By the end of 1937, Dirac was bereft of the company of experimenters with similar interests in physics, and some of his most valued colleagues among the Cambridge theoreticians were in decline. Following a debilitating stroke, Fowler’s health was failing, and, by early 1939, he had ‘faded out’, as he told Eddington.43 In the sometimes gory seminars in the mathematics department, Eddington was timorous and unable to defend himself against pillory by his younger colleagues. Dirac looked on, unmoved and dissatisfied with his own research. Quantum field theory was virtually at a standstill, and even the best minds were finding it hard to make progress. Dirac often reflected on the contrast with only a decade before, when quantum mechanics had just been discovered: ‘It was very easy in those days for any second-rate physicist to do first-rate work; it is very difficult now for a first-rate physicist to do second-rate work.’44 These words resonated with the theoretician Fred Hoyle, an independent-minded Yorkshire man who had attended Dirac’s undergraduate lectures and who had struggled in the late 1930s to find a subject ripe for development. Hoyle’s bottom-up approach to physics was the antithesis of Dirac’s style, but they got on well: the trick was, Hoyle said, to ask Dirac fewer questions than he asked you.45 Hoyle was amused by Dirac’s conversational eccentricities, though even he was stunned when he called Dirac to ask him a straightforward administrative question, only for Dirac to reply, ‘I will put the telephone down for a minute and think, and then speak again.’46 A few months later, Hoyle was told that he needed to find a supervisor, and Dirac took him on, partly because he was amused by the prospect of a relationship between a supervisor who did not want a student and a student who did not want a supervisor.47
Compared with many of the new ideas in quantum physics, the energy of an electron sounds a simple concept, but it was anything but simple to understand. This was because the energy that an electron has purely by virtue of its existence – its self-energy – turns out to be infinite. According to classical physics, the source of this embarrassment is the electric field of the electron (in some ways analogous to the gravitational field of a planet): the smaller the size of the particle, the stronger its field near by and the higher its energy. So if the electron were an infinitely small point, as it is usually assumed to be, its self-energy must be infinite. This makes no sense: how can a completely natural quantity have such an immeasurably huge value?
The theory of quantum electrodynamics, based on hole theory, had the same weakness: the self-energy of the electron was infinitely large. The most likely reason for this failure, Dirac believed, was that there was a fault in the classical theory on which his quantum theory was based: Maxwell’s classical theory of electromagnetism. Dirac hoped that if he could remove the errors in the classical theory, he would be able to deduce a quantum theory of the electron that did not suffer from the disease of infinite self-energy. This was an unpopular view: most of his colleagues thought the classical theory was fine and that the challenge was to solve the problems with quantum theory. But Dirac, as usual, was unperturbed by popular opinion and spent several months in late 1937 and early 1938 working out a new classical theory and finding equations to describe an electron with a tiny but non-zero size. It was an immaculate theory but failed at its first hurdle: when Dirac tried to use it to find an infinities-free quantum version of the theory, he failed.48
He may have wondered whether he had lost his edge. Besides his work, he was now a family man with other priorities: a wife and two bickering children, the employment of a cook and several domestic helpers, and his dependent mother, now sixty, living a hundred and twenty-five miles away and with no telephone. Flo was, however, in good spirits: she was pottering around in her house, writing verse in bed, occasionally packing her suitcase and taking a Mediterranean vacation funded by her now healthy bank account.49
Manci still found it hard to settle and never felt completely comfortable in 7 Cavendish Avenue, a damp house that somehow always seemed cold, even in high summer. Disappointed that Dirac had turned down Princeton University’s offer of a well-paid professorship, she thought Cambridge had nothing to commend it except its academic status and was beginning to dread the prospect of spending her life there.50 She resented the snobbery of the Cambridge academics who patronised her from the moment they heard she did not have a degree. The Kapitzas were her sort of people – respectful, without side, full of life – but they were fifteen hundred miles away and in touch only irregularly. Always a thoughtful and generous friend, Manci inundated them with supplies to help them overcome shortages; Anna tactfully requested her to send only English books, coffee beans and good-quality pipe tobacco for her husband. She also encouraged Manci to be more positive about Cambridge: ‘do you still feel lonely without your gay Budapest? If so, you are naughty and must not feel like this any more, because it worries people who like you and live with you (I mean Paul of course!)’51
Incessantly gloomy news bulletins on BBC radio about Hitler’s increasingly transparent intentions did nothing to improve Manci’s mood. In the spring of 1938, he had annexed Austria, where soldiers were welcomed with flowers and swastikas as they goose-stepped into towns. In late May, Dirac read an item in Nature that will probably have disturbed him: his friend Schrödinger was in Austria and appeared to be on Hitler’s side. The article reported that Schrödinger had written to a local newspaper in March 1938, ‘readily and joyfully’ affirming his loyalty to the new regime, having ‘misjudged up to the last the real will and true destiny of my land’.52
Dirac wanted to take his summer vacation in the Soviet Union, but this time the embassy in London refused his application and all others, in response to the British Government’s denial of visas to Soviet citizens. So Dirac made more modest plans: in August 1938, he travelled to the Lake District in the north-west of England and went walking and climbing with his friend James Bell and with Wigner, still recovering from the tragically early death of his wife almost a year before, barely eight months after their marriage.53 From their correspondence, it seems that Bell agreed with Wigner that the recent trials in the Soviet Union were frame-ups, though Bell thought they were no worse than ones organised by the English in their colony of India.54 Meanwhile, Manci took her children and Dirac’s mother to Budapest, where anti-Semitism was making her parents’ life intolerable: they were beginning to see that they had no future in Hungary.
