The Strangest Man Read online

  One of the postgraduate students who first heard in Cambridge that term about the discovery of spin was Robert Oppenheimer, a dapper, well-to-do American Jew just arrived from Harvard, then riddled with anti-Semitism. He was emotionally fragile, unsure of what he wanted to do with his life but outwardly confident and always keen to display the breadth and depth of his cultural interests. After Rutherford refused to accept him as a student, he spent a few unproductive weeks working with J. J. Thomson, then well over the hill. Oppenheimer disliked Cambridge life – the ‘rather pallid science clubs’, the ‘vile’ lectures, having to live in ‘a miserable hole’. He saw fellow American students ‘literally dying off under the rigors of disregard, climate, and Yorkshire pudding’.46 By the end of his first term in Cambridge, Oppenheimer was judged by a close American friend to have ‘a first class case of depression’.47

  Dirac mentioned none of his new student acquaintances in his postcards home, and virtually nothing about his work. His frustrated parents had to wait six weeks for him even to confirm that his lodgings were comfortable. Flo, having seen her son ratchet up his work rate after tumbling to the importance of Heisenberg’s first paper, began what was to become her ineffectual refrain: ‘Don’t work too hard; have some fun if it comes your way.’ Dirac’s father was still a broken man, suffering in the cold weather and – in his wife’s words – shuffling around ‘so slowly that he is like a block of ice’.48

  One of Flo’s favourite subjects was national and local politics, but that autumn she wrote little about them, probably because there was not much to write about: Britain was stable and quietly prospering. As the country entered the second half of the 1920s, it seemed at last to be coming to terms with its memories of the war, encouraged by the growing international consensus that disagreements should never again be resolved on the battlefield. This understanding was manifest in the hailed Treaty of Locarno, a non-aggression pact between France, Germany and Belgium, guaranteed by the two supposedly impartial powers, Italy and the UK. Some English schools celebrated by giving their pupils a day off when the treaty was signed in London on 1 December, the day the Royal Society published Dirac’s first paper on quantum mechanics. Fowler had managed to cut the time between the submission of the paper and its publication from the usual three months to three weeks.

  Word passed around the cognoscenti of quantum theory that a star had been born. Dirac’s earlier work had gone largely unnoticed, but here was a paper that appeared to have been written by a mature mathematician and physicist.49 One of those who had not heard of Dirac before his first work on the new theory was Heisenberg’s boss in Göttingen, Max Born.50 Though given to understatement rather than hyperbole, in his memoir he described his first reading of Dirac’s early work on quantum mechanics as ‘one of the greatest surprises of my life […] the author appeared to be a youngster, yet everything was perfect in its way and admirable’.51

  Heisenberg, too, was jolted by the paper. On 23 November, a few days after he received the proof copy Dirac sent him, Heisenberg replied in a two-page letter (in German) that began a fifty-year friendship.52 He began graciously by telling Dirac that he had read his ‘beautiful work with great interest’, adding that ‘There can be no doubt that all your results are correct, insofar as one believes in the new theory.’ The discoverer of the new theory was unsure of whether he had hit on ideas of lasting value.

  What followed must have made Dirac’s heart sink: ‘I hope you are not disturbed by the fact that part of your results have already been found here some time ago.’ Born had independently found the relationship between the position and momentum symbols, a connection that Dirac probably thought he had been first to make. Also, Heisenberg’s theory accounted for the Balmer formula for hydrogen atoms, according to a virtuoso calculation by Heisenberg’s slightly older friend Wolfgang Pauli, an Austrian theoretician known for his brilliance, his unsparing intellectual aggression and for drinking a glass of wine too many in the nightspots of Hamburg. Heisenberg’s note bore the disappointing message that other European theoreticians were on the same track and the deflating prospect that they would repeatedly beat him into print.

