The provenance of the hole theory is not entirely clear. The mathematician Hermann Weyl and others suggested that protons were related in some way to the negative-energy electrons, but their thinking was too woolly for Dirac. He later remarked that ‘it was not really so hard to get this idea [of the hole theory]’ as he was simply drawing an analogy with the theory of how atoms emit X-rays (high-energy light).28 This theory says that an electron close to the nucleus can be knocked out of the atom, leaving a gap into which another electron falls, accompanied by the emission of an X-ray. It is also possible that Dirac had acquired the germ of his idea when he was sailing down the river Volga fifteen months before. At the Russian Congress, he met the Soviet theoretician Yakov Frenkel: someone snapped a photograph of them lying on the deck of the steamer, in their dress suits. In 1926, Frenkel had produced a theory of crystals in which ‘empty spaces’ in the regular lattice structure of the crystal would behave like particles – again, precisely analogous to Dirac’s hole theory. Frenkel may have mentioned this theory to Dirac only for him to forget it and retrieve it later from his subconscious. But Dirac had no such recollection.29
Whatever the origins of the theory, there is no doubting the boldness of Dirac’s application of the idea. Nowhere in the paper does he pause to comment on the theory’s credibility. The crucial point for him was that he now had the beginnings of a viable theory of matter, based on an appealing equation and solid principles. Who was going to accept that the universe was full of unseen negative-energy electrons, an infinite sea of negative electrical charge? Yet his short paper ‘A Theory of Electrons and Protons’ bears no sign that he was expecting his idea to be greeted with incredulity. He wrote the article in his uncluttered style but with fewer equations than usual, free of the windiness that would have been excusable in the first presentation of a theory that suggested a new way of looking at the material universe.
Although Dirac never admitted to being nervous about the reception of his hole theory, he often talked of anxiety as the handmaiden of scientific daring.30 So it is likely that he feared his theory contained a humiliating fallacy, a concern stoked by a letter he received in late November from Bohr, who had heard about the hole idea on the grapevine. For Bohr, the existence of negative energy levels in Dirac’s theory of the electron undermined confidence in the entire concept of energy, a problem that – Bohr observed – also occurred in explanations of why some types of atomic nucleus can sometimes spontaneously eject a high-energy electron, a process known as radioactive beta decay. It seemed that energy was not conserved in this process – there was less energy before the decay than there was afterwards – so energy appeared to emerge out of nowhere. This was serious: Bohr was questioning quantum mechanics and even the law of conservation of energy. Dirac thought his mentor was overreacting and, in a roundabout way, recommended him to calm down. Dirac had already told Bohr that he believed that the law of conservation of energy had to be preserved at all costs and that, to keep it, he would be prepared to abandon the idea that matter consists of separate atoms and electrons. And Dirac thought it premature to be pessimistic about quantum mechanics, which had only just passed its fourth birthday:
I am afraid I do not completely agree with your views. Although I believe that quantum mechanics has its limitations and will ultimately be replaced by something better (and this applies to all physical theories) I cannot see any reason for thinking that quantum mechanics has already reached the limit of its development. I think it will undergo a number of small changes, mainly with regard to its method of application, and by these means most of the difficulties now confronting the theory will be removed.31
Dirac concluded by reiterating – almost word for word – his reasons for believing in his hole theory. Although his defence could be regarded as stubborn, he does make it clear that he expected his theory to be superseded; the task in hand was to develop the theory as far as it could be taken. Bohr’s criticisms do not seem to have shaken him in the least – he would need this thick skin during the coming barrage of scepticism and derision.
A week after he wrote to Bohr, Dirac gave his first public presentation of the hole theory to an audience in Paris, at the Henri Poincaré Institute. He will not have taken much pleasure from giving the lecture, as he reluctantly agreed to give it in French, bringing back abhorrent memories of meals with his father. When he returned to Bristol for Christmas, he had no choice but to speak French again. After his absence for nine months, his family was desperate to see him and to show him their latest plaything – the ‘Gramaphone’ (sic).32 But Dirac was, as always, downhearted even at the thought of returning to his enervating Bristol routine, his mother endlessly fussing over him, his father still intimidating him simply by his presence. Although Dirac appears to have told none of his physicist friends, he believed that his home life had stultified him as a child and was still grinding him down. He appears to have first shared the full extent of his pain only a few years later with a friend who was not one of his academic associates. In a letter, he wrote, ‘going to see my parents will change me very much, I am afraid, and makes me feel like a child again and unable to do anything for myself’.33 For now, like all his other emotions, his suffering was hidden.
