see how many constants there are and how many conditions there are. But I remember still that in some ways it was quite unique, and the easiest way of getting at it is to take care that the components which shouldn’t be there because there are no more levels — just as in the Zeeman effect — should vanish. [figure in transcript] Let us say L is equal to 1 and S is equal to one. J is equal to 0, 1, 2 and now take here the case L equals 2, S equals 1 and that would be 1, 2, 3. And you have from 2 to 2, from 2 to 1, and so on. And then here from the [highest] you can only combine with [2], so you have 6 lines. And then there are certain ones which are not [present]. You have here a [transition] from 2 to 3, but of course there is no 3 level in the lower multiplet so the formula should give a 0 intensity. From such relations, I think it comes out quite unique, but I can’t reconstruct it now.

Heilbron:

Then it’s not quite so arbitrary as it appears!

Kronig:

No.

Heilbron:

Now there is a question or two with which I was left, after “The Turning Point.” How important was this problem of the “relativistic” doublet separation taken to be at that time? Lande evidently was quite impressed with the difficulties that it involved.

Kronig:

Yes. Lande had written in 1924, when I was still in America, in the Phys. Zs., an article where he had collected –- [phone call interrupts]. Yes, Lande had realized that and had published a number of papers both on the optical doublets and the X-ray doublets. Also one of them had this problem of relativistic doublets. And, of course, it was a serious question. In the X-ray field you had the relativistic and the screening doublets, and there, too, one had to formally introduce an extra quantum number to account for the extra levels which one would not expect on the theory of simple orbital motion. Then the curious thing was that in the optical doublets this relativistic formula also fitted. Well, Lande really called attention to this difficulty very strongly. He was rather happy when I came with this calculation in which the electron with the magnetic moment moves in the field of the nucleus and where the relativistic transformation gives a coupling which led then to the fourth power law. I told Lande about it — that was the day before Pauli arrived — and Lande was rather enthusiastic. And Pauli, was very critical; when he arrived I told him about it. “Oh,” he said, “Das ist ja ein ganz witziges apercu aber so ist die Natur schon nicht.” Pauli’s opinion had a very strong way. I can’t reproduce it exactly, but if I recall rightly Lande said, “Ja wenn der Pauli das sagt, dann wird es schon nicht stimmen.”

Heilbron:

So Lande retreated too?

Kronig:

He retreated too. I don’t know if you —. Have you ever had contact with Lande? Does he recall any of this episode or of my visit? I haven’t seen him in many, many years. Though somehow most physicists one meets once in a while —. I don’t know if he leads a rather retreated life, or —

Heilbron:

I don’t know; he’s retired. But he doesn’t recall the particulars of that event. But were other people as impressed with this difficulty as Lande was? For instance, was the relativistic interpretation of the optical doublets still held after Lande’s criticism?

Kronig:

Well, the interpretation on the old model with the Rumpf — with the core — gave not the relativistic formula, but the formula with, the atomic number to the third power. And the curious thing to which Lande called attention was that the same formula but with z3 replaced by z4 gave the relativistic doublet splitting, which was quite unintelligible on the older interpretation with this core. So, one called it relativistic doublet from analogy with the hydrogen doublets but, of course, the explanation which Sommerfeld had given for the hydrogen doublets could never apply to these alkali doublets. The relativistic structure of the hydrogen spectrum, as originally given by Sommerfeld, rested essentially on the degenerate states of the hydrogen atom which are not present in the alkalis, where the orbit precesses quite rapidly in its plane.

Heilbron:

What was generally thought to be the explanation of the X-ray screening doublets? In Sommerfeld’s interpretation one has no room for them really.

Kronig:

No, one has no room. It was an unsolved problem at the time; one had too many levels. And one found that there were levels which fitted the relativistic formula known from hydrogen, but levels which really ought not to have been there at all. So it was a very mysterious situation at that time.

Heilbron:

Yes. I went through the first 4 editions of Atombau looking for his explanation of the screening doublets; he doesn’t even talk about it. He talks about them as if there is no way they can arise. I really wanted to get some feeling of the weight that was attached to this problem.

