The Strangest Man

by Graham Farmelo

  In the next presentation, given by the experimenter Isidor Rabi, of Columbia University in New York, the audience heard yet more unexpected news: the strength of the electron’s magnetism appeared to be weaker than the Dirac theory had predicted. The audience was euphoric: here were two observations that heralded the end of the reign of Dirac’s beautiful theory and provided crucial tests for any theory that presumed to succeed it. Oppenheimer steered the conference, incisively cross-examining the speakers and interspersing the proceedings with his elegant, if ostentatious, editorial arias. By the end of the meeting, it was clear that the main challenge was to explain Lamb’s result. But Dirac knew nothing of all this: he had declined an invitation to attend and read about the wounding of his theory on an autumn Sunday in Princeton, on the front page of the New York Times.10

  Within two years of the Shelter Island Conference, Lamb and Retherford’s results had been explained by two of the youngest theorists in the audience. One of them was Feynman, the other was a fellow New Yorker, Julian Schwinger, a loner with the manners of a prince and the self-belief of a boxer. Feynman and Schwinger were both the same age and had read Dirac’s book when they were precocious teenagers, and both based their theories on Dirac’s ‘little paper’. Yet the two versions appeared to be quite different: Schwinger’s mathematical approach was hard to understand, but Feynman’s approach was intuitive and involved special diagrams that made the underlying science easy to visualise, at least superficially. The two methods gave the same results, and everyone except Schwinger agreed that Feynman’s methods were quicker and easier.

  It turned out that the same results had been obtained several years earlier by the Japanese theoretician Sin-Itiro Tomonaga, who had based his ideas on Dirac’s version of quantum field theory. As a student, Tomonaga had been a fanatical student of Dirac’s book and was in the Tokyo audience when Dirac and Heisenberg gave their lectures during their tour of Japan in 1929. This pioneering work had been completed in Tokyo, where Tomonaga was one of the tens of thousands of starving citizens who were trying to rebuild the city after American bombers had flattened it towards the end of the war.11

  So there were now three versions of quantum electrodynamics that looked quite different and yet seemed to give the same results. It was Freeman Dyson, the student who had snapped at Dirac’s heels during his wartime lectures, who first demonstrated that the three theories were versions of the same underlying theory. Now, at last, physicists could claim they understood the interactions of the photon and the electron in terms of a theory that agreed with observation to within a few parts in ten thousand – roughly a human hair’s breadth compared with the width of a door. Four decades later, when much more accurate measurements were still in excellent agreement with the theory, Feynman referred to it as ‘the jewel of physics’.12 As he often stressed, its fundamental concepts had been set out by Dirac in his 1927 theory: Feynman, Schwinger, Tomonaga and Dyson had, in essence, introduced a collection of ingenious mathematical tricks and techniques that made the theory viable and showed how to remove the embarrassing infinities.

  Thoroughly pleased with himself for becoming ‘a big shot with a vengeance’ after his triumph, Dyson was keen to hear Dirac’s opinion on the new theory. He was expecting a few words of congratulation from his former teacher, but was disappointed:

  DYSON: Well, Professor Dirac, what do you think of these new developments in quantum electrodynamics?

  DIRAC: I might have thought that the new ideas were correct if they had not been so ugly.13

  The feature of the new theory that Dirac most loathed was the technique of renormalisation.14 According to this theory, the observed energy of an electron is the sum of its self-energy – resulting from the interaction between the electron and its field – and the bare energy, defined to be the energy the electron is supposed to have when completely separate from its electromagnetic field. But the bare energy is a meaningless concept because it is actually impossible to switch off the interaction between the electron and its field; only the observed energy can be measured.

