Tisza. A.I.Akhiezer and Laszlo Tisza in the Ukrainian Physico-Technical Institute in 1936 (Courtesy L.Tisza)

I. Introduction

I met Alexander Illich Akhiezer, for short Shura, in January of 1935 when I joined Landau's group of theoretical physics at the UFTI (Ukrainian Physico-Technical Institute) in Kharkov. For the next two years we followed a parallel course of passing the so-called "theoretical minimum" and then writing a research paper to qualify for the "candidate" degree. This is equivalent to the Ph.D. degree in Western Universities. I am therefore in a position to report my recollections of his struggle with his difficult problem: "The scattering of light by light" in Section III. Being the last surviving witness of the beginning of Shura's rich research career, I think this is the most significant contribution I can make to his memory. I should note, however, that I was not involved with this work; in fact our interests were different and we never worked together. Therefore In the next section I will sketch the working of the closely-knit Landau group as a framework in which friendly relations developed among all members. In Sec. IV I will indicate that Landau's methodology had a wide scope that let me respond to another aspect than the rest of the group.

II. Landau and his group

At the time of my arrival Landau's group consisted of Kompaneetz, E.M. Lifshitz (Zhenya), Pyatigorsky, and Alexander Illich Akhiezer (Shura). Kompaneetz had been the first on the list of Landau students, but he left soon after my arrival to rejoin Landau later in Moscow. Isaak Pomeranchuk (Chuk) was a new addition to the group arriving soon after me, while Piatigorski left the group over personal – political differences with Landau. The group was very friendly. My background was utterly different from theirs. If they were turned off by my separateness, they did not show it. At first I conversed in German. Landau or Dau as he was affectionately called was fluent in German and English; probably also in French, but that was hardly practiced in that period. If my memory is correct the linguistic ability of the group was rather good, but being in total immersion I picked up Russian surprisingly fast. I think in six months I spoke broken Russian and in twelve I qualified as fluent.

My studies in Gottingen, Leipzig and Budapest earned me a Ph.D. I had a couple of papers on the quantum mechanics of polyatomic molecules to my credit and no one suggested that I take the theoretical minimum. Yet I was aware that my training in physics was spotty. I had been a mathematics graduate student in Gottingen in 1928 and attended Max Born's first ever course on quantum mechanics. It was abstract and hard going and my understanding was rudimentary, yet I was fascinated to see rigorous mathematics applied to the real world and soon switched to theoretical physics. Gottingen offered a wide range of physics subjects, but all this amounted to a not quite adequate training. I wisely decided now to take this second chance and to avail myself of the famous Landau training. I announced my candidacy for the exams. It was somewhat delicate to join a much younger group, but they were very nice about it. My self-esteem was helped by the fact I made a small contribution to the theoretical minimum. Landau explained the absence of group theory by declaring it too complicated to be useful. After I presented my thesis to him, he added "group characters" to his syllabus.

We all admired and adored Landau, and this was obviously the glue that made a coherent group out of half a dozen distinct individuals. From a perspective of more than 60 years I feel like spelling out in more objective terms what made him so special. On the simplest level there was the famous Thursday Journal Seminar. Landau routinely reviewed the new arrivals in the library, a cozy room with well-provided stacks where Dau checked off 3-4 papers to distribute among members of his group to present each week to general attention and to his authoritative judgment. His instant sizing up of every paper was phenomenal. I remember that my first assignment was a paper by Lars Onsager on electrolytes. The choice of the author is noteworthy. Before his Ising model paper in 1944 made him a world famous mathematical physicist, Onsager was considered a chemist and was little known among physicists in the West. His papers on irreversible thermodynamics came to general attention only in the 1940s. By contrast, these papers were already in the theoretical minimum in the early 1930's. Dau emphasized his admiration for Onsager at a time when the latter was not yet widely appreciated. For us this judgment was the final word.

On the next deeper level came his ability to instantly answer every question you posed to him; he would start a calculation on the back of an envelope and carry it through until he had the answer. It was the greatest enjoyment for him to practice this uncommon ability.

