- Email: [email protected]
Some reminiscences about my early career
Physica A 168 (1990) 1-21 North-Holland
CHAPTER 1
PLENARY LECTURES
SOME REMINISCENCES ABOUT MY EARLY CAREER Cyril D O M B Department of Physics, Bar-llan University, Ramat-Gan, Israel The author recalls some of the highlights of his scientific career before he took up a professional appointment at King's College, London in 1954. The periods covered are: High School and undergraduate studies at Cambridge University 1932-1941; radar research for the British Admiralty 1941-1946; graduate studies at Cambridge University 1946-1949; post-doctoral research at the Clarendon Laboratory, Oxford University 1949-1952; faculty appointment at Cambridge University 1952-1954. A brief description is given of the personalities with whom the author was associated, the research problems in which he was involved, and of the early post world war 2 scientific conferences.
1. Introduction: high school and university 1932-1941 Let me first say how grateful I am for the many complimentary things which have been said about me at this Conference. My wife is a professional teacher, and she says that anyone who gives a lesson or delivers a lecture, is planting a seed; one never knows in advance how much fruit each seed may bear. It has been a wonderful revelation to me from the remarks of many of the speakers that my teaching and lecturing activities over many years did indeed bear fruit. I thought I would reminisce about the period in my life before I became a professor. This has two advantages. Firstly it should be new to everyone here (I met up with Michael Fisher, my oldest student at the Conference, only when I took up a professorship at King's College, London). Secondly, if I may quote the views of A.S. Besicovitch from an article which I wrote recently for the Mandelbrot Festschrift [1], before a person can be appointed to a Chair he must have become respectable, and once he is respectable, he ceases to be interesting. So hopefully for the period which I plan to cover, I and my associates were still interesting. My home background was not affluent, and my parents were not in a position to support my education financially. I am therefore eternally grateful to Britain, the country of my birth, for enabling me to obtain a first class education without calling on my parents. I started at a general elementary school, and obtained a scholarship to a medium grade high school, Hackney Downs School. I showed some mathematical ability, and the senior mathematics teacher, F.J. Swan, told me that if I really wanted to embark on a 0378-4371/90/$03.50 © 1990- Elsevier Science Publishers B.V. (North-Holland)
2
C. Domb / Some reminiscences about my early career
mathematical career, it was advisable to get to Cambridge University. Hackney Downs had no training programme for scholarships to Cambridge or Oxford; they would average perhaps one scholarship a year on the basis of individual tuition. The top class high schools like St. Pauls, City of London, or Manchester G r a m m a r ran special scholarship classes, and might well get 20 or 30 scholarships each year. In D e c e m b e r 1937 I went to Cambridge to compete against what Fred Hoyle termed the "trained greyhounds" (Bingley G r a m m a r School, which Hoyle attended [2], was comparable in standard to Hackney Downs). But Swan had prepared me well, and it was a pleasant surprise to learn that I, an "outsider", had been awarded a Major Open Scholarship by Pembroke College. My best paper was in projective geometry, my applied mathematics being quite weak. I went up to Cambridge in October 1938; it was just after Munich, and war clouds were gathering on the horizon. I can still recall vividly the freshness and inspiration of my introduction to real mathematics. There were several outstanding lecturers, the most notable being Philip Hall, the distinguished algebraist. I still have the notes which I took at his course on "Linear Algebra", and despite the plethora of books which have appeared on this subject during the intervening years, I still used these notes as the basis for a course which I gave recently at Bar-Ilan. War broke out in September 1939. Someone high up in government circles decided very intelligently that if we were allowed to complete degrees in science, we would be of much more help to the technology of war than if we were called up as undergraduates. I was advised to move in the direction of applied mathematics since this would provide far more opportunities of contributing to the war effort than pure mathematics. It should be pointed out that there was no theoretical physics at the Cavcndish Laboratory in those days. Dirac, Fowler and Eddington, who would have certainly been classified as theoretical physicists on the continent, held Chairs in applied mathematics in the Faculty of Mathematics. In my final year for Part 3 of the Mathematical Tripos, I was examined in courses on relativity, quantum mechanics and statistical mechanics, although I attended a variety of additional courses on other topics in pure and applied mathematics. I never regretted my training as a mathematician. In theoretical physics we are usually pragmatic, and far more concerned with deriving a practical solution to a problem than with establishing rigorously that the solution is correct. But a training in rigour enables one to decide with more confidence when it can be ignored. I graduated from Cambridge in June 1941, and joined the research group on radar (or R D F as it was then called) at the Admiralty Signal Establishment (ASE) in July 1941.
C. Domb / Some reminiscences about my early career
3
2. Radar research for the Admiralty 1941-1946 There were no appointments with the designation "theoretical" at the Admiralty. I was appointed as a T E A 3 (Temporary Experimental Assistant); others at a more advanced stage in their university work were appointed as Experimental Officers. Because of our experimental titles we were started on practical work, and I was introduced to the soldering iron. It was here that I first met Fred Hoyle. We were both so hopeless with the soldering iron that it was considered bad for morale to let us stay in the experimental group, and we were exiled to a hut on the outskirts of the establishment and told to occupy ourselves with theory. Fred was then a Junior Fellow at St. John's College, Cambridge, aged 25, whilst I was 20. He immediately pointed out that whilst it was our task at ASE to help win the war, he felt sure that we could fulfil this task without giving u p our interest in fundamental science. His own area of research was astrophysics, and he proceeded to give me a potted description of the current situation and major problems of astrophysics. He also provided brief profiles of the leading researchers in the field, who might be good mathematicians but had poor physical insight. Since I was undoubtedly looking around for a suitable field of research, he thought that astrophysics offered good prospects; if people with such poor appreciation of the physical aspects of a problem could get to the top, I should have no difficulty in establishing myself. Despite this encouragement I remained dubious since I was not convinced that physical insight was my forte. A week later Fred came in one morning triumphantly waving a copy of the "Monthly Notices" of the Royal Astronomical Society". "You have a unique opportunity of making your reputation overnight", he announced, "Eddington has published a paper with a serious flaw in it; if you write a brief note pointing out the flaw, you will immediately establish yourself in the field". Fred felt that it was not appropriate for him to do this since he was known to belong to the opposing school of thought. Since I had just attended Eddington's lectures, and he had been one of my Part 3 examiners, I could not really see myself filling the envisaged role. Also I was already fairly convinced that my area of research interest was statistical mechanics and condensed matter physics. Fortunately we were joined later by two new arrivals at ASE, Hermann Bondi and T o m m y Gold who were more sympathetic to astrophysics than I had been. Both came originally from Vienna, and had been interned in the Isle of Man during the 1940 panic. Some intelligent person in a position of authority had engineered their rapid transformation from spy suspects to members of a Top Secret Establishment. Hermann was a very capable mathematican who had distinguished himself at Cambridge, and the basis for his appointment was
4
C. D o m b / Some reminiscences about m y early career
clear. Tommy's situation was more mysterious. He had obtained a 4th class degree in engineering, not for lack of skill, but because he found it more exciting to climb King's College Chapel than to attend lectures. A short discussion with him on any scientific problem would soon provide evidence of his wide understanding and experience, and even though his formal mathematical knowledge was limited, I have never met anyone with greater physical insight #1. During his period at Cambridge he had made a number of important contacts, including that of E.D. Adrian, who was then engaged in his pioneering experiments on electrical conduction in nerves; strong recommendations from Bondi and Hoyle helped convince the government science recruiting team of his true calibre. Bondi and Gold were very interested by the many astrophysical problems which Hoyle put before them. In the early post war years the trio was nicknamed the "Cambridge Circus", and they contributed significantly to stimulating and invigorating British astrophysics during this period. The most widely known of their contributions is the steady state model of the universe [3]. Whilst this model has now been discarded in favour of the big bang model, its unequivocal predictions were the immediate cause of a number of exciting and crucial experiments in radio-astronomy [4]. We were soon constituted into a formal "Theoretical Group" with Hoyle as Head and Bondi as Deputy, and we began exercising an influence on the solution of the technological problems faced by the Admiralty. As far as the orderly routine of the Civil Service was concerned, Bondi and Gold were enfants terribles. We were stationed at Witley, Surrey, and they found it convenient to live in the neighbouring village of Dunsfold. Travel at our level of importance was by public transport only. The 8:30 am morning bus from Dunsfold arrived in time to sign on at 9:30 am. This was 30 minutes late. But Hermann and Tommy were liable to miss this bus and the next bus left at 1:30 pm! It is a remarkable achievement of British Society that an enfant terrible can be transformed into a pillar of the establishment. After a distinguished university career at Cambridge and King's College London, Hermann Bondi joined the Scientific Civil Service, and reached the top position of Chief Scientific Adviser to the Ministry of Defence; he was also knighted. I once called on him in his office in Whitehall to discuss a matter of mutual interest. "What time did you get in this morning"? I asked. "I was in by 8:00 am", came Hermann's proud reply, "my advice was needed urgently". By contrast, Tommy Gold has remained an enfant terrible, and is the best counterexample I know to Besicovitch's thesis quoted at the beginning of this ~ I was never privileged to m e e t Richard F e y n m a n personally, but he was described to me by D e n n i s Sciama (in a first a p p r o x i m a t i o n ) as a synthesis in one p e r s o n of T o m m y G o l d ' s physical insight and H e r m a n n B o n d i ' s mathematical skill.