  In the ten days following his first letter, Heisenberg wrote Dirac three more warm and complimentary notes, pointing out technical difficulties and minor errors in Dirac’s first paper and seeking to clarify details. He concluded his letter of 1 December: ‘Please do not take these questions that I write to you as criticisms of your wonderful work. I must now write an article on the state of the theory […] and still wonder at the mathematical simplicity with which you have overcome this problem.’53 Dirac knew that he was facing some of the toughest competition theoretical physics had to offer. Heisenberg was working in Göttingen not only with Born and his student Pascual Jordan but also in association with some of the world’s leading mathematicians. The trio of Born, Heisenberg and Jordan were working in the Göttingen tradition of a close relationship between the theoretical physicists, mathematicians and experimenters, in sharp contrast with the virtual separation of the communities in Cambridge, where individuality was prized. So, in the undeclared contest to be the first to develop quantum mechanics into a complete theory, the combined might of the mathematicians and physicists in Göttingen was pitted against the loner Dirac. He knew that Heisenberg had given his German competitors a head start of two months.

  It would take several years before quantum mechanics crystallised into a complete theory. During that time, it was a work in progress by about fifty physicists. In retrospect, they resembled a group of construction workers who had agreed on a common project – to build a new theory of the behaviour of matter – though not on how to accomplish it. In this case, the construction site was dispersed across north-western Europe, and virtually all the builders were male, under thirty, intensely competitive and craving the respect of their peers as well as the blessing of posterity. There was no official leader, so the workers were free to concentrate on any part of the project they liked. In this quasi-anarchy, some tasks were sure to be done by several people at the same time so, when useful results emerged, there would be quarrels about who most deserved the credit for them. All the workers had their favourite tools and their own preferred way of getting the job done. Some approached it philosophically, some mathematically and some with their eyes on what experiment could teach them. Some concentrated on the project’s grand plans and others on its details. Most of them liked to collaborate and to bounce ideas off their colleagues, while a few others – notably Dirac – had no wish to be in anyone’s team. It was rarely easy to see which of the new ideas were duds and which were gems, nor was it obvious whose approaches to the problem were the most promising. Not that any physicist felt bound by a need to take an entirely consistent approach; all that mattered was getting the job done, by whatever means were available. In the end, prizes for a new scientific theory tend to be awarded as they are in architecture for a new building – not to the people who talked most eloquently during the construction but to those who set out its vision and who did most to realise it.54

  Dirac knew that he and his colleagues had taken only the first step towards the building of a complete theory of quantum mechanics. There was much to do.

  Notes - Chapter six

  1 Reference for Dirac by Cunningham, April 1925, provided for Dirac’s application for

  a Senior Studentship, 1851COMM.

  2 Undated to Dirac from his mother, c. May 1924.

  3 Dirac was in room H7 on the first floor of New Court in Michaelmas (autumn) term.

  Later, he moved into other rooms: in Lent (winter) and Easter term 1925, he was in

  New Court room E12; from Michaelmas term in 1927 to Easter term 1930, he was

  in New Court room A4; in Michaelmas term in 1930, he was in Second Court room

  C4; from Michaelmas term 1936 to Michaelmas 1937, he was in New Court room

  I10.

  4 Letter from Dirac to Max Newman, 13 January 1935, Newman archive in
STJOHN.

  5 Letter to Dirac from his mother, undated, c. November 1924, Dirac Papers, 1/3/3

  (FSU).

  6 Letter from ‘Technical Manager’ (unnamed) at W & T Avery Ltd, 10 January 1925,

  Dirac Papers, 1/6/3 (FSU).

  7 Interview with Dirac, AHQP, 1 April 1962, p. 5; Salaman and Salaman (1986: 69). I

  am assuming that the date of Felix’s death on his gravestone, 5 March 1925, is correct; on his death certificate, the date of his death is given as the day after.

  8 Letter to Dirac from his Auntie Nell, 9 March 1925, Dirac Papers, 2/1/1 (FSU).

  9 Express and Star (local paper in Much Wenlock), 9 March 1925; Bristol Evening News, 27 March 1925.

  10 Interview with Mary Dirac, 21 February 2003; interview with Monica Dirac, 7

  February 2003. In an interview with Leopold Halpern, 18 February 2003, Halpern commented that Dirac found the suicide of Felix too painful to talk about.

  11 Bristol Evening News, 9 March 1925.

  12 Bristol Evening News, 10 March 1925.

  13 Dirac often remarked on this. His feelings are recorded in Salaman and Salaman

  (1986: 69). His close friend Leopold Halpern also mentioned that Dirac had mentioned

  this to him, quite independently (interview on 18 February 2002).