Personally Dau considered himself a student of Niels Bohr and he visited Copenhagen more than once; they had a warm personal relationship. I do not think he ever met Einstein. Yet in style of creation this ability of starting from an idea and connecting it through a mathematical argument with an observable result reminds me of Einstein. There is of course a vast difference of scale. Einstein recognized huge gaps in existing knowledge that he filled by creating entire new disciplines. By contrast Landau took these disciplines as pragmatically given. He did not handle the new physics as paradoxical extension of tradition, but as new tools to shed light on tradition and make a new tradition explicit on an encyclopedic scale. He was fortunate to have E.M. Lifshitz to help him realize this grand design; and of course the world is fortunate that they succeeded. The two cooperated already during my time. I saw Lifshitz emerge from their sessions, holding a manuscript in form of a scroll that arose from "cut and paste" with scissors and glue before the age of electronics. Landau worked at that time with 2-3 people, but the chemistry of the two eventual authors was clearly exceptional. I do not agree with the saying: "not a word by Landau, not a thought by Lifshitz", whoever may have framed it. It was vital for Landau that his fractured remarks at the blackboard be miraculously transformed into a text. Moreover, Lifshitz knew well what he was doing and he filled gaps and corrected mistakes in Landau's presentation.

Although Lifshitz had a very special relation to Landau, the rest of us had special relations as well in ways I will attempt to describe. However, this paper is about Akhiezer. The next section is devoted to his remarkable thesis research that qualified him for the leadership role he was to assume sooner than anyone expected.

III. Scattering of light by light

P.A.M. Dirac published in 1928 a remarkable paper in which he established a relativistically invariant form for quantum mechanics. This theory was at first plagued by a curious difficulty, it called for negative energy states for the electron. Dirac later showed that instead of reversing the sign of the energy, one might reverse the sign of its charge. At first this did not improve the situation much until the discovery of the positron in 1932 changed the difficulty into a most remarkable prediction of any theory. The use of the Dirac equation still was not obvious. The 4x4 gamma matrices involved in this equation made manipulations difficult. There was an International Theoretical Conference in May 1934 at the UFTI where these questions were discussed. By 1935 pair production problems were rather standard although they remained labor-intensive.

Shura and myself completed about the same time our theoretical minimum. We turned to Landau to start us off in research. The Dirac perturbation theory was ready for use, mainly as a result of the so-called Casimir method for handling gamma matrices; we all started along this line. Shura got the assignment of the "scattering of light by light". This was a very difficult problem of fourth-order perturbation calculus. After a while he and Chuk decided to join forces. This was a fortunate decision. I vividly remember the two sitting side by side at two desks, working through long sequences of calculations. They were doing the same step independently and proceeded to the next step only after their results checked. They reminded me of the famous cartoon characters: Max und Moritz by Wilhelm Busch, two mischievous boys, one of them with a funny hairdo. This one was clearly Chuk. He was always full of ideas, be it something funny, or some important physics. Landau said that Chuk reminded him of his younger self. They had both striking ironical faces, but Dau was tall and Chuk was short and boyish. Shura had his own benign sense of humor. The two were sitting at their desks, constantly joking and cursing while doing their ghastly calculations.

Eventually they finished and convinced Dau that all was right. (See Akhiezer's paper in Physics Today of 1994.) At the time the foremost expert Victor Weisskopf was visiting and he endorsed the work as well. When the secretary received the ms for typing, the title "Scattering of light by light" provoked her perceptive remark: "do chevo zhe dodumalis!" In free translation: "What will they dream up next?"

His hard work paid off, Akhiezer passed his grueling test to be ready to become Landau's successor in due time.

IV. The other Landau

About the same time as Shura I also finished my calculation: pair production and beta decay and we earned simultaneously our Candidate's degree. My problem was a first order perturbation calculation that was much simpler than Shura's. My heart was not in this problem and it did not affect my future research; Landau's influence on me was on a different plane. Though details of my work do not belong into this paper, the fact that Landau's contributions lend themselves to division into two categories is an issue of general interest that is unduly neglected.

Simultaneously with my assigned calculation I was involved in an indirect ways with Landau's papers on second order phase transitions. I translated the Russian manuscript for publication in the "Physikalische Zeitschrift der Sowiet Union". I was fascinated; I had learned from Born that thermodynamics was beautiful but completely finished. For Landau it was a living subject. This discrepancy was the reason that I had at first difficulties passing the thermodynamic test, until Piatigorskii gave me some lecture note to let me in on the Landau philosophy.