  The virtue of renormalisation is that it enables every mention of bare energies in the theory to be removed and replaced with quantities that depend only on observed energies. Using this technique, theorists could use quantum electrodynamics to calculate – to any degree of accuracy – the value of any quantity the experimenters cared to measure. Despite the success of the technique, Dirac abominated it, partly because he could see no way of visualising its mathematics but mainly because he felt that the process of renormalisation was artificial, an inelegant way of sweeping the fundamental problems of theory under the carpet. In his opinion, a fundamental theory of nature must be beautiful, whereas renormalisation seemed to Dirac’s taste to be as devoid of beauty as the dissonances of Arnold Schönberg.15

  Engineers, schooled to worry more about the reliability of their results and less about the rigour of their mathematics, might be expected to be happy with renormalisation, as the process gives answers that always tally with observations to extremely high accuracy. But, paradoxically, Dirac believed his engineering training was at the root cause of his hostility to the technique.16 At the Merchant Venturers’ College, he had learned the engineer’s art of using well-chosen approximations to simplify complicated, real-life problems so that they can be analysed mathematically. Dirac made this the theme of his 1980 lecture ‘The Engineer and the Physicist’: ‘The main problem of the engineer is to decide which approximations to make.’17 Good engineers make wise choices, often based on physical intuition, about the mathematical terms they can ignore in their equations: ‘The terms neglected must be small and their neglect must not have a big influence on the result. He must not neglect terms that are not small.’18

  Renormalisation entails a practice that no self-respecting engineer would countenance, Dirac pointed out: the neglect of large terms in an equation. To neglect infinitely large quantities in an equation was, for an engineer, anathema. Most physicists had no such compunctions, and leading theorists paid little heed to Dirac’s objections. As Dyson pointed out, although the infinities in the theory had not been eliminated, they were isolated in mathematical expressions that were quite separate from formulae representing the effects experimenters actually observe. Dirac was unconvinced. He, Schrödinger, Heisenberg, Pauli, Born and Bohr – the ‘old gang’, as Dyson dubbed them – had now joined Einstein in the wings of theoretical physics, while the next generation took centre stage. Of the ancien régime, only Pauli kept closely abreast of new developments in their subject; the rest withdrew into their own private worlds. Dyson and his friends were contemptuous of their elder colleagues:

  In the history of science there is always a tension between revolutionaries and conservatives, between those who build grand castles in the air and those who prefer to lay one brick at a time on solid ground. The normal state of tension is between young revolutionaries and old conservatives […] in the late 1940s and early 1950s, the revolutionaries were old and the conservatives were young.19

  In a sense, Dirac was the Trotsky of theoretical physics: he envisioned his subject progressing through one revolution after another, each an improvement on its predecessor. But new quantum electrodynamics did not constitute progress so far as Dirac was concerned: the theory offended the aesthetic sensibilities he had first developed in Bristol, when he was an Eton-collared cherub at junior school, a greasy-aproned engineering student – moonlighting in general relativity – at college, and a budding mathematician at university. Whether this unique aestheticism would be a dependable guide remained to be seen.

  When Dirac was a young man, he had been uninterested in human companionship, but he had come to value it. The result was that, after the war, Cambridge seemed to him like a ghost town – Fowler and Eddington had died, and all of Rutherford’s former ‘boys’ had left. Manci also felt the pain of the exodus, complaining to her brother Wigner in Princeton that ‘Life here is utterly and completely different.’20
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br />   With the ascendancy of American physics, Cambridge looked to Dirac to give leadership in the new era, but to no avail. Concerned only with his own research and in doing a modicum of teaching, he did nothing to improve the primitive facilities for students of theoretical physics in Cambridge: there were no offices for them in the department, and they even had to organise the programme of seminars.21 Dirac now preferred to work at home, as he had done during the war. Manci ensured that the children did not disturb him: woe betide them if they tried to attract his attention by banging on his study door.