C. Domb / Some reminiscences about my early career
5
article. He became and remained a professor at Cornell University without ever attaining respectability. Fred Hoyle spent much of his spare time reading science fiction. I found this very puzzling, but he said that familiarity with the sort of literature which was published could be of great help to him some time in the future. "The people who write this stuff know very little science, yet they made good money on their publications; I have a real knowledge of science, and I should surely be able to do far better". After the war Fred went back to Cambridge, and it did not take too long before he was elected to the Plumian Chair of Astronomy (and knighted). Some years later he became unhappy with the way applied mathematics was run at Cambridge, resigned his Chair, and went off to live in the Lake District. His earnings from science fiction and other writings dwarfed his former professorial salary! One of the most interesting personalities in the research section of ASE was Otto Bohm, who although attached to the aerials group, maintained close and cordial links with the theoreticians. For many years he had held a key position in the German radio industry as' research director of Telefunken. He was Jewish, and hints were dropped in the 1930's after Hitler's accession to power that in his specific case this would be overlooked if he wished to continue in his post. But he ignored these hints, and joined other refugees who left for the U.K. Like other refugees he was interned in 1940, and released to join ASE in the summer of 1941, when he was already over 60. Bohm played a key role in the development of aerials for centimetre wavelength radar. All of his calculations were relatively simple, many of them based on the standard formula for the impedance of a transmission line at any point on its length. He somehow managed to apply this formula to the new technology of wave guides and wave guide flares, and he estimated the illumination of the aperture from which the polar diagram could be calculated. The major parameter which he assigned intuitively was the characteristic impedance Z 0. The wave guide, the flare, and free space all had their specific Z 0. From the point of view of the mathematical physicist the problems he tackled were horribly complex involving the solution of Maxwell's equations for bodies of unusual sizes and shapes; but with remarkable perception he used empirical approximations which gave a solution correct to 10% or 15%. Further accuracy and refinement were obtained by a combination of empirical theory with experiment. It always seemed to me that the electrons themselves when faced with the solution of partial differential equations with appropriate boundary conditions must surely use pragmatic methods of Bohm's type rather than eigenfunction expansions. It is time to say something more precise about my scientific work during the
6
C. Domb / Some reminiscences about my early career
war years. My first mentor was M . H . L . (Maurice) Pryce who joined ASE at the same time as I and was assigned to the aerials group. Pryce had enjoyed a fabulous reputation at Cambridge; even as an undergraduate he had participated in colloquia and when Eddington published a paper putting forward some of his unconventiai views [5], the reply of conventional physics was given by Dirac, Peierls and Pryce [6]. Shortly before the war he had taken up an appointment as Reader in Theoretical Physics at Liverpool University. A few weeks after his arrival, Pryce produced an extremely neat and useful piece of theoretical work. In making practical use of radar it was important to be able to calculate simply and accurately the field strength due at a transmitter at any given height above the earth. The classic problem of the diffraction of electromagnetic waves by a sphere had been tackled by a number of investigators, the most comprehensive solution being that of G.N. Watson [7]. This solution is equally valid for the earth or a raindrop; but the generality of the solution exacts a price, and it cannot be readily used for practical calculation. Pryce suggested that for diffraction around the earth a meaningful approximation should be made at the outset, using a metric which takes account only of the first terms in the curvature; Maxwell's equations should then be solved for this metric. This leads naturally to a solution in terms of the Airy integral [8], which satisfies the simple second order differential equation y " = - x y . The Airy integral can be expressed in terms of Bessel functions of order but it is better treated as a simple function in its own right. Its values for real variables, had recently been tabulated by J.C.P. Miller [9], of Liverpool University. Pryce's solution required values along certain lines in the complex plane. Pryce was familiar with Miller's work, and sent me to Liverpool to undertake the new computations [10]. When they had been completed, we produced a set of curves [11] from which the field strength due to a radio transmitter could be derived with little effort at any point of interest. I think we did a good job because the curves were widely used on both sides of the Atlantic. The statistical distribution of noise, and noise and signal in receivers was a question of interest and importance. Bondi tackled this problem very effectively, and the work (in addition to an astrophysical investigation suggested by Hoyle) helped to secure him a Fellowship at Trinity. He never published his treatment, but he derived independently the results contained in the well known paper by S.O. Rice [12], which are reproduced in the widely used reprint volume edited by Nelson Wax [13]. There was great interest during the war years in "anomalous propagation" of centimetric waves. Certain meterological conditions were found to give rise to unusually long radar and signal ranges, and it was assumed that the waves were trapped by a type of wave guide effect near the surface of the earth which
C. D o m b / S o m e reminiscences about m y early career
7
prevented attenuation. Calculations for a variety of models of the atmosphere were undertaken by theoreticians working with the Air Force at TRE (Telecommunications Research Establishment). It was important to have basic factual information, and Fred Hoyle had the bright idea of stationing a transmitter at Aberporth on the shores of Cardigan Bay in Wales, and a receiver o n t h e summit of Snowdon, and taking records of propagation over Cardigan Bay for a long period of time. There was a hotel on the summit of Snowdon, which could be requisitioned to provide accomodation and technical facilities, and the height of Snowdon would correspond to a fairly low flying aircraft. The plan was accepted by the Admiralty, and enabled members of the theoretical group to carry out activities of importance in the beautiful Welsh countryside. The weather on top of Snowdon is often quite wild even in summer when the hotel had usually been open; it had always been closed during the winter. Fred's plan involved keeping it open and manned during the winter when the snow and ice would have to be braved. Hermann Bondi, who was familiar with mountainous winter conditions from his youth in Austria, volunteered to stay at the hotel and man the station, and naval ratings were assigned to look after his physical and technological needs. The experiments continued for many months and we all took part in them. Another problem of importance for sea borne radar was noise from sea reflections. Fred Hoyle suggested that the north coast of Cornwall (Bedruthan Steps) would provide a suitable location for a station at which to conduct a systematic study of long wave Atlantic breakers. Tommy Gold took charge of the project. Some of the conclusions played an important role later in the anti-radar "window" development. A question in which I became interested, and which belongs to the physics of disordered systems, was the calculation of radar scattering from rain clouds. It has always been assumed that droplets should be treated as random scatterers and this is reasonable when the wavelength is much shorter than the spacing between raindrops. But it is clear that for radiation of wavelengths long compared with the spacing between raindrops the cloud should be treated as a continuous medium with a dielectric constant differing from unity. How is the transition between these two approaches effected? Consideration of this problem led to the study of a special type of random walk problem, and to my first scientific publication [14]. I immediately came under fire from Coulson [15] (one of my predecessors in the Chair at King's College), who pointed out that there were limitations to the validity of the formulae which I had derived. In my reply [16] I showed that my results were satisfactory for the applications with which I had been concerned. In the course of discussions with experimentalists, questions often arose
8
C. Domb / Some reminiscences about my early career
which involved calculations relating to electric circuits, and I became very familiar with the technique of Laplace transforms. This stood me in good stead for a number of early calculations relating to probability theory [17]. In June 1945 the war in Europe came to an end, and Fred Hoyle announced that he would be going back to his Fellowship at Cambridge since he had an astrophysical problem of major importance on his mind, which needed intense concentration. In regard to the need to bring the war in the East to a successful conclusion, Fred argued that experience had shown a delay of 1-1½ years between any idea which he generated and its practical use by the Navy; he was absolutely convinced that before such a time the war with Japan would be over. His action put the Civil Service in a quandary. There was no mechanism by which he could resign or be dismissed since we were all "drafted". They therefore considered him on special duty at Cambridge, and continued to pay his salary. This was very embarrassing to Fred, and he came back to discuss the situation with the Captain Superintendent, the Naval Officer in charge of ASE. Interestingly enough Fred received a sympathetic hearing, and the Captain suggested that he spend some of his time at Cambridge thinking about ASE problems, with which he was by now very familiar; he could come back to report from time to time. Eventually a solution was found to the dilemma. The problem which Fred Hoyle had begun to think about was the origin and abundance of chemical elements in the universe. Within a year he had published a definitive paper [18] showing how it is possible to account for the abundances of the elements in stars by the statistical mechanics of nuclear reactions at high temperatures. He continued to think about the problem, and when accurate data on isotopic abundances became available, he collaborated with the Burbidges and W.A. Fowler to publish a classic paper [19], which accounted in remarkable detail for the observations. The citation in the award of the Nobel prize to Fowler in 1983 contained the phrase "for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe", thus recognizing the importance of this work. Fred's prognosis was correct, and the war with Japan came to an end a few months later. This initiated a major scramble among the temporary staff to get back to the university as quickly as possible. Hermann Bondi had no problem since his Trinity Fellowship was available immediately. My own position was more difficult since I had nothing specific; fortunately Pembroke College came to my rescue. A very able physics graduate student, Efraim Nahum, had been killed by the only bomb to fall on Cambridge during the war, and his parents had endowed a scholarship in his memory. The money had accumulated for
C. Domb / Some reminiscences about my early career
9
several years, and was enough to keep me from January to September 1946, when it was hoped that I would get a government award. As usual Tommy Gold had an original solution for his situation. He had become involved in discussions with R.J. Pumphrey, a distinguished biologist working at ASE, on the nature of the circuits in the human ear. Helmholtz had been led to think that these circuits are highly resonant [20], but current investigators had discounted his ideas [21], and assumed that the circuits were highly damped. Gold and Pumphrey [22] devised crucial experiments, which led back unequivocably to the Helmholtz picture. Gold submitted his work to Trinity and was awarded a Fellowship. It is to the credit of the referees that his 4th class degree was ignored.
3. Graduate studies at Cambridge 1946-1949
I had decided that the main area of research for my graduate studies would be statistical mechanics, and Fred Hoyle agreed to serve as my supervisor. He was not actively engaged in research in this area, but I hoped that I would be able to find problems by myself. Fred would let me work on my own and I could discuss my results with him if I felt that I was getting somewhere. I have always told graduate students who came to ask my advice that they should eliminate dependence on their research supervisor at the earliest opportunity. It seemed to me that there should be many problems to be tackled in relation to phase transitions, but I found the standard text by Fowler and Guggenheim, "Statistical Thermodynamics" (published in 1939), rather depressing. It gave me the impression that the theories were in a healthy state, and only minor points needed to be straightened out. I gained the same impression from the papers by Lennard-Jones and Devonshire on melting [23]. They seemed to achieve amazingly good agreement between theory and experiment, and the subject seemed to be tied up. Fortunately the year 1946 saw the publication in the famous Oxford monograph series of J. Frenkel's "Kinetic Theory of Liquids" and this gave me much more encouragement. The title is a misnomer and the book deals comprehensively with a variety of problems in condensed matter physics. On the Lennard-Jones and Devonshire theory of melting, Frenkel said (p. 111): "The considerable quantitative agreement between the calculated and observed positions.., can hardly be considered as a convincing confirmation.., such a numerical agreement being easily obtained by a proper choice of the parameters involved". Again in relation to a particular version of the hole theory of the liquid state he stated (p. 176): "Similar ideas have been put forward by Furth w h o . . , attempted, with a very poor degree of success, to apply this
10
C. Domb / Some reminiscences about my early career
conception to the quantitative interpretation of a number of properties of liquids". These assessments, and others of a similar kind throughout the book, convinced me that a lot of fundamental problems needed to be tackled. More important, I learned from Frenkel that the basic problem in dealing with the statistical mechanics of interacting systems is the calculation of the entropies of all the different possible configurations, and this is a mathematical problem in probability. Cambridge was a very exciting place in 1946 with large numbers of staff and students returning with enthusiasm after a prolonged absence. By general academic consensus there were 4 particularly bright young stars among those returning to the Cavendish Laboratory, Brian Pippard, Martin Ryle, Denys Wilkinson and Tommy Gold. This concensus view was confirmed by subsequent developments. Brian Pippard became Cavendish Professor; Martin Ryle was the pioneer of radio-astronomy and received a Nobel award in 1974; Denys Wilkinson moved to a Chair of Nuclear Physics at Oxford where he built up a lively research school. Tommy Gold contributed significantly to a variety of different problems, the most important being the identification of pulsars as neutron stars [24], and the most spectacular the demolishing of a "New Law of Nature" proposed by Patrick Blackett, Nobel Laureate and later President of the Royal Society. Blackett had been impressed by the experimental data on magnetic fields associated with rotating stars, and the origin of the earth's magnetic field was still an open question. He came forward with the dramatic suggestion that every rotating gravitating body generates a magnetic field. Tommy immediately realized that the idea had untenable implications, and at a public discussion organized by the Royal Astronomical Society he emphasized that among other things, the proposal contravened special relativity, and the principle of equivalence in general relativity [25]. The idea was never revived! After serving for a period as Assistant to the Astronomer Royal, Tommy moved to a professorship at Corneil. The first International Conference after the war took place in July 1946, and coincided with the opening of the new Austin Wing of the Cavendish Laboratory. It is amazing to think that it was devoted to "Fundamental Particles and Low Temperatures", and many of the leading personalities in the world of physics attended. Some highlights of the programme are reproduced in fig. 1. The opening address was delivered by Niels Bohr, and the speakers at the first session were Pauli, Dirac and Born, who dealt with the difficulties of field quantization and quantum electrodynamics. The following morning was devoted to the theory of liquid helium with F. London advocating the Bose-Einstein condensation model. V. Peshkov came from the Soviet Union, and told of Landau's alternative point of view, and for the first time we heard the terms "phonons" and "rotons". Each proponent
C. Domb / Someremin~cencesabout my ear~ career
11
Physical Society Conference - July 22nd - 27th, 1946 Fundamenta] Particles and Low Temperatures. Monday,
July 22rid. Chair - Sir W.L.Bragg.
