The Strangest Man

by Graham Farmelo

  At the end of July 1928, Dirac was preparing for his first visit to Russia, a two-month stay that combined the chores of lecturing with the pleasure of relaxing with Kapitza. Dirac’s mother was fearful: ‘If you go to Russia, do take care of yourself. We hear such dreadful accounts of the Bolshevists in the papers. There seems to be no law and order anywhere. I expect you know more about the facts than we do, though, as you are so much nearer.’23 Since 1918, the British press had reported on the Soviet regime’s growing repressiveness, which increased with the rise of Stalin to absolute power in 1926. The British Government did not officially recognise the Soviet Union, but profitable trade between the countries was easing relations between them, culminating in the Labour Prime Minister Ramsay MacDonald’s restoration in 1929 of full diplomatic relations.24

  After his arrival in Leningrad on 5 August, Dirac’s hosts introduced him to caviar, one of the few luxury foods for which he had a taste. Dirac blossomed in Russia – the scenery, the architecture, the museums and the art galleries – as he wrote in a long and chatty letter to Tamm:

  I spent the first two days in Leningrad with Born and his [Göttingen colleague] Pohl and we saw the sights and visited the Hermitage and the Museum of Russian Art and the Natural History Museum and also the Roentgen Institute [for physics research] […] I found Leningrad a very beautiful place, and was more impressed by it than by any other town during the journey, particularly as I came up the river in the steamer and first saw the large number of churches, with their gilded domes, quite different from anything I had ever seen […].25

  Moscow still resembled the city of Anna Karenina, with its squat wooden houses, multicoloured cupolas, horse-drawn cabs driven around the sprawl of zigzag streets by peasants in blue robes, bearded traders sipping vodka and eating cucumbers in the Slovenski Bazaar.26 Dirac was there to attend the no-expense-spared Congress of Russian Physicists, at his hosts’ expense. Physicists in the Soviet Union had been quick to realise the importance of quantum mechanics and wanted to learn from the innovators in western Europe. Of the one hundred and twenty physicists who attended the Congress, about twenty were foreign. Dirac was the star of the occasion, but he arrived in Moscow too late to give his talk, scheduled for the opening session. When he should have been giving his presentation, he was walking around one of the royal palaces on the outskirts of the city; in the evening, he went to a performance of Japanese theatre. The next day, Dirac went with the conference delegates to the Kremlin before setting off alone to walk the streets until sundown.

  The venue for the second part of the Congress was a steamer that sailed down the Volga to Stalingrad. During the week-long cruise, Dirac gave a talk on his theory of the electron and met the leaders of Soviet physics, including his admirer Lev Landau, a twenty-year-old graduate student, soon to be his country’s greatest theoretician – the most accomplished but least mature. Mangy and undernourished, he was so tall that in most company people could see his long, thin face standing out, topped with dark wavy hair that was piled on the right of his head like a burnt crest of meringue. As a critic, he was so aggressive that he made Pauli look demure; as a colleague, so socially inept that he made Dirac look suave.

  After the Congress, Dirac took a two-day train journey to the Caucasus. He stayed with Kapitza and joined a party of sightseers for a six-hour hike up a glacier near Vladikavkas. Dirac described his adventures in a letter to Tamm but did not mention that, during his time with Kapitza, he experienced an incident that was, in some way, his sexual awakening.27 Forty-five years later, he remembered that he first saw a naked young woman in the Caucasus: ‘[she was] a child, an adolescent. I was taken to a girls’ swimming pool, and they bathed without swimming suits. I thought they looked nice.’ He was twenty-six years old.