  By late 1950, Gabriel and Judy had left home. Gabriel was pursuing his career, and Judy – apparently settling down after her tempestuous adolescence – had married, leaving the Diracs to bring up their two youngest daughters. According to Manci, Dirac ‘kept himself too aloof’ from them, and she had to encourage him to kiss them.22 Neither Mary nor Monica recalled having any sense that their father was a famous or distinguished man – only that he was exceptionally quiet and good-natured, although unemotional and extremely slow to anger. Monica cannot recall seeing him laugh. But in many ways Dirac was a typical father, taking an interest in their hobbies, helping them do their homework and encouraging them to have pets, though he forbade them to bring dogs into the house because, as Monica recalls, ‘he did not like being startled when they barked’.23 Animal welfare was one of his concerns: when designing a flap for the girls’ cat, he measured the span of its whiskers to ensure that the animal would not be incommoded as it passed through the hole.

  Among the visitors to the Diracs’ home were Esther and Myer Salaman. Esther, born and raised in the Ukraine, had been a student of Einstein’s in the early 1920s, joined the Cavendish in 1925 and married Myer, a physiologist, a year later.24 She was the kind of fine-looking, self-assured woman Dirac admired. He listened carefully to her effusions on the leading nineteenth-century Russian novelists, including her favourite, Tolstoy, whose War and Peace took Dirac two years to complete, having digested every word of it. He brought this same attention to detail to Dostoevsky’s Crime and Punishment, which he thought was ‘nice’, though he pointed out that ‘In one of the chapters the author makes a mistake: he describes the sun as rising twice on the same day.’25

  Manci was still feeling out of place in Cambridge, contemptuous of its drab provincialism and despondent at the thought that she might have to spend the rest of her life in colourless England. Every day, newsreaders delivered discouraging news of the sluggish economy, continued rationing and product shortages; there was no sign of an end to the austerities of wartime. Manci, feeling the pinch, complained to Monica that ‘Uncle Eugene pays his cleaner more every week than your father gives me in housekeeping.’26 These were grim times, accurately summarised by the worldly-wise senior civil servant Bob Morris as ‘a right, tight, screwed-down society walled in in every way’.27

  The treatment of the dons’ wives by the colleges and university was still a sore point with Manci, though she saw a few hopeful signs. In 1948, the authorities symbolically enrolled Queen Elizabeth (later the Queen Mother) as the first woman to take a bona-fide degree, albeit an honorary one.28 A year later, under this legislation, women students at Cambridge first graduated. Slowly, much more slowly than Manci wanted, women in Cambridge University were making progress towards equality.

  To the emerging generation of physicists, Dirac was a cool and wary stranger, but for Heisenberg and other fellow pioneers of quantum mechanics, he was an attentive friend. After the war, Heisenberg knew he had to justify the work he had done for the Nazis, but this was an enervating struggle – several of his former colleagues, including his former friend and student Peierls, wanted nothing to do with him, and Einstein treated him with contempt.29 In 1948, when Heisenberg returned to Cambridge – at a time when Dirac was absent – he looked haggard and anxious but was excellent company, delighting his hosts one evening with an unrehearsed performance of Beethoven’s Emperor Concerto. He discreetly explained to everyone who would listen that he was never a Nazi and had stayed in Germany out of loyalty to his colleagues and to mitigate the worst of Hitler’s intentions. Determined to leave a good impression in Cambridge, as a gesture of remembrance he bought forty-eight rose bushes from a plant centre in nearby Histon and made it known he would plant them in his garden in Göttingen.30

  When Dirac first met Heisenberg after the war, he accepted Heisenberg’s explanation of his wartime conduct at face value and believed Heisenberg had behaved reasonably in an extremely difficult situation. ‘It is easy to be a hero in a democracy,’ Dirac would observe, as Manci laughed at his naivety.31 She scorned Heisenberg as a tricky character: ‘That Naaaaazi.’32