Notes - Chapter thirteen
1 Letter from Dirac to Oswald Veblen, 21 March 1929, LC, Veblen archive.
2 Scott Fitzgerald (1931: 459).
3 Letter from Dirac to Veblen, 21 March 1929, LC (Veblen archive).
4 Diaries of Dirac (DDOCS).
5 Fellows (1985); see the introduction (p. 4) and the conclusion.
6 Comment made by Bohr to Crowther, recorded by Crowther on 24 April 1932 in the
Crowther archive, SUSSEX, Book II of his notebooks, pp. 96–7. For one of many
retellings of this anecdote, see Infeld (1941: 171).
7 See the article on Roundy in the Wisconsin State Journal on the day after his death,
on 10 December 1971.
8 The article is reproduced in its entirety in Kragh (1990: 72–3). The original is in
Dirac Papers, 2/30/1 (FSU).
9 A check of the microfilm records of the Wisconsin State Journal reveals that the article
was not published between 1 April and 29 May 1929 (the microfilm for 30 May
is missing).
10 Van Vleck (1972: 7–16; see pp. 10–11).
11 Record of Dirac’s payment as ‘Lecturer in physics April and May 1929’ is in WISC.
Early in his stay, from 10–16 April, Dirac had spent almost a week based at the
University of Iowa.
12 Dirac left Madison on 27 May and travelled to the Grand Canyon via Minneapolis,
Kansas City and Winslow, Arizona.
13 Quoted in Brown and Rechenberg (1987: 134). This article gives much detail about
Dirac and Heisenberg’s preparations for their 1929 trip and the trip itself.
14 Mehra (1973: 816).
15 Brown and Rechenberg (1987: 136–7).
16 Interview with Leopold Halpern, 18 February 2003.
17 Brown and Rechenberg (1987: 139–41).
18 Heisenberg returned from the 1929 trip to be the best ping-pong player in the quantum
community: interview with von Weiszächer, AHQP, 9 July 1963, p. 11.
19 Mehra (1973: 816).
20 Mehra (1972: 17–59).
21 The jako was commonly used to scent clothes in Japan at that time. Hearn (1896: 31n).
22 Dirac gives his timetable in his letter to Tamm on 12 September 1929, Kojevnikov
(1993: 29); Brendon (2000: 234).
23 Letter to Dirac from his mother, 6 July 1929, Dirac Papers, 1/3/11 (FSU).
24 Letter to Dirac from his mother, 6 May 1929, Dirac Papers, 1/3/10 (FSU).
25 Postcards from Dirac to his parents, autumn 1929, DDOCS.
26 Interview with Oppenheimer, 20 November 1963, p. 23 (AHQP).
27 Fitzgerald (1931: 459).
28 Dirac (1977: 144).
29 Kojevnikov (2004: 56–9).
30 Pais, A. (1998: 36).
31 Letter from Dirac to Bohr, 9 December 1929, NBA.
32 Letter to Dirac from his mother, 11 October 1929, Dirac Papers, 1/3/10 (FSU). The spelling is the one used by Flo Dirac. Dirac expected to arrive home on 19 December
(postcard from Dirac to his parents, 27 November 1929, DDOCS).
33 Letter from Dirac to Manci, 26 February 1936 (DDOCS).
Fourteen
O hear the sad petition we electrons make to you
To free us from the dominion of the hated quantum view
For we are all abandoned to its dread uncertainty.
Except by you, our champion. O we pray you, set us free!
Once in a pleasant order our smooth-flowing time was spent
As the classical equations told us where to go, we went.
We vibrated in the atom, and a beam of light was freed;
And we hadn’t any structure – only mass and charge and speed.
We know not if we’re particles, or a jelly sort of phi,
Or waves, or if we’re real at all, or where we are, or why,
To protons – holes in ether – according to Dirac.