2.30 p.m.
Address of Welcome to the Conference
D.Brunt
FUNDAMENTAL PARTICLES (a) Opening addr_ees_~
Arts School
"A genaral survey".
N. Bohr. (b) Present state of general theory
Chair - N. Bohr.
W. Pau li.
"Difficulties of field theories and of field quantixation".
P.A.M.Dirac.
"Difficulties of quantum e le ct rodynamics".
M. Born.
"Relat iv ist ic Quantum Mechanics and the principle of reciprocity". Tuesday, July 23rd.
Arts School
LOW TEMPERATURES 9.30 a.m.
Chair - F. Simon
Liquid Helium II F. London
"Theory of Liquid Helium II".
K. Mendelssohn.
"Friekionless transport".
V. Peshkov (to be read by J.F. Allen).
"Propagation velocity of second sound in Liquid Helium II".
L. Onsager. 9.30 a.m.
~'Transition points". FUNDA~'~NTAL PARTICLES
Arts School
Chair - E. Schroedinger. N.F. Mott.
Closing address.
Fig. 1. Some items from the programme of the First International Scientific Conference after World War 2. (This figure represents the original duplicated programme.)
12
c. Domb / Some reminiscences about my early career
was very frank in his assessment of the opposing viewpoint. F. L o n d o n on Landau: " T h e quantization of the motion of a liquid as he proposed it is however quite u n c o n v i n c i n g . . . There is unfortunately no indication that there exists anything like a r o t o n " . Peshkov: " H o w e v e r the theoretical speculations of London and Tisza and very artificial and unconvincing". Among the speakers at one of the low temperature sessions was Lars Onsager on "Transition Points", but I must confess that I had to wait for the published version of the Proceedings [26] before I understood the content of his lecture. I then learned that he had been describing his work with Bruria Kauffman on correlations in the Ising model [27]. The Chairman on the last day was Schr6dinger, and one of the speakers was Heitler; both had recently moved to the Dublin Institute of Advanced Studies. The closing address was given by Mott. The G o v e r n m e n t of Eire had been prodding its citizens hard to put the Irish language, Erse, on the map. Mott congratulated Schr6dinger and Heitler on restraining themselves from speaking in their native Erse! My own researches in the statistical mechanics of interacting systems on lattices were sparked off by a colloquium given by A.R. Miller, a student of Fowler, on the Bethe approximation and its application to a variety of problems. I realized that for one-dimensional systems I could solve the problem exactly, and this led me naturally to the transfer matrix. But I soon found that I had been anticipated by three groups of workers [28]; this led me to chase up the literature, which was not difficult since there was only a handful of journals. I was struck by awe and admiration by Onsager's classic 1944 paper [29], and I found the 1945 review by Wannier [30] very useful since it contained more of Onsager's unpublished results. Wannier's paper ended with an optimistic hope, characteristic of the period, "It is to be hoped that a three-dimensional calculation will, before long, furnish the answer to these questions". I set about formulating transfer matrices for a variety of problems, and I found that they could all be reduced to a simple characteristic form with large numbers of zeros, which I called d u o - d i a g o n a l . At this period I hoped that it would be possible to deal with these matrices exactly, and I consulted with Philip Hall; but he was convinced that the problem was very difficult and had no practical suggestions to offer. I therefore developed perturbation expansions for the two-dimensional Ising model in zero and non-zero field. For a zero field certain simplifications were present, which enabled me to derive an indefinite number of terms of a series expansion; this was equivalent to Onsager's solution for a general asymmetric net. When the field was non-zero the situation became much more complicated, and only a limited number of terms could be derived. By examining the behaviour of those series I conjec-
C. Domb / Some reminiscences about my early career
13
tured that there were no singularities in non-zero field, a result proved rigorously a few years later by Yang and Lee [31], and I was able to estimate the critical behaviour of the spontaneous magnetization. This work constituted my Ph.D. thesis, and the results were published as a letter in Nature [32], and two papers in Proc. R. Soc. [33]. Early in 1948 I faced a sudden crisis in my personal career. I had been supported by a Senior Research Award of the DSIR (Department of Scientific and Industrial Research). Such awards were normally given for two years, and could be extended for a third year if the research was satisfactory. My work was going well and I anticipated no difficulty in securing a renewal. But with no preliminary warning a change of government policy was introduced that all such grants be terminated after two years. I had not applied for any alternative grant, and I was left suspended. The new policy threatened the careers of other research workers in the same situation, and senior professors intervened to try to get the decision revoked in individual cases (Hartree took up the cudgels on my behalf). But it seemed wise to explore alternative possibilities. Maurice Pryce had just been appointed to a new Wykeham Chair of Theoretical Physics at Oxford, and I went over to give a Colloquium and to find if he had anything to offer. The timing was fortunate. Pryce had a queue of graduate students, a substantial fraction being from overseas, who wished to do research in theoretical physics, and my work offered a number of promising lines (three-dimensional models, antiferromagnetism, distant neighbours, etc.). Stanley Rushbrooke had just been appointed to a Readership in Theoretical Physics at Oxford; his major interest was statistical mechanics and he reacted positively to my work. Pryce managed to secure an ICI Fellowship for me, and at the beginning of 1949 I moved to Oxford.
4. Clarendon Laboratory, Oxford 1949-1952 The years which I spent at Oxford were very fruitful. I had six graduate students. George (G.M.) Bell worked on closed form approximations for sophisticated models. He went on to a distinguished career in statistical mechanics, and became a professor in the mathematics department at Chelsea College, London. He is now at King's College, London, following a merger of the two colleges. Jack (J.E.) Brooks from the USA worked on antiferromagnetism, and after securing a Ph.D. returned to industry in the States. Renfrey (R.B.) Potts was a Rhodes Scholar from Adelaide, and I am sure that you are all familiar with his name from the P o t t s m o d e l . His thesis was concerned with
14
C. Domb / Some reminiscences about my early career
distant neighbour interactions in the Ising model and the new Potts model entered only marginally (I have told the story in detail elsewhere [34]). He returned to Adelaide where he later became Professor of Applied Mathematics. His interests have moved away from statistical mechanics; he has contributed with distinction in a number of different areas, and is a Fellow of the Australian Royal Society. Hugh (T.H.K.) Barron is the son of one of my former teachers at Hackney Downs. He worked in the area of lattice dynamics, became a world authority on thermal expansion, and Reader in the Chemistry Department at Bristol University. Lewis (L.S.) Salter came from Wabash College, Indiana, and worked on the thermodynamics of solids. He had a strong sense of public duty, and went from Oxford to Indonesia to serve in the Peace Corps. Eventually he returned to his Alma Mater, Wabash College. My last Oxford student, Martin (M.F.) Sykes, became my closest collaborator, and many of my papers in the 1950's and early 1960's were written together with him. Most people here will not have met him since he does not attend conferences, preferring to work in the quiet of the English countryside. His capacity for envisaging configurations of sites and bonds on lattices is quite incredible, and many of my subsequent students and collaborators benefited from his advice and help. During my first year at Oxford I worked on the three-dimensional Ising model using the matrix approach, but one of Rushbrooke's students, A.J. Wakefield, who also had a remarkable gift for configurational work, did far better than me, and I never published the results. The most important influence during my period at Oxford was Sir Francis (F.E.) Simon, who administered the Clarendon Laboratory. Lord Cherwell was the nominal Head, but he spent the whole week in London at the House of Lords, and came back to Oxford only for the weekends when Simon brought him up to date. Simon was a father figure who took a close personal interest in his staff and students. He was keen that they should be happy and free of anxiety, since he was convinced that under such conditions they would produce their best work. He would concern himself personally with their grants and research fellowships, and inspired such confidence that research staff preferred to stay at the Clarendon with temporary appointments rather than move to permanent appointments elsewhere. He was always throwing out ideas and suggestions for new lines which might be worth pursuing, and he involved the theoreticians in the planning and interpretation of experiments. Simon was pragmatic in his relationship with university administration. He obeyed all the rules, but tried to reduce the interference with the normal functioning of the laboratory to a minimum. An illustrative story, which circulated the Clarendon, concerned Arthur Cooke's Ph.D. oral examination.
C. D o m b / S o m e reminiscences about m y early career
15
A few days before the examination Simon ran into Cooke and said: "By the way Cooke, about your Ph.D. oral, come and have a chat with me to tell me what your thesis is about; and think of some clever questions, which I can ask you, which will impress the external examiner". The Colloquia of the low temperature group took place on Mondays. At the end of the colloquium Simon asked one or two dumb fool questions, which encouraged the audience to feel that if the professor could ask such questions, they risked little in having a go. I was interested to find a similar type of story relating to Niels Bohr in Mark Azbel's fascinating book [35]. He there tells the story of a lecture, which Bohr delivered during a visit to his distinguished friend Lev. D. Landau. After the lecture a question was asked: " H o w do you account for the incredibly high productivity which has emerged from your school?" Bohr answered: "I think it happened because we were never cautious. We were never afraid to look like fools before our students". This was so different from the attitude prevailing at the Landau Institute that the translator, Yevgeny Lifshitz, instinctively rendered "We were never afraid to let our students know they were fools". Simon had wide international contacts, and many visitors to England dropped in at Oxford. When Onsager came over from a sabbatical at Cambridge in 1952, Simon told him that he was continually losing his secretaries by marriage to his collaborators - this had happened seven times in the course of his career. Onsager commented that Simon must use discrimination in choosing his secretaries. In fact the news got around among the young ladies of Oxford, and, whenever a vacancy occurred, there were queues of applicants, even though the pay offered was very modest. I cannot in any way match Simon's record, but I was gratified to learn that my very capable former secretary, Jill, teamed up recently with my former colleague David Gaunt, who I am pleased to see participating in this conference. Elliott Montroll came to visit me at Oxford, he being one of the few people in the world interested in the Ising model at that time. We found that we had other interests in common, and became lifelong friends. Some years later Elliott invited me as a visiting professor to Maryland, and it was on this occasion that I first met another lifelong friend, George Weiss. Elliott could always find openings for bright young people, and Ren Potts and Michael Fisher both crossed the Atlantic for the first time at his invitation. Max Born was also a regular visitor to Oxford. In the early post war years he teamed up with Bert Green, a very able mathematician, and they started to tackle the major current problems in physics. It was the general academic consensus that Born felt the need to remind the Nobel Committee of his p r e s e n c e - all the other giants who founded the quantum theory had received Nobel prizes, Heisenberg in 1932, Schr6dinger and Dirac in 1933 (during the
16
C. D o m b / Some reminiscences about m y early career
war the awards were suspended), and Pauli in 1945; but Born seemed to be shelved. Then Born had an idea which even he considered dubious, that quantum zero point fluctuations are sufficient to break up perfect crystals into block structure at the absolute zero. His first paper on this topic appeared in the Proceedings of the Egyptian Academy of Sciences [36]. Born told Simon that there was a good chance that the idea would prove incorrect, and then no one would notice the paper; but if it proved correct it would be of major importance and he could then claim priority. As is well known Born eventually received his Nobel award in 1954. In the spring of 1952 I began to prepare for my first major international conference (now known as Statphys 2), which was being organized in Paris by Prigogine and de Boer. I had not been invited to Statphys 1 in Florence in 1949 presumably because my work was still unknown. Rushbrooke, who had attended it, brought back the news of Onsager's calculation of the long range order for the two-dimensional Ising model. I had also participated in the International Low Temperature Conference at Oxford in 1951 (LT2) but my contribution had been marginal. At Statphys 2 I presented two papers, one on the three-dimensional Ising model, and the other on the theory of the melting curve at high pressures, which had been stimulated by Simon's empirical formula. It was a very exciting conference with many highlights. I have already described elsewhere the laying of the ghost of John Maddox's exact solution of the three-dimensional Ising model [37]. Let me mention here two other incidents. Joe Mayer (of cluster integral fame) presented a paper in which he claimed that a summation of the cluster integral series led to the conclusion that the liquid-vapour co-existence curve has a flat top. Previous experimental work by Maass [38] had come to the same conclusion. Suggestions had been forthcoming that gravity might play a part because of high compressibility near the critical point, but they had been discounted. Fortunately W.G. Schneider refused to be cowed by this formidable combination of authority, and conducted a simple experiment by himself. He took a long tube in which one might expect a gravitational effect to be significant, and then turned the tube on its side so that the gravitational effect was minimized. The striking result is shown in fig. 2; ever afterwards gravity has always been taken into account in these experiments. Simon had been very concerned with the question whether the melting curve ends in a critical point at sufficiently high temperatures, comparable to the liquid-vapour critical point. I had answered firmly in the negative, but Simon was not completely convinced. At the beginning of the conference he came and whispered in my ear that Arnold Munster was presenting a paper [39] which
C. Domb I Some reminiscences about my early career
17
0.95
1.00
1.05
E ..= 1.1o
i,
0
1,15
1.20
1.2.5 I ~ 16.400
16.450
I I 16.500 16.550 Temperat ure('C)
I 16.600
Fig. 2. Liquid-vapour coexistence curves in the critical region: long tube DO, short tube O.
