Phys. perspect. 11 (2009) 46–97 1422-6944/09/010046–52 DOI 10.1007/s00016-008-0405-3

Adventures of a Theoretical Physicist, Part I: Europe Laszlo Tisza I was born in Budapest, Hungary, on July 7, 1907, and this first part of my interview with Andor Frenkel focuses on my life and work in Europe. After my elementary and secondary education I studied mathematics at the University of Budapest for two years. I went to the University of Göttingen in 1928 where I attended Max Born’s lectures on quantum mechanics, which influenced me to change from mathematics to physics, and as a consequence I focused on filling the gaps in my physics background.When ready to turn to research work I followed the advice of my friend Edward Teller and spent three months in Werner Heisenberg’s group at the University of Leipzig in the summer of 1930.That fall I returned to the University of Budapest, where I received my Ph.D. degree in the summer of 1932. Two months later, because I had become entangled in the illegal Communist Party, I was arrested and sentenced to fourteen months in prison. Fifteen months after my release, I joined Lev Landau’s group at the Ukrainian Physical-Technical Institute in Kharkov, passed Landau’s so-called “theorminimum” program on my second attempt, began research on the theory of liquid helium, and lost my faith in communism following Stalin’s repressive measures. I obtained an exit visa through the Hungarian Legation and returned to Budapest in June 1937.That September, again with the help of my friend Edward Teller, I attended a conference in Paris where I met Fritz London and Edmond Bauer, who arranged for me a small scholarship and an association with the Langevin laboratory at the Collège de France. Four months later, in January 1938, Peter Kapitza, and John F. Allen and A. Donald Misener reported their independent discovery of the superfluidity of helium, which London and I explored theoretically and I explained with my two-fluid theory later in 1938. Following the German invasion of France, my wife and I left Paris for Toulouse in June 1940, obtained exit visas to enter Spain and Portugal in February 1941, and boarded a Portuguese ship for New York the following month. The second part of this interview, covering my life and work in America, will appear in the next issue.

Key words: Alexander Akhiezer; John F. Allen; Edmond Bauer; Guido Beck; Niels Bohr; Max Born; S.N. Bose; Constantin Carathéodory; Richard Courant; Peter Debye; Paul Ehrenfest; Albert Einstein; Werner Heisenberg; David Hilbert; Fritz Houtermans; Peter Kapitza; Thomas S. Kuhn; Nicholas Kurti; Lev Landau; Evgenii Lifshitz; Fritz London; Heinz London; A. Donald Misener; John von Neumann; Emmy Noether; Rudolf Ortvay; George Placzek; Isaak Pomeranchuk; Martin Ruhemann; Francis Simon; Edward Teller; George E. Uhlenbeck; Bartel L. van der Waerden; Alexander Weissberg; Victor Weisskopf; Eugene Wigner; Matthias Gymnasium; University of Budapest; Loránd Eötvös University of Natural Sciences; Polytechnic University of Budapest; University of Göttingen; University of Leipzig; Ukrainian Physical-Technical Institute; Collège de France; Institut Henri Poincaré; mathematics; group theory; theoretical physics; thermodynamics; quantum mechanics; quantum electrodynamics; Born-Oppenheimer approximation; light quanta; statistical physics; Bose-Einstein con-

46

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

47

densation; Bose-Einstein statistics; Fermi-Dirac statistics; molecular vibrational-rotational spectra; superfluid helium; phase transition; superfluidity; two-fluid theory of superfluidity; nitrogen-fixation; communism.

Foreword by Jerome I. Friedman It was in the 20th century that the two major pillars of modern physics, relativity and quantum theory, were developed and physics started its grand march toward understanding the entire physical universe from the cosmos down to the subatomic world. Laslo Tisza’s career in physics spanned almost all of this century. He not only witnessed a number of the developments in physics at close hand and knew many of the major figures, he also made significant contributions of his own. Edward Teller, Lev Landau, and Fritz London were his mentors. He was born and raised in Hungary, a hothouse of great physicists and mathematicians in the early part of the 20th century. His primary professional training took place at Göttingen, Leipzig, and Budapest in the exciting time when quantum mechanics was in its infancy and being tested in applications to atomic and molecular problems. These were some of his first ventures into theoretical physics. After being awarded his Ph.D. at the University of Budapest, he served a productive apprenticeship with Landau in Kharkov, where he further honed his theoretical skills; but where he also witnessed the political oppression of the Soviet Union. He started his career with some self-doubt, but went on to provide the crucial idea that resolved the mystery of superfIuid helium. His two-fluid theory explained the surprising and paradoxical experimental observations of this strange state of matter that had been made at the time. He describes the development of the associated theory and his complex relationship with Landau and London. These events were occurring in the dangerous political environment that was overtaking Europe prior to World War II. His career took him from Germany to Hungary, the Soviet Union, back to Hungary, to France, and then to the United States when France was being invaded. He joined the Massachusetts Institute of Technology (MIT) physics faculty in 1941 and changed the direction of his research to developing a new generalized description of thermodynamics. In the latter part of his career, he turned his attention to the challenging problem of establishing a foundation for quantum mechanics. The Appendix following the second part of this memoir contains his unpublished paper, “The Meaning of Quantum Mechanics,” which gives his views on constructing a firmer basis for quantum mechanics. I first met Laszlo Tisza when I arrived at MIT in 1960 as a young faculty member. Over the years, he would often relate vignettes of his experiences to me and other faculty. His accounts of the intellectual developments were interwoven with the cultural and political milieu in which they took place. We invariably suggested that he write his memoir and share these experiences with a broader audience. It was clear that the history of his intersection with 20th-century physics should not be lost. He has finally done this, and we are all the richer for it. In this fascinating memoir, his description of his professional and personal experiences should be of great interest to anyone who would like a better understanding of how physics developed in the past century.

48

Laszlo Tisza

Phys. perspect.

Preface Andor Frenkel is a Hungarian theoretical physicist, a retired member of the Research Institute for Particle and Nuclear Physics in Budapest, Hungary. I first met him in 1979, when he spent eight months as a visiting scientist at the Theoretical Center of MIT. Subsequently, I met him during all of my visits in Hungary, and his visits in Boston. A few years ago he surprised me with the offer to interview me about my professional career, to tape-record our conversations and then to cooperate with me in editing the material for a possible publication of my memoirs. On some reflection I accepted his offer, as several of my colleagues had suggested that my memoirs would be of some general interest, but I did not feel up to carrying out this complex task on my own. In fact, I am grateful to Andor for his willingness to help this project along, which began in 2004 and ended in December 2006. He turned out to be very sensitive in lining up the right questions, and he proved also to be a good editor to make some of the answers more precise and to eliminate duplications unavoidable in the context of a freewheeling dialogue. It seems to me that his relentless questioning brought to the surface enough of the experiences of a long life to make it worthwhile reading for a younger generation.

Growing up in Budapest Frenkel: You told me many years ago that in your childhood you were attracted to mathematics, but later you turned to theoretical physics. Please tell me how this happened. Tisza: This is a fairly complicated story. As a child, I had a strange urge towards mathematics. I had no teacher or friends to stimulate me; it was simply a spontaneous urge. I think it first started at the age of 8. My father Béla [figure 1], a bookseller, occasionally took inventory and had long columns of numbers to add. I took inexplicable pleasure in this task. I vaguely sense that my interest in mathematics also had another root. Although my family circle was harmonious, there were occasional tensions I strongly resented, and I seemed to have formed the opinion that mathematics is the key to truth and the resolution of dissent. Sometime later I had a friend who was a few years older. He had lecture notes on algebra; I asked him to let me have a look at them. They covered the use of parentheses and similar topics. I found it eventually disappointing. Frenkel: Did you know these things already? Tisza: No. I browsed through his notes, found them of little interest, and dropped the matter. I came back to it when I was 12. I started to read popular books on problem solving and on geometrical constructions. I was maybe 14 when I took up an elementary introduction to calculus.

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

49

Fig. 1. The author’s father Béla and mother Camilla, Budapest late 1920s. Credit: Author’s personal collection.

My mother Camilla had a personal connection to Mano Beke, a retired professor of mathematics at the University of Budapest. He tested me and confirmed that I knew a lot for my age. Obviously, high-school math was never a challenge. I may mention at this point that from the third grade of high school (beginning at age 12) I went to a new school called Mátyás Gimnázium (Matthias Gymnasium; Matthias Hunyadi was one of the great kings of Hungary); it lacked laboratory facilities, but the faculty were both high quality and liberal. Even though I was not dissatisfied with the school, I was envious of the more prestigious Gymnasien attended by Edward Teller, Eugene Wigner, and John von

50

Laszlo Tisza

Phys. perspect.

Fig. 2. Portrait of the author at age 18 in Budapest. Credit: Author’s personal collection.

Neumann. They lived in Pest on the flat eastern side of the Danube river, whereas I lived in Buda on its hilly western side. They were challenged by their schools; I had to do with the challenges I generated myself. Then I had a rheumatic heart incident. It began with an ear infection at a time before antibiotics and sulfa drugs. When it was found that the fever continued after the infection had ended, this was attributed to a heart condition. My mother's theory was that I had overstrained myself with mathematics. I stopped reading mathematics for a while, to return to it gradually. I vividly remember that during my last year of high school the Mathematics Journal for High School was restarted by Professor Andor Farago. I [figure 2] enjoyed solving the monthly problem sets, but I did not gain much confidence that I had the stuff to become a professional. Frenkel: Why did you think this?

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

51

Tisza: Well, at first I was not sure. But very soon it became clear: I was quite unable to invent problems. For instance, Paul Erdös and his circle created problems in profusion. Frenkel: Did you know Erdös personally at that time? Tisza: I knew him from the time when he was 8 years old and I was 14; an uncle of mine was a friend of his father. We remained friends to the end of his life. Frenkel: So you felt that you probably would not be a mathematician. Tisza: Yes, I realized it. Eventually, when I was at the University of Budapest, Professor Farago repeatedly sent me word to visit him, and I always evaded it because I knew that he would ask me to contribute problems for the Journal, and I did not feel up to it. Frenkel: Still, as far as I know, you went to the University and studied mathematics for two years. It seems you enjoyed the study, even though you felt that you were not creative. Tisza: Yes. I was puzzled by myself. I had some talent and some obvious deficiencies. My career, as I will describe it here, turned around attempts to discover an area of creativity where I could achieve some success. The first decision to be made was the choice between pure mathematics and a field of activity where mathematics was applied only. I seriously considered engineering, but decided that it would not be scientifically satisfying; I was not convinced that the needed mathematics would interest me. Also, in those days engineers had to make a lot of drawings, and this did not attract me either. A part of the equation was my father’s hope and expectation that I would eventually take over his bookshop [figure 3]. I was his only child; a younger brother, Pali (Paul), had died at the age of 11. This was a painful blow for our family. My brother and I were very different. He had early talent for the violin, and his drawings were like those of an art student. Although I did not look forward to the bookseller option, I came to think of it as a safety net. If my mathematics should fail me, I could always fall back on selling books, although I did not like the idea and my mother was much against it. She confessed years later that her dream was for me to become a physician, but she did not push me because she wanted me to make my own decision. So, eventually I decided to take the chance to register at the University of Sciences, and to major in mathematics. Frenkel: University of Sciences meaning the University Péter Pázmány, the natural science branch of which became after the Second World War the Loránd Eötvös University of Natural Sciences (ELTE)? Tisza: Yes.

52

Laszlo Tisza

Phys. perspect.

Fig. 3. The building at Fö utca 12 in Budapest in which the author and his family lived and in which his father Béla’s bookstore was located. Photograph taken in the 1950s. Credit: Author’s personal collection.

Frenkel: Did you take courses in physics, too? Tisza: Yes, I was required to, but I did not like them. Frenkel: In those years the courses were aimed at forming research workers or highschool teachers? Tisza: The curriculum was not divided in this respect. In order to become a teacher, one had to take supplementary exams. The first was after the second year. I took it and passed. Frenkel: You also went to the Kürschak seminars in mathematics held at the Polytechnic University of Budapest, and you liked them very much. Were you a participant or just an auditor? Tisza: I was an active participant, particularly during the first year. We went through all of the Eötvös Competition problems. The problems were selected, you had to solve them and discuss the solution. The material was later published under the title, “Hungarian Problem Book.” I was very good in solving tricky elementary problems, and this seminar was a real pleasure. In the second year we read Helmut Hasse’s Higher Algebra.1 I wish to add that Jósef Kürschak was a lovely person. The small group in his seminar became a closely-knit family.

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

53

Frenkel: Could you say something more about him? Tisza: Professor Kürschak was one of the two senior mathematicians at the Polytechnic. He gave a calculus course taken by all first-year students of the school. In addition, undoubtedly for his own amusement, he led a seminar attended by a handful of university students who walked over the Danube bridge to reach the Polytechnic. The anchors of this seminar were László Kalmár and Rózsa Politzer-Péter who were seniors at that time; both were later to become university professors. They took me under their wing and steered me towards this seminar. My reputation as a math whiz preceded me. Also I was a winner of the mathematical Eötvös Competition after graduation from high school (Gymnasium). The first and second prizes were divided among three winners. While in school my mathematical interests separated me from everyone else; now I was pleased to discover that I was not alone and I acquired two friends with whom I shared interests. The more important was Edward (Edé) Teller, who became the father of the hydrogen bomb, but at that time was a student of chemical engineering, for a semester in Budapest and then in Karlsruhe. This was to be transitional as well. Our migration between professions was rather complicated and was also intertwined. The third winner of the competition, Rudolf Fuchs, may have been the best mathematician of the three of us, but he chose to train as a civil engineer at the Polytechnic University in Budapest. Rudolf and I attended a number of mathematics courses given by the lecturers (Dozenten) at the Polytechnic. We also loved to go on hikes in the surrounding mountains where we were experts at finding unusual trails where we did not meet other hikers. On my return visit to Budapest after the war I was saddened to hear that Rudolf was killed by the Hungarian Nazis.

