In Trieste a month later, at a symposium organised by Abdus Salam to mark Dirac’s seventieth birthday, Heisenberg and all the other guests saw the Diracs on their best form, the model of the contented elderly couple. But Dirac apparently did not want to put the unpleasantness of the previous few weeks completely behind him: he clipped Manci’s two notes together and filed them among the papers in his office. He appeared to regard all her attacks – and the makings-up that always followed – with an equanimity bordering on indifference; whether he suffered more deeply than others saw we shall probably never know, as he appears not to have discussed her behaviour – still less to have complained about her – with anyone.
To the Diracs’ acquaintances in their later years, Manci was a controversial figure. No one questioned that her gift for friendship hugely enriched his social life and that she was devoted to her husband, ‘my little Mickey Mouse’. Many colleagues attest to the care she took to look after him and make him look presentable; one visitor was touched to see her adjusting his clothes when he returned home one evening looking like a scarecrow. ‘She takes such good care of me,’ Dirac beamed as Manci adjusted his tie.15 Without her, he would probably have spent almost his entire adult life living alone in college, like Charlie Broad.
Yet many friends could not help flinching when she shouted at him, ‘Are you listening to me?’ and wondered how he felt when he silently bore her tirades against ‘nigger’ doctors and Jews (that Manci was both Jewish and occasionally anti-Semitic was one of the most baffling paradoxes of her personality).16 Yorrick Blumenfeld gives a bleak summary of the state of their thirty-four-year-old marriage: ‘She was tired of hen-pecking him, and he just wanted to live in his dream world.’ Helaine Blumenfeld is surprised that he could tolerate her: ‘He was a lovely man. She was simply an awful person.’17 But Lily Harish-Chandra, a frequent visitor to the Diracs’ home and a family friend, disagrees: ‘Manci was extremely warm and loyal, a great listener and a very caring woman. Paul cannot have been easy to live with. Their marriage worked because they gave each other what they wanted: he gave her status and she gave him a life.’18
*
In the early 1970s, Dirac was briefly optimistic about his research on particle physics. He had happened on a way of describing isolated elementary particles with a spin equal to a whole number, using an equation that he believed had a special mathematical beauty. Better yet, it described only positive energies – the mathematics yielded no embarrassing negative-energy solutions. But his excitement waned after he found it impossible to use the equation to describe how a particle interacts with other particles or with a field – the real-world case. Mathematical beauty had again proved a treacherous beacon.
Dirac then wound down his work on the theory of fundamental particles and returned to general relativity and his still-unproven large numbers hypothesis. He knew that Einstein’s theory and the hypothesis were incompatible because general relativity requires – in the language of Newtonian mechanics – that the strength of the gravitational force between two identical masses separated by the same distance has always had the same value, contrary to the hypothesis. So he tried to reconcile them using ideas set out by a former colleague at the Institute for Advanced Study, the German mathematician Hermann Weyl, whose approach to theoretical physics resembled Dirac’s. Weyl once said: ‘My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.’19 In 1922, Weyl had produced a prototype theory that gave a tantalising glimpse of how a mathematical account of gravity and electromagnetism might be given with a unified set of equations. Enthralled by their beauty, Dirac believed Weyl’s approach might furnish a link between the general theory of relativity and the large numbers hypothesis, in a way that involved a gradual weakening of gravity over time.20
Dirac was assisted in the project by Leopold Halpern, a general relativity specialist who arrived in Tallahassee in 1974, a year short of his fiftieth birthday. Born and raised in Austria, he and his family had fled, on Hitler’s invasion in 1938, when he was thirteen years old. He spent twenty-seven years working in several European research institutions, including a spell with Schrödinger, and Dirac had first met him at a conference in 1962. Halpern was a homoeopath and a certified African medicine man, a twenty-four-carat eccentric who slept outdoors all year round, sliced baked potatoes with karate chops and refused to wash with soap. He was not always popular in elevators. Colleagues with conventional manners were often disconcerted by the prickliness that disguised his shyness: when his phone rang, he would answer with a rasping, impatient ‘Hello’, his voice softening into a lilt the moment he realised that he was talking to a friend.