Kronig:

Yes, well, it was seen as a rather serious problem which at the time Lande wrote his papers was an open problem.

Heilbron:

But Pauli wasn’t impressed by the fact that you had removed the difficulties so much?

Kronig:

I think the idea that this electron should turn about its axis was especially unsympathetic to Pauli. He didn’t want to have a model for the fourth quantum number. He somehow had the feeling, which later proved to be quite right, that the spin was a thing which could not be visualized in classical terms. And the curious thing is for example, the nuclear spin which Pauli introduced himself. Then he was quite willing to say that in the nucleus there is an angular momentum in some form or other. But he would not do this with the electron. I think the real reason was that he felt that somehow if you tried to visualize that classically as a sphere rotating about an axis, you got into great difficulties about the energetic relationships. Because with the magnetic moment of one Bohr magneton the energy would have to be enormous — the energy of the magnetic field of this Bohr magneton concentrated in such a small space. I suppose; but I don’t think that he has stated it anywhere in that way.

Heilbron:

van der Waerden in his article tried to analyze that.

Kronig:

It’s, of course, a bit difficult since van der Waerden is a mathematician, and he thinks that everything happens so logically. But it doesn’t happen so logically. Things were rather in a mix. Pauli was, intuitively, probably very right, but if he could have put things in words at that time, I don’t know.

Heilbron:

Had you “translated” the then current models into that of the spinning electron for the purposes of elucidation of the multiplicity of levels and the different possibilities of multiplets?

Kronig:

Well, with Pauli’s explanation of the exclusion principle and the term multiplicity — that is, once one said this is the fourth quantum number, and a moment of momentum is assigned somehow to the electron individually — then the further conclusions are somewhat independent of whether one thinks of this electron as a rotating body. And after all, the whole terminology of the quantum numbers — the s, the spin quantum numbers as we now call it, and 1, and so on — the whole construction of the multiplicity, the vector rules for finding the number of terms — all that was not influenced by the interpretation of what these moments of momenta were.

Heilbron:

So really the main subject of the conversation, from your part of it, was the calculating to get the doublet separation?

Kronig:

Yes. And Bohr had never understood that. And, I think, that was the reason why when Goudsmit and Uhlenbeck’s paper came out — and that was still in Copenhagen — Bohr didn’t pay much attention to it.

Heilbron:

What was his feeling? Did he express any interest himself?

Kronig:

Well, I have a letter from Bohr where he says that he only became convinced of there being something in it when he heard of this interpretation of the relativistic doublet structure. I think I have a copy of this letter which I can let you have. This is the complete copy of the letter from Bohr from which I have quoted, I think, in the article. I haven’t quoted it entirely, but I have quoted passages. [Heilbron reads through the letter from Bohr.]

Heilbron:

So Bohr doesn’t recall your having mentioned the subject to him?

Kronig:

Well, the difficulty was that Bohr was very overburdened. He sat in the middle of all manner of problems of his own, and it was rather difficult to come in touch. Bohr sat mostly at home or in his out-of-door place — he has a little villa, or summer house, out in the country, and there he retired. So it wasn’t so easy to see much of Bohr. And when you saw him he was always hurried. Somehow, probably, I may have told him about some of the details and it simply didn’t get through to him. Because some other people I told about it do recall — Kramers, for example. Also, I remember telling it to Heisenberg, I know even where I told it to Heisenberg; I told it to him on the ferry between Gedser and Warnemunde. That was sometime in the spring, in April or March, 1925. But that is a little historical —. But this may help you, perhaps.

Heilbron:

Yes. And Heisenberg was unimpressed for the same reason — the factor of 2?

Kronig:

Well, he loved his duality, you see.

Heilbron:

He loved his mystic approach. And Kramers —?