At that time dealing with thermodynamics might have seemed to many people like turning away from the demands of the frontier. This I believe is a misjudgment. The main difficulty in our understanding of quantum mechanics is its disharmony with classical physics centered on Newtonian mechanics. All attempts failed to remedy this difficulty by adjusting quantum mechanics to canonical mechanics. I believe that Landau's approach to enrich thermodynamics and hence classical physics is an alternative move that might succeed by relating quantum mechanics to a richer classical physics. However, this structural relation between disciplines is a philosophical problem and Landau did not respect this activity. We may have to defy his words to do justice to his deeds. This is in keeping with Einstein's famous advice on understanding what the theoretical physicist is doing.

V. The End of Landau's Kharkov years

During the early times of my stay at the UFTI I asked Landau whether the repeated attacks in the party literature against relativity and particularly against quantum mechanics were of concern to him. He said all that was inconsequential because the Leader (Stalin) did not really care about dialectical materialism. He was of course essentially right; his magnum opus with Lifshitz turned around the two heretic disciplines and he was never inhibited in this context; in his group we felt rather insulated from the increasingly ominous developments in the outside world. However, the outside world started to close in on us, first by way of the University of Kharkov.

Landau and other members of UFTI did some teaching at Kharkov University. In December 1936 Landau was dismissed from his position. The conservative and not very capable faculty may not have liked his high level teaching. They alleged that the students did not understand him. This was unlikely since Landau was a great lecturer on all levels. There might have been also something ideological about it (See Akhiezer's paper quoted above.) As an outraged reaction to Landau's dismissal the entire UFTI staff resigned from their university post. They signed a formal statement, technically a "zayevlenie" to this effect. The party cell at UFTI made a great fuss out of the incident; it was a "strike against yourself" as the saying went. After a few stormy weeks the situation quieted down and there was a celebration arranged for the signers of the zayevlenie in the elegant Lifshitz home. (Zhenia's late father had been a respected physician). I was graciously included "because I would have signed had I been there!" Actually, I was fired already earlier.

Post script. A few weeks later Lifshitz found the rector of the University in the chair next to him in a barbershop. The rector told him that he was also dismissed from his job. "I can live without the University," replied Lifshitz: "so can I".

Actually, the case was not entirely closed. In a few weeks in early 1937 there was a series of Institute meetings at which Landau was viciously attacked. I don't remember details, except for two incidents that are completely sharp in my mind. The first is the berating of Landau by invoking his years in Leningrad when he formed a trio with Gamow and Ivanenko. They were the youths about town poking fun of everyone and everything. At this point Yuri Rumer got up and forcefully protested against this insinuation. "Gamow does good work, but he does it abroad and Ivanenko does nothing. Look at Landau's achievements."

The second incident was the dramatic end of the meetings. Landau got up and said he had just returned from Moscow where Kapitza invited him to direct a theoretical group to be established at the Institute of Physical Problems. He was leaving for Moscow next week. It was a bombshell. The meeting dissolved in dead silence.

VI. Epilogue

For now Landau escaped the grip of his local enemies. The enemies would regroup and Landau was arrested in April 1938. But in Moscow he had Kapitza as a powerful and courageous friend who freed him in another year. Five glorious years of Landau in Kharkov were over. There came a rash of arrests of highly respected people, some of my best friends.

Lifshitz went with Landau to the IFP. He brought the Course of theoretical physics to conclusion. Although he had written some noteworthy articles on his own the name E.M. Lifshitz conjures up only Landau-Lifshitz.

Akhiezer became the senior theorist at UFTI and then Professor at Kharkov University. He kept up the Landau standards both in quality and also in the breadth of application to all parts of theoretical physics. Landau was obviously proud of him. The same is true of Pomeranchuk.

My own case is different. I left the Soviet Union. It was a painful experience to witness the degradation of public life between 1934 and 1937. I went first to Budapest, then to Paris where I became associated with Fritz London. Landau's rejuvenation of thermodynamics and hence classical physics never left me as a guiding principle. It is exhilarating to have been part of his group. When Lifshitz visited at MIT around 1980 we continued as old friends.

In the last few years I took up e-mail contact with Shura Akhiezer. I was impressed that he overcame his poor health to continue his intense research activity. I helped him to acquire a well-deserved Soros fellowship. His passing saddens me; it leaves me the last survivor of those heady times.