  14 Letter to Dirac from his mother, 4 May 1925, Dirac Papers, 1/3/4 (FSU). Dirac

  always mentioned this when he opened his heart to friends and even mentioned it to

  his children.

  15 Flo wrote her poem ‘In Memoriam. To Felix’ on 5 March 1938. The poem is in Dirac

  Papers, 1/2/12 (FSU).

  16 Letter to Dirac from his mother, 22 March 1925, Dirac Papers, 1/3/4 (FSU).

  17 Death cerificate of Felix Dirac, registered 30 March 1925.

  18 Interview with Leopold Halpern, 18 February 2003.

  19 Interview with Christine Teszler, 22 January 2004.

  20 The problem that Dirac addressed was: if light consists of photons, as Compton had

  argued, how would these particles be affected by collisions with electrons swirling

  around on the surface of the Sun?

  21 Mehra and Rechenberg (1982: 96).

  22 Dirac (1977: 118).

  23 C. F. Weizsächer, in French and Kennedy (1985: 183–4).

  24 Pais (1967: 222). Pais gives a vivid description of Bohr’s strange oratory, noting

  ‘Bohr’s precept never to speak more clearly than one thinks.’

  25 Letters from Bohr to Rutherford, 24 March 1924 and 12 July 1924, UCAM

  Rutherford archive.

  26 Elsasser (1978: 40–1).

  27 In his AHQP interview on 1 April 1962 (p. 9) and in an interview on 26 June 1961

  (Van der Waerden 1968: 41), Dirac says he was not present, whereas elsewhere he

  says he was there (Dirac 1977: 119).

  28 Heisenberg recalls his experience at the Kapitza Club, and of staying with the

  Fowlers, in the BBC Horizon programme ‘Lindau’, reference 72/2/5/6025. The

  recording was made on 28 June 1965, in Dirac’s presence.

  29 The application is held by the 1851COMM.

  30 Letter to Dirac from his mother, with a contribution from his father, June 1925, in

  Dirac Papers, 1/3/4 (FSU). The application was advertised in the Times Higher

  Education Supplement, his mother says.

  31 This proof copy is in Dirac Papers, 2/14/1 (FSU).

  32 An English translation of this paper, together with other key papers in the early history

  of quantum mechanics, are reprinted in Van der Waerden (1967).

  33 Dirac (1977: 119).

  34 Interview with Flo Dirac, Stockholms Dagblad, 10 December 1933.

  35 Darrigol (1992: 291–7).

  36 Dirac (1977: 121).

  37 Letter from Albert Einstein to Paul Ehrenfest, 20 September 1925, in Mehra and

  Rechenberg (1982: 276).

  38 Dirac (1977: 121–5).

  39 Dirac (1977: 122).

  40 Here, X and Y are mathematical expressions of a type known as partial differentials.

  What is important is the superficial similarity between the form of the Poisson

  bracket and the difference AB – BA.

  41 Eddington (1928: 210).

  42 Elsasser (1978: 41).

  43 Reference for Dirac, written by Fowler in April 1925, for the Royal Commission of

  the Exhibition of 1851, 1851COMM.

  44 Dalitz and Peierls (1986: 147). The student was Robert Schlapp, who was studying

  under the veteran Sir Joseph Larmor.

  45 Van der Waerden (1960).

  46 Letters from Oppenheimer to Francis Fergusson, 1 November and 15 November

  1925; in Smith and Weiner (1980: 86–9).

  47 Bird and Sherwin (2005: 44).

  48 Letter to Dirac from his mother, 16 November 1925 (she repeats the image of ‘the

  block of ice’ in another letter to Dirac, written on 24 November), Dirac Papers, 1/3/4

  (FSU).

  49 Heisenberg later remarked that when he read Dirac’s first paper on quantum mechanics,

  he assumed that its author was a leading mathematician (BBC Horizon programme,

  ‘Lindau’, reference 72/2/5/6025).

