The Strangest Man

by Graham Farmelo

  36 St John’s awarded Dirac a praelectorship in mathematical physics, which enabled

  him to devote himself entirely to research, apart from the presentation of his lecture

  course.

  Thirteen

  [I]n England there is something very like a cult of eccentricity. […] With us [Americans], as more than one European has said, the trait is more distinguishable nationally than individually.

  GARDNER L. HARDING, New York Times, 17 March 1929

  In every branch of science, theorists vie with experimenters to set the agenda. Since Heisenberg’s publication of his path-breaking paper in the autumn of 1925, theoreticians had been pointing the way ahead in physics. Yet the foundations of some of the new theoretical ideas had not even been checked experimentally: according to Schrödinger’s quantum theory, for example, every material particle has an associated wave, but no experimenter had been able to prove the idea or to refute it. So there was an almost palpable sigh of relief among quantum physicists back in early 1927 when news reached Europe that the American experimenters Clinton Davisson and his student Lester Germer had shown that the electron could indeed behave like a wave. Dirac, often believed to regard experiments with a high-minded insouciance, belied his reputation by arranging to visit Davisson’s laboratory on West Street in south Manhattan, a few blocks from the meatpacking district, the first stop on his itinerary.1

  This was Dirac’s first sight of New York, then booming with wealth and new technology. The Jazz Age was, according to the man who named it, F. Scott Fitzgerald, past its ‘heady middle age’, though Americans were still enjoying ‘the most expensive orgy in history’.2 The hurried pace of American life was not at first to Dirac’s taste: it was somehow fitting that during the first night Dirac spent in his hotel on Seventh Avenue, he was kept awake until the small hours by revellers in an adjacent room.3 As soon as he awoke the next day, shortly before four o’clock in the afternoon, he realised he had missed his appointment with Davisson. Rather than waste the late afternoon, he spent it strolling around rush-hour midtown Manhattan, teeming with four-square black automobiles navigating around the skyscrapers, each of them a powerful symbol of America’s soaring prosperity.

  In Davisson’s laboratory the next day, Dirac saw the ingenious apparatus that first persuaded the electron to reveal its wave nature. Davisson and Germer had fired beams of electrons towards a nickel crystal and found that the number of electrons they detected at different angles had alternating peaks and troughs. These variations were impossible to understand if the electron is simply a particle: the only explanation was that the electrons behave as waves which are bent (‘diffracted’) by the crystal, like two waves combining on the surface of pond, forming peaks when the waves reinforce one another and troughs when they cancel each other out. Physicists had no choice but to conclude that the electron behaved sometimes like a particle and sometimes as a wave – a ‘wavicle’, as Eddington had dubbed it – precisely as quantum theory had supposed.

  Dirac quickly headed off on his five-month journey across North America, travelling mainly on the railroad. He kept a record of his trip in terms of numbers, not words: his diary contains no descriptions of his experiences, just a cumulative record of the number of nights he had spent on a train and on board ship.4

  After paying brief visits to Princeton and Chicago, Dirac travelled to Madison, capital of the Midwestern state Wisconsin. Like Göttingen, Madison was his sort of town, with a good university and surrounded by countryside offering plenty of opportunities for walks. He was the first foreign guest of John Van Vleck, newly appointed to the university faculty. Slightly older than Dirac, Van Vleck excelled at applying quantum physics and had no interest in the fundamentals of quantum mechanics. They spent hours together walking in the vast fields overlooking Lake Mendota, one of the four lakes around the town. For Dirac, Van Vleck was the perfect walking companion – fit, uninterested in small talk and content to say nothing for hours. Perhaps Van Vleck mentioned his passion for railroads and his feat of memorising the passenger railway timetable for the whole of Europe and the United States.5 Like Dirac, Van Vleck was fascinated by technology, numbers and order.

