Note - Chapter ten
1 Interview with Oppenheimer, AHQP, 20 November 1963, p. 5.
2Greenspan (2005: 137).
3Goodchild (1985: 20). Even if Dirac did not write these words, he agreed with their
sentiment; see interview with von Weizsächer, AHQP, 9 June 1963, p. 19.
4Dirac (1977: 139); Greenspan (2005: 141).
5Greenspan (2005: 142), and von Meyenn and Schücking (2001: 46). The student was
Otto Heckmann. Boys Smith’s comment is from a conversation with his former colleague
at St John’s College, Cambridge, Peter Goddard, 5 July 2006.
6 Information on scholarship from Angela Kenny, archivist, Royal Commission for the
Exhibition of 1851 (e-mail, 10 December 2007).
7 Letter from Dirac to James Wordie, 28 February 1927, STJOHN.
8 Letter to Dirac from his mother, 28 June 1928, Dirac Papers, 1/3/8 (FSU).
9 Greenspan (2005: 145).
10 Greenspan (2005: 146).
11 Letter to Dirac from his mother, 7 April 1927, Dirac Papers, 1/3/7 (FSU).
12 Letter to Dirac from his mother, 20 May 1927, Dirac Papers, 1/3/7 (FSU).
13 Letter to Dirac from his mother, 6 January 1927, Dirac Papers, 1/3/7 (FSU).
14 Letter to Dirac from his mother, 10 February 1927, Dirac Papers, 1/3/7 (FSU).
15 Letter to Dirac from his mother, 20 May 1927, Dirac Papers, 1/3/7 (FSU).
16 Letter to Dirac from his mother, c. 26 March 1927, Dirac Papers, 1/3/7 (FSU).
17 Flo enjoyed the company of several men in her classes and even put Dirac in touch
with one of them, a German-speaking insurance clerk Mr Montgomery (‘Monty’).
Letter to Dirac from his mother, 18 March 1927, Dirac Papers, 1/3/7 (FSU).
18 These recollections were given to Richard Dalitz in the 1980s.
19 Letter from Dirac to Manci Balázs, 7 April 1935, DDOCS.
20Letter from Dirac to Manci Balázs, 17 June 1936, DDOCS.
21 Their address was 173 Huntingdon Road. Fen (1976: 161); Boag et al. (1990: 78).
22 The conference was held at L’Institut de Physiology Solvay au Parc Léopold, from 24
to 29 October 1927.
23 Letter from John Lennard-Jones (of Bristol University) to Charles Léfubure (Solvay
official), 9 March 1928, SOLVAY.
24 See http://www.maxborn.net/index.php?page=filmnews (accessed 13 May 2008).
25 Heisenberg (1971: 82–8); interview with Heisenberg, AHQP, 27 February 1963, p. 9.The location of the hotel is specified in a letter to Dirac from the conference administrator
on 3 October 1927: Dirac Papers, 2/1/5 (FSU).
26 Dirac (1982a: 84).
27 Interview with Heisenberg, AHQP, 27 February 1963, p. 9.
28 Heisenberg (1971: 85–6).
29 In the early 1850s, the Punch humorist Douglas Jerrold quipped about the controversial
feminist writer Harriet Martineau, ‘There is no God, and Harriet Martineau is
her prophet.’ See A. N. Wilson (2002), The Victorians, London: Hutchinson, p. 167.
30 Dirac Papers, 2/26/3 (FSU).
31 Dirac (1977: 140).
32 Dirac (1977: 141).
Eleven
[T]he true and the beautiful are akin. Truth is beheld by the intellect which is appeased by the most satisfying relations of the intelligible: beauty is beheld by the imagination which is appeased by the most satisfying relations of the sensible.
