by Frank Field
The title of this little essay says it all: it is a memory after approximately 67 years of a man of whom I stood properly in awe at the time and for whom I have now even greater respect. I should say at the outset that I am writing this completely from memory with no reference to texts or other historical sources. Thus there may be minor errors in dates and even facts, but so be it; I have no desire at my present advanced age to engage in the game of academic scholarship.
I was a student at Duke University in the years 1939-1947, a chemistry major, and by the Fall of 1942 I had done all the undergraduate courses in physical chemistry, and it was a time for me to move up to a graduate level course. The next course available to me was Chemistry 265, Chemical Physics, Statistical Theory, in short, statistical mechanics. This course brought me in contact with Professor Fritz London, an eminent theoretical physicist who had been recruited to Duke in 1938 by Paul Gross, the Chairman of the Chemistry Department. Dr. Gross was a knowledgeable, effective, and energetic chairman, with a wide network of scientific acquaintances, and it was doubtless through this network that he learned of the availability of Professor London. Gross offered London a professorship at Duke. London had been the victim of the rampant Hitlerian anti-Semitism in the Europe of the 1930’s, which resulted in his having to move several times from academic post to academic post. According to the legend in the Duke Chemistry Department when I was there, London was in Paris in 1938, perhaps at the Sorbonne, and all Europe was threatened by Nazi expansionism. He was in conversation with a French colleague, possibly about the desirability of his accepting the offer from an obscure university in the southern part of the United States, and in the course of this discussion the matter of the fate of France (an thus of his university position in France) arose. The story has it that the French colleague proclaimed, “Ils résisteront”! London’s reply, based on his own bitter experience with the situation in Europe, was, “Non. Ils ne résisteront pas.” This opinion doubtless influenced his decision to accept the Duke offer.
He arrived at Duke in 1939. The University scientific community, especially the Chemistry community, was overjoyed to have obtained the services of a man with London’s scientific reputation: the Heitler-London theory of covalence, the theory of dispersion forces, and the role of Bose-Einstein condensation in superconductivity and superfluidity. He was assigned a small office just off the lobby of the old Chemistry Building on the West Campus, and he used this for all of the time that I knew him at Duke. I was told that when he started teaching in his first year his class was comprised, to a considerable extent, of the Duke Chemistry faculty, delighted to be able to learn startling new things at the feet of the world-renowned master. It must be remembered that in 1939 the quantum mechanics was only about 15 years old and was not widely known, except by the real scientific cognoscenti, so learning more about it was very attractive.
London’s office doubled as his classroom. It was longer than wide, and his desk was at the window end with the blackboard at the other end and desks for the students arranged in front of it, but allowing room for London to stand while he lectured. He did most of his work at home, so he mostly arrived in his office just in time for this class. He moved quite rapidly, and generally hurried in just before the lecture was to start. The class was scheduled for the period 11:30 AM-12:20 PM, but this was a nominal schedule. He usually paid little attention to time, and on more than one occasion we students had to attempt to stop his lecturing enough before 1:00 PM for us to get to the dining room for lunch before it closed. In my time the class consisted of about 5-7 students. London lectured rapidly and wrote rapidly, filling the blackboard with equations as he went. There was no text for the course, so we students tried to keep up with him as best we could. This resulted in a set of quite rough notes for us, and it was common practice for the students to make fair copies of their notes at some appropriate time after the class. As I recall, London made sparing use of lecture notes, and most of the very abstruse information that he was presenting came straight out of his head. He was as cavalier about setting limits on his writing as he was about setting limits on the extent of his lectures. The information on the blackboard was retained for continuity until erasures had to be made to enter new information, and he showed a considerable ingenuity in improvising writing space. Writing out onto the margins of the blackboard was a commonplace, and on one memorable occasion the last equations needed to complete a derivation were written on the horizontal shelf of the blackboard, the usual function of which was to hold chalk and erasers.
Things had shaken down a bit by the time I entered the statistical mechanics course in 1942. Professor Gross had been able to populate the Chemistry Department with a number of students who, like me, were eager to study with Professor London. He taught one of two courses on successive years: statistical mechanics and quantum mechanics. At least, that is the description given in the university catalog; in reality, for us students it was a three-year regimen. One started with one or the other of the courses; it didn’t much matter because the purpose of the first year was for the student to learn to understand the professor’s heavily German-accented English, European notation (figure sevens with crossed tails; figure ones that looked like teepees), and other idiosyncrasies. The next year one took the alternate course with the idea of learning the science, and when that was accomplished one took the first course over again with the hope of understanding the science that the professor had been talking about that first year. All of this was intellectually hard on me because I was only an undergraduate when I started, but it wasn’t a cakewalk for the other students either (and this went for the faculty students of the first year.) Indeed, it was a large intellectual quantum jump for all of us, for our previous training gave us little or no preparation for what London was trying to teach us. Thus in my statistical mechanics course classical mechanics, vector analysis, and elementary statistical concepts were presented in about three weeks, and then on to the real work of the course, the Liouville Theorem, LaGrangian multipliers, gamma space and mu space, and then Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac, and the manifold practical applications of statistical mechanics. It was tough, but exciting.