The oddities and coarse manners of Halpern grated on Manci, but they endeared him to Dirac, and the two men became close friends. At least once a week, they went swimming in Silver Lake and Lost Lake, two of Dirac’s favourite spots near Tallahassee, mainly because the waters there were so quiet. Dirac did not like to swim anywhere near motorboats, but on one trip, when he was seventy-six years old, he hailed one and asked the owner if he could have a go at water-skiing. The owner obliged. When Halpern told Manci, she was horrified: ‘Paul is still very immature!’21
Most weekends, the two men headed off in Halpern’s Volkswagen Super Beetle – his sixteen-foot canoe and a pair of paddles tied to the roof rack – on the hour-long drive to the Wakulla river.22 Minutes after setting off from the shore, they were alone in one of Florida’s most pleasant microclimates, a near wilderness. They would row for some two hours upstream on the slow-flowing river, through forests of sassafras and American beech trees, draped with Spanish moss. The alligators made scarcely a sound: the silence was broken only by the rhythmic sloshing of the paddles, the cry of a circling osprey, the occasional shuffling of wind passing through shoreline gaps in the forest. After a snack lunch at Snake Point, Dirac and Halpern would strip off and go for a swim, before they rowed back to their starting point, scarcely exchanging a word. These were idyllic, private hours. Occasionally, they would invite a visitor to join them – but it had to be someone who could be relied on to stay silent most of the time. One of the visitors was Kursunoglu, who went along dressed in his three-piece suit, tie and Stetson. Halfway through the trip, he stood up in the canoe to admire the scenery only for Dirac to dump him in the river and then collapse in a fit of laughter.
Dirac and Halpern often arrived home several hours late, half-heartedly suppressing shame – like a pair of errant schoolboys – when they were explaining themselves to a frantic Manci. Halpern assured her week after week that the Wakulla wildlife posed no danger at all: ‘If you leave the snakes and alligators alone, they will do nothing to harm you.’ Halpern could not understand what she was so worried about.23
In the 1970s, particle physics underwent what amounted to a revolution. After decades of uncertainty, physicists achieved a new clarity about the workings of the universe at the finest level: everything in the universe is made of a few basic particles – a handful of leptons and quarks and a small number of particles that mediate their interactions – and described by a quantum field theory simple enough to be spelt out on a T-shirt. The Dirac equation describes the electromagnetic interactions of all the leptons and quarks, each with the same spin as the electron.24
In the past fifty years, physicists had come up with quite a few attention-grabbing labels for their new concepts, but they allowed this description of weak, electromagnetic and strong interactions – one of the supreme syntheses of twentieth-century thought – to be given the most prosaic of names: the Standard Model. One of the first important steps towards the consensus was taken by Dirac’s former student Abdus Salam and by the American theorist Steven Weinberg, who independently suggested in 1967 that the weak and electromagnetic interactions might be understood in a unified way, by describing them in terms of a special type of gauge theory whose underlying mathematical symmetry is broken.25 For several years, the Weinberg–Sala
m theory was not taken seriously as it appeared to suffer an even more serious infestation of unwanted infinities than quantum electrodynamics, the theory of photons and electrons. All this changed in the early 1970s. After the Dutch theoreticians Gerard’t Hooft and Martin Veltman proved that the infinities in the theory – and in all other gauge theories – could be removed by renormalisation, the Weinberg–Salam theory quickly commanded wide interest and support.26 Also at around this time, theorists improved their understanding of renormalisation so that it was much more rigorous than the ‘sweeping under the carpet’ dodge that Dirac deplored. Renormalisation was now widely accepted as a rigorous branch of mathematical physics, with no sleights of hand; Dirac vehemently disagreed.