  Dirac’s hosts were aware of his reputation for eccentricity, and they soon saw that it was well justified and that his sangfroid was extreme even by the standards of the English. He left them several Dirac stories, including a classic that appears to have been first spread around by a tickled Niels Bohr.6 The story begins during one of Dirac’s lectures, moments after he has finished talking, when the moderator asks if anyone has any questions. Someone in the audience says, ‘I don’t understand the equation on the top-right-hand corner of the blackboard.’ Dirac says nothing. The audience shuffles nervously, but he remains silent, whiling away the time of day, looking unconcerned. The moderator, feeling obliged to break the silence, asks for a reply, whereupon Dirac says, ‘That was not a question, it was a comment.’

  Madison was also the venue of what would become the most widely quoted interview that Dirac ever gave, to the journalist Joseph Coughlin, known to everyone as Roundy owing to his substantial girth.7 Well known in the town, he was one of Wisconsin’s most popular columnists, delivering regular doses of homespun wisdom on sport and other topics in language that was often ungrammatical but always alive with quirky humour. Dirac kept a typed transcript of the four-page article, in which Roundy recounts verbatim his attempts to persuade his interviewee to utter more than one syllable at a time:8

  ROUNDY: Professor, I notice you have quite a few letters in front of your last name. Do they stand for anything in particular?

  DIRAC: No.

  ROUNDY: You mean I can write my own ticket?

  DIRAC: Yes.

  ROUNDY: Will it be all right if I say that P. A. M. stands for Poincaré Aloysius Mussolini?

  DIRAC: Yes.

  ROUNDY: Fine! We are getting along great! Now doctor will you give me in a few words the low-down on all your investigations?

  DIRAC: No.

  ROUNDY: Good. Will it be all right if I put it this way: ‘Professor Dirac solves all the problems of mathematical physics, but is unable to find a better way of figuring out Babe Ruth’s batting average?’

  DIRAC: Yes.

  The interview continues for another page. According to the transcript, Roundy’s interview was published in the ‘P. A. M. issue’ of the Wisconsin Journal on 31 April (sic). However, the records of the newspaper show that no such edition was published, so it appears that this much-anthologised interview is a spoof.9One possibility is that the typed document was a pastiche presented to Dirac by his Madison colleagues during his farewell dinner at the University Club, where – as Van Vleck later wrote – they played an elaborate game to tease out of Dirac the names designated by his initials P. A. M.10 Whatever the origins of the Roundy interview, it is an example of a probably apocryphal Dirac story that captures his behaviour so accurately that it somehow ought to be true.

  Dirac left Madison with a cheque for $1,800, more than enough to cover his costs for the remainder of his trip.11 In June, he combined business and pleasure, giving a series of lectures on quantum mechanics in Iowa and Michigan, also walking down and up the Grand Canyon and hiking in Yosemite National Park and the Canadian Rockies – his introductions to grand North American scenery, which he explored on foot during several trips in the coming decades.12 He again demonstrated his interest in the latest experimental tools when, during a stay at the California Institute of Technology, he visited the Mount Wilson Observatory, near Pasadena, whose telescope was the largest in the world and by far the most productive source of new information about the universe.

  A few months before, Heisenberg had proposed to Dirac that they should travel together to ‘bring European life into the American hurry’.13 When they met in early August at their hotel near the Old Faithful geyser, Heisenberg was surprised to find that Dirac had planned a route that would enable them to see the maximum number of geysers erupt.14 E
ven his scenic walks were informed by mathematical analysis. Heisenberg had arranged for them to travel first class to Japan on the steamer Shinyo Maru, sharing a roomy cabin with a sea view.15 Two leading theoreticians were about to spend weeks together, with every opportunity to talk and perhaps to crack the gnawing problem of how to interpret the negative-energy solutions to Dirac’s equation. The clubbable Heisenberg would probably have been game for a collaboration, but not Dirac. Although he admired Heisenberg and regarded him as a friend, Dirac felt no obligation to share any of his thoughts about physics with him. His motto was: ‘People should work on their own problems.’16