ANON.1
Those anonymous lines are from an ode to the electron, pinned to a noticeboard in the Cavendish Laboratory around 1930. Only the most hard-headed theorist could fail to sympathise with the poet’s nostalgia. A decade before, atomic physics had been a matter of common sense: electrons were just tiny particles, and they behaved predictably, according to straightforward laws of nature – the same ones that described everything else in the universe. How quaint those ideas now seemed: the classical laws that had held sway for a quarter of a millennium were now, in the atomic domain, obsolete, as Dirac liked to point out, the idea Jonathan Swift explored in Gulliver’s Travels – that no one would notice if naturally occurring things expanded or contracted in the same proportion – was wrong.2 The laws of the everyday world cannot be scaled down to the atomic domain: things are different there. Theorists could now reject every attempt to picture the electron as meaningless and therefore fraudulent. The particle did not even behave predictably: physicists were calculating odds like croupiers at nature’s gambling table, using waves that no one believed were real. To cap it all, Dirac had the temerity to argue that common-or-garden electrons, with positive energy, are outnumbered by negative-energy ones that cannot even be observed.
It was probably a Cavendish experimenter, one of many who were suspicious of hole theory, who wrote the anonymous poem. Only a few theoreticians, including Tamm and Oppenheimer, took the theory seriously, and even they soon found it wanting. In February 1930, Oppenheimer showed that the average lifetime of an atom was about a billionth of a second according to Dirac’s hole theory, because the atomic electron would quickly fall to its death in the negative-energy sea. Soon afterwards, Tamm and Dirac independently arrived at the same conclusion. Pauli suggested what became known as his Second Principle: whenever a physicist proposes a new theory, he should apply it to the atoms in his own body.3 Dirac would be the first victim.
Pauli’s jest appealed to Gamow, who was staying in Cambridge in the first academic term of 1930, mainly to work with Rutherford and his colleagues. Dirac was charmed by Gamow’s non-stop good humour and sense of fun: no one did more to show Dirac what he had missed in his youth. Gamow taught Dirac how to ride a motorcycle (and filmed him doing it), gave him a taste for Conan Doyle’s detective novels and apparently introduced him to the high jinks of Mickey Mouse, who first appeared on the screen two years before, in Steamboat Willy.4 Dirac adored Mickey Mouse films, the animated successors of the cartoons he had seen as a boy in the penny weeklies. A few years later, he made a point of attending a day-long festival of the films in Boston, though it seems that he kept this innocent pleasure secret from his highbrow Cambridge colleagues.5He was self-aware enough to know that his standing in the St John’s common room would not be increased if he were too enthusiastic in his praise of Peg-Leg Pete or Horace Horsecollar.
More respectable at High Table was Dirac’s appetite for mathematical games and puzzles that served no purpose at all beyond entertainment. Once, he gave a devastating performance in a game that had been introduced at Göttingen in 1929. The challenge was to express any whole number using the number 2 precisely four times, and using only well-known mathematical symbols. The first few numbers are easy:
1 = (2 + 2)/(2 + 2),
2 = (2/2) + (2/2),
3 = (2 × 2) – (2/2),
4 = 2 + 2 + 2 – 2.
Soon, the game becomes much more difficult, even for Göttingen’s finest mathematical minds. They spent hundreds of hours playing the game with ever-higher numbers – until Dirac found a simple and general formula enabling any number to be expressed using four 2s, entirely within the rules.6 He had rendered the game pointless.