Soon physicists found a gauge theory of strong interactions, called quantum chromodynamics, with the same underpinnings as the Weinberg–Salam theory. It turned out that it was possible to describe the strong interaction between quarks, mediated by massless particles which Gell-Mann named gluons. Quarks are never observed in isolation, the theory says, because the strong force prevents them being separated, though when quarks are close together they behave as if they were free. So the neutron, first observed by Chadwick just over thirty years before, could be re-envisaged as a compassionate prison for quarks – they cannot escape their confinement, but they are free when inside.
Rutherford’s vision of a typical atom as electrons orbiting a tiny nucleus of protons and neutrons (‘a gnat in the Albert Hall’) had been superseded. Now, the most fundamental way of imagining an atom was in terms of relativistic quantum field theory: the quarks in the nucleus were quantum excitations of the field associated with the strong interaction, just as the orbiting electrons were the quantum excitations of the electromagnetic field. Everything in an atom can be described in terms of such fields. Rutherford would have choked on such abstractions, yet they were the apparently inevitable consequence of a century of labour by his fellow experimenters and their theoretical colleagues.
Although the Standard Model left many questions unanswered – no one fully understood the particles’ masses, for example – its setting out in the 1970s was a high point in the history of science. But Dirac was unmoved: ensconced with Halpern in their Tallahassee redoubt, the new discoveries left him cold, and he appeared to take no great pleasure to see other theoreticians find a way of describing strong interactions using a field theory of the type he had pioneered, as scattering matrices fell into disuse. He no longer kept up to date with the latest physics journals and was beginning to make errors in his science, though no one was ungracious enough to say so in pub lic.27 By the mid-1970s, Dirac had lost interest in particle physics, and Halpern noticed that he was less interested in news about field theory than the renewed public debate about the origin of the Turin Shroud, believed by some to be the burial shroud of Jesus Christ.28
Although Dirac was impressed by the best young particle theoreticians, he thought they were deluded. Through his talks and occasional publications, he urged them to devote all their time to clearing and disinfecting the Augean stables of renormalisation, a job almost all physicists believed had already been done.29 By contrast, Heisenberg in Munich kept an open mind about new theoretical developments until liver cancer took his life in February 1976, six years after his former teacher and friend Max Born had died in Göttingen.30 All Dirac’s friends among the pioneers of quantum mechanics were now dead.
At one time, the historical perspective on atomic physics was not important to him, but now he was keen to put his side of the story to historians and other physicists. In these talks, he always took pains to emphasise the excitement of the early years of quantum mechanics – an emotion that, by all accounts, he rarely showed when he was living through them. He even included a reference to his feelings in the account that was the nearest he ever came to writing a scientific memoir: Recollections of an Exciting Era.31
In May 1980, while suffering from a bad dose of flu, Dirac travelled to Chicago to attend a conference on the history of particle physics at the Fermi National Accelerator Laboratory (Fermilab), where he spoke about the origins of quantum field theory. In a round-table session, he went out of his way to criticise the destructiveness of Pauli’s opposition when the idea of spin and the positron were first conceived.32 In another session, he presented his versions of the history of anti-matter in a talk that Leon Lederman recalled as ‘quintessential Dirac’ – clear, fluent and modest: ‘the content poured out of him like heavy cream’.33 When he had finished speaking, Vicki Weisskopf commented that Einstein had suggested the existence of a positive electron in 1925, some six years before Dirac’s prediction.34 But Dirac was unperturbed; he waved a hand dismissively, remarked, ‘He was lucky,’ and moved on. Even for Dirac, modesty had its limits.