  In the middle of August, after they had each given a series of lectures in Oppenheimer’s department at the University of California at Berkeley, they set off from San Francisco on their two-week cruise to Japan.17 On board, Heisenberg was a conventionally hedonistic tourist, honing his technique at ping-pong and dancing with the flapper girls.18 Dirac looked on, probably bemused. It is easy to imagine Dirac at one of the evening balls, sitting at a table and gazing quizzically at Heisenberg as he jived on the dance floor. Heisenberg long remembered being asked by Dirac, ‘Why do you dance?’ After Heisenberg replied, reasonably enough, ‘When there are nice girls it is a pleasure to dance,’ Dirac looked thoughtful. After about five minutes of silence, he said, ‘Heisenberg, how do you know beforehand that the girls are nice?’19

  As their steamer approached Yokohama, a reporter sought an interview with the two famous theoreticians. Unfamiliar with Dirac’s appearance but not with Heisenberg’s, the reporter said to Heisenberg, ‘I have searched all over the ship for Dirac, but I cannot find him.’ Heisenberg knew how to handle this: he talked affably to the journalist, no doubt giving him the story he wanted and not mentioning that Dirac was standing next to him, looking in another direction.20

  In Japan, the two physicists were greeted as heroes. Leading scientists in Japan knew that their science lagged well behind that of Europe and the USA, and physicists flocked from all over the country to see and hear two of the young founders of quantum mechanics. Dirac and Heisenberg were given round-the-clock obeisance and the full VIP treatment, their first taste of international celebrity. From the official photographs, it is clear that Heisenberg slipped easily into the role of the touring dignitary, looking poised and relaxed in the light summer suit he wore to stay cool in the searing heat. Looking less comfortable than his friend, Dirac made no such changes to his wardrobe: he wore the same three-piece suit and boots that he wore in the depths of the Cambridge winter.

  The itinerary was the usual one for academics making a short trip to the country: a stay in Tokyo followed by a visit to the old imperial city of Kyoto, lecturing to packed, hushed audiences of respectful men wearing Western suits splashed with jako perfume, scenting the auditorium with the fragrance of geraniums.21 The texts of the lectures were swiftly translated into Japanese and published as the Orient’s first authoritative book on quantum mechanics, a bible for Japan’s next generation of physicists, destined to make a huge impact. Dirac and Heisenberg, each of them only twenty-seven, were already training their successors.

  At the end of their stay in Japan, Dirac and Heisenberg parted company. Dirac wanted to return by the fastest practicable route, by traversing Russia on the Trans-Siberian Railway. The construction of the 5,785-mile railway in Siberia – with brutal extremes of climate, little local labour available and dreadfully primitive supply routes – had been an engineering project that would have daunted even Brunel. It took twenty-five years to complete. Dirac boarded the train on 24 September at Vladivostock on the eastern coast and, nine days later, arrived in Moscow. He met up with Tamm, and they went on a long walk to see the sights of the city, including the sixteenth-century St Basil’s cathedral, later converted into one of the country’s many anti-religion museums.22 Dirac then headed back to England after taking what seems to have been his first flight, from Leningrad to Berlin. This was probably not the most agreeable of experiences: for the next few decades, he preferred to admire aviation technology from a secure vantage point on the ground.

  While he was away, his family were ‘plodding along as usual’, as his mother put it.23 The highlight of the year had been the General Election in June. For Flo, new technology had taken much of the thrill out of politics: ‘The Election is being conducted mainly by “Wireless”,’ she wrote to Dirac, ‘so I don’t get any fun out of meetings.’ 24 She and Charles supported Lloyd George’s Liberal Party, which was trounced in Bristol by the Labour Party, consistent with the national swing that put Ramsay MacDonald back into 10 Downing Street.