On 20 February 1930, Dirac sent his parents the usual newsless weekly postcard, consisting of a ten-word summary of the Cambridge weather.7 The day after his mother received it, she visited the library and was astonished to read in a newspaper that her son had been elected a Fellow of the Royal Society, one of the highest honours in British science. Excited and flushed with pride, she dashed out to the post office and sent him a congratulatory telegram, keeping in check her annoyance that he had not mentioned the news on the card.8 Dirac was a ‘naughty boy’, she told him two days later in a letter, enquiring whether the society was organising a ceremony of induction. ‘Do tell me,’ she wrote, stressing each word in frustration.9
Dirac could now put the initials FRS after his name, letters that render all other aces, after they had been nominated and passed over several times, soademic qualifications redundant. The Society, which then had 447 Fellows, usually gave the honour to scientists in their forties and fifti it was extraordinary for Dirac to be appointed the first time he had been put up for election, when he was only twenty-seven. As the news spread among the High Tables and common rooms of Cambridge, it would not have escaped the dons’ notice that he had been elected a Fellow at a younger age than any of his senior colleagues.10
The announcement appears to have made Dirac’s parents realise how rapidly the reputation of their son had risen. ‘How hard you must have worked to get to the top of the tree like that,’ his mother wrote. ‘No wonder you didn’t take any interest in the Boat Racing.’11 The news was a welcome fillip for Flo, whose morale was low. Now that her husband was about to retire, her prospects were pitiable: only fifty-two years old, all she had to look forward to were years cooped up at home with a sick man whom she regarded as a browbeating ingrate and who, she knew, saw her as an inadequate nurse and servant. At school, Charles Dirac’s colleagues queued up to offer their congratulations, and he received several letters to congratulate him on raising such a successful son. Paul’s engineering teacher Andrew Robertson pointed out that he believed Dirac was the first Bristol graduate to have been elected an FRS; Ronald Hassé, who first steered Dirac towards a career in theoretical physics, wrote to say how much he was looking forward to Dirac’s first public speech in Bristol in September. The city was to host the annual meeting of the British Association for the Advancement of Science, where scientists and members of the public got together to hear a week of lectures on the latest science.12 At the Cotham Road School – formerly the Merchant Venturers’ School – they celebrated by taking a day off. Charles never quite knew when to expect the next plaudit: once, during a lesson, two complete strangers knocked on his classroom door, entered, complimented him on his son’s great achievement, and left.13
Perhaps to celebrate his latest success, Dirac took his mother’s advice and splashed out almost £200 on his first car, a Morris Oxford Tourer, capable of a then-impressive 50 mph.14 There was no driving test: after completing the sale, the garage owner gave him a short demonstration drive around Cambridge and then handed him the keys. He was then free to take his chances on the roads. With the scrapping
of the 20 mph speed limit that year, the highways became even more dangerous, not least because of Dirac’s presence. A colleague laughed that ‘Dirac’s car has two gears, reverse and top.’15 Only Mott left an account of being driven by Dirac, to London on an icy March day when ‘Dirac ran – very gently – into the back of a lorry and smashed a headlamp.’16 Like Kapitza, Dirac was a wild driver, and this appears to have been due both to his poor handling of the vehicle – his appreciation of machines always exceeded his competence at using them – and to the virtual absence of a highway code. Dirac was a stickler for obeying rules that he believed were rational and obviously for the common good, so, in the absence of regulations, he was free to drive as he wished.
Dirac was, at last, showing signs of mellowing. Leisure was not reserved only for Sundays: at lunchtimes, the bulk of his day’s work done, he would often motor out of Cambridge to the Gog Magog Hills, park his car near a tall tree and climb it, still wearing his three-piece suit.17 He wore it whatever the weather, whatever the occasion, and took it off only during his drives out to secluded sites by the river Cam and in the fens north-east of the city, where he bathed, as Lord Byron had done 125 years before. Later, when he returned to college or to his desk, he would do only the lightest of tasks. He was taking a leaf out of the book of G. H. Hardy, who believed that the longest a mathematician can profitably spend doing serious work is four hours.18
Of all the months in the Cambridge academic calendar, June was the most relaxed. The examinations over, it was time for the students to leave the university, but only after the catharsis of the summer ball. The intoxicating mix of music and dancing, free-flowing champagne, gorgeous frocks and sharply cut dinner suits could cheer up the most abject examinee. Dons could put on their summer suits and wind down to the ‘long vac’, when they had no administrative duties and were free to spend the long, languid afternoons doing nothing except sit in a deckchair and watch a game of cricket. Dirac was nonplussed by the appeal of an activity that involved twenty-two men spending hours – sometimes days – playing a game that often ended in a draw, which devoted spectators would often deem exciting. The game had no more ardent admirer than G. H. Hardy, for whom it was akin to pure mathematics: all the more beautiful for its lack of useful purpose. A few years later, he gave pride of place in his study to a photograph of the Australian batsman Donald Bradman, one of Hardy’s three greatest heroes (the others were Einstein and Lenin).19 Hardy was probably looking forward to Bradman’s first Test appearances on English soil, but the prospect will have left Dirac unmoved; he was busy preparing to spend the summer climbing and hillwalking with friends. He needed a break and some fresh inspiration if he was to sort out the problems with his hole theory and so answer his critics, including the mocking Pauli and the privately scornful Bohr. Several of Dirac’s colleagues would be lining up to attend his public lecture at the Bristol meeting at the end of the summer, he knew, to see if he had cracked the problem of negative-energy electrons.
The Strangest Man Page 25