But for me the real excitement came in the quantum mechanics course. Statistical mechanics is in large part a classical discipline with roots extending back to deep into the nineteenth century. Ludwig Boltzmann was a towering figure, but since he lived in about the years surrounding 1850 it was a difficult to personalize him—he was an important scientific figure, but an historical figure. But quantum mechanics was a completely different matter. One can date the beginning of quantum mechanics to 1925 (I here make the distinction that Professor London taught me of differentiating between the quantum theory of Bohr and the quantum mechanics of Heisenberg, Schrödinger, and Dirac), so that in the early 1940’s it was still a new, fascinating, and mysterious scientific discipline. And for me the real marvel of the London course was that London was contemporary with and acquainted with these early giants of quantum mechanics; indeed, he was one of them. Thus he was able to personalize them to the extent that they became real people for us students.
I shall give two examples of this. He started the course with a discussion of the ultra-violet catastrophe and Max Planck’s solution to the problem, and then he moved on to the Bohr theory of quantized orbits of the electrons. From there we learned of the limitations of this theory and the attempt to extend it with the Correspondence Principle. Of course this attempt met with but limited success, and the theoretical physics community was temporarily stumped. Enter Werner Heisenberg! Following a new scientific philosophy that was developing at this time, namely, that theories should be based solely on physically observable quantities, Heisenberg set out to develop a theory of atomic spectra that would involve the two indices that characterize a spectral line; that is, the quantum numbers characterizing the two states involved in the transition. London asserted that Heisenberg ab initio developed an algorithm that accomplished this, and London led us through the details of the development. I deeply regret that my class notes on this development have been lost, because I have never seen it expounded in any of the quantum mechanics texts that I have examined over the years. Heisenberg expanded his two-index array into a general theory of atomic mechanics, and it was later pointed out by one of the eminent mathematicians of the time (Hilbert?) that these two index arrays were in fact matrices, and Heisenberg’s procedure became known as matrix mechanics. For me it was really stunning to be exposed at close hand to Heisenberg’s monumental intellectual accomplishment, and it would never had happened without a teacher of London’s experience and stature.
The second example of personalizing the quantum science comes from London’s presentation of Dirac’s development of relativistic quantum mechanics. This involves the use of the Einstein relation between the mass of an object and its velocity, and Dirac used this variable mass in the Schrödinger equation. More regrets on my part, for over the years I have completely forgotten the details of London’s presentation, but I do remember the aspect of the matter that is of importance for this story. That is, the relation between mass and velocity contains a square root function, which, of course, has two roots. The consequence of this in relativistic quantum mechanics is that there is a set of energy levels for an electron in an atomic system corresponding to each root. The theory is quite clear that no distinction can be made with regard to the validity of each set of levels, which had the startling implication that negative energy levels for the electron exists. In explaining this London went on to say that Dirac was not overly upset about this, for he felt that there would be no probability of a transition between the two sets of states. However, he nevertheless calculated this probability and he found
(and here I wish that I could reproduce London’s look and his German-accented voice) that, to his horror, the probability was finite. Thus we had the prediction of the existence of the positron and the other anti-particles. I don’t have any idea about how London knew of Dirac’s feelings in the matter, but the core of the story vividly represents the reaction that a scientific worker of the time could have had.
Fritz London was obviously an intellectual giant, at least the equal of others that I have met in the course of my scientific career. Although I did no theoretical physics work myself, the learning he gave me proved to be very valuable. It hardly needs to be said that he played a very important role in the process whereby Duke University grew from a fledgling college to a major intellectual and scientific center.
29 April 2009
Frank Field obtained his B.Sc and PhD degrees at Duke University in 1943 and 1948. After various technical positions in the Standard Oil Co (New Jersey) and successors from 1952 - ‘70, he became the Camille and Henry Dreyfus Professor at the Rockefeller University, New York, 1970 -’88. Upon his retirement in 1988 he moved to Oak Ridge TN, later to Durham, N.C. where he passed away in 2013.