  Dirac’s father, in better health than he had been for some years, was drifting further away from his wife and ever closer to Betty. While Charles and his favourite child played with the family dog in the garden, Flo was left inside, dreaming of her favourite child thousands of miles away. She imagined him touring the Hollywood studios and riding a donkey down the Grand Canyon in a Panama hat, though she was disappointed to hear that he had done neither. Flo and Charles, having not seen their son for six months, were hoping to see him before the beginning of term and prepared the house for his visit. But in early October, Dirac perfunctorily informed them that he was back in Cambridge and mentioned no plans to visit Bristol.25

  He and other theoreticians had made virtually no progress with the problem of negative-energy electrons. Although most physicists wanted to be rid of them, the Swedish physicist Ivar Waller had shown a few months before that they were indispensable to the theory. Waller had found a strange result when he analysed what happens when a photon is scattered by a stationary electron: Dirac’s theory could reproduce the successful classical prediction at low energies only if the electron had access to negative-energy states. There could be only one conclusion for Dirac: his equation would survive only if someone could understand these negative-energy electrons.

  As he settled down for the new term, Dirac was aware that the critical chorus had swelled from a whisper to a roar. In the opinion of its most dominant soloist, Pauli, the equation’s sickness was incurable and its agreement with experiment was a fluke.26 The onus was on the equation’s discoverer, refreshed after almost six months’ vacation, to rescue it. So he set about the problem again.

  At the end of October, news broke from New York of the event that ended the calm of late-1920s politics and began the descent into global economic catastrophe. The Dow Jones index had reached its historic peak a month before. Then panic struck when the bubble burst. On Friday, 25 October, the newspapers in the St John’s common room all featured reports that made clear the scale of the crisis: the Manchester Guardian wrote of ‘Wild selling in record turnover of 13,000,000 shares’; The Times wrote, ‘a Niagara of liquidation took place on the American stock market today’. Four days later, on ‘Black Tuesday’, Wall Street all but melted down, and, as F. Scott Fitzgerald later noted, the decade of unparalleled prosperity had ‘leapt to its spectacular death […] as if reluctant to die outmoded in its bed’.27

  Britain braced itself for the aftershock. Dirac kept abreast of the news, but he was focusing mainly on solving the mystery of the negative-energy electrons. Why had no one observed jumps of the familiar, positive-energy electrons into negative-energy states? After a few weeks, he had found an answer. He imagined all the electrons in the universe gradually filling up the energy states: the states with negative energy will be populated first, because they have the lower energies. Only when they are full will electrons occupy positive energy states. Because the negative-energy states are full, there are no vacancies into which these positive-energy electrons can jump. It is ironic that the crucial idea that underpinned the theory was supplied by Dirac’s harshest critic, Pauli: according to his exclusion principle, every negative-energy state can be occupied by only one electron. This prevents each negative-energy state from being filled ad infinitum with electrons.

  The bizarre upshot of the theory is that the entire universe is pervaded by an infin
ite number of negative-energy electrons – what might be thought of as a ‘sea’. Dirac argued that this sea has a constant density everywhere, so that experimenters can observe only departures from this perfect uniformity. If this view is correct, experimenters are in rather the same position as a tribe that has spent its entire life hearing the unchanging background sound of a single musical note: this would not seem like torture because people are aware only of changes to their environment.

  Only a disturbance in Dirac’s sea – a bursting bubble, for example – would be observable. He envisaged just this when he foresaw that there would be some vacant states in the sea of negative-energy electrons, causing tiny departures from the otherwise perfect uniformity. Dirac called these unoccupied states ‘holes’. They would be observed, he reasoned, only when they are filled by an ordinary electron, which would then emit radiation as it makes the transition. It should therefore be possible to detect a hole in the sea when an ordinary positive-energy electron jumps into it. But what characteristics do the holes have? They mark the absence of a negative-energy electron. Within the general scheme of the ‘electron sea’, the absence of negative energy amounts to the presence of positive energy (two negatives make a positive: when debt decreases by £5, wealth increases by the same amount). Furthermore, a negative-energy electron is negatively charged, so its absence is equivalent to the presence of a positive charge.

  It follows that each hole has positive energy and positive charge – the properties of the proton, the only other subatomic particle known at that time. So Dirac made the simplest possible assumption by suggesting that a hole is a proton. What he could not explain was why the proton is almost two thousand times as heavy as the electron. That was a problem for the theory, he conceded, a ‘serious deficiency’.