From Mathematics to Theoretical Physics Frenkel: After two years at the University in Budapest, you left for Göttingen. Why Göttingen? Tisza: This is a very good question. It goes to the heart of the traditional German university system. Whereas in France the University of Paris excels over all the provincial universities, in Germany the provincial universities originated from different principalities, and developed their own characteristic individual features. Following a tradition established by Carl Friedrich Gauss, the princeps mathematicorum, the Göttingen chair, was always occupied by a first-class mathematician and the University of Göttingen was equally good in pure and applied mathematics. Recalling my time spent there, let me describe the distinctive atmosphere at the University. I knew all of the junior members of the faculty (Privatdozenten) personally, and this connection did not end as I shifted to physics. By contrast, during my stay in Leipzig I did not meet a single member of the mathematics faculty. Of course, in Leipzig I joined the physics department, without the detour through mathematics, but I had the impression that in Leipzig the relation between the two departments was not nearly as close. This much about the general background. Now I turn to my personal story leading me to Göttingen. I had made an agreement with my father that if I failed to become a

54

Laszlo Tisza

Phys. perspect.

mathematician, I would take over the bookstore. After two years at the university I was willing to honor this agreement, and my father arranged for an apprenticeship at a bookstore in Bonn. I was to spend the first year in the antiquarian bookstore, and the second year in the retail store, the only one of interest to my father. He had chosen to send me to Germany to express his satisfaction with my change of course. After my arrival in Bonn I had an interview with the manager of the bookstore. He asked me whether I was Jewish. It was a great surprise to him that I was, given the standing of my father’s professional connections in Germany. He would not have objected to my working in the antiquarian store, but he could not let me work in the retail store; his clients would not deal with a Jew. Frenkel: In what year did this happen? Tisza: In 1927. Since for us only the retail-store experience mattered, I rejected his offer, but agreed to stay in the antiquarian division until the end of February, the end of the first university semester. I held a student visa, the only practical way to enter Germany, and I registered at the University of Bonn while working at the store. I learned how to catalog collectible books, and had a good relation with the staff. I consulted with my parents for the sequel. They proposed that I should try to find volunteer employment at a Göttingen bookstore, and if unsuccessful I would be at the fountainhead of mathematics and might regain interest. This is what happened. I mentioned Göttingen’s singular role in mathematics; this was reinforced in Hungary, stemming from the friendship of Farkas Bolyai with Gauss while Bolyai was studying in Göttingen. (Farkas Bolyai was the father of Janos Bolyai, one of the two discoverers of non-Euclidean hyperbolic geometry, and Hungary’s most important mathematician.) And indeed, Göttingen did rekindle my interest in mathematics. Alas, the strongest causal factor was the booksellers’ lack of interest in me. I attended some lectures, but most important was that I signed up for two seminar presentations. One was the Prandtl seminar. Ludwig Prandtl was the director of the Fluid Dynamics Institute, but it was in the Göttingen spirit that he was assisted by senior mathematicians, namely, by Richard Courant, Albert Betz, and Gustav Herglotz. In fact, I was guided in my contribution by Courant. The theme was the application of conformal mapping to two-dimensional hydrodynamics. This topic was interesting mainly from the mathematical point of view, since real hydrodynamics is three-dimensional. The subject was explored mainly by Italian mathematicians. Courant suggested that I read Umberto Cisotti’s Idromeccanica Piana.2 I told him I didn’t know Italian. Courant countered: everyone knows Italian. This turned out to be correct, and I enjoyed applying mathematics to physics, even for an only marginally interesting problem. The second seminar I signed up for was led by Pavel S. Alexandrov, Heinz Hopf, and Bartel L. van der Waerden. It was on combinatorial topology. This was a high-powered seminar on a subject in vigorous development. A few years later Alexandrov published a booklet on the simplest concepts of topology.3 He pointed out two basic branches: the point-set topology based on point sets, and combinatorial topology based on polyhedra decomposed into simplexes, the simplest polyhedra of a given dimension. The simplex-

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

55

es are combined to form complexes. Alexandrov describes how the two branches were slowing down after an initial vigorous development, and were rescued mainly by Luitzen E.J. Brouwer in a synthesis called algebraic topology. This is a discipline in which I was to be interested in the years to come. Unfortunately, the seminar I took in 1928 was a dreary combinatorial topology. I undertook to prove the Jordan theorem: the Euclidian plane is divided by a closed curve into an interior and an exterior. This is, of course, intuitively evident, but the proof is very difficult. Instead of feeling satisfaction with my achievement, I felt rather letdown. Fortunately, at the same time a path to physics seemed to open. I had a Danish friend, Mogens Pihl, who was an enthusiastic romantic. In Copenhagen he had heard about quantum mechanics. He impressed on me that this was an exciting new discipline, saying we cannot miss the unique opportunity to attend the introductory lecture announced by Max Born for next fall. Frenkel: Did you hear about quantum mechanics in Budapest? Tisza: No. Theoretical physics there was in the hands of Izidor Fröhlich, for whom even Maxwell’s equations were too innovative. No one thought of or mentioned quantum mechanics in Budapest before I left for Göttingen. But in 1928, when I was already abroad, Rudolf Ortvay took over the Chair of Theoretical Physics and started a new era. He was interested in quantum mechanics. When I presented myself to him, he asked me to give the first talk in the series of Seminars on Theoretical Physics he was to organize, starting in 1929. The series is still alive under the name of the Ortvay Colloquium, held once a week at the ELTE. The course on quantum mechanics I attended in Göttingen was historically the first regular offering on the subject. It was headed by Max Born, but he went on sick leave and the course was given by his assistants, Walter Heitler, Lothar Nordheim, and Léon Rosenfeld. The basic material for the course was the finished, but as yet unpublished manuscript of the Born-Jordan book, Elementary Quantum Mechanics.4 This was pure matrix mechanics. Time evolution was calculated in the Heisenberg scheme, without the use of the Schrödinger equation. The idea was that there would be a next volume on the Schrödinger equation, which however never materialized. The course was about the general structure of the Hilbert space and the eigenvalue problem. I do not think that the hydrogen atom was discussed in the course, but we knew of Wolfgang Pauli’s solution of this problem,5 which is very complicated in the framework of matrix mechanics. The course was in more than one way a great experience. It was exciting to learn about the atomic world. Also, it was important for me that higher mathematics was applicable to the real world. During my early years of involvement with mathematics the cynics used to tease me that this discipline was utterly without practical use. This course seemed a personal justification in my belief that mathematics can account for the real world and prompted me to change my mathematical orientation to theoretical physics. I now turned to taking courses to fill my lack of physics background. Frenkel: Did you take other memorable courses in Göttingen?

56

Laszlo Tisza

Phys. perspect.

Fig. 4. Göttingen physicists in the 1920s (left to right): Max G.H. Reich, Max Born, James Franck, and Robert W. Pohl. Credit: American Institute of Physics Emilio Segrè Visual Archives, Franck Collection.

Tisza: Yes. I attended some remarkably good lecture courses on physics and some on mathematics. One was Max Born’s thermodynamics. This became significant for me when I later focused on this subject as my major interest, and when I had a chance to construct my own course on thermodynamics at MIT. Therefore I would like to describe Born’s version in some detail. The presentation of thermodynamics can be neatly divided into an elementary and an advanced subdiscipline. The former deals mostly with the equations of state of fluids and represents the thermodynamical processes as curves on the p-V plane (p and V stand for pressure and volume, respectively). The magisterial exposition of advanced thermodynamics is due to J. Willard Gibbs and somewhat later but independently to Max Planck. Gibbs’s presentation is extremely austere and quite unsuited for a pedagogical introduction. Although Born [figure 4] never said so in his lectures, I believe his real motivation might have been to rewrite the Gibbsian system in a more user-friendly form. The central concept of the discipline is the “fundamental equation,” U = U(V, S), in which the internal energy U of the system is represented as a function of its volume V and entropy S. The fundamental equation contains in a compact fashion all of the thermodynamic information about the system, both the equation of state as well as the specific heats. Maxwell was so impressed

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

57

that he prepared a plaster-of-Paris model of the fundamental equation of water and sent it as a gift to Gibbs. The minimum of the fundamental equation was to correspond to the thermodynamic equilibrium of the system. There are many things that call for elucidation. What is the entropy that Gibbs assumed to be known by his readers? This subtle concept was traditionally introduced in the context of Carnot engines extracting work from hot gases while undergoing a cyclic process. Born was quite explicit about his dissatisfaction with this method, which he felt was not a dignified way to introduce a fundamental concept. He found a better way by noting that the infinitesimal heat transfer to a system, dQ = dU + pdV, is not a perfect differential and therefore it is impossible to assign a heat content Q to a system. Born noticed, however, that under certain conditions there exists an integrating factor 1/T, where T is the absolute thermodynamic temperature, such that dQ/T = dS is the perfect differential of S, and it is possible to assign an entropy value to any system in thermodynamic equilibrium. Born presented the situation to his friend Constantin Carathéodory, a brilliant mathematician, who translated it into a precise and subtle mathematical formalism. He produced a rigorous proof that systems in thermodynamic equilibrium can be assigned an entropy value. This was quite amazing, given that a very empirical branch of physics was tied in with subtle higher mathematics. The trouble was that the proof was much too difficult for the physicists who were to make use of it. Born did not give up. First, he wrote a three-part paper in which he radically simplified Carathéodory’s proof,6 and this became the first part of his lectures. The second part was even more remarkable. Whereas in the foregoing the entropy was the final destination of a complex procedure, the greatest thermodynamicist of all, Willard Gibbs, simply took it for granted that entropy existed and showed how to make good use of it in terms of the fundamental equation introduced above. Actually, this formalism is not unique; the most important alternative is based on the free energy, F = U – ST, and F = F(V, T) is another fundamental equation that contains the same amount of information as the equation introduced above. In fact, there are altogether four fundamental equations, and even more if chemical reactions or electromagnetic phenomena are involved. This proliferation of schemes leads to a high measure of redundancy that enables the expert to transform the expressions to suit his specific needs. By contrast, the novice tends to be swamped by the profusion of formulas. Born invented a mnemonic square that brings simple order into the profusion and teaches the novice to navigate like an expert. I took over this helpful mnemonic device into my MIT course of thermodynamics. Born also gave a most stimulating course on special relativity. Walter Heitler gave an excellent course on statistical mechanics and another on group theory. Particularly the latter became important to me; group theory is a difficult subject, and Heitler’s pedagogical skills contributed a great deal to make it accessible. Knowing some of it made me a specialist, and led to my thesis subject. Frenkel: Was research in theoretical physics done in Göttingen at that time? Tisza: Well, Born suggested to Victor Weisskopf the problem of the natural line width. The idea was to use Paul A.M. Dirac’s time-dependent perturbation theory. It was

58

Laszlo Tisza

Phys. perspect.

known that in first approximation one gets a Dirac delta function that corresponds to a sharp line. It was hoped that in higher approximation one would account for the natural line width. But it didn’t happen. Then Weisskopf consulted Wigner in Berlin, and Wigner suggested that the exponential decay should be put in by hand, and then one can solve the problem rigorously. This is now a standard result in quantum mechanics, the so-called Weisskopf-Wigner formula.7 This work was started when I was in Göttingen and was finished after I left. Also, Max Delbrück was working on his Ph.D. thesis. He came from an old academic family; his father was a renowned historian. Max had great personal charm, but he was somewhat arrogant. In his oral doctoral exam Robert Pohl, the spectacular lecturer in the great physics class for physics and medical students, asked Delbrück about the sensitivity of a balance. Max made it clear that such questions were beneath his dignity. Pohl flunked him. Years later, in 1969, Delbrück was awarded the Nobel Prize in Physiology or Medicine for his genetic studies of the bacteriophage. It was known that Heitler would love to guide someone to develop the quantum chemistry of the van der Waals b-forces, which represent the intermolecular repulsion. However, no one seemed to have been interested. Frenkel: Did you try to find something to work on while you were there? Tisza: Born suggested to me to work on the improvement of the Born-Oppenheimer approximation applied to molecules, but nothing came of it. In early 1930 my friend Teller came to visit. He summed up his impression to me that the atmosphere in Göttingen was sterile and advised that I should transfer to Leipzig where he was working with Werner Heisenberg. Frenkel: But originally Heisenberg had been in Göttingen. Tisza: This was in 1925, before my time. Then he oscillated between Göttingen and Copenhagen. He was in very close contact with Niels Bohr. In those years Heisenberg, Pauli, Pascual Jordan, and Hendrik Kramers were the pioneers of the young generation who worked on translating Bohr’s heuristics into solid mathematics. They were in competition for getting a professorship. When the Leipzig position opened up, it went to Heisenberg, Pauli obtained a position in Zurich, and Jordan in Rostock. The Dutchman Kramers had a secure position in Leiden. I would like to say here a few words about the intensive interaction I had with the junior mathematics faculty. As I mentioned already, I established this interaction during my first term in the mathematics department, but it continued during my switching to physics. In fact, they observed this switch with bemusement. I kept going to selected seminars in the math department. I vividly remember David Hilbert’s first appearance after a prolonged illness (pernicious anemia, for which he was treated with an American experimental drug not yet in general use). He ruminated: “Next door the physicists run a seminar on the ‘Structure of Matter’. They deal with a newfangled mechanics called quantum mechanics. This is a mechanics somewhat like Newtonian mechanics, but not quite. The mathematicians will not get around learning this mechanics. But, of

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

59

Fig. 5. David Hilbert. Credit: American Institute of Physics Emilio Segrè Visual Archives, Landé Collection, photograph by A. Schmidt, Göttingen.

course, they may wonder whether it is the time to do so. The other day I asked an expert whether I should acquire a radio, and he suggested: ‘You might wait a while’.” Hilbert [figure 5] remembered his earlier active interest in the foundations of physics, but his weakened health did not let him resume where he left off. I remember also a talk by Emmy Noether, the center of modern algebra in Göttingen at the time. Reporting on her recent trip to Moscow, she was starry eyed talking on her experience. She mentioned the “House of Scholars,… an elegant palace that the government built for the scientists…; well, they did not build it, they bought it…; well, they did not buy it, they put it at their disposal.”

60

Laszlo Tisza

Phys. perspect.

Going to Habilitation talks of Privatdozenten was a favorite social occasion. This was a residue of the medieval history of German universities. Privatdozent was not an academic position, but a membership in the Guild of teachers marking the right to teach (venia legendi). I remember the talk of Stefan Cohn-Vossen, Hilbert’s coauthor of a book, Intuitive Geometry.8 The candidate gave a slide show without featuring a single mathematical formula. He demonstrated the distinction between vulgar art (Kitsch) as against real beauty, as seen in the 1000-fold enlarged photo of a louse. Hilbert watched all this with a somewhat pained expression. The mathematics department employed a large number of junior faculty; they had a large class of students of basic analysis who were given problem assignments that were corrected by faculty. The head of this group was Otto Neugebauer. He also became Director of the Mathematical Institute that was built with Rockefeller money obtained under the powerful influence of Courant; the innovative new Institute opened early in 1930. Belying its academic credentials, the University of Göttingen did not have a campus; the lectures in mathematics and physics were given in nondescript buildings spread over town. The Mathematical Institute was a consolidation of the physical plant into an efficient modern building, but with none of the medieval splendor of the Colleges of Oxford and Cambridge. When Hilbert was told that Neugebauer turned to the study of Babylonian mathematics, he commented: “aber Geschichte, das ist ja alles schon gewesen!” (“but history, that all happened already!”). Contrary to the rest of the scholarly world Hilbert did not appreciate Neugebauer’s contribution of learning ancient languages to decipher the first written manifestations of mathematics. Although I concentrated mostly on physics lectures, I also attended some on pure mathematics. Gustav Herglotz was a spectacular lecturer, and I enjoyed his course on differential equations. Harald Bohr lectured on almost periodic functions. Harald’s fame rested on several factors: He was Niels Bohr’s younger brother, a player on Denmark’s Olympic soccer team and, last but not least, a brilliant mathematician. His lectures were a virtuoso application of the method of eigenvalues on almost periodic functions. One of the phenomena on the Göttingen scene was Courant and Hilbert’s Methods of Mathematical Physics, the first volume of which had appeared in 1924.9 This book is centered on Hilbert’s original work dealing with linear vector spaces, function spaces, and eigenvalue problems. The Physics of the title may have seemed exaggerated at the time, since the problems covered, such as the vibrations of membranes and disks, were not very interesting. Many mathematicians believed that eigenvalues ought to be used for something more important. In fact, Bohr’s quantum theory of the hydrogen atom was a plausible candidate for an application of eigenvalues. However, the outlook was not immediately promising. The hydrogen spectrum consists of a discrete part that converges to the ionization limit where it is joined by the continuous spectrum. The trouble was that the Sturm-Liouville eigenvalue problems of CourantHilbert all had discrete spectra that converged to infinity. In the period 1924–1926 mathematicians tried hard to invent an eigenvalue problem that would let them break the Sturm-Liouville stranglehold. Harald Bohr’s almost periodic functions did achieve the mathematical aspect of the program; unfortunately, they were useless to