purported to prove quite generally that all first order phase transitions end in a critical point at sufficiently high temperatures; I should prepare to defend my view. When Munster was called upon to speak, he flashed one slide after another very quickly, each slide being filled with fluctuation formulae, grand partition functions, etc. At the end he proclaimed " T h e r e f o r e every first order transition must end in a critical point". How should I deal with this situation? Fortunately I happened to be sitting next to Fierz, who had the reputation of being Pauli's brightest student, and I had taken him into my confidence. Fierz turned to me and said: "You have nothing to worry about - he has made some fundamental mistake". " H o w could you possibly follow the argument presented at such a speed", I asked. " H e may have produced statistical mechanical formulae, but at no point has he introduced a specific model; therefore he has remained in the sphere of thermodynamics. I am quite sure that this issue cannot be settled by thermodynamics", came his reassuring reply. I returned to Oxford to face another career crisis, the renewal of my ICI
18
C. D o m b / Some reminiscences about my early career
Fellowship. Cherwell was the obstacle. I was in Oxford from Monday to Friday when Cherwell was in London. I returned to London for the week-end when Cherwell came back to Oxford. The general laboratory colloquium took place on Fridays at 4:30 pm, but I never attended; Simon had not objected to this, since I attended the low t e m p e r a t u r e colloquium regularly on Mondays. But now when he suggested renewing my Fellowship, Cherwell said: " W h o is this man D o m b , and why do I never see h i m - I d o n ' t believe that he exists". Simon pleaded plaintively to me: " C a n you not be an orthodox Jew in Oxford one Friday, and deliver a colloquium at which Cherwell will be present. H e can then see that you are real and renew your Fellowship". O f course I complied with his request, but just on that particular Friday Cherwell was delayed in L o n d o n and did not get to the colloquium. During the whole of my stay in Oxford I never met him! Shortly afterwards advertisements a p p e a r e d for a lectureship in mathematics at Cambridge, and for a prestigious Smithsonian Fellowship, which also contained a clause expressing a strong preference for Cambridge. I applied for them and was successful in both. Simon suggested that I could exercise pressure on the Smithsonian C o m m i t t e e to allow me to hold the Fellowship at Oxford. But I felt that the time had come to b e c o m e involved in University teaching, and, therefore, despite my happy relationship with all at Oxford, I decided to move over to the lectureship at Cambridge.
5. Lectureship at Cambridge 1952-1954 Most of the theoretical physics at Cambridge was still concentrated in the Mathematics D e p a r t m e n t , but those of us who were interested were given the opportunity to sit and work in a room in the laboratory; I had a seat in a large r o o m at the bottom of the Mond Laboratory. A m o n g other occupants of the r o o m were Dennis Sciama, who achieved distinction in astrophysics and cosmology, and is particularly well known because of his able students, a m o n g them Stephen Hawking; Oliver Penrose who collaborated with Onsager to establish a sound basis for the B o s e - E i n s t e i n transition in liquid helium, and went on to establish a fine reputation in statistical mechanics; A a r o n Klug who was then a crystallographer, and whose brilliant researches on the structure of viruses led to the award of a Nobel prize; he is now Director of the Molecular Biology Research L a b o r a t o r y at Cambridge. A year or so after my return to Cambridge an advertisement appeared inviting applications for the Chair of Theoretical Physics at King's College, London. The general consensus at Cambridge in those days was that one did not apply for such positions without some unofficial hint that an application
C. D o m b / Some reminiscences about m y early career
19
would be welcome. I ignored this view and sent in an application. I was among a short list of 4 chosen for interview. By good fortune Mott and Pryce were members of the selection committee, and both were familiar with my work; but I am sure that the decisive voice on the Committee was that of J.T. (Sir John) Randall, Head of the Physics Department at King's, a person whose judgement I learned to respect and admire. A few days after the interview I received a letter from Randall informing me that I had been appointed to the Chair. By a coincidence Hermann Bondi had been appointed at the same time to a Chair in Mathematics at King's College, so we were together again in the same Institution. Incidentally Mott had just been appointed to the Cavendish Chair at Cambridge in succession to Bragg, and he wrote to suggest to me that from the point of view of scientific advancement I might be better off staying in Cambridge. I replied that my desire to move to London was prompted by personal and social rather than scientific motives. Soon after arriving at King's I met Michael Fisher, who had just completed a doctorate on analogue computers under the supervision of Donald McKay. I convinced Michael that there was a brighter future in statistical physics, but it was important to secure a grant which would support his research at King's in this field. Here a distinguished Israeli came to our help, Aharon Katchalsky (Katzir). I had met Aharon during a visit to the Weizmann Institute, and he showed great interest in my work; he felt that there should be applications to the configurational problems of polymers and polyelectrolytes. He outlined a specific polyelectrolyte problem, which I passed on to Michael, and this served as a vehicle for a Senior DSIR Fellowship. The problem was complex, but Michael managed to get somewhere with it, and it gave him the opportunity to look at some of the other fascinating unsolved problems of statistical mechanics. I have little doubt that my most important contribution to science has been to introduce Michael Fisher to this field. I do not have to tell this audience of the massive contributions, which he has made subsequently, but I am privileged that he came and played such a prominent part in this conference. As anticipated in my opening remarks, I have brought you to the stage of my life at which I achieved respectibility. Let me conclude the story with a quotation from a Talmudic sage: "Much have I learned from my teachers, more from my colleagues, but most of all from my students". My own experience heartily endorses this view.
Acknowledgements I am indebted to my former A.S.E. colleagues Fred Hoyle, Hermann Bondi
20
C. D o m b / Some reminiscences about my early career
and Tommy Gold for correcting some errors of memory in the original manuscript.
References [1] C. Domb, Physica D 38 (1989) 64. [2] The Small World of Fred Hoyle (Michael Joseph, London, 1986). [3] H. Bondi and T. Gold, Mon. Not. R. Astron. Soc. 108 (1948) 252; F. Hoyle, Mort. Not. R. Astron. Soc. 108 (1948) 372; 109 (1949) 365. [4] M. Ryle (Halley Lecture) Observatory 75 (1955) 137; M. Ryle and R.W. Clark, Mon. Not. R. Astron. Soc. 122 (1961) 349. [5] A.S. Eddington, Proc. Camb. Phil. Soc. 35 (1939) 186. [6] P.A.M. Dirac, R. Peierls and M.H.L. Pryce, Proc. Camb. Phil. Soc. 38 (1942) 193. [7] G.N. Watson, Proc. R. Soc. A 95 (1919) 83. [8] M.H.L. Pryce, Adv. Phys. 2 (1953) 67. [9] J.C.P. Miller, Tables of the Airy Integral, British Association Mathematical Tables Part, vol. B (Cambridge Univ. Press, Cambridge, 1946). [10] C. Domb, Adv. Phys. 2 (1953) 96. [11] C. Domb and M.H.L. Pryce, J. Inst. Electr. Eng. 94 (1947) 325. [12] S.O. Rice, Bell Syst. Tech. J. 23 (1944) 282; 24 (1945) 46. [13] Nelson Wax, ed., Selected Papers on Noise and Stochastic Processes (Dover, New York, 1954). [14] C. Domb, Proc. Camb. Phil. Soc. 42 (1946) 245. [15] C.A. Coulson, Proc. Camb. Phil. Soc. 43 (1947) 583. [16] C. Domb, Proc. Camb. Phil. Soc. 43 (1947) 587. [17] C. Domb, Proc. Camb. Phil. Soc. 43 (1947) 329; 44 (1948) 335; 46 (1950) 429. [18] F. Hoyle, Mon. Not. R. Astron. Soc. 106 (1946) 343. [19] E.M. Burbidge, G.R. Burbidge, W.A. Fowler and F. Hoyle, Science 124 (1956) 611; Rev. Mod. Phys. 29 (1957) 547. [20] H. Helmholtz, On the Sensations of Tone (1885) (reprinted: Dover, New York, 1954). [21] D. Gabor, Nature 159 (1947) 591. [22] T. Gold and R.J. Pumphrey, Nature 160 (1947) 124; 161 (1948) 640. [23] J.E. Lennard-Jones and A.F. Devonshire, Proc. R. Soc. A 170 (1939) 464. [24] T. Gold, Nature 218 (1968) 731. [25] T. Gold, Rotation and Terrestrial Magnetism, Nature 163 (1949) 513. [26] Report of an International Conference on Fundamental Particles and Low Temperatures (The Physical Society, London, 1947). [27] B. Kauffman and L. Onsager, Phys. Rev. 76 (1949) 1244. [28] H.A. Kramers and G.H. Wannier, Phys. Rev. 60 (1941) 252; E.N. Lassettre and J.P. Howe, J. Chem. Phys. 9 (1941) 747; E.W. Montroll, J. Chem. Phys. 9 (1941) 706. [29] L. Onsager, Phys. Rev. 65 (1944) 117. [30] G.H. Wannier, Rev. Mod. Phys. 17 (1945) 50. [31] C.N. Yang and T.D. Lee, Phys. Rev. 87 (1952) 404. [32] C. Domb, Nature 163 (1949) 775. [33] C. Domb, Proc. Roy. Soc. A 196 (1949) 36; 199 (1949) 199. [34] C. Domb, J. Phys. A 7 (1974) 1335. [35] Mark Azbel, Refusenik- Trapped in the Soviet Union (Houghton Mifflin, Boston, 1983) p. 126. [36] M. Born, Proc. Math. Phys. Soc., Egypt 3 (1947) 35.
C. D o m b / S o m e reminiscences about m y early career
21
[37] Michael F. Shlesinger and George Weiss, eds., The Wonderful World of Stochastics (NorthHolland, Amsterdam, 1985) p. 50. [38] O. Maass, Chem. Rev. 23 (1938) 17. [39] A. Munster, Compt. Rend. 2 e Reunion de Chimie Physique (1952) 21.