JAMES JOYCE, A Portrait of the Artist as a Young Man, 1915, Chapter 5
Dirac always felt out of place at fancy college dinners. Rich food, vintage wines, antiquated formalities, florid speeches, the fetid smoke of after-dinner cigars – all were anathema to him. So he was probably not looking forward to the evening of Wednesday, 9 November 1927, when he was to be one of the toasts of a dinner to celebrate the election of three new Fellows to St John’s College. He was now certifiably a ‘first-rate man’, with a permanent seat at the college’s high table and the freedom to gather after dinner with his colleagues in their grand, candle-lit Combination Room, completed in 1602. In Hall, beneath the portrait of Lady Margaret Beaufort, Dirac celebrated his election to the fellowship in the traditional way, by consuming an eight-course meal that included oysters, a consommé, cream of chicken soup, sole, veal escalope and spinach, pheasant with five vegetables and side salad, and three desserts. For him, the meal was not so much a celebration as a penance.1
After the dinner, Dirac walked to his rooms, close to the Bridge of Sighs, a Gothic stone structure that crosses the river Cam in a brief undulation, leaving just enough room underneath for the punters. He probably went straight to bed, as his aim was always to be fresh for the morning, when he did his best work. His study was devoid of decoration, with only a folding desk of the sort used by schoolchildren, a simple chair, a coal fire and ‘a very ancient settee’, as one visitor described it.2 He worked at his little desk like a schoolboy in an empty classroom, writing in pencil on scraps of paper, sometimes pausing to erase an error or to consult one of his books.3 Now that he was a Fellow, he had a manservant (a ‘gyp’) on hand day and night.
In these austere but comfortable surroundings, Dirac made his most famous contribution to science. St John’s had created the best environment imaginable for him. He could work all day, taking breaks only to fulfil his modest lecturing duties, give the occasional seminar and visit the library.
He was now preoccupied with a single challenge: to find the relativistic equation that describes the electron.4 He believed that the electron was ‘a point particle’ but, like theoreticians, could not understand why it had not one but two states of spin. Several other physicists had suggested candidate equations – all of them contrived and ungainly – and Dirac was not satisfied with any of them, including the one by Klein that Bohr believed had solved the problem. Dirac was sure Klein’s theory was wrong, as it predicted, absurdly, that the chance of detecting an electron in a tiny region of space-time is sometimes less than zero.
Dirac knew that it was impossible to deduce the equation from first principles and that he would find it only through a happy guess. But what he could do was to narrow the options, by setting out the characteristics the equation must have and the characteristics it ought to have. Rather than tinker with existing equations, he took the top-down approach, trying to identify the most general principles of the theory he was seeking, before going on to express his ideas mathematically. The first requirement was that the equation conformed to Einstein’s special theory of relativity, treating space and time on an equal footing. Second, the equation must be consistent with his beloved transformation theory. Finally, when the equation describes an electron moving slowly compared with the speed of light, its predictions must resemble extremely closely ones made by ordinary quantum mechanics, which had already proved its worth.
Those were useful constraints, but there was still too much room for manoeuvre. If he stuck to them, Dirac could still have written down any number of equations for the electron, so he needed to use his intuition to narrow the possibilities. Believing that the relativistic equation would be fundamentally simple, he thought it most likely that the equation would feature the electron’s energy and momentum just as themselves, not in complicated expressions such as the square root of energy or momentum squared. Another clue came from the way he and Pauli had independently found to describe the spin of the electron, using matrices that each consisted of four numbers arranged in two rows and two columns. Might these matrices feature in the equation he was seeking?
Dirac tried out one equation after another, discarding each one as soon at it failed to conform to his theoretical principles or to experimental facts. It was not until late November or early December 1927 that he hit on a promising equation, consistent with both special relativity and quantum mechanics. The equation looked like nothing theorists had ever seen before, as it described the electron not using a Schrödinger
wave but using a new kind of wave with four interconnected parts, all of them essential.
Although the equation had an appealing elegance, that would count for nothing if it did not relate to real electrons. What did the equation have to say, for example, about the spin of the electron and its magnetic field? If his equation contradicted the experimenters’ observations, he would have had no choice but to abandon it and start all over again. But there was no need for that. In a few pages of calculations, Dirac showed that he had conjured something miraculous: his equation described a particle not only with the mass of an electron but with precisely the spin and magnetic field measured by experimenters. His equation really did describe the electron so familiar to experimenters. Even better, the very existence of the equation made it clear that it was no longer necessary to tack on the electron’s spin and magnetism to the standard description of the particle given by quantum theory. The equation demonstrated that if experimenters had not previously discovered the spin and magnetism of the electron, then these properties could have been predicted using the special theory of relativity and quantum mechanics.