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

61

account for the hydrogen spectrum. By 1926, when Erwin Schrödinger derived the hydrogen spectrum by solving a wave-mechanical eigenvalue problem, the CourantHilbert title did appear miraculously prophetic. On first seeing the new theory, Hilbert commented: “Wer hätte es gedacht dass die Singularität in der Differentialgleichung die Häufungsstelle des Spektrums ins Endliche bringen wird?” (“Who would have believed that the singularity in the differential equation would bring the convergence of the spectrum into the finite?”) Of course, Schrödinger did not play around with hypothetical eigenvalue problems. He was influenced by Louis de Broglie’s intuition of extending the wave-particle duality formulated by Albert Einstein for light to the electron. He came to the Coulomb potential for physical reasons; the mathematical singularity was a byproduct. The close interaction of mathematicians and physicists, an ancient tradition in Göttingen, lets us appreciate also their different ways of thinking. Let me mention here that there was a young German theorist, Walter Elsasser, who published a famous note as a first reaction to de Broglie’s bold new ideas.10 Walter pointed out that there are already known experimental facts that support the undulatory properties of the electron. However, this was before my time. When I made it to Göttingen Walter had already left. This scenario was repeated in Kharkov and Paris where I followed in Walter’s footsteps, after he already left. Finally, I caught up with him at the University of Pennsylvania where I gave a talk and found him in the faculty. We became friends until his death in 1991. His most important contribution was the theory of the Earth’s magnetic field. His interest in geophysics connected him with the Hungarian solid-state physicist Egon Orowan whom I first met at Wigner’s tea. Egon spent some time in Berlin, Birmingham, and Cambridge, England, to end up in the Mechanical Engineering Department at MIT, where we became close friends. Being one of the discoverers of dislocations, his best-known contribution is the mechanism of plastic deformation in solids. He also was interested in geophysical applications and had frequent discussions with Elsasser. I cannot close my story of Göttngen without saying a few words about Paul Ehrenfest. He was a theorist from Vienna, a close friend of Einstein, who could not get an academic position in Austria because he was Jewish. He found one in St. Petersburg. He married a Russian mathematician, Tatyana Afanassjewa, and they both moved to Leiden when he was appointed as Hendrik Antoon Lorentz’s successor in 1912.11 He and his wife wrote a famous article in the Encyclopedia of Mathematical Sciences on the fundamental problems of Ludwig Boltzmann’s kinetic theory.12 When Martin J. Klein worked on his Ehrenfest biography,13 he spent some time in Leiden and got fruitful information from Tatyana, Ehrenfest’s widow by that time. It was a widely mourned tragedy when Ehrenfest committed suicide in 1933. He also killed his retarded son, undoubtedly a part of the origin of his depression. However, his depression must have been aggravated by professional discontent. He had a strong compulsion to understand physics in depth. What for the community was only a disagreement of conflicting personalities concerning the interpretation of quantum mechanics, was for him an intolerable personal tension affecting scientific progress. For a few months in 1929, Ehrenfest [figure 6] was visiting professor in Göttingen. He did not give a course, but initiated an informal seminar from morning till night. He

62

Laszlo Tisza

Phys. perspect.

Fig. 6. Paul Ehrenfest. Credit: American Institute of Physics Emilio Segrè Visual Archives, Margrethe Bohr Collection.

pretended not to understand quantum mechanics, and put up for discussion such questions as the relation of the Heisenberg and the Schrödinger formalism, which at that time was widely discussed, but was carefully avoided by the Born staff, as they completely confined themselves to the Göttingen brand of matrix mechanics. One day Ehrenfest asked the following question: “Listen kids! We have learned in school that physical quantities are Minkowski tensors. Now comes Dirac with his electron theory and has four-component entities which are not Minkowski vectors; what are they?” Van der Waerden was in the audience, and in a few days he gave the answer: “They are composites of ‘spinors’, i.e., of two-component complex vectors, which are transformed by 2 ×2 complex matrices.” He did not mention that Elie Cartan had developed the spinor theory already in 1913. All this was illuminating, but taking the conjugate of matrices is beset by an ambiguity. One way to take the conjugate of a matrix is by taking the complex conjugate of each matrix element. This was the choice of both Cartan and of van der Waerden. Alternatively, in quantum mechanics it became usual to take the Hermitian conjugate of matrices. Jump-started by quantum mechanics, the mathematicians discovered the importance of the linear algebra of complex vector spaces, and they found mathematical reasons to prefer Hermitian conjugation.

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

63

Van der Waerden was an algebraist, a disciple of Emmy Noether. He was familiar with the mathematics of relativity, but at this time not yet with quantum mechanics. This was to change. His spinor theory became very popular and in time he wrote a book on Group Theory and Quantum Mechanics.14 He did include his spinor theory, but saw no reason to change his original convention and shift to Hermitian conjugation. Hence spinor theory persisted with its discordant method of conjugation. This is incorporated also in the spinor theory of Roger Penrose. I may note that neither the positivists nor Thomas S. Kuhn see any reason to prefer one mathematical formalism over another, so long as both agree with experiment. By contrast, I tend to believe that there is a natural harmony between a phenomenon and a well-chosen mathematics. Probably there is no more striking instance for an evolution of tradition toward harmony than the replacement of the geometrical language of Isaac Newton’s mechanics in his Principia with that of the analytical mechanics of Joseph Louis Lagrange, Pierre Simon Laplace, and successors. This progression from Euclid-Newtonian physics to analytical mechanics is thoroughly integrated in contemporary physics. However, the continued harmonization of mathematics and phenomenology after a new boundary will have been crossed was still open for critical examination. The next major boundary to be crossed was that separating atomic physics from macrophysics. The first thing to note about this boundary is that it does not lead us into a homogeneous domain of investigation, but we have: atomic and molecular physics, structure of condensed matter, nuclear physics, and particle physics. These can be taken up in proper sequence and there is also a proper beginning, the Rutherford nuclear model of the atom. At first there was a teasing relation between the Rutherford model of the hydrogen atom and the planetary system of a single planet. The analogy is deceptive, however, because the Rutherford model of the atom is unstable and strictly speaking not admissible on the atomic scale. There is a reliable way to get out of this difficulty. Newton had advanced two particle concepts, the mechanical in his Principia and an optical-chemical in his Opticks. However, only the first one received a mathematical elaboration, and at the beginning of the 20th century it would have been utterly impossible to find a formalization for the optical-chemical atom that would be both empirically and mathematically flawless. Accordingly, this model was not pursued at the beginning of the 20th century. The way out was found by Bohr, who discovered the method of “quantization” involving the ad hoc modification of classical mechanics to bring it somewhat in line with spectroscopic observations. Bohr had the boldness to advance a theory in which neither the mathematics nor the phenomenology was flawless. Bohr’s method of quantization was rudimentary, but this was remedied by the “canonical quantization” in the next generation. The resulting canonical quantum mechanics was highly satisfactory. I personally still thought that canonical quantum mechanics should be anchored in the particle concept of Newton’s Opticks. However, it took me a lifetime to figure out how to do this. I will give a brief account of it at the proper juncture.

64

Laszlo Tisza

Phys. perspect.

An Eventful Three Months in Leipzig Tisza: Following the advice Teller gave me on his visit in Göttingen, I moved to Leipzig at the beginning of the summer term in 1930. Frenkel: Was there no administrative problem in getting admitted to the university in Leipzig? Tisza: Surprisingly, there was none. I had been attending three universities in Germany. In each case I simply appeared at the Registration Office and announced my intention to register. The essential requirement of high school (Gymnasium) graduation was ensured by previous attendance at a university. In Göttingen I was supposed to take an exam of German proficiency. I could not get hold of the examiner. Finally the clerk said: “but you speak fluent German,” and the matter was settled. I had indeed learned German as a child from a governess. I do not know whether this easygoing style is still practiced in Germany. In Hungary a formal application was necessary; after all, the numerus clausus, a regulation to restrict the admission of Jews to higher education, had to be administered. Frenkel: How did your contact with Teller shape up? Tisza: Teller defended his Ph.D. thesis the day I arrived in Leipzig. It was being kept a secret, to become a birthday surprise for his father in a few weeks. It was an important landmark for Teller. The tedious machine calculation of his thesis with the primitive calculators of the day was over, and now he could turn to problems to give shape to his beginning career. He immediately told me about a matter that puzzled him, an apparent anomaly in the infrared spectrum of methane. We knew that the spacing of the rotational bands in the vibrational-rotational spectrum is determined by the moment of inertia of the molecule. We accepted the chemists’ view that the methane molecule is a regular tetrahedron; hence as a spherical top it should have only one moment of inertia. According to the then-prevailing rules of spectroscopy this meant a single rotational spacing. In reality, the methane molecule had two wellobserved infrared bands, and the two had substantially different rotational spacing. What do we make of that? Some physicists said: “Simple, the chemists are wrong. Instead of being a regular tetrahedron, the methane molecule is a square-based elongated pyramid.” This view was rejected out of hand by Teller. He held that the chemists knew what they were saying; the methane molecule must be a regular body with a single moment of inertia. It is the physicists who have to revise their simple rule connecting rotational spacing and moment of inertia. We must formulate a new rule by which a single moment of inertia can lead to more than one rotational spacing. This problem seemed at first impenetrable. However, Edward generated a stream of ideas that might work. My role became to convince him that they wouldn’t, and he came up with something new. Eventually he came up with an idea on which we could agree. The key was the validity of the Born-Oppenheimer approximation, the connecting link between quantum

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

65

mechanics and the geometry of the molecules. The essence of this formalism was to represent the energy of molecules as a sum of terms of different orders of magnitude. The largest term was the electronic energy, next the vibrational energy of the nuclei, and finally the rotational energy of the molecule as a rigid body. The gist of the BornOppenheimer approximation is to provide a basis for the hierarchy of electronic, vibrational, and rotational quanta. The tacit assumption of its validity was the nondegeneracy of the molecular ground state. This assumption would fail for such highly symmetric molecules as the methane molecule, and we had to adjust the Born-Oppenheimer approximation to this situation. This problem was not simple, and our first step was to formulate it for a simpler set of molecules, namely the methyl halides CH3X, where X = fluorine (F), chlorine (Cl), bromine (B). The line connecting carbon (C) and X is called the figure axis of the molecule. In view of the existence of this special direction, the vibrations can be divided into two classes: (1) vibrations parallel to the figure axis; let us call this direction z; (2) vibrations perpendicular to z. In this case the vibrations along x and y have the same frequency by symmetry. They can be superposed with an arbitrary phase lag. The situation is similar to the case of polarized light, where a 90° phase difference produces circularly polarized light. Its analog in the molecular context is an internal motion of the molecule that is a hybrid of vibration and internal rotation. Its energy is vibration-like; it is determined by its frequency, but it also has an angular momentum. This angular momentum associated with vibration can be expected to be coupled to the angular momentum of conventional rotation. The coupling of the internal and the external angular momentum is the effect we have been looking for. The result was indeed a changed rule connecting moment of inertia and rotational spacing. The details were more complicated than it sounds in retrospect, and they kept us busy till the end of the semester. We published the work in the Zeitschrift für Physik.15 Later Teller published a somewhat improved review of our paper in the Hand- und Jahrbuch der Chemischen Physik in 1934.16 This joint work was a landmark for both of us. The choice of the problem had been Teller’s, and was determined because Edward started his studies as a student of chemical engineering. Although he switched to physics before having graduated from chemistry, he did not want his knowledge of chemistry go to waste, and for a few years he explored the conceptual enrichment of physics stemming from borderline phenomena with chemistry. He proceeded to examine other limitations of the Born-Oppenheimer approximation, such as the Jahn-Teller effect dealing with vibronic states, i.e., the fusion of electronic and vibrational states. Frenkel: When Teller, Rudolf Fuchs, and you won the Eötvös Competition in mathematics, Teller also won the Competition in physics. Why did he start his university studies with chemistry instead of physics? Tisza: Physics and mathematics did not, at that time, seem practical professions with which to earn a living. Many cultured and knowledgeable fathers, especially in Jewish families, directed their sons towards chemistry. It is worth noting that three great Hungarians, von Neumann, Wigner, and Teller studied chemistry for a while and the latter two got a degree in it.

66

Laszlo Tisza

Phys. perspect.

Frenkel: After the Second World War physics dominated the realm of the natural sciences. Why was chemistry so popular in the 1920s? Tisza: There is a very good reason for that. During the First World War chemistry was of decisive importance, because the Central Powers (Germany and its allies) could not have continued the war beyond a year or so without the solution of the so-called nitrogen-fixation problem. Frenkel: Could you describe what this problem was? Tisza: There is plenty of nitrogen available in the atmosphere, but it is in its inert form. It was important to have nitrogen in “fixed” form as in ammonia, NH3, an ingredient of both explosives and fertilizers. In his presidential address to the British Association for the Advancement of Science in 1898, Sir William Crookes warned the scientific community that something has to be done with the nitrogen-fixation problem, because the world would exhaust its fixed-nitrogen sources, the saltpeter of Chile and the guano of the Pacific islands.17 Ammonia had to be produced synthetically. This was a difficult chemical problem, because if you just put nitrogen and hydrogen together, they will not react. Walther Nernst and Fritz Haber worked on the solution of this puzzle. Nernst established the proper domain of pressure and temperature at which the reaction would proceed to produce ammonia. However, the rate of reaction would be too slow for practical purposes. It was at this point that Haber addressed the problem from the point of view of the chemical engineer who can speed up reactions by selecting a proper catalyst. This he achieved in collaboration with the brilliant chemical engineer Carl Bosch. They started up a working large-scale factory in 1913, just before the war. This was the Manhattan Project of World War I, and well-informed laymen were as conversant with the term “catalyst” as the post-Hiroshima public was with “chain reaction.” When in the summer of 1914 the war broke out, the popular opinion in Germany and in the other Central Powers was that the war would be short, the soldiers would be home before Christmas. As we know, it was not to be, and Germany could not have continued the war if the nitrogen-fixation problem had not been solved. Frenkel: Because of a shortage in explosives, or in fertilizers? Tisza: Both. There was a serious food shortage in Germany. Hungary was a bread basket, although there was food rationing also in Hungary, but food was much more abundant than in Germany, where artificial fertilizers as well as ammonia for explosives were certainly essential. The naval blockade of the Allies severely curtailed imports. Frenkel: Did both the Central Powers and the Allies discover how to fix nitrogen? Tisza: The Allies had access to Chile; for them the solution of the problem was not as pressing. I think that they worked on the problem without solving it. After the war the excellent Haber-Bosch procedure was adopted everywhere.