Kronig:

Well, Kramers was, perhaps, too much under the “sun” of Bohr, I don’t know. You ask here [in the list of questions] “Your experience in this matter also suggests questions of a more general nature. For example, how much ‘approval’ in the form of conversations and letters with authorities did one seek before publishing a new idea?” Well, one did, of course, talk about things, and if a man like Bohr did not react, or if a man like Pauli said, “It is nonsense,” and you were 20, it required a great deal of obstinacy to publish such a thing, nevertheless. Goudsmit and Uhlenbeck had the fortune to be with Ehrenfest. And Ehrenfest was a man who — well, as I stated — was very encouraging for young people. And he really pushed them on; I have heard from Goudsmit that they owe it to Ehrenfest that they did publish something at all. He pushed them on to publish. He said, “You are young; if you publish something foolish, that may be forgotten soon or will not be noticed. I may not publish anything foolish, but you are so young, you can afford to publish something.” It was something of that nature; Uhlenbeck, I think, told me about that. He said that Ehrenfest really was the man who pushed them on. So there were authorities in a certain way. The number was limited because the theoretical physics happened in Copenhagen and in Munich and in Gottingen really. Born and Sommerfeld and Bohr were the authorities and also Ehrenfest, I would say at that time.

Heilbron:

What was thought in these various places about the other schools? I mean, for instance, how was Sommerfeld’s school regarded in Copenhagen or Gottingen?

Kronig:

Well, there were certain contrasts in style, of course; Bohr had the theory that one should never express things more exactly than one knew them. And he tried to adapt his language to the uncertainty or vagueness of the subject. The subject was vague. But he never would try to express it more sharply than he knew it. Sommerfeld was much more mathematical. Bohr, really, I wouldn’t say was non-mathematical, but with him the intuition played a much greater role while Sommerfeld was more a deductive sort of personality. Sommerfeld visualized the things much more than Bohr and expressed them much more sharply, and therefore had sometimes to retract things. And there was a certain contrast between the styles of Bohr and Sommerfeld, and each had its advantages, I think. They were not enemies in any way, but Sommerfeld probably said, “Bohr always writes so vaguely,” and Bohr would say, “Oh, Sommerfeld says things much more sharply than he ought to.” Something like that. You ask: “Were new ideas fairly well known to most physicists before ever reaching print?” Well, in this club of one-hundred people who did physics one knew of the interesting things beforehand. The correspondence was a very lively correspondence, and by letter each kept the others informed, or one sent copies of manuscripts before the manuscripts appeared in print.

Heilbron:

And getting into the club was a fairly straight-forward thing?

Kronig:

Well, I, after all, had come from America. I had met a few like Ehrenfest; I had heard Bohr and Sommerfeld once in a lecture in New York; but I was received, I would say, with open arms. I felt directly at home. Of course, I knew what one was talking about. Somehow I had read what one should have read to take part in the conversations. Though, I must say, afterwards, I am surprised how easy it was to have had access to all these people — some of whom were quite famous people.

Heilbron:

Yes. Well, that’s the impression one gets reading about the episode.

Kronig:

They were all very kind. When I went to Berlin I looked up von Laue; I wrote him a letter asking if I might meet him, and he said, “Come once some afternoon.” I went to his house and had a talk with him, and I was a young man of 20, and Laue was, after all, a man who had the Nobel Prize. And he was very kind. It was the same with Sommerfeld; I spent a few days in Munich and looked up Sommerfeld, and so on. Then I had published these multiplet things, and he had published the same formula with Honl. And so he, of course, knew something of my work, so there I wasn’t quite an unknown figure. Now, of course, the great difference is that the number of physicists is so large. Then one could know everybody and knew what everybody was doing, or approximately what he was doing. And now the number of physicists is so large that one constantly meets people that one hasn’t met before.

Heilbron:

What about the refereeing policies of journals?

Kronig:

Well, if you sent a nonsensical paper to the Zs. f. Phys., then it probably would be returned, but, otherwise, there was not a very rigorous —. It differed; the Royal Society, of course, you could not send a paper to except through a member. In the Amsterdam Academy, even now, you can only get a paper published if you have a member present it to the Society. But the Zs. f. Phys. or the Ann. d. Phys. or the Jour. d. Phys., unless it was clear-cut nonsense, in general accepted things. I’ve never had difficulties; I’ve never heard of people having difficulties except perhaps if the size was too large. There were some limitations as to the size; if the paper was many pages, the editor might say, “Well, this is too long; cut it down.”