CHAPTER 1
PLENARY LECTURES
SOME REMINISCENCES ABOUT MY EARLY CAREER Cyril D O M B Department of Physics, Bar-llan University, Ramat-Gan, Israel The author recalls some of the highlights of his scientific career before he took up a professional appointment at King's College, London in 1954. The periods covered are: High School and undergraduate studies at Cambridge University 1932-1941; radar research for the British Admiralty 1941-1946; graduate studies at Cambridge University 1946-1949; post-doctoral research at the Clarendon Laboratory, Oxford University 1949-1952; faculty appointment at Cambridge University 1952-1954. A brief description is given of the personalities with whom the author was associated, the research problems in which he was involved, and of the early post world war 2 scientific conferences.
1. Introduction: high school and university 1932-1941 Let me first say how grateful I am for the many complimentary things which have been said about me at this Conference. My wife is a professional teacher, and she says that anyone who gives a lesson or delivers a lecture, is planting a seed; one never knows in advance how much fruit each seed may bear. It has been a wonderful revelation to me from the remarks of many of the speakers that my teaching and lecturing activities over many years did indeed bear fruit. I thought I would reminisce about the period in my life before I became a professor. This has two advantages. Firstly it should be new to everyone here (I met up with Michael Fisher, my oldest student at the Conference, only when I took up a professorship at King's College, London). Secondly, if I may quote the views of A.S. Besicovitch from an article which I wrote recently for the Mandelbrot Festschrift [1], before a person can be appointed to a Chair he must have become respectable, and once he is respectable, he ceases to be interesting. So hopefully for the period which I plan to cover, I and my associates were still interesting. My home background was not affluent, and my parents were not in a position to support my education financially. I am therefore eternally grateful to Britain, the country of my birth, for enabling me to obtain a first class education without calling on my parents. I started at a general elementary school, and obtained a scholarship to a medium grade high school, Hackney Downs School. I showed some mathematical ability, and the senior mathematics teacher, F.J. Swan, told me that if I really wanted to embark on a 0378-4371/90/$03.50 © 1990- Elsevier Science Publishers B.V. (North-Holland)
2
C. Domb / Some reminiscences about my early career
mathematical career, it was advisable to get to Cambridge University. Hackney Downs had no training programme for scholarships to Cambridge or Oxford; they would average perhaps one scholarship a year on the basis of individual tuition. The top class high schools like St. Pauls, City of London, or Manchester G r a m m a r ran special scholarship classes, and might well get 20 or 30 scholarships each year. In D e c e m b e r 1937 I went to Cambridge to compete against what Fred Hoyle termed the "trained greyhounds" (Bingley G r a m m a r School, which Hoyle attended [2], was comparable in standard to Hackney Downs). But Swan had prepared me well, and it was a pleasant surprise to learn that I, an "outsider", had been awarded a Major Open Scholarship by Pembroke College. My best paper was in projective geometry, my applied mathematics being quite weak. I went up to Cambridge in October 1938; it was just after Munich, and war clouds were gathering on the horizon. I can still recall vividly the freshness and inspiration of my introduction to real mathematics. There were several outstanding lecturers, the most notable being Philip Hall, the distinguished algebraist. I still have the notes which I took at his course on "Linear Algebra", and despite the plethora of books which have appeared on this subject during the intervening years, I still used these notes as the basis for a course which I gave recently at Bar-Ilan. War broke out in September 1939. Someone high up in government circles decided very intelligently that if we were allowed to complete degrees in science, we would be of much more help to the technology of war than if we were called up as undergraduates. I was advised to move in the direction of applied mathematics since this would provide far more opportunities of contributing to the war effort than pure mathematics. It should be pointed out that there was no theoretical physics at the Cavcndish Laboratory in those days. Dirac, Fowler and Eddington, who would have certainly been classified as theoretical physicists on the continent, held Chairs in applied mathematics in the Faculty of Mathematics. In my final year for Part 3 of the Mathematical Tripos, I was examined in courses on relativity, quantum mechanics and statistical mechanics, although I attended a variety of additional courses on other topics in pure and applied mathematics. I never regretted my training as a mathematician. In theoretical physics we are usually pragmatic, and far more concerned with deriving a practical solution to a problem than with establishing rigorously that the solution is correct. But a training in rigour enables one to decide with more confidence when it can be ignored. I graduated from Cambridge in June 1941, and joined the research group on radar (or R D F as it was then called) at the Admiralty Signal Establishment (ASE) in July 1941.
C. Domb / Some reminiscences about my early career
3
2. Radar research for the Admiralty 1941-1946 There were no appointments with the designation "theoretical" at the Admiralty. I was appointed as a T E A 3 (Temporary Experimental Assistant); others at a more advanced stage in their university work were appointed as Experimental Officers. Because of our experimental titles we were started on practical work, and I was introduced to the soldering iron. It was here that I first met Fred Hoyle. We were both so hopeless with the soldering iron that it was considered bad for morale to let us stay in the experimental group, and we were exiled to a hut on the outskirts of the establishment and told to occupy ourselves with theory. Fred was then a Junior Fellow at St. John's College, Cambridge, aged 25, whilst I was 20. He immediately pointed out that whilst it was our task at ASE to help win the war, he felt sure that we could fulfil this task without giving u p our interest in fundamental science. His own area of research was astrophysics, and he proceeded to give me a potted description of the current situation and major problems of astrophysics. He also provided brief profiles of the leading researchers in the field, who might be good mathematicians but had poor physical insight. Since I was undoubtedly looking around for a suitable field of research, he thought that astrophysics offered good prospects; if people with such poor appreciation of the physical aspects of a problem could get to the top, I should have no difficulty in establishing myself. Despite this encouragement I remained dubious since I was not convinced that physical insight was my forte. A week later Fred came in one morning triumphantly waving a copy of the "Monthly Notices" of the Royal Astronomical Society". "You have a unique opportunity of making your reputation overnight", he announced, "Eddington has published a paper with a serious flaw in it; if you write a brief note pointing out the flaw, you will immediately establish yourself in the field". Fred felt that it was not appropriate for him to do this since he was known to belong to the opposing school of thought. Since I had just attended Eddington's lectures, and he had been one of my Part 3 examiners, I could not really see myself filling the envisaged role. Also I was already fairly convinced that my area of research interest was statistical mechanics and condensed matter physics. Fortunately we were joined later by two new arrivals at ASE, Hermann Bondi and T o m m y Gold who were more sympathetic to astrophysics than I had been. Both came originally from Vienna, and had been interned in the Isle of Man during the 1940 panic. Some intelligent person in a position of authority had engineered their rapid transformation from spy suspects to members of a Top Secret Establishment. Hermann was a very capable mathematican who had distinguished himself at Cambridge, and the basis for his appointment was
4
C. D o m b / Some reminiscences about m y early career
clear. Tommy's situation was more mysterious. He had obtained a 4th class degree in engineering, not for lack of skill, but because he found it more exciting to climb King's College Chapel than to attend lectures. A short discussion with him on any scientific problem would soon provide evidence of his wide understanding and experience, and even though his formal mathematical knowledge was limited, I have never met anyone with greater physical insight #1. During his period at Cambridge he had made a number of important contacts, including that of E.D. Adrian, who was then engaged in his pioneering experiments on electrical conduction in nerves; strong recommendations from Bondi and Hoyle helped convince the government science recruiting team of his true calibre. Bondi and Gold were very interested by the many astrophysical problems which Hoyle put before them. In the early post war years the trio was nicknamed the "Cambridge Circus", and they contributed significantly to stimulating and invigorating British astrophysics during this period. The most widely known of their contributions is the steady state model of the universe [3]. Whilst this model has now been discarded in favour of the big bang model, its unequivocal predictions were the immediate cause of a number of exciting and crucial experiments in radio-astronomy [4]. We were soon constituted into a formal "Theoretical Group" with Hoyle as Head and Bondi as Deputy, and we began exercising an influence on the solution of the technological problems faced by the Admiralty. As far as the orderly routine of the Civil Service was concerned, Bondi and Gold were enfants terribles. We were stationed at Witley, Surrey, and they found it convenient to live in the neighbouring village of Dunsfold. Travel at our level of importance was by public transport only. The 8:30 am morning bus from Dunsfold arrived in time to sign on at 9:30 am. This was 30 minutes late. But Hermann and Tommy were liable to miss this bus and the next bus left at 1:30 pm! It is a remarkable achievement of British Society that an enfant terrible can be transformed into a pillar of the establishment. After a distinguished university career at Cambridge and King's College London, Hermann Bondi joined the Scientific Civil Service, and reached the top position of Chief Scientific Adviser to the Ministry of Defence; he was also knighted. I once called on him in his office in Whitehall to discuss a matter of mutual interest. "What time did you get in this morning"? I asked. "I was in by 8:00 am", came Hermann's proud reply, "my advice was needed urgently". By contrast, Tommy Gold has remained an enfant terrible, and is the best counterexample I know to Besicovitch's thesis quoted at the beginning of this ~ I was never privileged to m e e t Richard F e y n m a n personally, but he was described to me by D e n n i s Sciama (in a first a p p r o x i m a t i o n ) as a synthesis in one p e r s o n of T o m m y G o l d ' s physical insight and H e r m a n n B o n d i ' s mathematical skill.