Soon, the Diracs’ home became a popular hostel for physicists and their families fleeing Nazism. Among the first to arrive were the Schrödingers, who later settled in Dublin, after Schrödinger accepted a post at the newly created Institute for Advanced Studies.55 During the stay, Schrödinger will have explained to the Diracs why he had earlier declared his support for the Nazis – he had been forced to make public his approval of the Nazi regime, he said, and had done this as ambiguously as he could.56 Dirac appears to have accepted this explanation and not to have questioned that his friend’s integrity had wavered for a minute.
The house guest whose courtesy Manci most admired was Wolfgang Pauli, en route to the Institute for Advanced Study in Princeton, where he spent most of the war. Dirac told Kapitza: ‘[Pauli] has got much milder after his second marriage.’57
Dirac agreed with the political left that the British Government had been weak and negligent in failing to tackle Hitler after his armies had invaded the Rhineland in March 1936. The left also, however, opposed rearmament and defence expenditure, a policy it would later regret. When Neville Chamberlain became British Prime Minister in 1937, he tried to mollify Hitler and waved away the warnings of his despised colleague Winston Churchill from the back-benches that the ambitions of the Führer would have to be opposed by force. The mood in Cambridge alternated from hope that a war could be avoided to fear that a conflict was inevitable.58Chamberlain brought about the most famous of these swings on 30 September 1938 when he returned from talks in Munich with Hitler, Mussolini and the French Prime Minister Édouard Daladier to declare ‘peace for our time’, having agreed that Hitl
er’s troops would be free to enter Czechoslovakia. Crowds cheered Chamberlain’s return until they were hoarse; the entire country was euphoric even after it became clear that Czechoslovakia had been betrayed. But Churchill thought the agreement was a travesty: ‘[The] German dictator, instead of snatching his victuals from the table, had been content to have them served course by course.’59
As he spoke those words, two German chemists, Otto Hahn and Fritz Strassman, were making a discovery that would change the course of history. The experiment they had done superficially looked recondite: when neutrons were fired at compounds of uranium, the new chemical elements that were formed were much lighter than had previously been thought. Within a few weeks, by the beginning of January 1939, it was clear that Hahn and Strassman had observed individual uranium nuclei breaking apart into two other nuclei, each with roughly half the mass of the original nucleus, as if a stone had split into two parts of about the same size. Analogous to cell division in biology, the process came to be called ‘nuclear fission’. The key point was that the amount of energy released in the fission of a nucleus exceeds the energy produced when atoms change partners during the burning of gas, coal and other fossil fuels by a factor of about a million – this is energy release on a huge scale.
Eddington had long foreseen the possibility of harnessing nuclear energy and in 1930 looked forward to the time when there would be no need to fuel a power station with ‘load after load of fuel’ but that ‘instead of pampering the appetite of our engine with delicacies like coal or oil we shall induce it to work on a plain diet of subatomic energy’.60 Just over three years later, at the 1933 annual meeting of the British Association, Rutherford had ridiculed his colleague’s vision as ‘moonshine’. On the following day, after Leó Szilárd read about the prediction in The Times, it occurred to him as he traversed a pedestrian crossing in Bloomsbury that it might be possible to capture nuclear energy more easily than Rutherford had imagined: ‘If we could find an element which is split by neutrons and which would emit two neutrons when it absorbs one neutron, such an element, if assembled in sufficiently large mass, could sustain a nuclear chain reaction.’61
When Szilárd heard about the discovery of fission, he realised that the chemical element he had in mind could be uranium. If more than one neutron was emitted when the uranium nucleus fissioned, those neutrons could go on to fission other uranium nuclei, which would emit more neutrons, and so on. Szilárd later recalled that ‘All the things which H. G. Wells predicted appeared suddenly real to me.’62
The discovery of nuclear fission on the eve of a catastrophic conflict is one of history’s most tragic coincidences. What made the prospect of nuclear weapons worrying for Dirac and other scientists who understood the implications of the discovery was that it had been made in Berlin, Hitler’s capital.
Physicists and chemists were about to be drawn from the tranquillity of their offices and laboratories into a world of warfare, secrecy and power politics. The stakes could not have been higher, nor could the new work have been more troubling to their consciences. Scientists who regarded it as their duty to be open about their findings found themselves worrying that their results were too sensitive to be made public.63 Szilárd believed that if uranium was in principle capable of sustaining a nuclear chain reaction, then the results should be kept secret from Hitler’s scientists, including Heisenberg and Jordan.
