At the end of January, as he was preparing to leave Copenhagen, Dirac posted his paper to the Royal Society. It turned out that he was the first to introduce the mathematics of creation and annihilation into quantum theory, though his results had been reached independently by John Slater, studying in Cambridge with Fowler. Slater was one of the many who admired Dirac’s paper for its content but found its presentation perversely complicated: ‘his paper was a typical example of what I very much distrusted, namely one in which a great deal of seemingly unnecessary mathematical formalism is introduced’.34
Dirac’s time in Copenhagen was an unqualified success. The two theories that he had nurtured there had underlined his status as a leading player on the international stage of science. Although he was still the archetypal individualist, he had come to see the value of taking different approaches to his subject and of having his views cross-examined. Apart from Bohr, the interrogator who most fascinated him was Paul Ehrenfest, an intense and disturbed theoretician based at the University of Leiden in the Netherlands. Ehrenfest got on well with Dirac, who was almost half his age, the two no doubt especially comfortable in each other’s company because – unusually among the Institute’s members – they disliked both alcohol and smoking. Ehrenfest’s aversion to smoking was in part due to his extremely sensitive sense of smell. One victim of this was the amiable Dutch graduate student Hendrik Casimir. Soon after he arrived in Leiden, Casimir had his hair cut before a meeting with Ehrenfest, who soon sniffed the perfume of the barber’s dressing. Ehrenfest quickly became angry and shouted, ‘I will not tolerate perfume here. Get out. Go home, get out. Get out. Get out.’ A few days later, Casimir was dismissed.35
Ehrenfest was at his best during seminars. Unafraid of ridicule, he would politely but persistently interrupt speakers, seeking clarification of every unclear point. When he first met Dirac, Ehrenfest was uncomfortable with quantum mechanics and was worried that his close friend Einstein was unhappy about the central role played in the theory by probability. Einstein had been the first to identify that when an atom spontaneously jumps to a lower energy level, quantum theory cannot predict either the direction of the emergent photon or the precise time of its ejection. This was also true of ordinary quantum mechanics and of Dirac’s new quantum field theory. Einstein was sure that a satisfactory theory had to do better than just predict probabilities: ‘God is not playing dice,’ he wrote to Max Born.36 Dirac thought his hero worried too much about the philosophical issues of quantum mechanics. All that mattered to Dirac – true to his mathematical and engineering training – was that the theory was logical and accurately accounted for the results of experiments.
At the end of January 1927, Dirac was preparing to travel to Göttingen. Soon he would be leaving the company of Niels Bohr, whom Dirac would later describe as ‘the Newton of the atom’ and ‘the deepest thinker that I ever met’.37 But it was Bohr’s warmth and humanity that most impressed Dirac. At Christmas – while Charles, Flo and Betty Dirac were going through the family rituals – Dirac had been welcomed into the Bohrs’ loving fold and witnessed familial joy for the first time. Dirac had seen that it was possible to be both a great physicist and a dedicated family man and that perhaps – just perhaps – there might be more to life than science.
For Bohr, Dirac was ‘probably the most remarkable scientific mind which has appeared for a very long time’ and ‘a complete logical genius’.38 Also intrigued by Dirac’s personality, Bohr never forgot one incident, during a visit to an art gallery in Copenhagen, of his young visitor’s eccentricity. When they were looking at a French impressionist painting showing a boat sketched by just a few lines, Dirac observed, ‘This boat looks as if it was not finished.’ Of another picture, Dirac remarked, ‘I like that because the degree of inaccuracy is the same all over.’39 Such anecdotes became part of scientific lore, and physicists vied with one another to relate the most amusing instances of Dirac’s verbal economy, his literal-mindedness, mathematical precision and otherworldliness. With no psychological framework available to help understand him, his personality became an object of collective amusement, through a myriad of ‘Dirac stories’.
No one relished telling the stories more than Bohr, who entertained visitors with them over afternoon tea in his office. Four years before he died, he told a colleague that, of all the people who had visited his institute, Dirac was ‘the strangest man’.40
Note - Chapter eight
1 Wheeler (1998: 128–9). On 24 April 1932, Jim Crowther wrote of hearing a similar
anecdote from Bohr over afternoon tea (Book I of Crowther’s notes from his meeting
with Bohr, pp. 99–100 [SUSSEX]).
