A week after Christmas, Rutherford was ennobled at the end of his five-year stint as President of the Royal Society. But the pleasure the honour gave him was eclipsed by a family tragedy: his daughter and only child, Fowler’s wife, died in childbirth two days before Christmas. Lord Rutherford, grieving as he approached his sixtieth birthday, must have thought his years of glory were over. He was not doing much research of his own, so his remaining hopes of being involved in more of the ground-breaking discoveries that he longed for were in the hands of his ‘boys’.
Dirac showed none of the confidence that might be expected of a young man at the top of his game. Chandrasekhar wrote home to his father that he was disappointed that Dirac did not show a bit more swagger: ‘[Dirac is a] lean, meek shy young “Fellow” (FRS) who goes slyly along the streets. He walks quite close to the walls (like a thief!), and is not at all healthy. A contrast to Mr Fowler […] Dirac is pale, thin, and looks terribly overworked.’52
Work was not Dirac’s only concern. Having read his mother’s letters, he may have sensed that his parents’ relationship, tense and unstable, was fast approaching a flashpoint. Charles Dirac, dreading retirement, was pleading with the Bristol education authorities to be allowed to stay on in his job, but they were resisting. Betty, now with a car of her own, was doing little except chauffeur him three times a day to and from Cotham Road School. Dirac was watching his sister become another of his father’s servants.
Meanwhile, Flo knew that, in only a few months, she would be spending most of her life at home alone with her husband: ‘It simply won’t bear thinking about.’53
Notes - Chapter fourteen
1 Cavendish Laboratory Archive, UCAM. The poem was apparently written as a
Valentine’s card to the electron.
2 Dirac, ‘Symmetry in the Atomic World’, January 1955. The draft, which features this
analogy, is in Dirac Papers, 2/27/13 (FSU).
3 Cited in Kragh (1990: 101).
4Gamow (1970: 70); letter from Dirac to Tamm, 20 March 1930, in Kojevnikov
(1993: 39).
5 On Saturday, 16 February 1935, Van Vleck took D to ‘A Disney Day’ at a cinema in
Boston. The documents, marked with Van Vleck’s comment ‘Dirac loved Mickey
Mouse’, are in the Van Vleck papers at AMS.
6 Dirac’s formula is n = – log2 [log2 (2√(√ . . . √2))], where the ellipsis (. . .) denotes the
taking of n square roots. The story is related in Casimir (1984: 74–5), where the author
asserts that Dirac killed the game using only three 2s. Each symbol in the formula is
very common in mathematics, so Dirac’s solution is within the rules of the game.
7 Postcard from Dirac to his parents, 20 February 1930 (DDOCS).
8 Telegram to Dirac from his mother, 22 February 1930, Dirac Papers, 1/3/12 (FSU).
9 Letter to Dirac from his mother, 24 February 1930, Dirac Papers, 1/3/12 (FSU).
10 The certificate of Dirac’s election to the Fellowship of the Royal Society is available
on the Society’s website. The names of the 447 Fellows of the Society on 31
December 1929 are given in the Yearbook of the Royal Society 1931.
11 Letter to Dirac from his mother, 24 February 1930, Dirac Papers, 1/3/12 (FSU).
12 Letter from Hassé to Dirac, 28 February 1930, Dirac Papers, 2/2/1 (FSU).
13 Letter from Arnold Hitchings to the Bristol Evening Post, 14 December 1979.
14 In 1935, Dirac traded in this car. Dirac Papers, 1/8/2 (FSU).
15 Interview with John Crook, 1 May 2003.
16 Mott (1986: 42).
17 Dirac was well known for this practice. It is described explicitly by his climbing tutor
Tamm in the course of the letter to his wife on 27 May 1931, Kojevnikov (1993: 55). See also Mott (1972: 2).
18 Interview with Monica Dirac, 7 February 2003; see also M. Dirac (2003: 42).
19 Letter from Taylor Sen (1986: 80). Howarth (1978: 104).
20 See, for example, Daily Telegraph, 12 February 1930, Manchester Guardian, 12–18
February 1930.