The sometimes bad-tempered exchanges about whether to keep the fission properties of uranium secret involved most of the leading nuclear scientists, including Bohr, Blackett, Fermi, Joliot-Curie, Szilárd, Teller and Wigner. By early summer 1939, the campaign to keep the new science secret had failed. It was now public knowledge that uranium should be able to sustain a nuclear chain reaction: nuclear weapons were a practical possibility.
Dirac was only peripherally concerned with these discussions, having been asked by Wigner to support Blackett in the campaign to keep sensitive results confidential.64 In Cambridge, the euphoria of Chamberlain’s Munich agreement had faded into despair by the spring of 1939, when Hitler contemptuously absorbed previously unoccupied parts of Czechoslovakia into Nazi protectorates and client states. War now looked inevitable. During those grim early weeks of 1939, Dirac prepared his first lecture as a self-styled philosopher of science who professed no interest in philosophy. Although the two living scientists he most admired – Einstein and Bohr – were both accomplished at talking about science to wide audiences, Dirac had shown no interest in following their lead until the Royal Society of Edinburgh awarded him their Scott Prize and invited him to give the Scott lecture on their favoured theme of the philosophy of science to an audience that included many who knew little or no science.65 Late on a Monday afternoon early in February 1939, he spoke for an hour on the relationship between the mathematician, who ‘plays a game in which he invents the rules’, and the physicist, ‘who plays a game in which the rules are provided by Nature’.
Dirac’s themes were the unity and beauty of nature. He identified three revolutions in modern physics – relativity, quantum mechanics and cosmology – and hinted that he expected them one day to be understood within a unified framework. Although he did not mention John Stuart Mill, Dirac was seeking to answer the same question posed in A System of Logic: ‘What are the fewest general propositions from which all the uniformities existing in nature could be deduced?’66 Whereas Mill never used the beauty of a theory as a criterion of its success, an appreciation for the value of aesthetics had been part of Dirac’s education. He now gave vent to his feelings by proposing the principle of mathematical beauty, which says that researchers who seek the truly fundamental laws of nature in mathematical form should strive mainly for mathematical beauty. Ignoring centuries of philosophical analysis about the nature of aesthetics, he declared that mathematical beauty was a private matter for mathematicians: it is ‘[a quality that] cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating’.67
The success of relativity and quantum mechanics illustrates the value of the principle of mathematical beauty, Dirac said. In each case, the mathematics involved in the theory is more beautiful than the mathematics of the theory it superseded. He even speculated that mathematics and physics will eventually become one, ‘every branch of pure mathematics having its physical application, its importance in physics being proportional to interest in mathematics’. So he urged theoreticians to take beauty as their principal guide, even though this way of coming up with new theories ‘has not yet been applied successfully’.
The physicists in the Edinburgh audience heard Dirac’s enthusiasm for the discovery that the universe is expanding, which he said ‘will probably turn out to be philosophically even more revolutionary than relativity or the quantum theory’. Focusing on how the universe developed from its birth, he suggested that classical mechanics will never be able to explain the present state of the universe because the conditions at the very beginning of the universe would be too simple to seed the complexity we now observe. Quantum mechanics might provide the answer, he believed: unpredictable quantum jumps early in the universe should be the origin of the complexity and ‘now form the uncalculable part of natural phenomena’. Cosmologists rediscovered this idea forty years later, when it became one of the foundations of the quantum origins of the universe. While the world was heading into the gutter of war, Dirac was looking up at the stars.
In Cambridge, the students could not bring themselves to face the consequences of the expected war. In April, the students’ sixpenny magazine Granta looked forward to another summer of croquet on the lawns, cucumber sandwiches, paprika salad and crème brûlées washed down with chilled Bollinger. For students wanting to wind down after the examinations, there were performances of Mozart’s Idomeneo and more opportunities to see Disney’s Snow White and the Seven Dwarfs.68 The captain of the university cricket team knew that the party was soon to be over, though he said that h
e hoped to God that Hitler would not start a war before the end of the cricket season. But he was disappointed: after Hitler’s invasion of Poland, Chamberlain declared war on 3 September, before the final overs had been bowled.
Ten days before, Dirac – on holiday with his family on the French Riviera – read that Stalin had signed a non-aggression pact with Hitler, a moment that George Orwell called ‘the midnight of the century’. Stalin’s opportunism was incomprehensible to Dirac. He still tended to expect politicians to practise with the consistency of mathematicians, and it is probably no coincidence that Dirac’s disillusion with politics and politicians began that summer. From then on, he turned away from public affairs and concentrated on his family, which was about to expand – Manci was pregnant.
Notes - Chapter twenty-one
1 Dirac, M. (1987: 4).
2 Letter from Dirac to Manci, 18 February 1937 (DDOCS).
3 Letter from Dirac to Manci, 6 February 1937 (DDOCS).
4 Letter from Dirac to Manci, 20 February 1937 (DDOCS). Dirac writes ‘How soon after the new moon comes will I be alone with my beloved, and have her in my arms […]’.
5 Letter from Dirac to Manci, 19 February 1937 (DDOCS).
The Strangest Man Page 43