2Book I of Crowther’s notes from his meeting with Bohr, 24 April 1932, pp. 96–101,
SUSSEX. See also the article on Dirac by John Charap in The Listener, 14 September
1972, pp. 331–2.
3 Book I of Crowther’s notes from his meeting with Bohr, p. 99, SUSSEX.
4 Dirac (1977: 134).
5 Bohr’s words (Nicht um zu kritisieren aber nur um zu lernen) are quoted in Dirac
(1977: 136).
6 Postcard from Dirac to his parents, 1 October 1926 (DDOCS).
7 Letter from Dirac to James Wordie, 10 December 1926, STJOHN; Dirac (1977: 139).
8 The phrase ‘liked the sound of his own voice’ is taken from the letter John Slater
wrote to John Van Vleck on 27 July 1924, John Clarke Slater papers APS. See also
Cassidy (1992: 109).
9Crowther notes, p. 99, SUSSEX.
10 The wave is what is known mathematically as a complex function, which means that
the wave at any point has two parts: one real, the other imaginary. The ‘size’ of the
wave at any point, related to both parts, is called its modulus. According to Born, the
probability of detecting the quantum in a tiny region near a point is related to the
square of the modulus of the wave.
11 Pais (1986: 260–1).
12 Heisenberg (1967: 103–4).
13 Interview with Oppenheimer, AHQP, 20 November 1963.
14 Weisskopf (1990: 71).
15 Interview with Dirac, AHQP, 14 May 1963, p. 9.
16 Garff (2005: 308–16, 428–31).
17 Interview with Monica Dirac, 3 May 2006.
18 Quoted in Garff (2005: 311); interview with Dirac, AHQP, 14 May 1963, p. 9.
19 Møller (1963).
20Dirac had also seen the need for the function when he was studying Eddington’s The
Mathematical Theory of Relativity (1923). On page 190, Eddington uses nonrigorous
mathematics, and he drew attention to this in a footnote, which Dirac read.This was an example of the case where the delta function is needed to make some
sense of a scientific equation which would otherwise be mathematically unintelligible.
See interview with Dirac, AHQP, 14 May 1963, p. 4.
21 Interview with Dirac, AHQP, 6 May 1963, p. 4.
22 Heaviside (1899: Sections 238–42).
23 Lützen (2003: 473, 479–81).
24 Interview with Heisenberg, AHQP, 19 February 1963, p. 9.
25Dirac (1962), report of the Hungarian Academy of Sciences, KFKI-1977-62.
26 Letter from Einstein to Conrad Habicht, 24 December 1907, see Pais (1982: 441).
27 Dirac mentioned this in a press release issued by Florida State University on 24
November 1970; Dirac Papers, 2/6/9 (FSU).
28 Letters to Dirac from his mother, 19 November, 26 November, 2 December, 9
December 1926, Dirac Papers, 1/3/6 (FSU).
29 It is possible that Charles wrote other letters to Dirac. If so, Dirac did not keep them
– uncharacteristically, as he appears to have kept most of his family correspondence.
Moreover, the frequent letters from Dirac’s mother often send messages from his
father, indicating that his father was communicating to his s
on via her, a common
arrangement in family correspondence of this type.
30 Letter to Dirac from his father, 22 December 1926, Dirac Papers, 1/1/7 (FSU).
31 Letter to Dirac from his mother, 25 December 1926, Dirac Papers, 1/3/6 (FSU).
32 Mehra (1973: 428–9).
33 Postcard from Dirac to his parents, 10 January 1927, DDOCS.
34 Slater (1975: 135).
35 Elsasser (1978: 91).
36 Born (2005: 88).
37 ‘The deepest thinker’: Dirac (1977: 134).
38 ‘The most remarkable scientific mind . . .’: Crowther notes, p. 21, SUSSEX. The ‘logical
genius’ comment is in the interview with Bohr, AHQP, 17 November 1962, p. 10.
39 Both quotes from the Crowther notes, p. 97, SUSSEX.
40 ‘PAM Dirac and the Discovery of Quantum Mechanics’, Cornell colloquium, 20
January 2003, available at http://arxiv.org/PS_cache/quant-ph/pdf/0302/
0302041v1.pdf (accessed 24 September 2007).