21 Peierls (1987: 36).
22 Letter to Dirac from his mother, 12 June 1930, Dirac Papers, 1/3/12 (FSU).
23 Kojevnikov (1993: 40), note on letter from Dirac to Tamm, 6 July 1930.
24 The Guardian, ‘World Conference of Scientists’, 3 September 1930. Crowther was
probably the author of this report.
25 Ross (1962).
26 The venue and the time of the talk are in the records of the British Association for the
Advancement of Science, BOD.
27 Delbrück (1972: 280–1).
28 The report of the Science News Service is in Dirac Papers, 2/26/8 (FSU).
29 New York Times, 10 September 1932.
30 I have translated the German word quatsch as ‘crap’. Another, similar version of
this anecdote is given in the interview with Guido Beck, AHQP, 22 April 1967, p. 23.
31 Among the most able students who were dissatisfied by Dirac’s talks was Freeman
Dyson, who recalls: ‘I read Dirac’s book hoping to learn quantum mechanics from it,
and found it totally unsatisfactory.’ E-mail from Dyson, 19 August 2006.
32 Nature, Vol. 127, 9 May 1931, p. 699.
33 Pauli’s review is in Kronig and Weisskopf (1964: 1,397–8).
34 Einstein (1931: 73).
35 Leisure reading anecdote: Woolf (1980: 261); ‘Where’s my Dirac?’ anecdote is from
Tallahasse Democrat, 29 November 1970.
36 Hoyle (1994: 238).
37 Freeman (1991: 136–7).
38 Quoted in Charap (1972: 331).
39 Letter from Tamm to Dirac, 13 September 1930, in Kojevnikov (1993: 43).
40 Einstein (1931: 73).
41 Comment made by Einstein on his arrival in New York on 11 December 1930,reported in the LA Times, 12 December 1930, p. 1.
42 Letter to Dirac from Tamm, 29 December 1930, Kojevnikov (1993: 48–9).
43 Letter from Kemble to Garrett Birkhoff, 3 March 1933 (AHQP).
44 Dirac attended the dinner on 17 December 1932, Dirac Papers, 2/79/6 (FSU).
45 Letter from Kapitza to his mother, 16 December 1921, in Boag et al. (1990: 138–9).
46 Da Costa Andrade (1964: 48).
47 Da Costa Andrade (1964: 162).
48 Records of the Cavendish dinners (CAV 7/1) 1930, p. 10 (UCAM).
49 Records of the Cavendish dinners (CAV 7/1) 1930, p. 10 (UCAM).
50 Snow (1931).
51 Snow (1934). Dirac features in the book, and some of his opinions also appear,
unattributed. See Snow (1934: 97–8 and 178–83).
52 Letter from Chandrasekhar to his father, 10 October 1930, quoted in Miller (2005:
96).
53 Letter to Dirac from his mother, 8 November 1930, Dirac Papers, 1/3/13 (FSU).
Fifteen
Russian politics like opium seems infallibly to provoke the most fantastic dreams and imaginings on the part of the people who study them.
E. A. WALKER, British Embassy, Moscow, 1931
In Cambridge, during the spring of 1931, Dirac happened upon a rich new seam of ideas that would crystallise into one of his most famous contributions to science. In the thick of this project, he received a letter from his mother, beginning:
27 April 1931
My dear Paul
Pa and I had quite a row yesterday all about some wine upset on some cheap stamps. He got in the most awful rage for a few minutes & then said he had had enough of me & should go if I did anything more to upset him.
I apologised most humbly as usual but on thinking it over, I am pretty certain he meant it.