C. Domb / Some reminiscences about my early career
5
article. He became and remained a professor at Cornell University without ever attaining respectability. Fred Hoyle spent much of his spare time reading science fiction. I found this very puzzling, but he said that familiarity with the sort of literature which was published could be of great help to him some time in the future. "The people who write this stuff know very little science, yet they made good money on their publications; I have a real knowledge of science, and I should surely be able to do far better". After the war Fred went back to Cambridge, and it did not take too long before he was elected to the Plumian Chair of Astronomy (and knighted). Some years later he became unhappy with the way applied mathematics was run at Cambridge, resigned his Chair, and went off to live in the Lake District. His earnings from science fiction and other writings dwarfed his former professorial salary! One of the most interesting personalities in the research section of ASE was Otto Bohm, who although attached to the aerials group, maintained close and cordial links with the theoreticians. For many years he had held a key position in the German radio industry as' research director of Telefunken. He was Jewish, and hints were dropped in the 1930's after Hitler's accession to power that in his specific case this would be overlooked if he wished to continue in his post. But he ignored these hints, and joined other refugees who left for the U.K. Like other refugees he was interned in 1940, and released to join ASE in the summer of 1941, when he was already over 60. Bohm played a key role in the development of aerials for centimetre wavelength radar. All of his calculations were relatively simple, many of them based on the standard formula for the impedance of a transmission line at any point on its length. He somehow managed to apply this formula to the new technology of wave guides and wave guide flares, and he estimated the illumination of the aperture from which the polar diagram could be calculated. The major parameter which he assigned intuitively was the characteristic impedance Z 0. The wave guide, the flare, and free space all had their specific Z 0. From the point of view of the mathematical physicist the problems he tackled were horribly complex involving the solution of Maxwell's equations for bodies of unusual sizes and shapes; but with remarkable perception he used empirical approximations which gave a solution correct to 10% or 15%. Further accuracy and refinement were obtained by a combination of empirical theory with experiment. It always seemed to me that the electrons themselves when faced with the solution of partial differential equations with appropriate boundary conditions must surely use pragmatic methods of Bohm's type rather than eigenfunction expansions. It is time to say something more precise about my scientific work during the
6
C. Domb / Some reminiscences about my early career
war years. My first mentor was M . H . L . (Maurice) Pryce who joined ASE at the same time as I and was assigned to the aerials group. Pryce had enjoyed a fabulous reputation at Cambridge; even as an undergraduate he had participated in colloquia and when Eddington published a paper putting forward some of his unconventiai views [5], the reply of conventional physics was given by Dirac, Peierls and Pryce [6]. Shortly before the war he had taken up an appointment as Reader in Theoretical Physics at Liverpool University. A few weeks after his arrival, Pryce produced an extremely neat and useful piece of theoretical work. In making practical use of radar it was important to be able to calculate simply and accurately the field strength due at a transmitter at any given height above the earth. The classic problem of the diffraction of electromagnetic waves by a sphere had been tackled by a number of investigators, the most comprehensive solution being that of G.N. Watson [7]. This solution is equally valid for the earth or a raindrop; but the generality of the solution exacts a price, and it cannot be readily used for practical calculation. Pryce suggested that for diffraction around the earth a meaningful approximation should be made at the outset, using a metric which takes account only of the first terms in the curvature; Maxwell's equations should then be solved for this metric. This leads naturally to a solution in terms of the Airy integral [8], which satisfies the simple second order differential equation y " = - x y . The Airy integral can be expressed in terms of Bessel functions of order but it is better treated as a simple function in its own right. Its values for real variables, had recently been tabulated by J.C.P. Miller [9], of Liverpool University. Pryce's solution required values along certain lines in the complex plane. Pryce was familiar with Miller's work, and sent me to Liverpool to undertake the new computations [10]. When they had been completed, we produced a set of curves [11] from which the field strength due to a radio transmitter could be derived with little effort at any point of interest. I think we did a good job because the curves were widely used on both sides of the Atlantic. The statistical distribution of noise, and noise and signal in receivers was a question of interest and importance. Bondi tackled this problem very effectively, and the work (in addition to an astrophysical investigation suggested by Hoyle) helped to secure him a Fellowship at Trinity. He never published his treatment, but he derived independently the results contained in the well known paper by S.O. Rice [12], which are reproduced in the widely used reprint volume edited by Nelson Wax [13]. There was great interest during the war years in "anomalous propagation" of centimetric waves. Certain meterological conditions were found to give rise to unusually long radar and signal ranges, and it was assumed that the waves were trapped by a type of wave guide effect near the surface of the earth which
C. D o m b / S o m e reminiscences about m y early career
7
prevented attenuation. Calculations for a variety of models of the atmosphere were undertaken by theoreticians working with the Air Force at TRE (Telecommunications Research Establishment). It was important to have basic factual information, and Fred Hoyle had the bright idea of stationing a transmitter at Aberporth on the shores of Cardigan Bay in Wales, and a receiver o n t h e summit of Snowdon, and taking records of propagation over Cardigan Bay for a long period of time. There was a hotel on the summit of Snowdon, which could be requisitioned to provide accomodation and technical facilities, and the height of Snowdon would correspond to a fairly low flying aircraft. The plan was accepted by the Admiralty, and enabled members of the theoretical group to carry out activities of importance in the beautiful Welsh countryside. The weather on top of Snowdon is often quite wild even in summer when the hotel had usually been open; it had always been closed during the winter. Fred's plan involved keeping it open and manned during the winter when the snow and ice would have to be braved. Hermann Bondi, who was familiar with mountainous winter conditions from his youth in Austria, volunteered to stay at the hotel and man the station, and naval ratings were assigned to look after his physical and technological needs. The experiments continued for many months and we all took part in them. Another problem of importance for sea borne radar was noise from sea reflections. Fred Hoyle suggested that the north coast of Cornwall (Bedruthan Steps) would provide a suitable location for a station at which to conduct a systematic study of long wave Atlantic breakers. Tommy Gold took charge of the project. Some of the conclusions played an important role later in the anti-radar "window" development. A question in which I became interested, and which belongs to the physics of disordered systems, was the calculation of radar scattering from rain clouds. It has always been assumed that droplets should be treated as random scatterers and this is reasonable when the wavelength is much shorter than the spacing between raindrops. But it is clear that for radiation of wavelengths long compared with the spacing between raindrops the cloud should be treated as a continuous medium with a dielectric constant differing from unity. How is the transition between these two approaches effected? Consideration of this problem led to the study of a special type of random walk problem, and to my first scientific publication [14]. I immediately came under fire from Coulson [15] (one of my predecessors in the Chair at King's College), who pointed out that there were limitations to the validity of the formulae which I had derived. In my reply [16] I showed that my results were satisfactory for the applications with which I had been concerned. In the course of discussions with experimentalists, questions often arose
8
C. Domb / Some reminiscences about my early career
which involved calculations relating to electric circuits, and I became very familiar with the technique of Laplace transforms. This stood me in good stead for a number of early calculations relating to probability theory [17]. In June 1945 the war in Europe came to an end, and Fred Hoyle announced that he would be going back to his Fellowship at Cambridge since he had an astrophysical problem of major importance on his mind, which needed intense concentration. In regard to the need to bring the war in the East to a successful conclusion, Fred argued that experience had shown a delay of 1-1½ years between any idea which he generated and its practical use by the Navy; he was absolutely convinced that before such a time the war with Japan would be over. His action put the Civil Service in a quandary. There was no mechanism by which he could resign or be dismissed since we were all "drafted". They therefore considered him on special duty at Cambridge, and continued to pay his salary. This was very embarrassing to Fred, and he came back to discuss the situation with the Captain Superintendent, the Naval Officer in charge of ASE. Interestingly enough Fred received a sympathetic hearing, and the Captain suggested that he spend some of his time at Cambridge thinking about ASE problems, with which he was by now very familiar; he could come back to report from time to time. Eventually a solution was found to the dilemma. The problem which Fred Hoyle had begun to think about was the origin and abundance of chemical elements in the universe. Within a year he had published a definitive paper [18] showing how it is possible to account for the abundances of the elements in stars by the statistical mechanics of nuclear reactions at high temperatures. He continued to think about the problem, and when accurate data on isotopic abundances became available, he collaborated with the Burbidges and W.A. Fowler to publish a classic paper [19], which accounted in remarkable detail for the observations. The citation in the award of the Nobel prize to Fowler in 1983 contained the phrase "for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe", thus recognizing the importance of this work. Fred's prognosis was correct, and the war with Japan came to an end a few months later. This initiated a major scramble among the temporary staff to get back to the university as quickly as possible. Hermann Bondi had no problem since his Trinity Fellowship was available immediately. My own position was more difficult since I had nothing specific; fortunately Pembroke College came to my rescue. A very able physics graduate student, Efraim Nahum, had been killed by the only bomb to fall on Cambridge during the war, and his parents had endowed a scholarship in his memory. The money had accumulated for
C. Domb / Some reminiscences about my early career
9
several years, and was enough to keep me from January to September 1946, when it was hoped that I would get a government award. As usual Tommy Gold had an original solution for his situation. He had become involved in discussions with R.J. Pumphrey, a distinguished biologist working at ASE, on the nature of the circuits in the human ear. Helmholtz had been led to think that these circuits are highly resonant [20], but current investigators had discounted his ideas [21], and assumed that the circuits were highly damped. Gold and Pumphrey [22] devised crucial experiments, which led back unequivocably to the Helmholtz picture. Gold submitted his work to Trinity and was awarded a Fellowship. It is to the credit of the referees that his 4th class degree was ignored.
3. Graduate studies at Cambridge 1946-1949
I had decided that the main area of research for my graduate studies would be statistical mechanics, and Fred Hoyle agreed to serve as my supervisor. He was not actively engaged in research in this area, but I hoped that I would be able to find problems by myself. Fred would let me work on my own and I could discuss my results with him if I felt that I was getting somewhere. I have always told graduate students who came to ask my advice that they should eliminate dependence on their research supervisor at the earliest opportunity. It seemed to me that there should be many problems to be tackled in relation to phase transitions, but I found the standard text by Fowler and Guggenheim, "Statistical Thermodynamics" (published in 1939), rather depressing. It gave me the impression that the theories were in a healthy state, and only minor points needed to be straightened out. I gained the same impression from the papers by Lennard-Jones and Devonshire on melting [23]. They seemed to achieve amazingly good agreement between theory and experiment, and the subject seemed to be tied up. Fortunately the year 1946 saw the publication in the famous Oxford monograph series of J. Frenkel's "Kinetic Theory of Liquids" and this gave me much more encouragement. The title is a misnomer and the book deals comprehensively with a variety of problems in condensed matter physics. On the Lennard-Jones and Devonshire theory of melting, Frenkel said (p. 111): "The considerable quantitative agreement between the calculated and observed positions.., can hardly be considered as a convincing confirmation.., such a numerical agreement being easily obtained by a proper choice of the parameters involved". Again in relation to a particular version of the hole theory of the liquid state he stated (p. 176): "Similar ideas have been put forward by Furth w h o . . , attempted, with a very poor degree of success, to apply this
10
C. Domb / Some reminiscences about my early career
conception to the quantitative interpretation of a number of properties of liquids". These assessments, and others of a similar kind throughout the book, convinced me that a lot of fundamental problems needed to be tackled. More important, I learned from Frenkel that the basic problem in dealing with the statistical mechanics of interacting systems is the calculation of the entropies of all the different possible configurations, and this is a mathematical problem in probability. Cambridge was a very exciting place in 1946 with large numbers of staff and students returning with enthusiasm after a prolonged absence. By general academic consensus there were 4 particularly bright young stars among those returning to the Cavendish Laboratory, Brian Pippard, Martin Ryle, Denys Wilkinson and Tommy Gold. This concensus view was confirmed by subsequent developments. Brian Pippard became Cavendish Professor; Martin Ryle was the pioneer of radio-astronomy and received a Nobel award in 1974; Denys Wilkinson moved to a Chair of Nuclear Physics at Oxford where he built up a lively research school. Tommy Gold contributed significantly to a variety of different problems, the most important being the identification of pulsars as neutron stars [24], and the most spectacular the demolishing of a "New Law of Nature" proposed by Patrick Blackett, Nobel Laureate and later President of the Royal Society. Blackett had been impressed by the experimental data on magnetic fields associated with rotating stars, and the origin of the earth's magnetic field was still an open question. He came forward with the dramatic suggestion that every rotating gravitating body generates a magnetic field. Tommy immediately realized that the idea had untenable implications, and at a public discussion organized by the Royal Astronomical Society he emphasized that among other things, the proposal contravened special relativity, and the principle of equivalence in general relativity [25]. The idea was never revived! After serving for a period as Assistant to the Astronomer Royal, Tommy moved to a professorship at Corneil. The first International Conference after the war took place in July 1946, and coincided with the opening of the new Austin Wing of the Cavendish Laboratory. It is amazing to think that it was devoted to "Fundamental Particles and Low Temperatures", and many of the leading personalities in the world of physics attended. Some highlights of the programme are reproduced in fig. 1. The opening address was delivered by Niels Bohr, and the speakers at the first session were Pauli, Dirac and Born, who dealt with the difficulties of field quantization and quantum electrodynamics. The following morning was devoted to the theory of liquid helium with F. London advocating the Bose-Einstein condensation model. V. Peshkov came from the Soviet Union, and told of Landau's alternative point of view, and for the first time we heard the terms "phonons" and "rotons". Each proponent
C. Domb / Someremin~cencesabout my ear~ career
11
Physical Society Conference - July 22nd - 27th, 1946 Fundamenta] Particles and Low Temperatures. Monday,
July 22rid. Chair - Sir W.L.Bragg.