Nine
[For young Germans after the great inflation they experienced in 1923] their aims were to live from day to day; and to enjoy to the utmost everything that was free: sun, water, friendship, their bodies.
STEPHEN SPENDER, World Within World, 1951
In Göttingen, Dirac made another of his unlikely friendships. This one was with Robert Oppenheimer, who had fled Cambridge and was flourishing in Max Born’s Department of Theoretical Physics as a Ph. D. student of rare ability, self-confidence and superciliousness. Ever the intellectual peacock, Oppenheimer ensured that his colleagues knew he was thinking about more than physics: his eclectic reading list included F. Scott Fitzgerald’s collection of short stories Winter Dreams, Chekhov’s play Ivanov and the works of the German lyric poet Johann Hölderlin.1 He was also composing verse, a hobby that puzzled Dirac. ‘I don’t see how you can work on physics and write poetry at the same time,’ he remarked during one of their walks. ‘In science, you want to say something nobody knew before, in words everyone can understand. In poetry, you are bound to say something that everybody knows already in words that nobody can understand.’ For decades to come, Oppenheimer liked to recount this anecdote over cocktails, no doubt having polished Dirac’s original phrasing to give it the bite of one of Wilde’s paradoxes.2
Dirac kept normal working hours, while Oppenheimer was nocturnal, so the two young men could not have seen much of each other.3 They boarded with the Cario family in a spacious granite villa on Giesmarlandstrasse, which led from the town centre out to the local countryside.4 From the outside, the home appeared to be just another of the town’s many lavish residences, but there was a bitterness and penury inside. During the unstable early years of the Weimar Republic, the Carios had been victims of the precipitate fall of the German currency: the number of deutschmarks that could be purchased with an American dollar rose from 64.8 in January 1920 to 4.2 trillion in November 1923.5 Worse, the family’s breadwinner, a doctor, had been disqualified for malpractice. Now that the Republic had stabilised, the Carios made a living by turning their home into a guesthouse for the stream of foreign visitors, many of them American students visiting the Georgia Augusta University, one of the most prestigious academic addresses in Europe. With his fellow boarders, Dirac sat down every evening to a meal based on the local fare of potatoes, smoked meats, sausages, cabbages and apples.
It took Dirac and Oppenheimer only five minutes to stroll from their lodgings to Born’s department in the Second Physics Institute, located in an ugly red-brick building with all the charm of a Prussian cavalry barracks. Born – a handsome, clean-shaven man, who looked younger than his forty-four years – was reserved but warmer than most of his professorial colleagues. He cultivated a competitive environment but was sensitive to the needs of the brightest students and tolerant of their peccadilloes. Dirac and Oppenheimer were among the many students Born invited to his villa on the Planckstrasse, a quiet road on the outskirts of the town. To be invited there was always a pleasure: dinner would be followed by good-humoured conversation and a concert in the huge front room, which contained two grand pianos.6Heisenberg, a close friend of the family, took every opportunity to display his pianistic skills in flamboyant renditions of Beethoven, Mozart and Haydn.7
Dirac lived just a few steps away from the historic centre of Göttingen, one of the best-preserved medieval towns in Lower Saxony: its half-timbered houses and shops, its churches and cobbled backstreets had remained virtually unchanged for centuries. Nor was it yet overrun by the motor car. Most people got around on foot or by bicycle, many of the cyclists sporting garishly coloured caps to show their affiliation to one of the clubs and societies.8 Like Cambridge, Göttingen was a tranquil academic town, dominated by the needs and whims of its academics and students. Seniority and intellectual distinction were at a premium there. Its most revered citizens were the most venerable of its distinguished professors, including the gruff David Hilbert, sixty-three years old and the most celebrated mathematician alive.