In three pages of brief, matter-of-fact sentences, she described to Dirac – apparently for the first time – the charade of her marriage. She told him of a young woman who had visited the family when he was a baby, staye
d to supper and had been escorted home by Charles to Bedminster. Flo had written to her that she ‘wouldn’t have it any more and thought it was all finished’. But she was deluding herself, as she realised when she visited Charles’s Esperanto exhibition at Bishop Road School and saw that the woman who was presenting it with him, wearing a huge pair of tortoise-shell glasses, was the young woman who had visited them decades before. ‘Fancy if they have kept up the acquaintance for 29 years,’ Flo wrote. By this account, his father had been cheating on the woman who had spent most of her life looking after him. Her conclusion was: ‘She has nothing to do but humour him, I have to keep the house clean, dress him, bath him & worst of all find something to feed him on.’1
As usual, Dirac appears to have said nothing of this to anyone, even to his close friends. In the early months of 1931, a quiet time for his fellow theoreticians, he was working on the most promising new theory he had conceived for years.2 The theory broke new ground in magnetism. For centuries, it had been a commonplace of science that magnetic poles come only in pairs, labelled north and south: if one pole is spotted, then the opposite one will be close by. Dirac had found that quantum theory is compatible with the existence of single magnetic poles. During a talk at the Kapitza Club, he dubbed them magnons, but the name never caught on in this context; the particles became known as magnetic monopoles.3
The idea arose accidentally, he later said, when he was playing with equations, seeking to understand not magnetism but electrical charge.4 The American experimenter Robert Millikan had demonstrated that this charge exists only in discrete amounts, each of them exactly equal to a whole number multiplied by the size of the electron’s charge, usually denoted by e. So the electrical charge of a piece of matter can be, for example, five times the charge of the electron (5e) or minus six times its charge (–6e), but never two and a half times its charge (2.5e). The question Dirac wanted to answer was: why does electric charge come only in discrete amounts?
At first, Dirac worked in traditional ways, with quantum mechanics and Maxwell’s equations of electromagnetism. Then, like a jazz musician working with two intertwining melodies, he began the riff that led to the monopole. Dirac pictured the magnetic lines of force that end on a quantum particle, much like the ones that terminate on the pole of a bar magnet, usually displayed by patterns of iron filings, each of them obediently aligned to the magnetic force acting on it. He asked: if quantum mechanics and Maxwell’s equations of electromagnetism are assumed to be true, what can be said about the magnetic field associated with a quantum particle? To answer the question, he used an innovative combination of geometric thinking – picturing the possible waves in space and time – with powerful algebraic reasoning. He found a way of building on the existing structure of quantum theory, without changing any of its essential foundations and preserving all the rules that governed the interpretation of the theory. If quantum mechanics can be likened to a house of playing cards – with a fragile balance between its interconnected parts – then Dirac can be said to have added a few more cards, preserving the structure’s balance, while extending its range to include a new type of particle. The theory furnished a new connection between electricity and magnetism, an equation that relates the smallest-possible electrical charge with the weakest-possible magnetic charge.
The equation enabled him to draw some startling conclusions. First, the strength of the magnetic field of a monopole is quantised – it can have only certain allowed values, whole-number multiples of the minimum quantity, whose value he could easily calculate. It turned out that two monopoles of opposite sign are hard to separate: the force pulling them together is almost five thousand times the force that attracts an electron to a proton.5 This, Dirac suggested, might be why magnetic poles of opposite sign have never been separated and therefore appear in pairs.
His second conclusion was still more striking: the observation of just one monopole anywhere in the universe would explain why electrical charge is quantised – the very thing Dirac had set out to understand. Having checked his final calculations and having found no errors, he came to a bold conclusion: if an experimenter happens on a single monopole anywhere in the universe, the new theory can explain why nature had chosen to apportion electric charge only in discrete amounts.
Dirac’s theory did not guarantee the existence of monopoles but did show that quantum mechanics can describe such particles if they occur in nature. Centuries earlier, other scientists had speculated that monopoles might exist, but those ideas were just hunches, with no logical underpinning.6 Dirac was the first to give clear reasons why such particles might be observed. He may well have thought that the idea was too beautiful to be wrong, but he followed the convention of presenting his conclusion as an understatement: ‘one would be surprised if Nature made no use of it’. And he chose not to go the whole hog by trumpeting the magnetic monopole as a prediction of his theory. Like all physicists at that time, he accepted that experimenters had found the need for only two fundamental particles – the electron and the proton – and that it was not the job of theorists to complicate matters by proposing new ones. Ironically, the first physicist to buck the trend was an experimenter, Rutherford, when he proposed in 1920 that most atomic nuclei contain a hitherto undetected particle, roughly as heavy as the proton. He called the new particle ‘the neutron’.