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

67

Frenkel: Thank you for this interesting piece of history. It explains why von Neumann, Wigner, and Teller started their university studies with chemistry. Were they really interested in it, or did they just follow their fathers’ advice? Tisza: Von Neumann and Teller were interested in mathematics, Wigner in theoretical physics. But they had to agree with their fathers that these were not promising careers. Wigner recounted that to the question of his father, “How many theoretical physics positions are there in Hungary?” he answered that there are three or four. I understand that Wigner felt later that he had exaggerated. “And do you expect you will get one of them?” asked his father. So the parents argued, and the sons accepted the argument. Anyway, they were exceptionally gifted and had to succeed in any career. Wigner knew how to put to use his expertise in chemical engineering when he was already a worldfamous physicist. He took a leading role in the design of the plutonium factory in advancing the atomic-bomb project. I mentioned already that Teller, too, started his studies in chemical engineering, namely, at the Polytechnic University in Budapest, but he finished only the first semester. He told me that the scientific standard of the University did not satisfy him, and he went to Karlsruhe to study chemistry. In addition, he attended there the lectures of Peter Paul Ewald, a famous X-ray spectroscopist. Ewald was impressed by the bright Teller. He called in Teller senior, and told him that his son was exceptionally talented, and since he wanted to do physics, he shouldn’t be prevented from doing it. The outcome was that Edward went to Munich to work with Arnold Sommerfeld. He started investigating the excited states of the hydrogen molecular ion, establishing the solutions of the Schrödinger equation by numerical integration. As Sommerfeld left for a sabbatical, Edward transferred to Leipzig to join the team of Heisenberg. There he completed his work begun with Sommerfeld. The case of Johnny von Neumann was very different. With his prodigious capacity for absorbing and initiating new disciplines, such as the theory of games and of economic activities, computer science, and meteorology, he did not feel that his studies of chemical engineering had to be integrated into his professional activity. I once had a freewheeling chat with him on a variety of topics. Frenkel: Could you say something more about this chat? Tisza: The setting was Shelter Island facing the northeastern tip of Long Island, New York. On this island, in the early spring of 1947, before the beginning of the tourist season, a fashionable resort hotel was the seat of a conference on quantum electrodynamics.18 This event proved phenomenally successful, as it stimulated entirely new developments. A recently discovered experimental fact, the so-called Lamb shift, could be explained by the extraction of observable effects from the vacuum fluctuations of the quantized electromagnetic field. The result was the generation of a new method of calculation, called renormalization, initiating a new era in quantum electrodynamics. The success of the Shelter Island Conference made it tempting to achieve a repeat performance in1948. The idea was to try to center it on cryogenics. The stars of the proceedings would be Fritz London and I. However, we already had said what we knew

68

Laszlo Tisza

Phys. perspect.

Fig. 7. Werner Heisenberg with his students in the Winter Semester of 1930–1931, the semester after the author left Leipzig. Front sitting left: Rudolf Peierls, Heisenberg; standing left: Giovanni Gentile, Jr., George Placzek, Felix Bloch, Victor Weisskopf, Fritz Sauter; behind Placzek: Gian-Carlo Wick. Credit: American Institute of Physics Emilio Segrè Visual Archives, Peierls Collection.

and had not much new to add. The conference was not a success with a lot of time to fill. Among the more interesting padding was William (Bill) Shockley’s presentation of the physical basis of the transistor, soon to be announced. Among others, not strictly cryogenic participants, was Johnny von Neumann. I don’t remember any contribution of his to the proceedings, but there was a free afternoon and the two of us found a scenic rock on the seashore, and were free associating on a number of topics. The gist of Johnny’s point was not very novel; he repeated his often-expressed view that the failure of mathematics to yield solutions of the equations of hydrodynamics would be remedied by the advance of high-speed computing. I remember one of his statements: in order to predict the weather for tomorrow, the computer technology of the day would call for computer time of a month. He hoped there is chance for improvement. Let me add that although it is true that computers enlarged the scope of applied mathematics, it is more remarkable the extent to which they transformed the style of everyday living. I think Johnny worked on computers because he knew how to increase their power. Also, he bitterly complained about Einstein’s relentless critique of quantum mechanics. He did not consider this critique well taken. Let me now come back to Leipzig. The physics department was an international meeting place [figure 7]. Among foreign visitors in my time was John H. Van Vleck

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

69

from Harvard; Nevill Mott from Bristol; Boris Podolsky, who was to become a central figure in the famous Einstein-Podolsky-Rosen paper; Nathaniel H. Frank, who became my colleague at MIT, put in a short visit interrupting his stay with Sommerfeld. Heisenberg’s assistant was Guido Beck, a German from Prague, same as George Placzek, and both were equally witty. With the Nazi regime on the horizon, Guido’s position was drawing to a close and I was to meet him again in the Ukraine. Personally for me what mattered was having gained some research experience to alleviate my doubts about my creative potential. The next step was to follow up with a work independent enough to serve as a Ph.D. thesis. Teller came through by suggesting a problem on polyatomic molecules. Our joint work just finished dealt with a few specific molecules; my new work was to deal with the rules of selection and intensity for all molecules classified by their symmetries. The proper mathematical method involved group theory. Teller knew that I had taken a course on this with Heitler in Göttingen, and that I was eager to build on this knowledge. I carried through this program in Budapest, where I returned in 1930, after the end of the semester in Leipzig. Before turning to this further stage in my career, I wish to recall an amusing anecdote centered on Heisenberg, which I mentioned also in a recent interview I gave to Péter Horváthy (in Hungarian). It was a beautiful summer day when the Heisenberg group descended to the Academy of Saxony to attend a lecture of Peter Debye. He was at that time Chair of the Department of Experimental Physics in Leipzig. He was to demonstrate his reputation of enlivening his lectures with brilliant demonstrations, and the lecture room was packed. In addition to the expected fine lecture, the audience was treated to an unexpected event: the announcement of Heisenberg’s election to membership in the Academy. We felt that this event was surrounded by a certain drama that struck us as amusing. All the academicians sported long white beards and were wearing solemn black coats. By contrast, Heisenberg was cleanshaven and wore a white summer suit. This was a Tuesday afternoon, to be followed by a traditional ping-pong party in the lab the same evening. On leaving the Academy Edward and I were pondering the proper way to celebrate Heisenberg’s induction to this august body. We stopped by at the nearby theater and acquired a stage beard. Back in the lab, we conspired with Professor Friedrich Hund to produce a formal black coat, and all that would be presented to Heisenberg even while Hund produced a little speech: “people engaged in useless activities, such as Egyptology and theoretical physics, like to establish academies to celebrate their own importance. They spend beautiful summer afternoons listening to lectures instead of playing tennis. Dear Heisenberg, we are saddened that you too were caught up in such an undertaking.” To be frank, I doubt that Heisenberg fully appreciated the affectionate humor of our celebration.

Back Home and Involvement with the Communists Frenkel: So in 1930 you returned to Budapest. Why didn’t you stay in Leipzig longer? Tisza: My father called an end to his willingness to finance my studies. I did not question his decision, and my stay in Leipzig was the final stage of my all-too-long study in Germany.

70

Laszlo Tisza

Phys. perspect.

Frenkel: Did your contacts with Teller survive? Tisza: Yes. We were in touch by correspondence, and he always came home for vacations to spend in his parents’ home and to keep in touch with his friends. I was one of these. Our contacts were partly social, parties and hiking, but more importantly for me they aimed to keep my thesis work on an even keel. An important part of Teller’s input was to convey to me an interesting contribution by George Placzek to molecular spectroscopy centered on the Raman effect. This is a variety of inelastic scattering, where the difference between the energies of the primary and scattered quanta is equal to the energy of a transition in the vibrational-rotational spectrum. However, the selection rules are different from those of the infrared spectrum. The first theories of the Raman effect were very complicated, involving the Schrödinger equation of the molecule. Placzek established a much simpler method based on a phenomenological polarization tensor, the matrix elements of which governed the selection and intensity rules in much the same way as the matrix elements of the electric-dipole moment govern these rules for the infrared spectra. A plausible problem was to establish which matrix elements would vanish because of symmetry. Placzek worked out the results for many molecules intuitively. His results were mostly right, but sometimes wrong, and he welcomed the idea that I should do this more reliably with group theory. This was a very suitable idea for me and I followed it up. I met Placzek personally in Leipzig and later in Kharkov during my stay in the Landau group. However, I learned about his ideas on the Raman effect mainly from his publications and from discussions with Teller. Eventually I presented and defended my Ph.D. thesis at the University of Budapest, with Rudolf Ortvay the official supervisor. Ortvay was interested in the work and sent the manuscript to Eugene Wigner for appraisal. Wigner mainly approved, and offered some helpful criticism. My thesis was submitted originally in Hungarian, but I prepared a German translation that appeared in the Zeitschrift für Physik.19 I had my degree; I had two solid papers to my credit. It might have been a turning point in my career that had started with much self-doubt. Alas, there was also an unhappy event that was most embarrassing, but it became entangled with my professional life, and I have to come to terms with it. I got involved with a communist group. My first contact with communism had been under the Béla Kun regime in 1919. I was too young to form an independent opinion, but my parents and everyone around me was thoroughly anticommunist, and I went along. However, I had a good friend, Johnny Antal, whose father was an educator with a midlevel position in the communist Education Commissariat. My connection with Johnny turned around our complementary interests; he was interested in art and literature, while I cared about mathematics and science; we agreed to disagree on political philosophy. In the course of 1920 Johnny and his family left Hungary and he disappeared from my life, to reappear unexpectedly, without his family, shortly after I returned to Budapest from my lengthy studies in Germany. During my stay in Germany I was quite apolitical; I didn’t even read newspapers. Once, talking with two of my best friends among student colleagues, Mogens Pihl and Martin Strauss, I ventured to remark that “no one in his right mind could be a com-

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

71

munist.” They replied: “We are of such minds!” The conversation stopped, but I was startled and got sensitized to the growing political tension that became palpable during my semester in Leipzig. There also was a deepening of the economic depression. As I mentioned earlier, days after my arrival in Budapest my friend Johnny appeared out of the blue. He was now the correspondent of the Soviet News Agency. We resumed where we left off ten years before, but I was shaken in my confident anticommunism. I was ready to be instructed by him and started to read Karl Marx’s Das Kapital. I also made contact with old university friends, particularly with Emmi Balog (later married Tarján) who had been a first-year mathematics student the same time with me. She also became politically sensitized in the interim, and was involved in a nonacademic group whose main interest was hiking and skiing in the Buda mountains, and carrying out discussions among adherents of Marx and the American political philosopher Henry George. Discussing political philosophy was a harmless occupation even in Hungary. It was another matter that two members of Emmi’s group were members of the illegal Communist Party. One of them asked me to render some apparently small favors to the Party, such as transmitting material from the one who wrote it to the typist to copy it. Although foolishly I may have considered it a minor matter, it was illegal in Hungary. Being influenced by friends and by the deepening economic depression were rather typical motivations for turning politically left in those times. I also had a more personal motivation that pushed me in the same direction. As a physicist I tended to look at relativity and quantum mechanics as products of scientific revolution, and to consider “revolution” as a legitimate engine of change. Teller, Wigner, and von Neumann saw no connection between the two revolutions; their acceptance of the scientific revolution was not in conflict with their opposition to political revolution. The tendency to draw a parallel between the two kinds of revolution cuts both ways. At that period in Budapest it rendered me open to political entrapment. Three years later, after an extensive acquaintance with the socialist experiment in the Soviet Union, there was not a shred of illusion left in me as to its attraction. However, I am getting ahead of myself; let me go back to the summer of 1932. Two months after I defended my thesis I was arrested, and although I was not a Party member I was sentenced to 14 months in jail. In Hungary the Communist Party was illegal at that time, and any communist activity was heavily apprehended. After that it was out of the question for me to obtain an academic position in Hungary. My scientific career seemed at an end before having started. Yet Teller remained the faithful friend. Although he had no sympathy with my political views, he helped me to find a way out. Frenkel: Was he still in Leipzig? Tisza: No, he had moved to Göttingen. Frenkel: But he told you not to stay in Göttingen! Tisza: Oh, he said that Göttingen was not a good place for me to get started on a Ph.D. thesis, but he went there to work as an assistant to Arnold Eucken, a prominent pro-

72

Laszlo Tisza

Phys. perspect.

Fig. 8. A day at the beach near Budapest in the fall of 1933. Left to right: The Japanese physicist Fujiyoka, Edward Teller, and the author. Credit: Author’s personal collection.

fessor of physical chemistry. Also, he got a Rockefeller fellowship to work with Enrico Fermi in Rome and with Bohr in Copenhagen. He commuted between these cities. Frenkel: Teller was an assistant of Eucken to provide a link to quantum mechanics? Tisza: Exactly. It was at that time common for senior professors to have assistants knowledgeable in quantum mechanics to help them to adjust their classical expertise to new developments.

Apprenticeship with Landau Tisza: Edward [figure 8] had the idea that I ought to join Landau’s group at the Ukrainian Physical-Technical Institute (UFTI) in Kharkov. Lev Davidovich Landau had a marvelous reputation both for his research and for his method of training, yet he was not overrun, because the people he would have liked to get, like Weisskopf or Placzek, were happy to visit but were unwilling to accept a position under the repressive regime, and they had other options. Frenkel: How did Teller get to know Landau? Tisza: Landau traveled in the West in 1929–1930. He did not come to Leipzig during my stay, but the manuscript of his paper on the diamagnetism of free electrons circu-

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

73

Fig. 9. Participants in the meeting at the Ukrainian Physical-Technical Institute in Kharkov, May 1934 (left to right): Dimitri D. Ivanenko, the author (obscured), Léon Rosenfeld, Unknown (obscured), Yuri B. Rumer, Niels Bohr, J.G. Crowther, Lev D. Landau, Milton S. Plesset, Yakov I. Frenkel, Ivar Waller, Evan J. Williams, Walter Gordon, Vladimir A. Fok, Igor E. Tamm. Credit: American Institute of Physics Emilio Segrè Visual Archives, Physics Today Collection.

lated there and created a great deal of interest. Van Vleck and Teller published their comments. It is a beautiful paper.20 I think Teller met Landau in Copenhagen and called his attention to me. The first result was an invitation to a small but prestigious theoretical meeting at the UFTI in May 1934 [figure 9]. The prestige of the meeting was assured by the presence of Niels Bohr; it was attended also by a group of French and British theorists. The proceedings had two leitmotifs: the development of Dirac’s theory of the electron to cover the new experiments on pair production (the production of an electron-positron pair by two light quanta), and the interpretation of cosmic-ray showers as multiple processes. A noteworthy aspect of the meeting was that the general political atmosphere could not have been better. A good harvest seemed to have ended the agricultural crisis of several years, and the friends of the regime were optimistic as to the future. These expectations were to some extent fulfilled. Not only was the shortage of bread ended, but even gourmet food had become easily available in the stores of the grocery chain Gastronome. However, and I shall come to this shortly, the expected mellowing of the political suppression did not materialize; the situation went from bad to worse.

74

Laszlo Tisza

Phys. perspect.