  Dirac was in no hurry to return to Bristol: the journey took him almost a month.28 The disparity between the excitement of his work and the dreariness of his home life had never been so stark. He was lionised by many of his colleagues, he was financially independent, and he was benefiting from international travel at a time when it was a luxury. Charles, Flo and Betty, on the other hand, were locked in their routine and left their hometown only rarely. Betty was happy to do nothing at all when she was not looking after her new dog; Charles was overworked and run down; Flo was trying to make the most of every opportunity to leave the house. At her elocution classes, she wrote and practised giving speeches, including one opposing the notion that there might one day be a woman prime minister. She rehearsed her speech on the Bristol Downs, beginning with the flourish ‘I rise to oppose the motion of a woman prime minister – to oppose most decidedly and definitely.’ For one thing, Flo argued, women do not have sufficiently strong constitutions to take on such a responsibility: ‘As regards physique – women today are wonderful: but none can say when a woman may faint! None when she may scream! Is it becoming for a Prime Minister to suddenly fall to the ground, or to burst into hysterics at a crucial moment?’29

  Although Flo was not in the vanguard of feminism, Dirac knew that underneath his mother’s apparent submissiveness lay stoicism and an independence of spirit. These qualities would, over the next three years, be tested to breaking point.

  When Dirac returned to Cambridge in October 1928, he knew that the onus was on him to cure the sickness of his theory of the electron. Somehow, he needed to find a rational explanation for the negative-energy states which were undermining confidence in the Dirac equation; some of his colleagues were becoming worried that the equation might not be right after all.30

  That autumn, he was, unusually, working on several projects at the same time: his hole theory, his textbook and a brief paper on one of his favourite subjects – the relationship between classical mechanics and quantum mechanics. The paper was based on the ultra-rigorous work of von Neumann, who had derived one result that caught Dirac’s eye. Von Neumann had found a way of describing the overall behaviour of an enormously large number of non-interacting quantum particles, when nothing is known about their individual behaviour. It turned out, surprisingly, that the statistical description given by quantum mechanics is just as simple as the account given by classical mechanics; in both, the behaviour of the individual particles averages out to a smooth overall pattern, just as the behaviour of a swarming crowd can be described without referring to any of its individuals. In this bijou paper, Dirac developed von Neumann’s ideas and laid bare the precise analogy between the classical and quantum understandings of vast numbers of particles. This was a divertimento composed during a holiday from fixing his troublesome symphony.

  In those politically tranquil times, the favourite topic of conversation in Cambridge was poetry.31 The eighty-five-year-old poet laureate Robert Bridges had written the most talked-about poem of the year, A Testament to Beauty, 5,600 lines about the nature of beauty. It is now read only rarely, but then it struck a chord with tens of thousands of lay readers and some literary critics, including one in the Cambridge Review who described it as ‘a high philosophical explanation of Keats’s “Beauty is truth, Truth beauty”’.32 To some extent, Bridges was reacting against modernist art – such as Arnold Schönberg’s atonal music, Picasso’s cubism, Eliot’s fragmented poetry. Bridges sought beauty and found it not only in music, art and nature but also in science, food and even in football matches. Dirac knew, too, that beauty was about much more than art and nature. He had seen it in Einstein’s equation for the general theory of relativity and he now had an equation of his own that was no less of a contribution to aesthetics. But aesthetic judgements like that count for nothing in science if a theory fails to agree with experiment. Unless someone could explain the meaning of the negative-energy solutions to the Dirac equation, it was doomed to be remembered only as just another scientific fad.

  A few of Dirac’s colleagues in Cambridge would not have been distraught if fortune had clipped his wings: his ascending reputation had led, inevitably, to envy. No longer were the two leading lights of the university’s experi
mental and theoretical physics cited as Rutherford and Eddington, but as Rutherford and Dirac. Eddington’s star was waning, and he knew it. Meanwhile, the old guard of Cambridge physics looked pitifully out of touch. The proud Irishman Sir Joseph Larmor, holder of the most prestigious chair in Cambridge, the Lucasian Professorship of Mathematics, once held by Newton, was living in the past, unable to understand relativity theory and disdainful of quantum mechanics. He and his friend J. J. Thomson wandered the streets of Cambridge, each of them wearing a bowler hat, a black three-piece suit and an immaculate white shirt, and each wagging a stick behind his back. When they peered into one of the shop windows on Trinity Street, the two superannuated professors looked like a pair of penguins.