  50 Frenkel (1966: 93).

  51 Born (1978: 226).

  52 Letter to Dirac from Heisenberg, 23 November 1925, Dirac Papers, 2/1/1 (FSU).

  53 All these letters from Heisenberg to Dirac at this time are in Dirac Papers, 2/1/1 (FSU).

  54 Beller (1999: Chapter 1); see also Farmelo (2002a: 25–6).

  Seven

  A door like this has cracked open five or six times since we got up on our hind legs. It’s the best possible time to be alive, when almost everything you knew is wrong.

  TOM STOPPARD, Arcadia, 1993, Act 1, Scene 4

  Einstein admired the new quantum mechanics, but he was suspicious of it. On Christmas Day 1925 in Berlin, he wrote to a close friend that it seemed implausible to him that something so simple as a number representing a quantum particle’s position should have to be replaced by an array of numbers, ‘a genuine witches’ multiplication table’.1 Seven weeks later, he was coming to the conclusion that the theory was wrong.2

  Dirac had no such qualms – he was sure that Heisenberg had pointed the best way ahead. Yet although Dirac was working with Heisenberg’s theory, their approaches to it were quite different: whereas Heisenberg thought the theory was revolutionary, for Dirac it was an extension of classical theory.3 While Heisenberg and his Göttingen colleagues strove constantly to account for experimental results, Dirac’s priority was to lay the theory’s ‘substrata’, following a favourite term of Eddington’s. Dirac was following Einstein in taking a top-down approach, beginning with mathematically precise formulations of fundamental principles and only afterwards using the theory to make predictions.

  A few weeks after Christmas – the first the Dirac family had spent without Felix – Dirac gave a talk at the Kapitza Club about his just-published paper on quantum mechanics. Two days later, he sent off for publication the proof that his theory reproduced Balmer’s formula, the first of three papers on the new theory that he wrote in the first four months of the year. In these first papers on quantum mechanics, Dirac was trying both to understand the theory and to apply it. Puzzled by the symbols in Heisenberg’s theory, he spent months unsuccessfully trying to relate them to projective geometry; none of his ideas worked. He was using mathematics that was unknown or at least unfamiliar to most of his colleagues, yet he rarely gave details of the mathematical techniques he was using or the experimental observations he was trying to explain. He thus managed to perplex both physicists and mathematicians. Nearly fifty years later, Dirac admitted that his attitude to mathematics was cavalier:

  I did not bother at all about finding a precise mathematical nature for [some of my symbols] or about any kind of precision in dealing with them.
I think you can see here the effects of an engineering training. I just wanted to get results quickly, results which I felt one could have some confidence in, even though they did not follow from strict logic, and I was using the mathematics of engineers, rather than the rigorous mathematics which had been taught to me by Fraser.4

  Those words would have puzzled Dirac’s peers in the spring of 1925. Most of them would have been hard pressed to identify in his papers any remnants of an engineer’s training, nor did his writings flaunt the quick-and-dirty approach to calculations favoured by engineers. Rather, Dirac’s papers appeared to be impenetrable to all but the mathematically adept. One reason why Dirac’s approach was so puzzling was that he was an unusual hybrid – part theoretical physicist, part pure mathematician, part engineer. He had the physicist’s passion to know the underlying laws of nature, the mathematician’s love of abstraction for its own sake and the engineer’s insistence that theories give useful results.

  Wearing the hat of the physicist, Dirac knew that, for all the mathematical elegance of quantum mechanics, it had yet to make a single prediction whose confirmation would demonstrate its superiority over Bohr’s theory. Such a test of the new theory was not easy to find. The best that Dirac could do was to use the theory to describe the most-investigated example of subatomic collision – the scattering of a photon (a particle of light) by a single electron. This process always involves particles travelling at extremely high speeds, close to the speed of light, so any theory that seeks to describe it must be relativistic – consistent with Einstein’s special theory of relativity. The problem was that Heisenberg and Dirac’s theory of quantum mechanics was not relativistic, and it was unclear how to incorporate relativity into the theory. Dirac made a start on this by tweaking the theory to improve its consistency with relativity and then used it to make testable predictions, using the ideas he had developed at home in Bristol soon after he received Heisenberg’s original paper. The theory was rough and ready, but it enabled Dirac to make the first prediction of quantum mechanics: using a graph, he compared observations of electron scattering with his ‘new quantum theory’ and showed that it was in better agreement than the classical theory.