Under the influence of the prevailing euphoria I expressed to Landau my desire to join his group, and he accepted me with a complete absence of formality. The deal was confirmed by the temporary director of the Institute, Gey, who filled the gap between Aleksandr Leipunsky, an excellent physicist who was the scientists’ favorite director, and the party hack Davidovich, who was in power by the time I joined the UFTI in January 1935, and stayed in this position during my whole tenure there. Accordingly, I have two quite different stories to tell. I will start with the positive professional experience at the UFTI and will describe the deteriorating political background later. Frenkel: The Hungarian right-wing government let people go to the communist Soviet Union? Tisza: This is indeed surprising, but international relations were distinct from the objection to communism at home. There were Hungarian engineers employed to work on the Five Year Plan. They were welcomed along with German, British, and American engineers and scientists, and received privileged treatment. Extension of protection to its citizens who went East because of unemployment at home may have been the main reason for Hungary to recognize the Soviet Union at that time. There was no Soviet Consulate yet in Budapest; I had to pick up my visa in Vienna. Frenkel: Which branches of physics were pursued at the UFTI? Tisza: There was an experimental low-temperature group under Lev Schubnikow, Boris Lasarev, and Abram Kikoin; there was also a low-temperature group with Martin and Barbara Ruhemann oriented toward industrial application. By the way, the Ruhemanns wrote a fine book on low-temperature physics,21 one of the first along this line. It was intended that this group should become an independent institute, the OSGO (Experimental Station of Deep Cooling). The idea of this institute was conceived by Alexander Weissberg, a Viennese engineer and a communist. He joined the UFTI in the early thirties. He convinced the Commissariat of Heavy Industry of the soundness of applied cryogenics, and he was commissioned to build the new institute. During my May 1934 visit I was enormously impressed by his story, and during my entire stay there beginning in January 1935 he acted as a contractor. I considered it impressive that the apparently rigid system could act with such flexibility. However, all ended differently, as I will report in the context of the events of 1937. Furthermore, an electronics group was working on secret radar problems, and a successful neutronphysics group was established by Fritz Houtermans, a German communist. Last but not least, there was the theory group, headed by Landau. Frenkel: Had you a contract for a year or so with Landau? Did you know how long you would stay? Did you get a salary? Tisza: I got a position that now would be called a postdoc, not clearly distinguished from a graduate student working for a Ph.D. I already had a Ph.D. and formally fitted more into the category of a “foreign specialist.” However, I was aware that my training

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

75

was far from solid. I was willing to accept the role of a trainee in the theory group. I did get a salary, maybe more like a scholarship, but I did not know how long this arrangement would last. Frenkel: Did you attend any courses? Tisza: There were no courses. This was not a university, but a research institute. There were seminars. Landau reviewed the physics journals each week. There was an excellent research library, and he assigned papers to be reported on in the seminars, threeto-four papers for each session. Landau expressed his appreciation or dismissal with sovereign assurance, and his judgment was accepted without any question. Frenkel: I guess the famous Landau-Lifshitz textbook series on theoretical physics did not yet exist. Tisza: Well, the series existed as a project. Landau was a young man and his ability and potential exceeded his actual professional standing. He was deliberately working on improving this situation. Producing an “encyclopedia of theoretical physics” was an important factor in his master plan. The idea was to demonstrate Landau’s truly unique abilities. First, there was his view on the role of relativity and quantum mechanics in the body of theoretical physics. Whereas many authors stressed the strange, not to say paradoxical nature of modern physics, Landau emphasized first of all that the modern disciplines increased the power and coherence of physics. A second point was his uncanny mathematical ability. He could invoke sophisticated mathematical tools to produce coherent conceptual structures in physics. Landau [figure 10] did not like the minutiae needed to complete manuscripts on his own; work with collaborators to fill in details came naturally to him. His reputation was enough for attracting people to work with him. At first he planned to collaborate in preparing the textbooks with every member of his group. However, eventually the chemistry with Evgenii Lifshitz was so perfect that all the others fell by the wayside, and the eventual format took shape quite naturally. I saw Landau and Lifshitz disappear behind the closed doors of Landau’s office, and emerge after a while with a scroll of paper obtained by cutting and pasting Lifshitz’s draft. Frenkel: Did you choose a problem to work on? Tisza: In this respect there was a ritual. First of all, every one had to pass the so-called “theorminimum” program, later called the Landau minimum, distributed in the format of a syllabus. I could have claimed exemption, but I decided not to. Landau kept track of all successful candidates. I am number 5 in his lifelong list, the only one from outside the Soviet Union. The material was divided into subfields, each part taken privately as an informal oral quiz by Landau. I got a waiver on mathematics and classical mechanics, and my first quiz was on thermodynamics. I ran immediately into trouble. As I mentioned already, I had taken a thermodynamics course with Max Born. Landau’s version could not have been more different. According to Born, thermodynamics was a beau-

76

Laszlo Tisza

Phys. perspect.

Fig. 10. Lev Landau at work, ca. 1930. Credit: Author’s personal collection.

tiful but completely finished branch of physics; for Landau, it was in a state of continued evolution. This he achieved by deconstructing various dividing boundaries that Born built to keep his discipline separate. Born’s thermodynamics was classical, and quite separate from both statistical physics and quantum mechanics. For Landau thermodynamics was statistical, quantal, and in a state of evolution. When Landau tested me in this discipline, I did not know what he was talking about: I failed. A member of the group, Lazar Moysevich Piatigorsky, took pity on me and presented me with an informal summary of Landau’s thermodynamics. Once I saw it presented, I was delighted and passed the exam. Simultaneously with these happenings, there was another development that demonstrated the creative evolutionary features of Landau’s approach. He wrote a number of papers on the so-called higher-order phase transitions. This category was conceived by Paul Ehrenfest.22 Shortly thereafter there was a spate of papers in which the phenomena in question were accounted for in terms of approximate statistical theories. I am

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

77

referring to the well-known papers of Hans Bethe and Rudolf Peierls.23 They were based on a distinction between long-range and short-range order expressed through appropriate order parameters. A similar development was initiated by Pierre Weiss who developed a phenomenological theory of ferromagnetism based on the concept of an internal magnetic field, produced by the near neighbors of a selected elementary magnet.24 William L. Bragg and Evan J. Williams generalized the Weiss theory by creating the concept of a nonmagnetic internal field accounting for the short-range order in nonmagnetic systems.25 Landau continued the path of abstraction initiated by the above authors; he introduced order parameters into the thermodynamic formalism without using approximations suggested by specific models. He presented the cumulative effect of these innovations in two papers on phase transitions, leading to a systematic classification. These papers made a great impression on me, and led me to plan my own work along his line. At first this resolve resulted in a very modest project. As usual, Landau wrote his papers in Russian and published them in a domestic publication. However, there existed at that time a German-language research journal, the Physikalische Zeitschrift der Sowjetunion, whose Editorial Office was at the UFTI. By that time I already had a good reading knowledge of Russian, and I was commissioned to translate Landau’s papers into German.26 I went at this task with enthusiasm, and it helped me to get a thorough familiarity with the papers. My role in the translation of the Landau papers had some unexpected reverberations. In 1979 Lifshitz visited MIT, and on this occasion we had a friendly musing about common memories. He suddenly told me: “Do you realize that while translating the phase-transition papers into German you improved the papers?” I had no recollection of this sort. However, Lifshitz added that on the occasion of preparing Landau’s Collected Papers for publication, it was noticed that the German version of the papers was improved over the Russian originals. As a result my German version was retranslated into Russian for inclusion into the Collected Papers. I still have no recollection of having done any deliberate editing, but I must assume that Lifshitz knew what he was saying, and that I did do some smoothing of the text that I did not consider important enough to bring to Landau’s attention. I suspect that I may have had another small input into the Landau papers. As soon as I was given the circulating version of the theorminimum, I was impressed by the total absence of group theory. I commented to Landau on this feature. He replied that group theory was overrated. Its actual usefulness is not commensurate with the complexity of its formal structure. I pointed out to Landau that my thesis work was an example of a simple group formalism producing useful results by manipulating group characters. I definitely remember that I gave him a private presentation of my thesis. Since the entry “group characters” appeared in the next edition of the theorminimum, I think I am justified in taking some credit for Landau’s change of mind. Also, some group theory was built into the phase-transition papers. I did not publicize my private lecture in the group; Alexander Akhiezer has given another explanation for Landau’s change of heart about group theory. In his 1994 “Recollections of Lev Davidovich Landau,” he attributes Landau’s turnaround to a morning of playing tennis with the famous mathematician Nikolai Chebotarev.27

78

Laszlo Tisza

Phys. perspect.

My involvement with Landau’s phase-transition papers had a decisive influence on my turning to Landau’s thermodynamics as an intended style of research. My venture into the theory of liquid helium was the first manifestation of this program.28 Later papers included in my book, Generalized Thermodynamics,29 were additional instances. Landau’s phase-transition papers generated a great deal of interest. Landau himself was very proud of them and felt that this confirmed him as a “class-two” physicist. To explain the meaning of this statement, I have to refer to Landau’s hagiography. At the time of my original visit in May 1934, his office was decorated with thirteen pictures of class-one theorists. My recollection is probably not much off the mark: Newton, Augustin Jean Fresnel, Lord Kelvin, Rudolf Clausius, James Clerk Maxwell, Boltzmann, Gibbs, Planck, Lorentz, Einstein, Heisenberg, Dirac, Schrödinger. I have no definite recollection of the class-two theorists. Maybe Pauli, Born, Jordan, Wigner, Peierls. Class three was a huge group: Felix Bloch, Bethe, Teller, Placzek, Hendrik Casimir, Mott, Kramers, George Gamow, Carl Freidrich von Weizsäcker, Vladimir Fok, Igor Tamm, and others. He definitely considered Heitler, Fritz London, Yakov Frenkel, Léon Brillouin, and Ralph H. Fowler below this group: class four was competent without remarkable achievements. Class five was incompetent. In the Landau literature there are other versions. Thus, Newton and Einstein are sometimes lifted above everyone else, as a sort of zero class. Frenkel: I am surprised that Bohr and de Broglie are not on the list. How can one explain this? Tisza: Landau was a brilliant physicist with an uncanny mathematical ability. He appreciated rigorous mathematical formalisms closely related to intuitive concepts. Let me give an example. Huygens’ spherical waves along with Huygens’ principle provided an easy intuitive interpretation of waves. However, there was neither wavelength nor directionality, necessary for a mathematical theory. All this was implicit in the wave vector that was developed by Fresnel into a mathematical theory, which in turn was also connected with experiment through diffraction. This, it seems to me, is the reason why Landau raised Fresnel to a much higher level than Huygens. The situation is similar with Bohr. His concept of quantum state opened microphysics for quantitative description, but it was nowhere near a mathematical theory. This came about only through Heisenberg, Dirac, and Schrödinger. I know that Landau later on included Richard Feynman. This apparent lowering of Bohr’s stature does not alter the fact that he had the highest regard for Bohr’s intuition. Likewise, de Broglie conceived the wave-particle dualism, but the formalism was given only by Schrödinger. Formalism too far from an intuitive counterpart was not to Dau’s liking either. Thus he did not really appreciate Nikolai Bogolubov. Although I was greatly influenced by the phase-transition papers, I think they are somewhat overrated. The modern theory of critical points operates in terms of critical exponents, based on the idea that critical points are mathematical singularities. These two lines of research seem to proceed on inconsistent lines. However, in a later effort developed in the Statistical Physics volume of the Landau-Lifshitz series, there are

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

79

extensive arguments focused on reconciling the two types of approaches to critical points. I must admit I am insufficiently prepared to evaluate the success of this effort at synthesis. Frenkel: How large was the Landau group? Tisza: When I arrived, the group consisted of Aleksandr Kompaneets, Lifshitz, Piatigorsky, and Akhiezer. Kompaneets and Piatigorsky soon left, while Isaak Pomeranchuk, Michael Koretz, and Veniamin Levich joined the group. I think Landau worked with a larger group later in Moscow at Peter Kapitza’s Institute of Physical Problems. Pomeranchuk had a great future. Landau said he reminded him of his own younger self. There was indeed a physical likeness in addition to similarity of personalities. Levich founded the field of electrochemical hydrodynamics and in 1958 became head of the theoretical department of the Institute of Electrochemistry of the USSR Academy of Sciences. Korec was not a noteworthy physicist, but Landau valued him as a personal friend and an adviser in human relations. Frenkel: How was the work of the theory group organized? Were there subgroups? Tisza: Not really. People worked on their problems. At the time, the favorite subject was pair production, a new line of research extensively discussed at the above-mentioned international meeting at the UFTI. Landau assigned me such a problem as well: the internal pair production in beta decay. A free electron does not radiate, therefore it cannot produce even a single light quantum, let alone creating a pair. However, an electron created in the beta decay of a nucleus is moving in the electric field of the daughter nucleus and can produce an electron-positron pair by the emission of an intermediary (“virtual”) light quantum. The energy needed for this process is provided by the nucleus. At the same time, Akhiezer and Pomeranchuk [figure 11] worked on the scattering of light by light, which called for a fourth-order perturbation in the relativistic Dirac formalism. They had to calculate an inordinate number of integrals involving Dirac’s gamma matrices. We all solved our problems and received a so-called “candidate” degree, which corresponded to a Ph.D. in the West, while the Soviet “doctor” degree was of a higher level, corresponding, say, to Habilitation at the German universities. The scattering of light-by-light problem was originally assigned to Akhiezer. The calculations were extremely long-winded and by common consent Pomeranchuk joined him. I vividly remember them sitting at nearby desks and performing the same steps independently until their results matched. Frenkel: The renormalization of quantum electrodymanics did not yet exist at that time. How were the infinities handled? Tisza: I don’t have a precise answer, but I think that in the 1930s the procedure was to select problems in which the infinities could be bypassed. Cases to the point were papers by Heisenberg and Hans Euler and by Weisskopf.30 I believe gauge invariance

80

Laszlo Tisza

Phys. perspect.

Fig. 11. Colleagues at the campus of the Ukrainian Physical-Technical Institute in Kharkov, 1936 (left to right): Isaak Pomeranchuk, Alexander I. Akhiezer, the author, unknown. Credit: Author’s personal collection.

was a criterion. The innovation in the 1940s was to seek out problems in which the vacuum polarization had to be explicitly faced. Weisskopf was actively interested in this problem and he assigned it to Bruce French who did not make much headway. Then in 1947 came the famous Shelter Island Conference where the Lamb shift was identified as an experimental result to serve as a test case for the need to face the divergence problem. Returning from the conference, Hans Bethe was the first to achieve this in a makeshift fashion, triggering the careful calculations of Julian Schwinger, Feynman, and Freeman Dyson who succeeded in exploiting relativistic invariance along with gauge invariance. It turned out later that Sin-itiro Tomonaga did it independently. I was near Weisskopf at the American Physical Society meeting where Schwinger first presented his results. Weisskopf was depressed, because he was among the few who appreciated self-energy as an important and solvable problem. He blamed himself for not pushing and guiding Bruce French hard enough to get through before the others. Frenkel: Were there people working in other branches of theoretical physics?

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

81

Tisza: Landau himself worked on everything: on solid-state physics, statistical physics, molecular physics, cosmic rays, astrophysics, and least of all on nuclear physics, which does not have a volume of its own in the Landau-Lifshitz Course of Theoretical Physics. This omission is presumably because nuclear physics cannot be radically simplified by selecting proper concepts.