Although Dirac apparently showed his usual Trappist calm, he was jubilant. In a few squiggles of his pen, he had described the behaviour of every single electron that had ever existed in the universe. The equation was ‘achingly beautiful’, as theoretical physicist Frank Wilczek later described it: like Einstein’s equations of general relativity, the Dirac equation was universal yet fundamentally simple; nothing in it could be changed without destroying its power.5 Nearly seventy years later, stonemasons carved a succinct version of the Dirac equation on his commemorative stone in Westminster Abbey: iγ.∂ψ = mψ. When set out in full, in the form he originally used, the equation looked intimidating even to many theoreticians simply because it was so unusual, not that this would have disturbed Dirac: all that mattered to him was that it was based on sound principles and that it worked. It might even have crossed his mind that he had done something that John Stuart Mill had articulated as one of the aims of science – to unify disparate theories to explain the widest possible range of observations.
When Dirac was an old man, younger physicists often asked him how he felt when he discovered the equation.6 From his replies, it seems that he alternated between ecstasy and fear: although elated to have solved his problem so neatly, he worried that he would be the latest victim of the ‘great tragedy of science’ described in 1870 by Thomas Huxley: ‘the slaying of a beautiful theory by an ugly fact’.7 Dirac later confessed that his dread of such an outcome was so intense that he was ‘too scared’ to use it to make detailed predictions of the energy levels of atomic hydrogen – a test that he knew it had to pass.8 He did an approximate version of the calculation and showed that there was acceptable agreement but did not go on to risk failure by subjecting his theory to a more rigorous examination.
During November and December, he shared with no one the pleasure he took in his discovery or his occasional panic attacks. Not a single significant letter or record of a conversation with anyone exists from those months. He broke his silence only before he set off to Bristol for the Christmas vacation when he bumped into his friend Charles Darwin, a grandson of the great naturalist and one of Britain’s leading theoretical physicists. On Boxing Day, in a long letter to Bohr, Darwin wrote: ‘[Dirac] has now got a completely new system of equations for the electron which does the spin right in all cases and seems to be “the thing”.’9That was how Bohr learned that the remark he had made to Dirac at the Solvay Conference – that the problem of finding a relativistic equation for the electron had already been solved – was completely wrong.
Fowler sent Dirac’s paper ‘The Quantum Theory of the Electron’ to the Royal Society on New Year’s Day 1928, and a month later sent off a second paper that cleared up a few details. While the first paper was in press, Dirac wrote to Max Born in Göttingen, not mentioning his new equation except in a ten-line postscript, where he spelt out the reasoning that had led to it. Born showed these words to his colleagues, who regarded the equation as ‘an absolute wonder’.10 Jordan and Wigner, who were working on the problem that Dirac had solved, were flabbergasted.11 Jordan, seeing his rival walk off with the prize, sank into depression.
When the equation appeared in print at the beginning of February, it was a sensation. Though most physicists struggled to understand the equation in all its mathematical complexities, the consensus was that Dirac had done something remarkable, the theorist’s equivalent of a hole in one.12 For the first time in his career, he had shown that he was capable of tackling one of the toughest problems of the day and beating his competitors to the solution, hands down. The American theoretician John Van Vleck later likened Dirac’s explanation of electron spin to ‘a magician’s extraction of rabbits from a silk hat’.13 John Slater, soon to be a colleague of Van Vleck’s at Harvard, was even more effusive: ‘we can hardly conceive of anyone else having thought of [the equation]. It shows the peculiar power of the sort of intuitive genius which he has possessed more than perhaps any of the other scientists of the period.’14
Even Heisenberg, more confident than ever after his recent appointment to a full professorship in Leipzig, was taken aback by Dirac’s coup. One physicist later recalled Heisenberg speaking of an English physicist – unquestionably Dirac – who was so clever that it was not worth competing with him. Heisenberg was, however, concerned that despite the equation’s beguiling beauty, it might be wrong: he was one of many who underlined a problem that Dirac had pointed out in his first paper on the equation – it made a strange prediction about the values of energy that an electron can have.