2.30 p.m.
Address of Welcome to the Conference
D.Brunt
FUNDAMENTAL PARTICLES (a) Opening addr_ees_~
Arts School
"A genaral survey".
N. Bohr. (b) Present state of general theory
Chair - N. Bohr.
W. Pau li.
"Difficulties of field theories and of field quantixation".
P.A.M.Dirac.
"Difficulties of quantum e le ct rodynamics".
M. Born.
"Relat iv ist ic Quantum Mechanics and the principle of reciprocity". Tuesday, July 23rd.
Arts School
LOW TEMPERATURES 9.30 a.m.
Chair - F. Simon
Liquid Helium II F. London
"Theory of Liquid Helium II".
K. Mendelssohn.
"Friekionless transport".
V. Peshkov (to be read by J.F. Allen).
"Propagation velocity of second sound in Liquid Helium II".
L. Onsager. 9.30 a.m.
~'Transition points". FUNDA~'~NTAL PARTICLES
Arts School
Chair - E. Schroedinger. N.F. Mott.
Closing address.
Fig. 1. Some items from the programme of the First International Scientific Conference after World War 2. (This figure represents the original duplicated programme.)
12
c. Domb / Some reminiscences about my early career
was very frank in his assessment of the opposing viewpoint. F. L o n d o n on Landau: " T h e quantization of the motion of a liquid as he proposed it is however quite u n c o n v i n c i n g . . . There is unfortunately no indication that there exists anything like a r o t o n " . Peshkov: " H o w e v e r the theoretical speculations of London and Tisza and very artificial and unconvincing". Among the speakers at one of the low temperature sessions was Lars Onsager on "Transition Points", but I must confess that I had to wait for the published version of the Proceedings [26] before I understood the content of his lecture. I then learned that he had been describing his work with Bruria Kauffman on correlations in the Ising model [27]. The Chairman on the last day was Schr6dinger, and one of the speakers was Heitler; both had recently moved to the Dublin Institute of Advanced Studies. The closing address was given by Mott. The G o v e r n m e n t of Eire had been prodding its citizens hard to put the Irish language, Erse, on the map. Mott congratulated Schr6dinger and Heitler on restraining themselves from speaking in their native Erse! My own researches in the statistical mechanics of interacting systems on lattices were sparked off by a colloquium given by A.R. Miller, a student of Fowler, on the Bethe approximation and its application to a variety of problems. I realized that for one-dimensional systems I could solve the problem exactly, and this led me naturally to the transfer matrix. But I soon found that I had been anticipated by three groups of workers [28]; this led me to chase up the literature, which was not difficult since there was only a handful of journals. I was struck by awe and admiration by Onsager's classic 1944 paper [29], and I found the 1945 review by Wannier [30] very useful since it contained more of Onsager's unpublished results. Wannier's paper ended with an optimistic hope, characteristic of the period, "It is to be hoped that a three-dimensional calculation will, before long, furnish the answer to these questions". I set about formulating transfer matrices for a variety of problems, and I found that they could all be reduced to a simple characteristic form with large numbers of zeros, which I called d u o - d i a g o n a l . At this period I hoped that it would be possible to deal with these matrices exactly, and I consulted with Philip Hall; but he was convinced that the problem was very difficult and had no practical suggestions to offer. I therefore developed perturbation expansions for the two-dimensional Ising model in zero and non-zero field. For a zero field certain simplifications were present, which enabled me to derive an indefinite number of terms of a series expansion; this was equivalent to Onsager's solution for a general asymmetric net. When the field was non-zero the situation became much more complicated, and only a limited number of terms could be derived. By examining the behaviour of those series I conjec-
C. Domb / Some reminiscences about my early career
13
tured that there were no singularities in non-zero field, a result proved rigorously a few years later by Yang and Lee [31], and I was able to estimate the critical behaviour of the spontaneous magnetization. This work constituted my Ph.D. thesis, and the results were published as a letter in Nature [32], and two papers in Proc. R. Soc. [33]. Early in 1948 I faced a sudden crisis in my personal career. I had been supported by a Senior Research Award of the DSIR (Department of Scientific and Industrial Research). Such awards were normally given for two years, and could be extended for a third year if the research was satisfactory. My work was going well and I anticipated no difficulty in securing a renewal. But with no preliminary warning a change of government policy was introduced that all such grants be terminated after two years. I had not applied for any alternative grant, and I was left suspended. The new policy threatened the careers of other research workers in the same situation, and senior professors intervened to try to get the decision revoked in individual cases (Hartree took up the cudgels on my behalf). But it seemed wise to explore alternative possibilities. Maurice Pryce had just been appointed to a new Wykeham Chair of Theoretical Physics at Oxford, and I went over to give a Colloquium and to find if he had anything to offer. The timing was fortunate. Pryce had a queue of graduate students, a substantial fraction being from overseas, who wished to do research in theoretical physics, and my work offered a number of promising lines (three-dimensional models, antiferromagnetism, distant neighbours, etc.). Stanley Rushbrooke had just been appointed to a Readership in Theoretical Physics at Oxford; his major interest was statistical mechanics and he reacted positively to my work. Pryce managed to secure an ICI Fellowship for me, and at the beginning of 1949 I moved to Oxford.
4. Clarendon Laboratory, Oxford 1949-1952 The years which I spent at Oxford were very fruitful. I had six graduate students. George (G.M.) Bell worked on closed form approximations for sophisticated models. He went on to a distinguished career in statistical mechanics, and became a professor in the mathematics department at Chelsea College, London. He is now at King's College, London, following a merger of the two colleges. Jack (J.E.) Brooks from the USA worked on antiferromagnetism, and after securing a Ph.D. returned to industry in the States. Renfrey (R.B.) Potts was a Rhodes Scholar from Adelaide, and I am sure that you are all familiar with his name from the P o t t s m o d e l . His thesis was concerned with
14
C. Domb / Some reminiscences about my early career
distant neighbour interactions in the Ising model and the new Potts model entered only marginally (I have told the story in detail elsewhere [34]). He returned to Adelaide where he later became Professor of Applied Mathematics. His interests have moved away from statistical mechanics; he has contributed with distinction in a number of different areas, and is a Fellow of the Australian Royal Society. Hugh (T.H.K.) Barron is the son of one of my former teachers at Hackney Downs. He worked in the area of lattice dynamics, became a world authority on thermal expansion, and Reader in the Chemistry Department at Bristol University. Lewis (L.S.) Salter came from Wabash College, Indiana, and worked on the thermodynamics of solids. He had a strong sense of public duty, and went from Oxford to Indonesia to serve in the Peace Corps. Eventually he returned to his Alma Mater, Wabash College. My last Oxford student, Martin (M.F.) Sykes, became my closest collaborator, and many of my papers in the 1950's and early 1960's were written together with him. Most people here will not have met him since he does not attend conferences, preferring to work in the quiet of the English countryside. His capacity for envisaging configurations of sites and bonds on lattices is quite incredible, and many of my subsequent students and collaborators benefited from his advice and help. During my first year at Oxford I worked on the three-dimensional Ising model using the matrix approach, but one of Rushbrooke's students, A.J. Wakefield, who also had a remarkable gift for configurational work, did far better than me, and I never published the results. The most important influence during my period at Oxford was Sir Francis (F.E.) Simon, who administered the Clarendon Laboratory. Lord Cherwell was the nominal Head, but he spent the whole week in London at the House of Lords, and came back to Oxford only for the weekends when Simon brought him up to date. Simon was a father figure who took a close personal interest in his staff and students. He was keen that they should be happy and free of anxiety, since he was convinced that under such conditions they would produce their best work. He would concern himself personally with their grants and research fellowships, and inspired such confidence that research staff preferred to stay at the Clarendon with temporary appointments rather than move to permanent appointments elsewhere. He was always throwing out ideas and suggestions for new lines which might be worth pursuing, and he involved the theoreticians in the planning and interpretation of experiments. Simon was pragmatic in his relationship with university administration. He obeyed all the rules, but tried to reduce the interference with the normal functioning of the laboratory to a minimum. An illustrative story, which circulated the Clarendon, concerned Arthur Cooke's Ph.D. oral examination.
C. D o m b / S o m e reminiscences about m y early career
15
A few days before the examination Simon ran into Cooke and said: "By the way Cooke, about your Ph.D. oral, come and have a chat with me to tell me what your thesis is about; and think of some clever questions, which I can ask you, which will impress the external examiner". The Colloquia of the low temperature group took place on Mondays. At the end of the colloquium Simon asked one or two dumb fool questions, which encouraged the audience to feel that if the professor could ask such questions, they risked little in having a go. I was interested to find a similar type of story relating to Niels Bohr in Mark Azbel's fascinating book [35]. He there tells the story of a lecture, which Bohr delivered during a visit to his distinguished friend Lev. D. Landau. After the lecture a question was asked: " H o w do you account for the incredibly high productivity which has emerged from your school?" Bohr answered: "I think it happened because we were never cautious. We were never afraid to look like fools before our students". This was so different from the attitude prevailing at the Landau Institute that the translator, Yevgeny Lifshitz, instinctively rendered "We were never afraid to let our students know they were fools". Simon had wide international contacts, and many visitors to England dropped in at Oxford. When Onsager came over from a sabbatical at Cambridge in 1952, Simon told him that he was continually losing his secretaries by marriage to his collaborators - this had happened seven times in the course of his career. Onsager commented that Simon must use discrimination in choosing his secretaries. In fact the news got around among the young ladies of Oxford, and, whenever a vacancy occurred, there were queues of applicants, even though the pay offered was very modest. I cannot in any way match Simon's record, but I was gratified to learn that my very capable former secretary, Jill, teamed up recently with my former colleague David Gaunt, who I am pleased to see participating in this conference. Elliott Montroll came to visit me at Oxford, he being one of the few people in the world interested in the Ising model at that time. We found that we had other interests in common, and became lifelong friends. Some years later Elliott invited me as a visiting professor to Maryland, and it was on this occasion that I first met another lifelong friend, George Weiss. Elliott could always find openings for bright young people, and Ren Potts and Michael Fisher both crossed the Atlantic for the first time at his invitation. Max Born was also a regular visitor to Oxford. In the early post war years he teamed up with Bert Green, a very able mathematician, and they started to tackle the major current problems in physics. It was the general academic consensus that Born felt the need to remind the Nobel Committee of his p r e s e n c e - all the other giants who founded the quantum theory had received Nobel prizes, Heisenberg in 1932, Schr6dinger and Dirac in 1933 (during the
16
C. D o m b / Some reminiscences about m y early career
war the awards were suspended), and Pauli in 1945; but Born seemed to be shelved. Then Born had an idea which even he considered dubious, that quantum zero point fluctuations are sufficient to break up perfect crystals into block structure at the absolute zero. His first paper on this topic appeared in the Proceedings of the Egyptian Academy of Sciences [36]. Born told Simon that there was a good chance that the idea would prove incorrect, and then no one would notice the paper; but if it proved correct it would be of major importance and he could then claim priority. As is well known Born eventually received his Nobel award in 1954. In the spring of 1952 I began to prepare for my first major international conference (now known as Statphys 2), which was being organized in Paris by Prigogine and de Boer. I had not been invited to Statphys 1 in Florence in 1949 presumably because my work was still unknown. Rushbrooke, who had attended it, brought back the news of Onsager's calculation of the long range order for the two-dimensional Ising model. I had also participated in the International Low Temperature Conference at Oxford in 1951 (LT2) but my contribution had been marginal. At Statphys 2 I presented two papers, one on the three-dimensional Ising model, and the other on the theory of the melting curve at high pressures, which had been stimulated by Simon's empirical formula. It was a very exciting conference with many highlights. I have already described elsewhere the laying of the ghost of John Maddox's exact solution of the three-dimensional Ising model [37]. Let me mention here two other incidents. Joe Mayer (of cluster integral fame) presented a paper in which he claimed that a summation of the cluster integral series led to the conclusion that the liquid-vapour co-existence curve has a flat top. Previous experimental work by Maass [38] had come to the same conclusion. Suggestions had been forthcoming that gravity might play a part because of high compressibility near the critical point, but they had been discounted. Fortunately W.G. Schneider refused to be cowed by this formidable combination of authority, and conducted a simple experiment by himself. He took a long tube in which one might expect a gravitational effect to be significant, and then turned the tube on its side so that the gravitational effect was minimized. The striking result is shown in fig. 2; ever afterwards gravity has always been taken into account in these experiments. Simon had been very concerned with the question whether the melting curve ends in a critical point at sufficiently high temperatures, comparable to the liquid-vapour critical point. I had answered firmly in the negative, but Simon was not completely convinced. At the beginning of the conference he came and whispered in my ear that Arnold Munster was presenting a paper [39] which
C. Domb I Some reminiscences about my early career
17
0.95
1.00
1.05
E ..= 1.1o
i,
0
1,15
1.20
1.2.5 I ~ 16.400
16.450
I I 16.500 16.550 Temperat ure('C)
I 16.600
Fig. 2. Liquid-vapour coexistence curves in the critical region: long tube DO, short tube O.