Manci was a generous hostess, able to make everyone in the room feel special and at ease. She often threw dinner parties, attentively filling her guests’ glasses, serving generous portions of her favourite dishes, ensuring that the conversation kept moving. Dirac, sitting at the head of the table, would apparently spend most of the evening asleep. He could, however, be drawn into conversation if he were approached by a young woman, especially if she was friendly and attractive.35 His advice was often sought but he usually declined to offer any; however, when pressed, he would sometimes offer a few words. One of his favourite replies was: ‘Think about yourself first. If nobody gets hurt, do it’ – a slightly egoistic summary of the view of the individual’s moral responsibility in the opinion of John Stuart Mill.36
Manci would point out to guests a favourite photograph of Dirac warmly shaking hands with Pope John Paul II in the Vatican. ‘Paul and the Pope get on so well,’ Manci would beam, as if the two men met every weekend for a round of golf.37 The photograph was taken at one of several meetings between Dirac and the Pope at the Papal Academy, a group of distinguished scientists that offers the Pope disinterested scientific advice. Dirac had been elected to the Academy in 1961, the year after his friend the cosmologist George Lemaître became President. The Diracs’ friend Kurt Hofer recalls Manci’s pride in her husband: ‘After showing guests the papal photograph, she unpacked a collection of postal stamps from all over the world, each bearing a portrait of Paul. He pretended to be embarrassed, but he never did anything to prevent her.’38
It was during one of Hofer’s weekly visits to 223 Chapel Drive that Dirac unexpectedly disgorged his recollections of his father. Dirac trusted only his closest friends with these unexpurgated memories, although the circumstances of Felix’s death were still too distressing for him to share with anyone, even with Manci.39 Dirac did, however, speak of his happiest memories of Felix’s life to Betty in October 1969 when she was in an Amsterdam hospital, lying in a coma after a stroke and a seven-hour brain operation.40 Alone at her bedside, he tried to coax her back into consciousness by telling her stories of their childhood – playing on the Downs with Felix, the three of them bathing on Portishead beach, sharing each other’s books and comics. She regained consciousness a few weeks later and gradually made a partial recovery.
Hofer recalls that Dirac thought organised religions were primitive and socially manipulative ‘myths’. Once, as he walked past a local Mormon church with a huge satellite dish, he scoffed that the church needed such a large dish ‘so that it can communicate directly with God’.41 Yet Dirac was now much more willing to introduce the concept of God into discussions about science. In June 1971, he had startled his audience at the Lindau meeting by considering ‘Is there a God?’ to be one of the five most important questions in contemporary physics. He said it would be useful to approach the question scientifically:
A physicist would need to make this question precise by understanding what is meant by a universe with a God and what is a universe without a God, having a clear distinction between the two types of universes, and then looking at the actual universe and seeing which class it belongs to.42
The audience laughed nervously and went quiet when he sugges
ted a way of detecting the presence of a God. If future scientists demonstrated that the creation of life is overwhelmingly unlikely, then, in his opinion, this would be evidence for the existence of God. Until that time, the hypothesis must be regarded as unproven.43 Dirac was taken to task by the press for these speculations but he was not to be deflected and often returned to the topic, in public and private. He took a dim view of any religion declaring itself to offer the only hope of salvation, Hofer remembers: ‘Paul believed it was the height of arrogance for any group of people to claim that they alone know the truth. He often pointed out there are hundreds of religions on this planet and that it is impossible to know which one, if any, is correct.’44
There was ‘no trace of religiosity’ in Dirac, Halpern later wrote. He remembered that Dirac was especially critical of Catholicism and other religions that acknowledged miracles, because, in his view, the existence of a miracle implies a temporary breaking of the underlying laws of nature, whose beauty he regarded as sacred.45 Like Einstein, and largely following the philosopher Spinoza, Dirac appeared to take the pantheist view that the universe is either identical with God or in some way an expression of God’s nature, a view that – though vague almost to the point of tautology – appears to rule out the notion of a God that can influence human affairs. Dirac’s pantheism was an aesthetic faith: that observations on nature at the most fundamental level will be described perfectly by theories whose mathematical beauty is also perfect. If he had a religion, this was it.
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