The background to the problem with the equation was that, like time, energy is a relative quantity, not an absolute one. The energy of motion of a free electron – one that has no net force acting on it – can be defined as zero when the particle is stationary; when the particle gathers speed, its energy of motion is always positive. Dirac’s problem was that his equation predicted that, in addition to perfectly sensible positive energy levels, a free electron has negative energy levels, too. This arose because his theory agreed with Einstein’s special theory of relativity, which said that the most general equation for a particle’s energy specifies the square of the energy, E2. So if one knows that E2 is, say, 25 (using some chosen unit of energy), then it follows that the energy E could be either +5 or –5 (each of them, when multiplied by itself, equals 25). So, Dirac’s formula for the energy of a free electron predicted that there were two sets of energy values – one positive, the other negative. In classical physics, the negative-energy ones could be ruled out, simply because they are meaningless, but this cannot be done in quantum mechanics as it predicts that a positive-energy electron could always jump into one of them.
No one had observed such a jump, so the Dirac equation was in serious trouble. Despite this unsightly canker, however, the consensus was that his theory of the electron was a triumph. Yet Dirac seemed to take no pleasure from his success and showed none of the relief and elation that Einstein had demonstrated after he published his equation of general relativity. Dirac’s younger colleague Nevill Mott later described the extent of Dirac’s detachment from his fellow physicists in Cambridge. Mott was – like hundreds of other theorists – concentrating not on extending quantum mechanics but on applying it.
According to Mott, no one in the Cambridge mathematics department knew anything about Dirac’s equation until they read his paper in the library. Dirac was, Mott said, passive and forbidding, the kind of expert no one quite dares to consult. Dirac did not seem to appreciate the narrowness of his understanding of companionship: he liked to be among fellow physicists, when they were friendly – as they were in Bohr’s Institute – but felt no obligation to talk to them about his work or even to disclose his first name. Charles Darwin had known him for six years before writing him a postcard asking him about his signature: ‘What does P. A. M. stand for?’15
Whereas at Copenhagen and Gö
ttingen there were many premier-league quantum physicists, Fowler and Darwin were the only ones in Cambridge, so Dirac believed that it was his duty to deliver his seminars and lectures on the basics of quantum mechanics.16 But that, in his view, was where his departmental teaching obligations ended. But, surprisingly for a young research scientist, he did agree to write a textbook on quantum mechanics, scheduled to be the first publication in the ‘International Series of Monographs on Physics’, edited by Kapitza and Fowler. The series was the brainchild of Jim Crowther, the science reporter of the Manchester Guardian, the unofficial writer-in-residence at the Cavendish Laboratory and the only journalist Dirac regarded as a friend. A passionate Marxist, Crowther had joined the Communist Party in 1923 and managed to be close to both Bernal and Rutherford – sworn enemies – making the most of the talents and influence of each of them.17 By subtly cultivating relationships with all the finest young scientists in the Cavendish, including Dirac, Crowther became an influential bit-part player in the emerging group of radical scientists in Cambridge. One of his strengths was his sensitivity: he will have realised quickly that, to make friends with the great young theoretician, he had to overcome Dirac’s reluctance to have anything to do with importuning journalists. Dirac just wanted to be left in peace.
Dirac’s family knew nothing of his equation. For Charles, always keen to find out about Dirac’s work, his son’s unwillingness to share his science was cruel. In April 1928, when he read an anonymous article in The Times about quantum physics, Charles may have been discouraged by the conclusion: ‘Far past is the day when the scientist could talk to the layman as man to man […] the world loses much when science has got into such deep waters that only a Channel swimmer can follow it.’18 When Charles pressed his son to explain something of his new physics – as he surely did – Dirac almost certainly gave his usual response of shaking his head or remarking unhelpfully that the new quantum theories ‘are built up from physical concepts which cannot be explained in words at all’.19 Although Dirac used his visual imagination to think about quantum mechanics, he declined every request to describe images of the quantum world. As he would later remark: ‘To draw its picture is like a blind man sensing a snowflake. One touch and it’s gone.’20
The Strangest Man Page 21