Heilbron:

But they were set up for refereeing?

Kronig:

Well, that depended on the journal. I think with the Zs. f. Phys. the editor simply looked at the papers, looked to see where they came from and perhaps in cases when he was a bit in doubt might have consulted a colleague. And, of course, many papers — papers which came from Born’s Institute or from Bohr — were accepted without question.

Heilbron:

I was interested in what sort of arrangements you might have made with Columbia — If when you left, you were expected to return there?

Kronig:

When they gave me this traveling fellowship, at their own suggestion, I received that and I had no ties at all. But I considered coming back to America; my family lived in America, and I came back at the end of 1926. I returned to America, and they had already suggested that I could become a lecturer, and they appointed me as a lecturer. In fact, they had asked me to come back in the fall of 1925, but I had still some money left over, and then I asked if I might wait until the spring term to begin my lecturing duties. So I came back in January, 1926, and started my duties as a lecturer then.

Heilbron:

And did, you then have any success in introducing new physics into the curriculum?

Kronig:

It was left to my own choice. I would say on structure of matter in a general way. And I had to supervise some laboratory exercises, some elementary laboratory work of the younger students. And in my course, of course, I dealt with things which interested me and which went in the direction of modern physics.

Heilbron:

Did you teach the matrix mechanics?

Kronig:

Well, in 1926 I don’t think the students were yet quite right for the matrix mechanics. I dealt with some dispersion problems, magnetic moments of atoms, and so on. I can’t recall exactly how I did it; that was quite a while ago. Of course, during that year — in 1926 — then Schrodinger came along. And one of the men with whom I had close contact who was in the same department was Rabi. Rabi and I knew each other well; Rabi was then working on his thesis on the magnetism of various crystals. And I think he was finishing that. And we spent quite a little time together with (a Chinese) to learn Schrodinger, and from this effort a paper resulted by Rabi and myself on the energy levels of the symmetrical top. It really was the problem at the hand of which we learned to use Schrodinger’s theory; it was a sort of exercise for us to learn wave mechanics.

Heilbron:

Had you any feelings at the time about which was more fundamental?

Kronig:

Well, the thing was, of course, one wanted to see the connection between the two. And that came very soon! Schrodinger came himself showing that the wave mechanics gives the answer to the problems of finding energy levels and so on, and intensities and calculated the matrix elements which in the matrix formulation it was so very difficult to answer. That really was the method of solution of the problems, too, of matrix mechanics. But this paper of Schrodinger where this was demonstrated came rather soon after his first papers, so one wasn’t left very long in doubt as to what the connection was. Another thing was — and that was the thing requiring quite a little thought and we discussed it a lot — was the interpretation of the wave equation. You may recall that Schrodinger wanted to return to a sort of deterministic physics, or had that hope. I remember very clearly that we spent quite a lot of time — Rabi and Wong and I — on understanding Born’s interpretation of the wave function and the probability amplitudes. I think Born was the man who first clearly stated the physical meaning of Ψ as the probability amplitude. That was something one had just to get accustomed to. It took us some discussion before we got the meaning of what Born really wanted.

Heilbron:

Had you earlier been sympathetic to the sort of thing Schrodinger was trying to do in his long introduction to the second paper where he talks about the analogy with Hamilton’s —

Kronig:

Oh, I think, the analogy of geometrical optics — physical optics versus classical mechanics — quantum mechanics sounded very agreeable and convincing.

Heilbron:

What about wave packets and so forth?

Kronig:

Yes. At that time one didn’t yet quite know; it was all in a very formative period. I must say when Born came along with his probability interpretation I think we were much charmed by the idea. Also because one could then treat collision problems. That had been left quite in the dark — I mentioned that already even with matrices. But even now when Schrodinger came along — Schrodinger had never spoken about it in any of those papers. Then Born came along with the probability amplitude and showed how one should consider a collision problem by the use of their function.