Social Life at the UFTI Frenkel: From what you told me it is clear that in the Landau group there was an extraordinarily fertile scientific atmosphere. What can you say about the social atmosphere? You spent a few years in Germany and in France. Was life in the Soviet Union much different? Tisza: I am pleased you asked this question. It gives me a chance to point out the double aspect of my stay in Kharkov. While the professionally important aspect was my connection to Landau, my life there also had aspects determined by my being a member of the UFTI [figure 12]. I would like to recall a few episodes of this exotic interval of my life that could have had a more ominous outcome than it actually did. The UFTI campus was at the edge of the city. It contained a dormitory, a cafeteria, three-room apartments for the senior staff, and a tennis court, apart from the laboratories and workshops. I arrived in January 1935, in the dead of winter; there was snow on the ground. I was soon escorted to a Dynamo sporting-goods store, where I bought a pair of skis and bindings. The store did not undertake to mount the bindings, but this was readily done in the UFTI machine shop. On Sundays we did some cross-country skiing. The nearest mountain to Kharkov was some thousand miles away, in the Caucasus. There was a mountaineering club in Kharkov, and I heard of expeditions in past years to the Altai Mountains in Central Asia, but none of this was going on in my time. In late spring and summer a pick-up truck equipped with benches took off for swimming parties to the banks of the Donets river. There were occasional parties of dancing and singing, involving both the scientists and the technicians of the UFTI. These were enlivened by amateur productions of Anton Chekhov’s one-act plays. These are comic masterpieces, very different from the full-length dramas, such as The Three Sisters or The Cherry Orchard, which are better known outside of Russia. There were political events that affected the whole of Soviet society. The “Stalin Constitution” was announced in a radio address by Joseph Stalin in May 1936. This format was itself innovative. People were bemused by his Georgian accent. Even more striking was the completely democratic phraseology; it was such a departure from the Leninist-Stalinist tradition that it took everyone by surprise. A “wait-and-see” attitude was the best that could have been expected from skeptical observers, such as Landau and Alex Weissberg. A few days after the Constitution an ordinance on initiating human rights to replace secret-police procedures was published. This seemed even more stunning than the Constitution. Within a few months the radical change in direction of the regime turned out to be altogether fictitious. Whereas the whole country learned about the allegedly democra-

82

Laszlo Tisza

Phys. perspect.

Fig. 12. The author at the entrance to the Ukrainian Physical-Technical Institute in Kharkov, 1937. Credit: Author’s personal collection.

tic new Constitution from Stalin’s radio presentation, the reality check came to everyone through his own individual experience. Mine came soon and forcefully through the visit of a Hungarian friend who worked as an engineer in the Donets region. He visited officially in Kharkov, and called on me personally. He had an amazing story to tell. He recently ran into a colleague in the factory who summoned him to go to a meeting. It was a misunderstanding. This was not a production meeting, but a party meeting; he was not supposed to be there, but he was, and this is what he heard: the secret-police procedures were to be reinforced. It was the exact opposite of the recently publicized human-rights’ ordinance. It was not hard to guess which of the two was for real, and this was confirmed by events soon enough.

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

83

The next message came about early June. A colleague asked me: “Will you come to the abortion meeting?” “No, why should I?” I replied. “Well, you should.” It appeared that the government suggested that the legality of abortion should be abolished, but the matter was put up for discussion, and the Kharkov party secretary wrote an article in the local paper to oppose the change. This was a signal that a real debate was authorized. There was great excitement and in the evening the room was packed. A heated discussion followed and carried over for two more nights. Eventually there was a move to put the question to a vote. The chairwoman got very excited: “We are not supposed to vote!” However, the matter was out of hand and two motions were put forward: (1) Abortion should be allowed with some limitations; (2) Abortion should be forbidden with some exceptions. Motion (1) carried the day. Next morning the papers announced the news: “The population overwhelmingly accepted the criminalization of abortion.” A meeting was called at which party members who had spoken out for abortion had to apologize for their mistake. It clearly had been a social experiment: can the leadership count on the population to go along with their minor wishes? The answer was a clear NO! The next event was more serious. The old Bolsheviks Grigory Zinoviev and Lev Kamenev, who had been tried and sentenced to jail in January 1935, were retried and sentenced to death in August 1936. The stage was set for many capital sentences to follow. The scientific work described above took place at the UFTI during 1935–1936. That was a golden period during which the life of the Landau group was sheltered from political events going on outside. This splendid isolation was to end in the fall of 1936. While the UFTI was not a university, much of the Landau group and other members of the UFTI were engaged in teaching at the University of Kharkov. Quite unexpectedly, Landau was fired from his teaching job. There seems to have been tension between him and the old-fashioned faculty. This was construed as Landau being against dialectical materialism, the official religion. This was a shock for his group and they simultaneously submitted their resignations. The Ukrainian Department of Education took violent exception: This was a strike that was illegal in the socialist state; you were not supposed to “strike against yourself.” Personally I was not involved in the whole affair. At the time when teaching by the Landau group at the University was initiated, my name was submitted as part of the group, but I was immediately rejected as being a foreigner. Instead I got a teaching assignment at the local technical university where I gave a course on quantum mechanics. This arrangement suited me well; the students were better than at the University. Evgenii Lifshitz’s younger brother, the very talented Ilya Lifshitz, was among my students; I was also left out of the whole turmoil I am about to describe. The situation was whipped up into a major political issue. The “strikers” were called on the carpet in Kiev at the Commissariat of Education.31 Eventually, the strikers went back to work, and the affair was winding down. There was a New Year’s Eve celebration in the elegant apartment of Lifshitz, whose late father had been a practicing physician. In the first weeks of 1937 the circus was reopened at staff meetings at the UFTI, where Landau was openly attacked as counterrevolutionary. Landau was fed up with

84

Laszlo Tisza

Phys. perspect.

these increasingly virulent attacks. He went to Moscow and asked for Kapitza’s help, who indeed invited him to join his newly founded Institute of Physical Problems. At the next UFTI meeting, Landau quietly announced that he was resigning his position and was leaving next week for Moscow. This was a bombshell; the meeting came to a halt. Landau escaped his enemies, at least for a while. Moscow was beyond the reach of the Kharkov NKVD (the secret police). However, Landau was arrested in the spring of 1938 and was freed only a year later thanks to the direct intervention of Kapitza. Meanwhile in Kharkov there was a rash of arrests at the UFTI, among others Alexander Weissberg, Fritz Houtermans, and Lev Schubnikow. Alex played a central role among the foreigners at the UFTI. His wife, Eva Stricker, was the niece of Michael Polanyi, a chemist who was Wigner’s mentor when he studied chemical engineering in Berlin. As I mentioned already, during my first visit in Kharkov in May 1934 I was particularly fascinated by Alex. When he first arrived at the UFTI, the strong cryogenic work there sparked in him the idea that this line of research might be of great practical use. The gases that are the waste products of the metallurgical industry could be collected and separated into constituents at low temperatures to serve as the raw material of the chemical industry. Now that the institutional result of this insight, the OSGO (Experimental Station of Deep Cooling), was near completion, Weissberg, its motivating spirit, was removed from the scene. Martin Ruhemann, who could hardly wait to put his beloved cryogenics to practical use, was let go. With Landau leaving, I had no reason to stay on; nor was I welcome to stay. After a long wait for an exit visa, I turned to the Hungarian Legation for help. End of June 1937 I arrived in Budapest. Having the protection of a foreign Legation was probably the reason that I was allowed to leave the country. The other foreigner to get away was Martin Ruhemann; although he was an ethnic German, he had for some reason a British passport, and was not arrested either. At the time of the Hitler-Stalin pact of August 23, 1939, Houtermans and Weissberg were handed over to the Gestapo. Houtermans, not being Jewish, was allowed to do nuclear physics in Germany. The Jewish Weissberg knew that his outlook was not as good; he jumped train in Poland, joined the Polish underground, and survived to go into business in London after the war. The truly tragic outcome was Shubnikov’s execution. He was an excellent experimental physicist and an unusually fine person. Let me mention here that before leaving the Soviet Union, I went to Odessa to explore, in vain, a possible employment. I met there my colleague Guido Beck whom I knew from Leipzig, but who was now at the University of Kiev, and had previously arranged for me a visiting lectureship there for a month in electrodynamics. Now we spent a pleasant weekend by boat to Sebastopol, from where we took a taxi to Yalta. The bulk of the trip was through arid country, like the American West, up the mountain to the Baidarsdkie Vorota and from there down through a subtropical forest to Yalta. That was a nice closing episode of my stay in the Ukraine. Shortly thereafter I met Guido in Paris; he left France for Portugal in 1942 and the following year emigrated to Argentina.32 We were in occasional correspondence. Just about three years had passed since my introductory meeting in May 1934 at the UFTI. What a change from my innocent optimism to the witnessing of total political

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

85

corruption! Whereas I had no hesitation to abandon all confidence in the regime, there was a long search ahead, in the course of which I asked myself: what went wrong? I was unwilling to confine all the blame to Stalin, and was intent to find the flaw in the theory. It would take me years to deal with this puzzle. Yet, on the other hand, I had received a solid apprenticeship, and I was prepared for both research and teaching.

Paris and Superfluidity Frenkel: I know that the next period of your life led to your involvement with superfluidity and to the invention of the two-fluid theory. How did this come about? Tisza: This is a simple question with a complicated answer. The main features of the two-fluid theory emerged over a sleepless night, but this could not have happened without the input extended over two years. I have explained how Landau influenced me toward a creative use of thermodynamic methods. The identification of an appropriate problem emerged for me in interaction with Fritz London. Frenkel: Had you known London already? Tisza: No, I hadn’t known him. Back from Kharkov in Budapest at the end of June 1937, I got in touch with my old friend Teller, who asked Leo Szilard to write to Fritz London on my behalf. London had recently moved from Oxford to Paris, where he worked in the Institut Henri Poincaré.33 He was maître de recherche à la Caisse Nationale de Recherches Scientifiques (senior researcher at the National Foundation of Scientific Research). This was an elegant position, but he had not much contact with French physicists. He was eager to interact with me, and I with him. I still have the copy of the letter I wrote to him from Budapest. He suggested that I go to Paris to attend the Congrès du Palais de la Découverte in September 1937. This was the last “hurrah” of the interaction of the French scientific community with the government of the Front Populaire. London referred me to Edmond Bauer, who granted me a small scholarship and an association with the Langevin laboratory at the Collège de France, where he was associate director. I was to act as a consultant in thermodynamics. I developed close relations with the colleagues there, particularly with Michel Magat [figure 13], a Russian-born physical chemist who had a French wife and was firmly rooted in the local setting. We soon became close friends. The lab was oriented toward the physicochemical properties of materials. I was consultant for them in the interpretation of many of their experiments. Frenkel: You said that London arrived in Paris from Oxford. Was he an Englishman? Tisza: No, he was an assimilated German Jew. He left Germany and immigrated to England in 1933 [figure 14]. In Oxford he got into touch with Franz Simon, later Sir Francis. Until that time he worked in quantum chemistry, but under the influence of Simon, who was an outstanding experimental physicist with deep theoretical insight, London quite suddenly switched to cryogenics. This was a new period in his life, I think

86

Laszlo Tisza

Phys. perspect.

Fig. 13. Colleagues at the Collège de France, 1938 (left to right): Michel Magat, Edmond Bauer, Mlle. Ochs (a junior coworker), the author. Credit: Author’s personal collection, photograph by Paul Gross, Duke University.

a very refreshing one. He felt that in quantum chemistry the Americans like John Clarke Slater, Linus Pauling, and Robert S. Mullikan took over the field, and that the Heitler-London theory of molecular bonding could not compete with their more flexible approach. Frenkel: Why did he move to Paris? Tisza: In England he had a grant from the Imperial Chemical Industries, which was not renewed. This was a painful surprise to him; there might have been some misunderstanding about the scope of the original offer. Fortunately, he got a suitable position in Paris. From there, in 1939, just at the outbreak of the Second World War, he went to the United States, accepting a call from the Chemistry Department of Duke University. My contact with London soon turned into friendship. I was glad to find a new mentor (he was about six years older than I), and he was glad to have someone with whom to discuss the cryogenic interests he recently acquired in Oxford. As soon as we met in Paris, he gave me the booklet on the macroscopic theory of superconductivity he had published in 1937.34 He enjoyed explaining the details to me. I found his interests very congenial and him to be personable compared to Landau, who was much less approachable. I may mention in this context that my two other mentors, Teller and Landau, were a year younger than I. They were born in 1908, and so was Weisskopf, the senior theorist at MIT.

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

87

Fig. 14. Erwin Schrödinger and Fritz London in Berlin in 1928. Credit: Author’s personal collection.

After superconductivity, London explained to me what Simon and he had done on liquid helium. Of course not on superfluid helium, which was not yet discovered; but it was already known that liquid helium had the unique property of not crystallizing on the approach to absolute zero, unless the pressure is more than 25 atmospheres. Simon proved through ingenious thermodynamic reasoning that this unusual property is brought about by a high quantum-mechanical zero-point energy.35 London explored an atomic model to support this conclusion.36 All of this genuinely interested me, and I found it very much in harmony with the thinking I acquired from Landau. It was an amazing coincidence that London’s recent cryogenic interests matched so well with the research program I made up under Landau’s influence. However, it took some time before I became aware of this. It never ceased to puzzle me why Landau did not mention the Oxford results of Simon and London. Frenkel: Could you give some details of Simon’s and London’s work on liquid helium? Tisza: I would like to come back to this later; let me now move towards superfluidity as it came to our attention. I felt that my acclimatization in Paris was proceeding well enough. This process was accelerated by events in the coming months. Two important factors were responsible for the burst of my scientific activities during 1938-1939: The experimental discovery of superfluidity in liquid helium in January 1938, generating a deep perplexity in both of us, and London’s surprising idea on the role of the Bose-Ein-

88

Laszlo Tisza

Phys. perspect.