purported to prove quite generally that all first order phase transitions end in a critical point at sufficiently high temperatures; I should prepare to defend my view. When Munster was called upon to speak, he flashed one slide after another very quickly, each slide being filled with fluctuation formulae, grand partition functions, etc. At the end he proclaimed " T h e r e f o r e every first order transition must end in a critical point". How should I deal with this situation? Fortunately I happened to be sitting next to Fierz, who had the reputation of being Pauli's brightest student, and I had taken him into my confidence. Fierz turned to me and said: "You have nothing to worry about - he has made some fundamental mistake". " H o w could you possibly follow the argument presented at such a speed", I asked. " H e may have produced statistical mechanical formulae, but at no point has he introduced a specific model; therefore he has remained in the sphere of thermodynamics. I am quite sure that this issue cannot be settled by thermodynamics", came his reassuring reply. I returned to Oxford to face another career crisis, the renewal of my ICI
18
C. D o m b / Some reminiscences about my early career
Fellowship. Cherwell was the obstacle. I was in Oxford from Monday to Friday when Cherwell was in London. I returned to London for the week-end when Cherwell came back to Oxford. The general laboratory colloquium took place on Fridays at 4:30 pm, but I never attended; Simon had not objected to this, since I attended the low t e m p e r a t u r e colloquium regularly on Mondays. But now when he suggested renewing my Fellowship, Cherwell said: " W h o is this man D o m b , and why do I never see h i m - I d o n ' t believe that he exists". Simon pleaded plaintively to me: " C a n you not be an orthodox Jew in Oxford one Friday, and deliver a colloquium at which Cherwell will be present. H e can then see that you are real and renew your Fellowship". O f course I complied with his request, but just on that particular Friday Cherwell was delayed in L o n d o n and did not get to the colloquium. During the whole of my stay in Oxford I never met him! Shortly afterwards advertisements a p p e a r e d for a lectureship in mathematics at Cambridge, and for a prestigious Smithsonian Fellowship, which also contained a clause expressing a strong preference for Cambridge. I applied for them and was successful in both. Simon suggested that I could exercise pressure on the Smithsonian C o m m i t t e e to allow me to hold the Fellowship at Oxford. But I felt that the time had come to b e c o m e involved in University teaching, and, therefore, despite my happy relationship with all at Oxford, I decided to move over to the lectureship at Cambridge.
5. Lectureship at Cambridge 1952-1954 Most of the theoretical physics at Cambridge was still concentrated in the Mathematics D e p a r t m e n t , but those of us who were interested were given the opportunity to sit and work in a room in the laboratory; I had a seat in a large r o o m at the bottom of the Mond Laboratory. A m o n g other occupants of the r o o m were Dennis Sciama, who achieved distinction in astrophysics and cosmology, and is particularly well known because of his able students, a m o n g them Stephen Hawking; Oliver Penrose who collaborated with Onsager to establish a sound basis for the B o s e - E i n s t e i n transition in liquid helium, and went on to establish a fine reputation in statistical mechanics; A a r o n Klug who was then a crystallographer, and whose brilliant researches on the structure of viruses led to the award of a Nobel prize; he is now Director of the Molecular Biology Research L a b o r a t o r y at Cambridge. A year or so after my return to Cambridge an advertisement appeared inviting applications for the Chair of Theoretical Physics at King's College, London. The general consensus at Cambridge in those days was that one did not apply for such positions without some unofficial hint that an application
C. D o m b / Some reminiscences about m y early career
19
would be welcome. I ignored this view and sent in an application. I was among a short list of 4 chosen for interview. By good fortune Mott and Pryce were members of the selection committee, and both were familiar with my work; but I am sure that the decisive voice on the Committee was that of J.T. (Sir John) Randall, Head of the Physics Department at King's, a person whose judgement I learned to respect and admire. A few days after the interview I received a letter from Randall informing me that I had been appointed to the Chair. By a coincidence Hermann Bondi had been appointed at the same time to a Chair in Mathematics at King's College, so we were together again in the same Institution. Incidentally Mott had just been appointed to the Cavendish Chair at Cambridge in succession to Bragg, and he wrote to suggest to me that from the point of view of scientific advancement I might be better off staying in Cambridge. I replied that my desire to move to London was prompted by personal and social rather than scientific motives. Soon after arriving at King's I met Michael Fisher, who had just completed a doctorate on analogue computers under the supervision of Donald McKay. I convinced Michael that there was a brighter future in statistical physics, but it was important to secure a grant which would support his research at King's in this field. Here a distinguished Israeli came to our help, Aharon Katchalsky (Katzir). I had met Aharon during a visit to the Weizmann Institute, and he showed great interest in my work; he felt that there should be applications to the configurational problems of polymers and polyelectrolytes. He outlined a specific polyelectrolyte problem, which I passed on to Michael, and this served as a vehicle for a Senior DSIR Fellowship. The problem was complex, but Michael managed to get somewhere with it, and it gave him the opportunity to look at some of the other fascinating unsolved problems of statistical mechanics. I have little doubt that my most important contribution to science has been to introduce Michael Fisher to this field. I do not have to tell this audience of the massive contributions, which he has made subsequently, but I am privileged that he came and played such a prominent part in this conference. As anticipated in my opening remarks, I have brought you to the stage of my life at which I achieved respectibility. Let me conclude the story with a quotation from a Talmudic sage: "Much have I learned from my teachers, more from my colleagues, but most of all from my students". My own experience heartily endorses this view.
Acknowledgements I am indebted to my former A.S.E. colleagues Fred Hoyle, Hermann Bondi
20
C. D o m b / Some reminiscences about my early career
and Tommy Gold for correcting some errors of memory in the original manuscript.
References [1] C. Domb, Physica D 38 (1989) 64. [2] The Small World of Fred Hoyle (Michael Joseph, London, 1986). [3] H. Bondi and T. Gold, Mon. Not. R. Astron. Soc. 108 (1948) 252; F. Hoyle, Mort. Not. R. Astron. Soc. 108 (1948) 372; 109 (1949) 365. [4] M. Ryle (Halley Lecture) Observatory 75 (1955) 137; M. Ryle and R.W. Clark, Mon. Not. R. Astron. Soc. 122 (1961) 349. [5] A.S. Eddington, Proc. Camb. Phil. Soc. 35 (1939) 186. [6] P.A.M. Dirac, R. Peierls and M.H.L. Pryce, Proc. Camb. Phil. Soc. 38 (1942) 193. [7] G.N. Watson, Proc. R. Soc. A 95 (1919) 83. [8] M.H.L. Pryce, Adv. Phys. 2 (1953) 67. [9] J.C.P. Miller, Tables of the Airy Integral, British Association Mathematical Tables Part, vol. B (Cambridge Univ. Press, Cambridge, 1946). [10] C. Domb, Adv. Phys. 2 (1953) 96. [11] C. Domb and M.H.L. Pryce, J. Inst. Electr. Eng. 94 (1947) 325. [12] S.O. Rice, Bell Syst. Tech. J. 23 (1944) 282; 24 (1945) 46. [13] Nelson Wax, ed., Selected Papers on Noise and Stochastic Processes (Dover, New York, 1954). [14] C. Domb, Proc. Camb. Phil. Soc. 42 (1946) 245. [15] C.A. Coulson, Proc. Camb. Phil. Soc. 43 (1947) 583. [16] C. Domb, Proc. Camb. Phil. Soc. 43 (1947) 587. [17] C. Domb, Proc. Camb. Phil. Soc. 43 (1947) 329; 44 (1948) 335; 46 (1950) 429. [18] F. Hoyle, Mon. Not. R. Astron. Soc. 106 (1946) 343. [19] E.M. Burbidge, G.R. Burbidge, W.A. Fowler and F. Hoyle, Science 124 (1956) 611; Rev. Mod. Phys. 29 (1957) 547. [20] H. Helmholtz, On the Sensations of Tone (1885) (reprinted: Dover, New York, 1954). [21] D. Gabor, Nature 159 (1947) 591. [22] T. Gold and R.J. Pumphrey, Nature 160 (1947) 124; 161 (1948) 640. [23] J.E. Lennard-Jones and A.F. Devonshire, Proc. R. Soc. A 170 (1939) 464. [24] T. Gold, Nature 218 (1968) 731. [25] T. Gold, Rotation and Terrestrial Magnetism, Nature 163 (1949) 513. [26] Report of an International Conference on Fundamental Particles and Low Temperatures (The Physical Society, London, 1947). [27] B. Kauffman and L. Onsager, Phys. Rev. 76 (1949) 1244. [28] H.A. Kramers and G.H. Wannier, Phys. Rev. 60 (1941) 252; E.N. Lassettre and J.P. Howe, J. Chem. Phys. 9 (1941) 747; E.W. Montroll, J. Chem. Phys. 9 (1941) 706. [29] L. Onsager, Phys. Rev. 65 (1944) 117. [30] G.H. Wannier, Rev. Mod. Phys. 17 (1945) 50. [31] C.N. Yang and T.D. Lee, Phys. Rev. 87 (1952) 404. [32] C. Domb, Nature 163 (1949) 775. [33] C. Domb, Proc. Roy. Soc. A 196 (1949) 36; 199 (1949) 199. [34] C. Domb, J. Phys. A 7 (1974) 1335. [35] Mark Azbel, Refusenik- Trapped in the Soviet Union (Houghton Mifflin, Boston, 1983) p. 126. [36] M. Born, Proc. Math. Phys. Soc., Egypt 3 (1947) 35.
C. D o m b / S o m e reminiscences about m y early career
21
[37] Michael F. Shlesinger and George Weiss, eds., The Wonderful World of Stochastics (NorthHolland, Amsterdam, 1985) p. 50. [38] O. Maass, Chem. Rev. 23 (1938) 17. [39] A. Munster, Compt. Rend. 2 e Reunion de Chimie Physique (1952) 21.