Yet, in his paper on the monopole, Dirac implied for the first time that he no longer believed there are only two fundamental particles. In the introduction, he declared that he had suggested that a proton is a hole in the negative-energy sea of electrons: Oppenheimer and Weyl had convinced him that the hole must have the same mass as the electron (he did not mention Pauli, who had also come to the same conclusion). So Dirac followed the logic of Sherlock Holmes: ‘When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth.’7 The conclusion was that each hole corresponded to a new, hitherto undetected type of particle with exactly the same mass as the electron:
A hole, if there were one, would be a new kind of particle, unknown to experimental physics, having the same mass and opposite charge to an electron. We may call such a particle an anti-electron. We should not expect to find any of them in nature, on account of their rapid rate of recombination with electrons, but if they could be produced experimentally in high vacuum they would be quite stable and amenable to observation.
Again, Dirac is surprisingly circumspect. Although he states the properties of his new particle and even names it, he seems less keen to stress the inevitability of its existence than the difficulty of detecting it. If Dirac had been confident, he would have included a plainspoken sentence such as ‘According to this version of hole theory, the anti-electron should be detectable,’ but he held back. Paradoxically, he did underline a radically new interpretation of protons: they were nothing to do with electrons, he suggested, but have their own negative-energy states, ‘an unoccupied one appearing as an antiproton’. Within twenty lines of prose, he had foreseen the existence of the anti-electron and the anti-proton.
Though chary about predicting new particles, Dirac showed no timidity at all when he introduced what amounted to a new way of doing theoretical physics. In two paragraphs, consisting of 350 words and no equations, he argued that the best way to make progress was to seek ever-more-powerful mathematical foundations for fundamental theories, not to tinker with existing theories or look to experiment for inspiration. He envisaged the future of physical science as an unending series of revolutions, driven by mathematical imagination, not by opportunistic responses to the latest announcements from experimenters. This was tantamount to a new style of scientific investigation: seeking laws of ever-greater generality – as Descartes, John Stuart Mill and others had recommended – but relying on mathematical inspiration to find them, rather than taking their cues mainly from observations.
He began by pointing out that before Einstein used non-Euclidean geometry as the basis of the general theory of relativity
and before Heisenberg used non-commutative algebra in quantum mechanics, these branches of mathematics were ‘considered to be purely fictions of the mind and pastimes for logical thinkers’. The solution to the hardest problems in fundamental physics, Dirac inferred, will ‘presumably require a more drastic revision of our fundamental concepts than any that have gone before’. He set out his manifesto with the blazing confidence of a young scientist at the height of his powers:
Quite likely these changes [to our fundamental concepts] will be so great that it will be beyond the power of human intelligence to get the necessary new ideas by direct attempts to formulate the experimental data in mathematical terms. The theoretical worker will therefore have to proceed in a more indirect way. The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalise the mathematical formalism that forms the existing basis of theoretical physics, and after each success in this direction, to try to interpret the new mathematical features in terms of physical entities …
His message was clear: theorists should concentrate much more on the mathematical foundations of their subject and much less on the latest bulletins from the laboratories – to abandon centuries of tradition. No wonder Dirac became known as ‘the theorist’s theorist’.8
Early in May 1931, when Dirac was writing his paper, Tamm arrived in Cambridge to spend a few months in St John’s College, having left his wife and children in Moscow.9 He had no trouble securing permission to work in the UK, as Dirac was officially a favoured scientist in the Soviet Union, having been elected a corresponding member of the USSR Academy of Sciences three months before.
The Strangest Man Page 27