stein condensation to account for the specific-heat anomaly of liquid helium. Our subsequent theoretical advance was triggered by this idea. The status of the Bose-Einstein condensation went through many ups and downs; its invocation to unravel the puzzles of liquid helium calls for a sketch of some of the historical events that culminated at the time of my narrative. S.N. Bose entered the picture in June 1924 when he asked Einstein’s help to have his manuscript published. Publication had been refused by the Philosophical Magazine. Bose’s objective was to improve the light-quantum statistics introduced by Einstein in his famous March 1905 paper.37 Einstein’s statistics, which was in fact Boltzmann’s statistics applied to light quanta, led to the Wien distribution law, and Bose constructed a light-quantum statistics that yielded the experimentally favored Planck distribution. Bose achieved this improvement by modifying Boltzmann’s statistical counting method without, however, being aware of the nature of this modification, or even of having tampered with the classical Boltzmann procedure. Einstein acted fast. He translated Bose’s paper from English to German and ensured its publication in the Zeitschrift für Physik.38 He also went a long way in identifying Bose’s intuitive modification of Boltzmann statistics. Bose replaced the Boltzmann statistics of particles with the statistics of cells, and Einstein recognized that this meant abandoning the distinguishability of identical particles in a quantum-mechanical many-body system. Moreover, he sent off for publication a paper of his own in which he applied Bose’s light-quantum statistics to an ideal gas with molecules of finite rest mass.39 He noted that this change of statistical method ensured the validity of the Nernst principle for the Bose gas, whereas that principle failed for the Boltzmann gas. Einstein was on to something important, but he failed to see through all the intricacies of the novel situation. Here are the developments as they are actually documented. The paper by Bose and the follow-up by Einstein were criticized in a letter by Ehrenfest to Einstein, as reported in a second paper by Einstein.40 I invoke Einstein’s words, as quoted by Abraham Pais in his biography of Einstein: “the quanta and molecules, respectively, are not treated as statistically independent, a fact that is not particularly emphasized in our papers.” 41 Einstein admitted that this objection of Ehrenfest was justified, and he added that the differences between the Boltzmann and the Bose-Einstein counting “express indirectly a certain hypothesis on a mutual influence of the molecules which for the time being is of a quite mysterious nature.” 42 Pais continues: “With this remark, Einstein came to the very threshold of the quantum mechanics of identical particle systems. The mysterious influence is, of course, the correlation induced by the requirement of totally symmetric wave functions.” 43 Einstein indeed came to this threshold, but he did not cross it. Nor could he have been expected to, since the “totally symmetric wave functions,” although not many years in the future, emerged only after a considerably involved conceptual evolution. Einstein recognized that the Bose-Einstein statistics implied a strange coupling of undulatory entities that is nowadays called “entanglement,” considered by Schrödinger the most characteristic aspect of quantum mechanics. It means in essence that two (or more) quantum particles may be in a superposition of different, strictly correlated states. This can happen even if they are at macroscopic distances from each other and do not interact in the conventional sense. Within classical mechanics this would be a

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

89

thoroughly unacceptable feature; by contrast, atomic and molecular entangled states are part and parcel quantum mechanics. Familiar examples are the spin-singlet states formed by two electrons in an atom. It would have been conceivable for Einstein to take a positive view of the emerging recognition that quantum theory deals with indistinguishable particles. Might this not foreshadow the ability to provide a mathematical theory of chemistry? In this discipline the nondistinguishability of particles emerges from the nature of the chemical processes. That the mechanical and chemical particles differ could have been inferred from the well-known rule that, in order to yield the correct entropy, the entropy based on Boltzmann’s kinetic theory had to be corrected by the factor 1/N!, where N is the total number of particles. This correction was built into the Bose counting. Einstein constructed the intricate formalism of the Bose-Einstein condensation, but failed to recognize the supreme appropriateness of the Bose-Einstein statistics to play the role of quantization as a transformation of the mechanical particle concept into the chemical one. This could have explained the puzzle that Einstein established the BoseEinstein condensation six months before Heisenberg injected the notion of quantum mechanics into the body of atomic physics. Had Einstein taken his own insights more seriously, this would have achieved the most rational introduction into the quantum world. Unfortunately, the experimental verification of the existence of the Bose-Einstein condensation was out of reach at the time when the theory was born; it was achieved in a series of experiments from 1995 onward. There were other important manifestations of this alternative history. Following the publication of the Bose-Einstein statistics as the first instance of quantum statistics, a second soon followed, the Fermi-Dirac statistics. It is interesting that Wigner wrote a paper suggesting that pairs of fermions form a boson. For some reason he published this paper in a Hungarian version. As a consequence I had the opportunity to report on this paper in Heisenberg’s seminar. The same theorem also appeared in a more accessible paper by Ehrenfest and J. Robert Oppenheimer.44 The relation of the two kinds of statistics was for a while mysterious, until George E. Uhlenbeck [figure 15] in his seminal thesis developed a systematic and comprehensive presentation of both versions of quantum statistics and their relation to the classical Boltzmann statistics.45 However, this important paper also launched a misconception. It claims that the Bose-Einstein condensation is based on a mathematical error. Some mathematicians call a proposition that sounds plausible, although it is incorrect, a “folk theorem.” Such a folk theorem is the proposition, upheld by Uhlenbeck, that “the limit function of a sequence of continuous functions is continuous.” The correct statement is that the continuity of the limit function is assured only if the convergence of the sequence of functions is uniform. Uhlenbeck’s thesis was the first authoritative monograph on quantum statistics, and the unfounded rejection of Bose-Einstein condensation by him was not challenged for ten years. A break in the dismissal of the Bose-Einstein condensation was triggered somewhat indirectly at the Van der Waals Centenary Conference in November 1937 in Amsterdam, where Max Born presented an improved version of Joseph Mayer’s theory of the condensation of the van der Waals gas.46 This event was the sensation of the confer-

90

Laszlo Tisza

Phys. perspect.

Fig. 15. George E. Uhlenbeck, Hendrik A. Kramers, and Samuel A. Goudsmit in the late 1920s. Credit: American Institute of Physics Emilio Segrè Visual Archives, Goudsmit Collection.

ence, as I heard from Fritz London on his return to Paris: “This young American chemist [Mayer] did not know that this cannot be done, and he did it!” The discontinuity of phase equilibrium that Mayer claimed to have obtained from rigorous statistical mechanics violated the same folk theorem that Uhlenbeck had invoked ten years earlier against Bose-Einstein condensation, according to which the partition sum of analytic functions cannot yield the phase discontinuity, evident from experiment and accounted for by thermodynamics. There was a lively and inconclusive discussion whether or not to accept Mayer’s claim and abandon the cautionary view. Kramers, the chairman of the session, suggested that a discontinuity might emerge from the partition sum in the thermodynamic limit as the number of particles N and volume V tend to infinity at constant density N/V. Kramers put the question to a vote. The parties were at first evenly divided, but the suggestion was soon to be generally accepted. This was a useful suggestion, but I would prefer a somewhat more general formulation and introduce uniform and nonuniform convergence into the vocabulary of physics. Many an inconclusive argument can be resolved in terms of this subtlety. In his report on the conference, London did not mention to me the Bose-Einstein condensation, although there is evidence that the analogy between the two types of

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

91

condensation was discussed. Boris Kahn and Uhlenbeck soon published a theory to subsume both condensations under the same formalism.47 Thus, just before the discovery of superfluidity Uhlenbeck implicitly withdrew his critique of the Bose-Einstein condensation. The superfluidity of helium was discovered independently by Kapitza in Russia and by John F. Allen and A. Donald Misener in England, whose papers appeared in the same January 1938 issue of Nature.48 Kapitza sent in his paper first. The editor of Nature knew that Allen and Misener had been working for a while on superfluidity. He sent Kapitza’s manuscript to Allen, and encouraged him to send in his results. No one doubted that the results of Allen and Misener were independent; they just needed some prodding to publish. Frenkel: Could you say a few words about these experiments? Tisza: They have shown that below the so-called λ-point temperature, which at normal pressure equals 2.19 degrees kelvin, liquid helium penetrates and flows easily through slits and leaks (“superleaks”), which at higher temperatures are completely tight, not only for liquid, but even for gaseous helium. Frenkel: You learned that superfluidity exists from that issue of Nature? Tisza: Yes. The papers of Kapitza and of Allen and Misener came to us as exciting and welcome events. We were stunned. To London superfluidity was reminiscent of superconductivity, another macroscopic quantum state. His next thought was the SimonLondon quantum delocalization of the atoms in liquid helium, caused by the large zero-point energy. He ventured that the atoms in liquid helium may have “gas-like” properties, similar to those of Bloch’s electrons in metals. He suggested that I examine this idea for helium in terms of the Fermi-Dirac statistics. He came to see me at my hotel room where I nursed a cold, and asked for my results. Of course, I had none. Then he said: “Look at this!” and he showed me a calculation of the specific heat of an ideal Bose-Einstein gas. He got a discontinuous specific heat. As a matter of fact, he made a mistake in the calculation. After correction there was a kink rather than a discontinuity in the specific heat. In Ehrenfest’s language this was not a second, but a third-order phase transition. I told him this is wonderful, this was the right way to proceed; the Fermi-Dirac gas idea was nonsense. So we shifted gears and decided to go ahead with the Bose-Einstein calculation. I do not believe that Fritz would have maliciously sent me on a wild goose chase; I am sure that the afterthought of the November conference concerning the Bose-Einstein statistics came to him only after he asked me to deal with the fermionic Bloch states. For a while nothing much happened, and we were rather clueless how to proceed. Two or three weeks later there was another paper in Nature by Allen and Harry Jones.49 They immersed a capillary in a superfluid helium bath. One end of the capillary continued into a vertical tube leading to the surface of the bath. With the help of a flashlight the capillary was slightly heated. The aim of the experiment was to study the heat conductivity of liquid helium. Quite unexpectedly, as a result of the heating, a

92

Laszlo Tisza

Phys. perspect.

flow of helium rushed though the capillary and tube and flew spectacularly high, a few centimeters above the surface of the bath. This phenomenon became known as the fountain effect. It left us in a shock, because, on the one hand, these experiments indicated that below the λ-point liquid helium can flow without any friction with practically vanishing viscosity, but, on the other hand, the viscosity measurements carried out in Toronto and in Leiden with the method of oscillating disks had shown a nonvanishing viscosity. The following weekend we went on a hike in the Bois de Verrière. By now the area is strongly developed, but at that time it was a picturesque excursion site. Our wives talked to each other while Fritz and I pondered our agenda. We concluded that the fountain effect was so crazy that we cannot fail to find a solution. For me there followed a sleepless night, and by morning the rough outline of the two-fluid idea was in place. My idée fixe was that if we have a single fluid, the new observations cannot be reconciled with the existing measurements of the viscosity by the method of oscillating disks. I came to the conclusion that the only way to resolve this contradiction was the radical idea that passing the λ-point into what is called helium II, liquid helium cannot continue as a homogeneous liquid. It has to consist of two components, one normal, the other one superfluid, each having its own velocity field. With decreasing temperature the fraction of the superfluid component increases. In the rotating-disk experiment the viscosity of the normal component manifests itself, while in the fountain effect and in the capillary-flow experiments the superfluid component becomes dominant. What is the meaning of the term “superfluid”? Most of my efforts went into giving an intelligible answer to this question. Superfluid is something negative: the normal viscosity mechanism is inoperative. It was an important thought that there are in general two mechanisms responsible for the viscosity in fluids. One is the kinetic viscosity found also in nearly ideal gases, coming about by transport of momentum; another is an activation mechanism, sometimes called the dynamic liquid-type viscosity.50 In order to explain the superfluidity of helium, we have to rationalize the absence of both mechanisms. The absence of the dynamic viscosity was taken care of by the SimonLondon idea of the large quantum-mechanical zero-point energy preventing the atoms from settling down at the minima of the potential energy. This can be taken as a rational definition of the quantum liquid that was markedly different from that of Landau. Whereas Landau explained superfluidity in terms of the excitation spectrum, according to London the important feature was the property of the ground state. I accepted London’s view that the loosened-up structure of the fluid rendered plausible a certain measure of gas-like translation and the invocation of Bose-Einstein condensation. The coherence of the Bose-Einstein ground state is a justification for the vanishing of the kinetic viscosity. It was apparent to me that this interpretation of the two-fluid concept would provide a ready framework for describing the experiments that appear paradoxical in the language of traditional hydrodynamics. Next morning I proudly reported my first contribution to our joint work to London. Alas, he was outraged. From the distance of sixty years it is easy to assess our disagreement. I considered myself as London’s disciple and collaborator. I agreed with

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

93

him that liquid helium is a macroscopic quantum state, and also in the relevance of Bose-Einstein condensation. However, I went beyond, as my analysis of the experiments called for the two-fluid concept, and I assigned to the viscous and the superfluid components their own velocity fields. Here London demurred. He felt that I arbitrarily advanced the properties needed without doing any honest work. He resented that I gained a jump on him by lowering the standards of theorizing, and he refused to continue our collaboration. I understood his feelings, but I thought that I correctly sized up the unusual situation. Six years later London was to change his mind, and came around to my view. Meanwhile, he published his interpretation of the λ-singularity as a manifestation of Bose-Einstein condensation in a note in Nature,51 without entering into the discussion of the hydrodynamic effects. True, for the moment all I produced was not in terms of received concepts of physics, and lacked in mathematical rigor. However, I felt that no honest work would do any good within conventional hydrodynamics; I knew that a new hydrodynamics was to come. While I was defeatist about my ability to establish it, I thought that my analysis of the problem was already useful for those struggling with apparently incoherent experiments. No such people were in Paris at the time, but Simon and Nicholas Kurti repeatedly spent weeks there in order to work with the big magnet of the Bellevue Observatory. Kurti was an old friend; my crazy ideas percolated to Oxford and Cambridge and aroused interest. I decided to send off a note to Nature with the prediction of the inverse of the thermomechanic effect.52 Whereas in the fountain effect heating produces flow, in the inverse effect flow produces a temperature difference. This was readily verified by John Daunt and Kurt Mendelssohn.53 My paper created quite a commotion. The experimentalists felt it was just what they needed; the theorists were scandalized. They were unimpressed by an explanation of perplexing experiments in terms of unorthodox assumptions. The next event was a paper by Heinz London who gave a thermodynamic derivation of the fountain effect.54 He referred to my paper but not to that of Fritz. For this he was scolded by his brother. However, his paper was ambiguous. It did not necessarily endorse my superposed volume currents, and Fritz interpreted the superflow hinted at by his brother as a surface effect, reaffirming his opposition to me. This paper appeared in Nature in October. In my recollection I reacted to it before the small lowtemperature conference in London in early July 1938. Heinz must have sent his manuscript sometime in the spring to his brother, who showed it to me. Heinz’s paper gave me a jolt. I realized that I should and could have written this paper myself, except for my lack of self-confidence. That I did not expect to produce a flawless theory should not have precluded my groping toward an expedient one; this is what I decided to do at this point. Specifically, I proposed to search for an observable implication to decide between my volume currents and Fritz’s surface currents. I knew that Leonhard Euler had derived his hydrodynamics by concentrating the mass of a volume element into a point mass to which Newtonian mechanics was applied. I proceeded to replace the mass of the volume element by two point masses, each with its own velocity field. Next I remembered from Landau’s theorminimum that the linearization of the Euler equation leads to the wave equation of sound propaga-

94

Laszlo Tisza

Phys. perspect.

tion. In the two-fluid context I readily arrived at two wave equations, one for pressure and one for temperature, the latter with a strongly temperature-dependent velocity of propagation. I was happy with this result and presented it at the small low-temperature conference in London. I even proposed an experimental test for the propagation of the temperature waves by immersing a paramagnetic salt in helium and exposing it to an alternating magnetic field. This was indeed performed many years later, but nothing happened in the West before and during the war. Frenkel: Why are you pointing out the West? Did something happen in the East? Tisza: Yes, I am coming to this part of the story shortly. For the time being I would like to go on with my doings in 1938–1939. I published my two-fluid hydrodynamics including the temperature waves still in 1938 in two notes in the Comptes rendus of the Paris Academy of Sciences.55 These papers were written unashamedly in an ideal-gas language. Actually, I was ashamed. I knew that Landau had disapproved of treating interacting systems as ideal gases. He used the term “quantum liquid” for systems of interacting particles, the wave function of which cannot be factorized into single-particle functions. I think he was mainly influenced by Niels Bohr’s theory of the compound nucleus published in February 1936.56 In contrast to most people, Landau talked even of metal electrons as an electron liquid. Landau’s technique of dealing with the situation was to expand the energy near the ground state in terms of quasiparticles. He developed a real virtuosity in getting practical results from this method, which in condensed-matter physics he considered greatly superior to the use of independent particles. I had the intention to bring to bear Landau’s method to the helium problem, but the severe limitation of length of the Comptes rendus notes precluded inclusion of such subtleties into this publication. I immediately started to write a two-part paper for the Journal de Physique et le Radium, where no such limitations applied. I submitted it in 1939 and it appeared in 1940.57 The highlight of the paper was the prediction of temperature waves, but expressed in Landau’s exciton language. Allan Griffin wrote me some time ago that he finds this paper impressive even today and wondered whether I would translate it into English. I think the paper made some positive contributions at the time. I tried to integrate the concepts of quantum liquid of London and of Landau. However, although I did my best to adapt Landau’s quasiparticle concept to the London-Tisza theory, my “best” did not fully measure up to Landau’s theory produced two years later. I would not think of republication at this late date, as occasionally suggested. It is unfortunate that my paper became known, and not very widely at that, only after the war. I saw it first in 1945, while it seems to have come to Landau’s attention already in 1943! Meanwhile, in 1941 Landau overtook me with his seminal theory of superfluidity.58 This two-part paper is the best that I produced on liquid helium. Because of the war situation it received no attention whatever at the time, and my prediction of the temperature wave was not checked experimentally. Ironically, my paper commanded interest only after London called attention to it as a partial anticipation of Landau’s theo-

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

95

ry. A comparison of the two theories became desirable. All this happened about two years later, after I had moved from France to the United States.