  The two men knew that their views counted for nothing among physicists who were once their admiring students and who were now running physics. No one symbolised the new generation’s ascendancy more powerfully than Dirac, but he still did not have a permanent job. He had turned down Arthur Compton’s offer of a post in Chicago and had later declined an offer of a professorship in applied mathematics at Manchester University, commenting that ‘my knowledge of and interest in mathematics outside my own special branch are too small for me to be competent [in such a post].’33 If the spurned mathematicians in Manchester found his modesty hilarious, Dirac would have been uncomprehending, as he was simply being candid. As Mott said: ‘He is quite incapable of pretending to think anything that he did not really think.’34

  If Dirac and Fowler were away, Cambridge University would struggle to teach quantum mechanics, as Harold Jeffreys virtually admitted when he wrote to Dirac in March 1929, pleading with him to set the questions on quantum mechanics for the summer examinations. Jeffreys and his fellow ‘ignorant and philistine’ faculty colleagues were in the embarrassing position of having to admit that ‘the candidates know more than we [do]’.35 Fowler led the campaign to ensure that Dirac remained in Cambridge, and he soon had some success: in June 1929, St John’s College awarded Dirac a special lectureship, though it was funded for only three years.36 Dirac’s loyalty to Cambridge was to be tested, repeatedly.

  As Dirac was getting nowhere with his top priority of sorting out the difficulties with his equation, he decided to devote himself to other things. In late 1929, he spent most of his time drafting his book and working on another research project, the theory of heavy atoms. This was by no means his favourite branch of physics, but it was closer to the work of the great majority of quantum theorists, who were applying the theory to complicated atoms and molecules. Dirac was, however, in no doubt that quantum mechanics would be successful:

  The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.

  Those words became one of the clarion calls of reductionists, who believe that complex things can be explained in terms of their components, right down to the level of atoms and their constituents. Extreme reductionism implies, for example, that quantum mechanics lies at the bottom of an inverted pyramid of questions that begins, for example, with ‘Why does a dog bark?’ A reductionist seeks to answer the question by understanding the chemical reactions going on inside the dog’s brain, and those reactions are ultimately understood by the interactions of the chemicals’ electrons, whose behaviour is ultimately described by quantum mechanics. Although popular with many scientists, the approach does not describe how to make the links between the layers of explanation.

  In his paper, Dirac applied quantum mechanics to atoms that contain more than one electron, such as carbon atoms. Such atoms are much harder to describe than hydrogen atoms because, in every multi-electron atom, the complicated and unwieldy interactions between all the electrons have to be taken into account. Dirac found a way of describing these interactions approximately and investigated the consequences of the fact that it is impossible to detect experimentally if two of the electrons swapped places. As usual, Dirac left it to others to work out the theory’s consequences: the American theoretician John Van Vleck, based in Minneapolis, quickly saw the potential of Dirac’s ideas and spent years using them to explain the origin of magnetism, the various ways that atoms can bond to form molecules and the patterns of light emitted by multi-electron atoms. This was to be the main legacy of Dirac’s excursion into atomic physics – his first paper on the subject, and his last.

  At the end of term, he visited his family briefly and then, in what was becoming a ritual, set off on another long journey. At Southampton, on the freezing Wednesday morning of 13 March, he boarded the liner Aquitania with his travelling companion, Isabel Whitehead’s son Henry. In the crowd at quayside was Florence Dirac, who by then had got the message: her only son wanted to spend as little time at home as he could. Just as she must have dreaded, he would be away for as long as his teaching obligations in Cambridge allowed, on his first visit to the United States of America. His reputation had preceded him.

  Note - Chapter twelve

  1 Kojevnikov (1993: 7–8).

  2 Peierls (1985: 62–3).

  3 Kojevnikov (2004: 64–5).

  4 Letter from Tamm to his wife, 4 March 1928, in Kojevnikov (1993: 7).

  5 ‘The tulip fields are all in flower now’: postcard from Dirac to his parents, 29 April

  1928 (DDOCS). ‘[Leiden] is below sea level and there are nearly as many canals as

  streets’: postcard from Dirac to his parents, 29 June 1927 (DDOCS).