Heilbron:

So that you would say that it was not an uncomfortable interpretation to you —?

Kronig:

No. I think, when it came along, we were all quite willing to accept it. Of course, as you know, in Copenhagen there were long discussions between Bohr and Einstein. And Einstein was always constructing new cases, new models to show that you could somehow come back to a deterministic viewpoint. And then Bohr applied the uncertainty principle, and showed that he had just shifted it to somewhere else. And that must have been quite exciting; I was not in Copenhagen when these discussions took place. But people who attended said that it was very amusing to see these two together with one trying to catch the other on something he had forgotten.

Heilbron:

Then you became quite an expert in the Schr3dinger treatment, quite soon.

Kronig:

Yes. Well, we tried to learn it as quickly as possible, and as I say, this problem of the symmetrical top was exercise to get acquainted with it.

Heilbron:

Then the band spectra.

Kronig:

Yes. I really became interested in the band spectra from this problem of the dielectric constant of dipole molecules. There was this old calculation of Pauli’s where it appeared that the result for the dielectric constant even in the limit of high temperatures did not check with the classical equation. You might say that the Correspondence Principle was not satisfied. This always gave a strong feeling of unpleasantness. That made me recalculate on the basis of quantum, mechanics the dielectric constant of the gas of dipole molecules which then appeared to give the classical result again in the limit of high temperatures. That way, I might say, I got into molecular physics and got interested in questions of the behavior of molecules and that led on to band spectra. I had contacts with some experimental band spectroscopists. Those were Mullikan, who was then still at Harvard, later at Chicago; and Dieke, whom I knew from the time when I first was in Leiden in 1924; and then a Swedish band spectroscopist, Hulthen, whom I met when I came back to Copenhagen in 1927. They had all manner of problems arid they wanted a theoretical man to look into these partly empirical selection rules they had found, and that way I really became interested in band spectra. Later when I was in Zurich with Pauli, I met Professor Henri, a physical chemist who had discovered experimentally this phenomenon of what be called pre-dissociation, and that made me look into the theoretical interpretation of this pre-dissociation. So it was partly theoretical researches which led me into this and partly the contact with experimentalists who came to me with very concrete problems.

Heilbron:

That was an extraordinary letter you quoted from Pauli in “The Turning Point” when he issues the invitation to become his assistant.

Kronig:

Oh yes. I think I have kept everything from Pauli. The first letter I have from Pauli is one in which he returned to me 50 Danish Crowns which I had lent him when we went out one evening and amused ourselves in Copenhagen, and he got short of money; that’s from 1925. [Kronig locates Pauli’s letter of Nov. 22nd, 1927, and reads it. The letter is reproduced on the microfilm of letters to Kronig.] This was then the contact which led to my coming to Zurich.

Heilbron:

You were already in Copenhagen — you had already left?

Kronig:

I was still in Copenhagen. It was in November of ‘27. This was the second time after I came in June, ‘27, I went for the second time to Copenhagen.

Heilbron:

So you had left for Europe before you had obtained the invitation from Pauli?

Kronig:

Yes. …Well, I had a Rockefeller Foundation Fellowship from the International Education Board to take me to Europe for a second time. While my inclination, I would say, at that time, was to stay in Europe where, of course, much more was happening than in the United States. When I was in Zurich with Pauli, the thing which occupied him to a very large extent was the formulation of quantum electrodynamics. You may remember that in ‘27 — the summer of ‘27, just when I was in, Copenhagen the second time — the second quantization was introduced by Jordan and Klein for Bosons and by Jordan and Wigner for Fermi particles. But that was still a non-relativistic theory, and then when I was in Copenhagen, Pauli and Heisenberg were occupied — and Jordan, too, I think — in trying to formulate the quantum electrodynamics starting from Hamiltonians for vacuum fields, and later with interactions. And. there the well-known difficulties which later led to renormalization’ became already apparent. So that was one of the things we talked about. Another thing which occupied us at first was the problem of X-ray scattering. Scherrer, of course, being an X-ray man, was interested from the experimental side in problems of X-ray scattering by atoms — form factors and that sort of thing. And Weyl was in Zurich, and Weyl had just written his book on group theory and quantum mechanics, so that, too, was a topic.