Acknowledgment I thank Roger H. Stuewer for his thoughtful and careful editorial work on my interview with Andor Frenkel.

References 1 Helmut Hasse, Höhere Algebra. I. Lineare Gleichungen. II. Gleichungen höheren Grades (Berlin and Leipzig: Walter de Gruyter, 1926–1927). 2 Umberto Cisotti, Idromeccanica Piana (Milan: Libreria Editrice Politechica, 1921–1922). 3 Paul Alexandroff [Pavel S. Alexandrov], Einfachste Grundbegriffe der Topologie. Mit einem Geleitwort von David Hilbert (Berlin: Julius Springer, 1932). 4 Max Born and Pascual Jordan, Elementare Quantenmechanik (Zweiter Band der Vorlesungen über Atommechanik) (Berlin: Julius Springer, 1930). 5 W. Pauli, “Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik,” Zeitschrift für Physik 36 (1926), 336–363; reprinted in Wolfgang Pauli, Collected Scientific Papers, ed. R. Kronig and V.F. Weisskopf. Vol. 2 (New York, London, Sydney: Interscience Publishers, 1964), pp. 252–279. 6 M. Born, “Kritische Betrachtungen zur traditionellen Darstellung der Thermodynamik,” Physikalische Zeitschrift 22 (1921), 218–224; idem, 249–254; idem, 282–286; reprinted in Max Born, Ausgewählte Abhandlungen. Mit einem Verzeichnis der wissenschaftlichen Schriften. Herausgegeben von der Akademie der Wissenschaften in Göttingen. Erster Band (Göttingen: Vandenhoeck & Ruprecht, 1963), pp. 161–176. 7 V. Weisskopf and E. Wigner, “Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie,” Zeit. f. Phys. 63 (1930), 54–73. 8 D. Hilbert and S. Cohn-Vossen, Anschauliche Geometrie (Berlin: Julius Springer, 1932). 9 R. Courant and D. Hilbert, Methoden der mathematischen Physik. Erster Band (Berlin: Julius Springer, 1924). 10 Walter Elsasser, “Bemerkungen zur Quantenmechanik freier Elektronen,” Die Naturwissenschaften 13 (1925), 711. 11 Pim Huijnen and A.J. Kox, “Paul Ehrenfest’s Rough Road to Leiden: A Physicist’s Search for a Position, 1904–1912,” Physics in Perspective 9 (2007), 186–211. 12 P. and T. Ehrenfest, “Begriffliche Grundlagen der statistischen Auffassung in der Mechanik,” Encyklopädie der mathematischen Wissenschaften. Vol. 4, Part 2 (Leipzig: B.G. Teubner, 1912), 3–90; reprinted in Collected Scientific Papers, ed. Martin J. Klein (Amsterdam: North-Holland, 1959), pp. 213–300; translated by Michael J. Moravcsik as The Conceptual Foundations of the Statistical Approach in Mechanics (Ithaca: Cornell University Press, 1959). 13 Martin J. Klein, Paul Ehrenfest. Vol. 1. The Making of a Theoretical Physicist (Amsterdam and London: North-Holland and New York: American Elsevier, 1970). 14 B.L van der Waerden, Die Gruppentheoretische Methode in der Quantenmechanik (Berlin: Julius Springer, 1932). 15 E. Teller and L. Tisza, “Zur Deutung des ultraroten Spektrums mehratomiger Moleküle,” Zeit. f. Phys. 73 (1932), 791–812. 16 E. Teller, “Theorie der langwelligen Molekülespektren,” in Hand- und Jahrbuch der Chemischen Physik. Band 9. Die Spektren Entstehung und Zusammenhang mit der Struktur der Materie. Abschnitt II (1934), pp. 43–160. 17 Sir William Crookes, “[Presidential] Address,” in Report of the Sixty-Eighth Meeting of the British Association for the Advancement of Science held at Bristol in September 1898 (London: John Murray, 1899), pp. 3–38; especially pp. 14–19.

96

Laszlo Tisza

Phys. perspect.

18 Silvan S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (Princeton: Princeton University Press, 1994), pp. 156–205. 19 L. Tisza, “Zur Deutung der Spektren mehratomiger Moleküle,” Zeit. f. Phys. 82 (1933), 48–72. 20 L. Landau, “Diamagnetismus der Metalle,” Zeit. f. Phys. 64 (1930), 629–637; reprinted in Collected Papers of L.D. Landau, ed. D. ter Haar (New York, London, Paris: Gordon and Breach, 1965), pp. 31–38. 21 M. and B. Ruhemann, Low Temperature Physics (Cambridge: Cambridge University Press, 1937). 22 P. Ehrenfest, “Phasenumwandlungen in üblichen und erweiterten Sinn, classifiziert nach den entsprechenden Singularitäten des thermodynamischen Potentiales,” Koninklijke Akademie van Wetenschappen te Amsterdam. Proceedings of the Section of Sciences 36 (1933), 153–157 [Communications from the Kamerlingh Onnes Laboratory of the University of Leiden 20, Supplement 75b (1933), 8–13; reprinted in Collected Scientific Papers (ref. 12), pp. 628–632. 23 H.A. Bethe, “Statistical Theory of Superlattices,” Proceedings of the Royal Society [A] 150 (1935), 552–575; reprinted in Selected Works of Hans A. Bethe With Commentary (Singapore, New Jersey, London, Hong Kong: World Scientific, 1997), pp. 247–270; R. Peierls, “Statistical Theory of Superlattices with Unequal Concentrations of the Components,” Proc. Roy. Soc. [A] 154 (1936), 207–222; reprinted in Selected Scientific Papers of Sir Rudolf Peierls With Commentary, ed. R.H. Dalitz and Sir Rudolf Peierls (Singapore, New Jersey, London, Hong Kong: World Scientific and London: Imperial College Press, 1997), pp. 182–197. 24 Pierre Weiss, “L’Hypothèse du champ moléculaire et la propriété ferromagnétique,” Journal de Physique 6 (1907), 661–690. 25 W.L. Bragg and E.J. Williams, “The Effect of Thermal Agitation on Atomic Arrangement in Alloys,” Proc. Roy. Soc. [A] 145 (1934), 699–730; idem, “II,” ibid. 151 (1935), 540–566. 26 L. Landau, “Zur Theorie der Phasenumwandlungen. I,” Physikalische Zeitschrift der Sowjetunion 11 (1937), 26–47; idem, “II,” ibid., 545–555; published originally in Russian in the Zhurnal Eksperimental-noi i Teoreticheskoi Fiziki 7 (1937), 19–32; idem, “II,” ibid., 627–632; translated and reprinted together as “On the Theory of Phase Transitions,” in Collected Papers of L.D. Landau (ref. 20), pp. 193–216. 27 Alexander I. Akhiezer,”Recollections of Lev Davidovich Landau,” Physics Today 47 (June 1994), 35–42; on 39. 28 L. Tisza, “Transport Phenomena in Helium II,” Nature 141 (1938), 913. 29 Laszlo Tisza, Generalized Thermodynamics (Cambridge, Mass. and London: The M.I.T. Press, 1966). 30 W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie der Positrons,” Zeit. f. Phys. 98 (1936), 714–732; reprinted in Werner Heisenberg, Collected Works, ed. W. Blum, H.-P. Dürr, and H. Rechenberg. Series A/Part II. Original Scientific Papers (Berlin, Heidelberg, New York: Springer-Verlag, 1989), pp. 162–180; V. Weisskopf, “Über die Elektrodynamik des Vakuums auf Grund der Quantentheorie des Elektrons,” Mathematisk-Fysiske Meddelelser Det Kgl. Danske Videnskabernes Selskab 14, Nr. 6 (1936), 1–39. 31 Akhiezer, “Recollections of Landau” (ref. 27), p. 40. 32 Peter Havas, “The Life and Work of Guido Beck: The European Years: 1903–1943,” in H. Moysésg Nussenzveig and Antonio Augusto Passos Videira, ed., Guido Beck Symposium, Rio de Janeiro August 29–31, 1934 [Anais da Academia Brasileira de Ciências 67, Supl. 1 (1995), pp. 11–36]; Arturo López Dávalos and Norma Badino, “Guido Beck in Argentina 1943–1951,” in ibid., pp. 67–72; Augusto José dos Santos Fitas and António Augusto Passos Videira, “Guido Beck, Alexandre Proca, and the Oporto Theoretical Physics Seminar,” Phys. in Perspec. 9 (2007), 4–25. 33 For London’s movements in Europe and emigration to the United States, see Kostas Gavroglu, Fritz London: A scientific biography (Cambridge, New York, Melbourne: Cambridge University Press, 1995). 34 F. London, Une Conception Nouvelle de la Supra-Conductibilité (Paris: Hermann & Cie, 1937); based in part on F. and H. London, “The Electromagnetic Equations of the Supraconductor,” Proc. Roy. Soc. [A] 149 (1935), 71–88. 35 F. Simon, “Behaviour of Condensed Helium near Absolute Zero,” Nature 133 (1934), 529. 36 F. London, “On Condensed Helium at Absolute Zero,” Proc. Roy. Soc. [A] 153 (1936), 576–583.

Vol. 11 (2009)

Adventures of a Theoretical Physicist, Part I: Europe

97

37 A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik 17 (1905), 132–148; reprinted in The Collected Papers of Albert Einstein, ed. John Stachel. Vol. 2. The Swiss Years: Writings, 1900–1909 (Princeton: Princeton University Press, 1989), pp. 150–166; translated by Anna Beck, idem, pp. 86–103. 38 [S.N.] Bose, “Plancks Gesetz und Lichtquantenhypothese,” Zeit. f. Phys. 26 (1924), 178–181. 39 A. Einstein, “Quantentheorie des einatomigen idealen Gases,” Sitzungsberichte der Preussischen Akademie der Wissenschaften. Physikalisch-Mathematische Klasse (1924), 261–267. 40 A. Einstein, “Quantentheorie des einatomigen idealen Gases. Zweite Abhandlung,” Sitz. Preus. Akad. Wissen. Phys.-Math. Kl. (1925), 3–14. 41 Quoted in Abraham Pais, ‘Subtle is the Lord…’: The Science and the Life of Albert Einstein (Oxford: Clarendon Press and New York: Oxford University Press, 1982), p. 430. 42 Quoted in ibid. 43 Ibid. 44 P. Ehrenfest and J.R. Oppenheimer, “Note on the Statistics of Nuclei,” Physical Review 37 (1931), 333–338; reprinted in Collected Scientific Papers (ref. 12), pp. 597–602. 45 G.E. Uhlenbeck, “Over statistische methoden in de quantum theorie,” Ph.D. Thesis, University of Leiden (‘s Gravenhage: Martinus Nijoff, 1927). 46 Max Born, “The Statistical Mechanics of Condensing Systems,” Physica 4 (1937), 1034–1044; reprinted in Ausgewählte Abhandlungen. Erster Band (ref. 6), pp. 699–709. 47 B. Kahn and G.E. Uhlenbeck, “On the Theory of condensation,” Physica 4 (1937), 1155–1156. 48 P. Kapitza, “Viscosity of Liquid Helium below the λ-point,” Nature 141 (1938), 74; J.F. Allen and A.D. Misener, “Flow of Liquid Helium II,” ibid., 75. 49 J.F. Allen and H. Jones, “New Phenomena Connected with Heat Flow in Helium II,” Nature 141 (1938), 243–244. 50 Fritz London, Superfluids. Vol. II. Macroscopic Theory of Superfluid Helium (New York: John Wiley and Sons and London: Chapman and Hall, 1954; reprinted New York: Dover, 1961), p. 38, Fig. 19. 51 F. London, “The λ-Phenomenon of Liquid Helium and the Bose-Einstein Degeneracy,” Nature 141 (1938), 643–644. 52 Tisza, “Transport Phenomena,” (ref. 28). 53 J.G. Daunt and K. Mendelssohn, “Transfer of Helium II on Glass,” Nature 141 (1938), 911–912. 54 H. London, “A Ponderomotive Effect associated with the Flow of Heat through Liquid Helium II,” Nature 142 (1938), 612–613. 55 Lasislas Tisza, “Sur la supraconductibilité thermique de l’hélium II liquide et la statistique de Bose-Einstein,” Comptes rendus hebdomadaries des séances de l’Académie des Sciences 207 (1938), 1035–1037; L. Tisza, “La viscocité de l’hélium liquide et la statistique de Bose-Einstein,” ibid., 1186–1189. 56 Niels Bohr, “Neutron Capture and Nuclear Constitution,” Nature 137 (1936), 344–348; reprinted in Niels Bohr Collected Works. Vol. 9. Nuclear Physics (1929–1952), ed. Sir Rudolf Peierls (Amsterdam, Oxford, New York, Tokyo: North-Holland, 1986), pp. 152–156; Roger H. Stuewer, “Niels Bohr and Nuclear Physics,” in A.P. French and P. Kennedy, ed., Niels Bohr: A Centenary Volume (Cambridge, Mass.: Harvard University Press, 1985), pp. 197–220, 362–363. 57 L. Tisza, “Sur la théorie des liquides quantiques. Application a l’hélium liquide. I,” Le Journal de Physique et le Radium 1 (1940), 164–172; idem, “II,” ibid., 350–358. 58 L. Landau, “The theory of superfluidity of helium II,” Academy of Sciences of the USSR Journal of Physics 5 (1941), 71–90; reprinted in Collected Papers (ref. 20), pp. 301–330. Department of Physics Massachusetts Institute of Technology Cambridge, MA 02139 USA e-mail: [email protected]