Also like Cambridge, many of Göttingen’s (mainly male) students were there not so much to be well educated as to spend a few hedonistic years in the fug and cacophony of the town’s taverns and coffee bars.9 No doubt having left Dirac to get his sleep, Oppenheimer and his friends spent many a night on the razzle; he happily picked up the tab after downing a few pints of frisches Bier in the Black Bear pub or dining on Wienerschnitzel at the four-hundred-year-old Junker Hall.10 The atmosphere in the pub had hardly changed in generations: most evenings, the din of the students would often dissolve into bibulous choruses of favourite folk songs, while virile young men sloped off to put on their chain mail, don their swords and do some ‘academic fencing’. When the combatants returned, their faces were ‘decorated’ with scars, each a bloody badge of honour.11
At weekends, Oppenheimer and other affluent students often took the two-and-a-half-hour train journey to Berlin, the city of Bertolt Brecht, Arnold Schönberg and Kurt Weill. But Dirac had no interest in broadening his horizons much beyond the towns and villages of Lower Saxony, where he went on long Sunday walks, if he was not snowbound. Within twenty minutes of leaving his lodgings, he was walking in the gently rolling countryside, following the fast-flowing rivers and pausing at the scattered monuments to Bismarck. By early spring, the walking conditions were perfect: almost all the winter snow had melted, and the linden trees, shrubs and flowers were scenting the air. He passed occasional groups of young men in the German Youth Movement but otherwise saw scarcely another person, which was just as he preferred – his empathies lay more with uncommunicative forms of nature than with human beings.
So Göttingen gave Dirac everything he wanted in a town – a great university with a world-leading physics department and comfortable lodgings close to walking country, where he could escape from other people. Göttingen was a German Cambridge, with hills.
In early February 1927, within days of Dirac’s arrival in Göttingen, he had set Oppenheimer’s imagination alight. Oppenheimer was completing his Ph. D., on the quantum mechanics of molecules, and looking to the future which appeared to lay in the direction that Dirac had opened up. Near the end of Oppenheimer’s life, when he looked back on his career, he remarked that ‘perhaps the most exciting time of my life was when Dirac arrived [in Göttingen] and gave me the proofs of his paper on the quantum theory of radiation’. While others found Dirac’s field theory mystifying, to Oppenheimer it was ‘extraordinarily beautiful’.12
Oppenheimer had been an outsider at Cambridge and Harvard and so he was pleased at last to feel part of the small community of Göttingen physicists, gradually recovering from his clinical depression. Among his colleagues was Pascual Jordan, born a few weeks after Dirac and the youngest of the quantum innovators. Intense, haunted and private, his eyes stared out from behind elliptical glasses with lenses as thick as jam jars. Oppenheimer later remarked that Jordan’s peculiarities may have led him to be underestimated: ‘it was i
n part because he was really an unbelievably queer duck with tics and mannerisms and […] apparent brutalities, which put people off very much.’13 According to Oppenheimer, Jordan had a stutter so crippling that ‘it was difficult to get through’, though Oppenheimer may have to some extent admired it – he began to affect a stutter, muttering ‘njum-njum-njum’ before some of his finely crafted declamations.14
Although Jordan and his colleagues admired Oppenheimer’s quick-fire intelligence – one of them likened him to ‘an inhabitant of Olympus who had strayed among humans’ – they found his arrogance irritating, to the point that it became unacceptable.15 One morning, Born found on his desk a letter from several of his colleagues threatening to boycott seminars unless he stopped Oppenheimer from disrupting them with his continual interruptions. Always fearful of showdowns, Born chose to leave the letter – a large sheet of parchment lettered in ornamental script – on his desk for Oppenheimer to see. It did the trick. Relations between Born and Oppenheimer were superficially cordial, but Oppenheimer regarded Born as a ‘terrible egotist’ who continually complained that he had not been given enough credit for pioneering quantum mechanics.16 Born had good reason to feel slighted. He had been one of the creators of quantum mechanics, having used his battery of mathematical skills to develop Heisenberg’s initial idea. Most physicists gave the lion’s share of the credit to Heisenberg, but Born believed that it was he who first fully appreciated the idea’s potential and he who led its development in Göttingen.
By the time Dirac arrived there, Born was confident that he had found the right way to develop quantum mechanics, using Heisenberg’s ideas, not Schrödinger’s. Although Born knew of Dirac’s reputation, he was not expecting his young visitor to be so adept and knowledgeable. The American physicist Raymond Birge, then visiting Göttingen, observed that ‘Dirac is the real master of the situation […] when he talks, Born just sits and listens to him open-mouthed.’17
The Strangest Man Page 18