Heilbron:

What did Pauli think of the book?

Kronig:

Oh, he appreciated it; of course, it was written by a mathematician. But, Pauli, I think, had great admiration for Weyl for having worked himself so quickly into the problems of quantum physics and spectroscopy. I mean the book is really putting it in a form which was, in many ways, quite new. Physicists didn’t know group theory at that time. Well, Wigner tried to apply group theory and applied group theory to spectroscopic problems with success, but there was no book in group theory which was very easily readable for physicists. There was a book by Speiser which was written from a purely mathematical point of view, and, I think, we all welcomed the fact that Weyl took the trouble, as a mathematician, to put group theory into such a form that the physicists could work with it. So I think that Pauli and Weyl made a very good combination; they appreciated each other very much.

Heilbron:

Did you discuss complementarity and such questions as well?

Kronig:

Well, the complementarity question actually was settled already at that time; at least, the majority of physicists had become reconciled, or had accepted it, with a few exceptions. de Broglie has always had his misgivings, and Einstein was still hungering after the old flesh pots, if I may put it that way; but they were exceptions. I mean, the idea of Bohr and the interpretation of Heisenberg, and so on, in 1928, already, was not a subject one discussed very much anymore. Another thing which was then, of course, was Dirac’s theory of the electron. It came along in the beginning of 1928 extending what Pauli already, with his two-component spin, had tried to do, and that, of course, was a very important thing and gave rise to a great deal of work — working out the consequences of the Dirac equation. As you mention here, the difficulties that the holes and the protons did not fit; positrons were not known yet, and the idea of Dirac was that the holes corresponded to the protons. But there was no possibility of explaining the difference in mass; that was a situation which one did not understand then. The elementary particles at that time were electrons, and protons. So Dirac naturally thought that there must be some modification in the equations to make the number of states somehow distended in the energy scale so that the protons corresponded to the negative energy levels — to the holes. Some such idea was rampant.

Heilbron:

What did people in Zurich think about that?

Kronig:

I don’t know. Nobody was very much satisfied about this. No, one didn’t feel very happy about the proton in this way, but one had nothing else at the time, so that was left a bit in the dark.

Heilbron:

Now I’d just like to ask you how you happened to go to Groningen and get involved with the Dutch school?

Kronig:

When I was first in Copenhagen, Kramers was lecturer at Bohr’s Institute and was the right hand of Bohr, you might say. Kramers was appointed, I think, in 1926 professor of theoretical physics in Utrecht. And Kramers asked me if I cared to spend a year in Utrecht to work together with him and at the same time look after the written estate — the papers — of Lorentz. Lorentz had died, I think, in 1927, and one felt that all the papers he left should be looked into to see if there was anything which might be worthwhile preserving or worthwhile publishing. So I spent some time at the house of old Mrs. Lorentz to look through the papers Lorentz had left. I had been, of course, in’ Holland in Leiden at the time, and I knew the Dutch physicists — by the way my mother is of Dutch descent.

Heilbron:

Had you spoken Dutch, as well, at home?

Kronig:

Well, not much; no I didn’t know much, but I learned it when I was in Holland. Then Professor Coster in Groningen asked me if I cared to come to his institute. Professor Coster worked a lot on X-ray physics at that time, X-ray spectroscopy, and so on. That interested me, and I liked the atmosphere of the laboratory, so I came to him, and I stayed there a number of years. I actually was the successor to Dieke; Dieke had filled the lecturer’s place in Groningen, and I took over from Dieke. He went to Japan, I think, at that time, and then later went to the United States, to California.

Heilbron:

Well, if other matters occur to you, we shall be delighted to have them, if not, I thank you.