  6 Letter from Tamm to his wife, undated, Kojevnikov (1993: 8).

  7 Casimir (1983: 72–3).

  8Brown and Rechenberg (1987: 128).

  9 Letter from Heisenberg to Pauli, 31 July 1928, in Kronig and Weisskopf (1964).

  10 Peierls (1987: 35). In this account, Peierls remembers going to the theatre, but it

  seems from his letter to Dirac of 14 September 1928 (Lee [2007: 50]) that they went

  to the opera. I am grateful to Professor Olaf Breidbach for his comments on early

  twentieth-century Prussian politesse.

  11 Born (1978: 240) and Greenspan (2005: 151–3).

  12 Schücking (1999: 27).

  13 Bohr nicknamed Gamow ‘Joe’ after the standard name for cowboys in western

  movies, which Bohr especially liked (interview with Igor Gamow, 3 May 2004). See

  also Reines (1972: 289–99; see pp. 280); Mott (1986: 28).

  14 The only exception is the paper that Dirac co-authored with Rutherford’s student

  J. W. Harding, ‘Photoelectric Absorption in Hydrogen-Like Atoms’, in January 1932.

  15 Gamow (1970: 14).

  16 Wigner (1992: 9–15).

  17 Letter from Gabriel Dirac to Manci Dirac, 5 September 1940: ‘It may interest you to

  know that everybody (Prof [Max] Born, Morris [Pryce] and Daddy [Paul Dirac]) says

  that Johnny von Neumann is the world’s best mathematician’ (DDOCS).

  18 Fermi (1968: 53–9).

  19 Wigner (1992: 37–43).

  20 Interview with Pat Wigner, 12 July 2005.

  21 Dirac wrote to his parents on 18 July 1928: ‘The woods here are full of fireflies in the

  evening. I have been to the top of the Harz mountains’ (DDOCS).

  22 Dirac’s wife would later write to him: ‘It seems the beautiful scenery has the same

  effect on you as a beautiful book has on me’, 12 August 1938 (DDOCS).

  23 Letter to Dirac from his mother, 12 July 1928, Dirac Papers, 1/3/8 (FSU).

  24 Sinclair (1986: 32–3).

  25 Letter from Dirac to Tamm, 4 October 1928, Kojevnikov (1993: 10). The conference

  lasted from 5 August to 20 August.

  26 Brendon (2000: 241).

  27 Salaman and Salaman (1986: 69). In this article, Dirac is quoted as giving 1927 as

  the date of the experience; this is impossible as he did not visit Russia that
year.

  28 He first took a boat to Constantinople (renamed Istanbul in the following year), then

  sailed on to Marseilles via Athens and Naples, before travelling across France and

  then home. He planned to arrive in Bristol on Monday, 10 September (letter from

  Dirac to his parents, 8 September 1928, DDOCS).

  29 Letter to Dirac from his mother, 28 October 1928, Dirac Papers, 1/3/8 (FSU). A copy

  of the speech is in this file of the archive.

  30 In mid-December, Dirac read a paper by Klein showing that the Dirac equation pre-dicted that if a beam of electrons is fired at a barrier, more electrons will be reflected

  than were present in the original beam. It was as if a tennis ball struck a player’s

  racket and not one but several balls flew off it.

  31 Howarth (1978: 156).

  32 Cambridge Review, 29 November 1929, pp. 153–4. See also the rhapsodic review in the

  Times Literary Supplement, 24 October 1929.

  33 Draft letter to Dirac from L. J. Mordell, 4 July 1928, Dirac Papers, 2/1/7 (FSU).

  34Mott (1986: 42–3).

  35Letter from Jeffreys to Dirac, 14 March 1929, Dirac Papers, 2/1/8 (FSU).