  Dirac was supportive of Heisenberg even when he was working for Hitler. Max Born had been startled when Dirac asked him to support Heisenberg for foreign membership of the Royal Society. ‘Heisenberg’s discovery will be remembered when Hitler is long forgotten,’ Dirac commented.33 Dirac also strongly supported Schrödinger’s election to a reluctant Royal Society. The consensus among its officials was that ‘one hunch, however good and however important […] needed more following up with sustained evidence of ability’, an insider told Dirac.34 Probably incredulous, Dirac took up Schrödinger’s cause and helped to ensure his election in 1949. Schrödinger was profuse in his thanks, telling Dirac, ‘You really are very nearly a saint.’35 Dirac showed no such conscientiousness when it came to supporting his former peers for the Nobel Prize: strong candidates for the award – Pauli, Born, Jordan or even Dirac’s Cavendish friends Blackett, Chadwick, Cockcroft and Walton – received no support from him.36 The only physicist Dirac nominated was Kapitza.37

  Dirac had heard little from Kapitza during the war, though he had read in his copy of Moscow News of Kapitza’s invention of a method of liquefying oxygen that did much to raise the productivity of the hard-pressed steel manufacturers and several branches of the Soviet chemical industry.38 Stalin never met Kapitza but showed every sign of having a soft spot for him, telephoning him occasionally and showering him with awards, including the USSR’s highest civil title ‘Hero of Socialist Labour’.39 By the end of the war, Kapitza had proved himself the scientist best able to work with the Government and with Stalin, whom he flattered shamelessly: ‘The country has always been fortunate to have leaders [such as you and Lenin].’40

  Two weeks after Americans dropped the bomb on Japan, Kapitza’s fortunes took a turn for the worse when Stalin set up a special committee to develop nuclear technology and weapons, headed by his first lieutenant Lavrentiy Beria. Of all Stalin’s courtiers, Beria was the most feared – a bully, a serial rapist and a casual murderer – but he was a consummate manager, the kind of man who would have no trouble running an industrial conglomerate. At Stalin’s request, Beria took over leadership of the Soviets’ nuclear project and soon fell out with Kapitza, who complained to Stalin in the autumn of 1945 about Beria’s scientific ignorance and incompetence.41 When Kapitza realised that he could not oust his boss, he asked to be released from the project. Stalin agreed and, though apparently ensuring that Kapitza’s life was not in danger, did nothing when all his responsibilities were removed. By early 1946, Kapitza was in disgrace. Dirac knew nothing of this – he did not know that Kapitza had survived the war until the summer of 1949.42

  In September 1947, Dirac began his most productive year for a decade. Accompanied by his family, he was on sabbatical at the Institute for Advanced Study, which had relocated eight years before to Fuld Hall, a four-storey red-brick building with a spire like a New England church. It stood, symmetric as a crystal, in almost three hundred acres of meadows, fields, woods and wetlands, about half an hour’s walk from the centre of Princeton. This was a realisation of Abraham Flexner’s vision of a small academic institution focusing on a few disciplines and with a world-class faculty, all of them unencumbered by administration and unwanted students. The Institute was, for Dirac, a ‘paradise’.43

  Manci felt at home in Princeton and thrived in its
prosperous academic milieu and – compared with Cambridge – its liveliness and informality. The community treated her with the respect she wanted, not just as Dirac’s wife but as a bright woman in her own right. The institute had become even more attractive to Dirac in 1946, when Oppenheimer became its director and gave him an open invitation to visit. Fresh from the Manhattan Project, Oppenheimer was ‘ablaze with power’, though ill at ease: ‘I feel I have blood on my hands,’ he had told President Truman.44

  It was a relief for Dirac and his family to be far away from the austerities of post-war Britain, and they took away from Princeton an album of memories: their young daughters scurrying around in the empty tea room at the weekend, their yells shattering the institute’s chapel-like quiet; Einstein, visiting the Diracs for afternoon tea, signing a portrait of himself for Manci; Oppenheimer showing off his van Gogh; setting off with Veblen at the weekends, axes slung over their shoulders, to clear a path in the local woods.45 Freeman Dyson recalls meeting the Diracs during their visit to the institute in early September 1948: