Dirac was aware of the exclusion principle’s power. But he knew that there was much more to do before theorists could understand, at an atomic level, what was going on in the chemistry experiments that he had done at Bishop Road School. There, chemistry was about describing how the elements and other substances behaved: the prize was to move beyond these descriptions to explanations in terms of universal laws. Quantum mechanics promised to do just this, but in 1926 it was not even possible to apply it to atoms that contain more than just one electron, the so-called ‘heavy atoms’.
In his college room, Dirac reflected on how Schrödinger waves might describe heavy atoms and the importance of the Pauli exclusion principle. At the back of Dirac’s mind was Heisenberg’s tenet that theories should be set up only in terms of quantities that experimenters can measure. He thought about the Schrödinger waves that describe two electrons in an atom and wondered whether each wave would be any different if the electrons swapped places. No experimenter could tell the difference, he concluded, because the light given out by the atom would be the same in each case. The way to describe the electrons was, he realised, in terms of waves with the property that they change sign (that is, are multiplied by minus one) when any two electrons are switched. In a few pages of algebra, he used this idea to work out how energy is shared out by groups of electrons as they fill the available energy states. The formulae Dirac derived that summer are now used every day by researchers who study metals and semiconductors; the flows of heat and electricity in them are determined by their electrons, collectively dancing to the tunes of his formulae.
Yet the practical applications were of no interest to Dirac. He was concerned only with understanding how nature ticks at the most fundamental level and why there is such a sharp contrast between the waves that describe electrons and those that describe photons. He concluded that, while the wave describing a group of electrons changes sign if two electrons swap places, the corresponding wave describing a group of photons behaves in the opposite way – if two photons swap places, the wave remains the same.
This tied in neatly with the abortive work he had done on blackbody radiation and led him to explain one of the most puzzling problems of quantum mechanics, a problem that was beyond the ken of Einstein. As Dirac had first heard in Tyndall’s lectures in Bristol, quantum theory had begun in the closing weeks of 1900 when Max Planck suggested that energy is delivered in quanta. The problem was that no one understood how the new theory of quantum mechanics explained Planck’s formula. In the months of grief after Felix’s death, Dirac had lost the scent of the solution because his theoretical tools were inadequate.20 Now he had discovered the tool he needed to explain the black-body radiation spectrum: the waves that describe the photons remain unchanged when any two photons are switched. Two pages of calculations in Dirac’s notebooks had brought to an end a research project that had been going on for twenty-five years. He must have known he had done something special, but he did not intend to share it with his parents. On 27 July, the message he wrote on his weekly postcard was ‘There is not much to say now.’21
At the end of August, Dirac sent off an account of his new theory to the Royal Society. He had every reason to be pleased with himself, but disappointment was in store, as he had again been beaten into print. At the end of October, a month after his paper was published, he received a short, typewritten letter from a physicist in Rome who had published a quantum theory of groups of electrons eight months before. The letter was from Enrico Fermi, an Italian physicist a year older than Dirac. In a short note, written in Berlitz-enhanced English, Fermi drew attention to his paper, which he presumed that Dirac had not seen, and concluded without rancour: ‘I beg to attract your attention to it.’22 But Dirac had seen Fermi’s paper several months before and thought it was unimportant; it had slipped his mind. Although Dirac’s paper was very different in approach to Fermi’s, their predictions for energies of groups of electrons were identical.
It later turned out that another physicist had also done work similar to Fermi’s. In Göttingen, Pascual Jordan had independently derived the same results, had written them up in a manuscript and had given it to his adviser Max Born to read during a trip to the USA. Born put the paper at the bottom of his suitcase and forgot all about it until he returned to Germany several months later, but it was too late. Today, physicists associate the quantum description of groups of electrons only with Fermi and Dirac – in this project, Jordan was, unjustly, a loser.23
In September 1926, Dirac was preparing to leave Cambridge to spend a year in Europe funded by his scholarship from the 1851 Commission. His preference was to spend his first year as ‘an 1851 man’ with Heisenberg and his colleagues in Göttingen, but Fowler wanted him to go to Bohr’s Institute for Theoretical Physics in Copenhagen. They agreed on a compromise: Dirac would spend half the time in each, beginning with six months in Denmark.
Dirac arrived in Copenhagen exhausted, having spent much of the sixteen-hour voyage across the North Sea vomiting.24 The experience led him to a surprising resolution: he would keep sailing in stormy seas until he had cured himself of the weakness of seasickness. His colleague Nevill Mott was flabbergasted: ‘he is quite indifferent to cold, discomfort, food etc. […] Dirac is rather like one’s idea of Gandhi.’25
Notes - Chapter Seven
1 Letter from Einstein to Michel Besso, 25 December 1925, quoted in Mehra and
Rechenberg (1982: 276).
2Letter from Einstein to Ehrenfest, 12 February 1926, quoted in Mehra and
Rechenberg (1982: 276).
3 Bokulich (2004).
4Dirac (1977: 129).
5 Slater (1975: 42).
6 Jeffreys (1987).
7 Bird and Sherwin (2005: 46).
8Interview with Oppenheimer, AHQP, 18 November 1963, p. 18.
9‘The Cambridge Review’, ‘Topics of the Week’ on 14 March and 12 May 1926.
10Letters to Dirac from his mother, 16 March 1926 and 5 May 1926, Dirac Papers,
1/3/5 (FSU).
11 Morgan et al. (2007: 83); Annan (1992: 179–80); Brown (2005: 40 and Chapter 6);
Werskey (1978: 93–5).
12Quoted in Brown (2005: 75).
13Wilson (1983: 564–5).
14 Morgan et al. (2007: 84).
15Morgan et al. (2007: 80–90).
16Dirac Papers, 2/1/2 (FSU).
17 This description follows the one given by Kapitza of his Ph.D. graduation ceremony
three years before, when the proceedings were the same. See Boag et al. (1990: 168–9).
18 Letter to Dirac from his mother, 28 June 1926, Dirac Papers, 1/3/5 (FSU).
19 The Cambridge newspapers reported a wave of heat deaths in July. See the
Cambridge Daily News, 15 August 1926, the hottest day in the town for three years.
20 Dirac had carefully studied a derivation of the radiation spectrum produced by the
previously unknown Satyendra Bose, a student in Calcutta. No one had understood
quite why his derivation worked. Einstein developed Bose’s ideas to produce a theory
that is now named after both men.
21 Postcard from Dirac to his parents, 27 July 1926, DDOCS.
22 Letter to Dirac from Fermi, Dirac Papers 2/1/3 (FSU).
23 Greenspan (2005: 135); Schücking (1999: 26).
24 Letter to Dirac from his mother, 2 October 1926, Dirac Papers 1/3/6.
25 Mott (1986: 42).
Eight
MR PRALINE: […] I wish to complain about this parrot what I purchased not half an hour ago from this very boutique.
PET SHOP OWNER: Oh yes, the, uh, the Norwegian Blue … What’s, uh … What’s wrong with it?
MR PRALINE: I’ll tell you what’s wrong with it, my lad.’ E’s dead, that’s what’s wrong with it!
Monty Python’s Flying Circus, script by JOHN CLEESE and GRAHAM CHAPMAN, 1970
Monty Python’s famous sketch uncannily resembles a parable Rutherford told Bohr
soon after Dirac had arrived in Copenhagen. ‘This Dirac,’ Bohr grumbled, ‘he seems to know a lot of physics, but he never says anything.’ This will not have been news to Rutherford, who decided that the best way of answering Bohr’s implied criticism was to tell a story about a man who went to a pet store, bought a parrot and tried to teach it to talk, but without success. The man took the bird back to the store and asked for another, explaining to the store manager that he wanted a parrot that talked. The manager obliged, and the man took another parrot home, but this one also said nothing. So, Rutherford continued, the man went back angrily to the store manager: ‘You promised me a parrot that talks, but this one doesn’t say anything.’ The store manager paused for a moment, then struck his head with his hand, and said, ‘Oh, that’s right! You wanted a parrot that talks. Please forgive me. I gave you the parrot that thinks.’1
Dirac did a lot of thinking in Copenhagen, mostly alone. No one at Bohr’s institute had ever seen anyone quite like him – even by the standards of theoretical physicists he was profoundly eccentric, a retiring figure, happiest when he was alone or listening in silence. His predisposition to answer questions with either yes or no reminded Bohr of Lewis Carroll’s description, in Alice through the Looking Glass, of the frustration involved in talking to cats: ‘If they would only purr for “yes” and mew for “no”, or any rule of that sort, so that one could keep up a conversation! But how can one deal with a person if they always say the same thing?’2Once in a while, however, Dirac did extend his binary vocabulary of response. When Bohr or one of his friends fussed over him or pressed him to state his preference about something or other, he would bring the interrogation to an end with a curt ‘I don’t mind.’3
Perhaps surprisingly, Dirac thrived in the friendliness and informality of the institute, a world apart from the chilly formalities of Cambridge.4 Bohr had taken great care to nurture this congeniality since the opening of the building in 1921. Located on the Blegdamsvej, a wide straight road on the north-western edge of the city, from the outside the institute looked anonymous, much like every other new building in the city. But inside, the institute’s atmosphere was unique: for most of the day, it hummed with high-minded debate, most of it free of pomposity; individuality was prized, but collaboration was supported; the administration was efficient, free of asinine bureaucracy. Bohr encouraged his colleagues to relax together – to play silly games, to commandeer library tables for ping-pong tournaments, to spend the occasional evening at the cinema, followed by boozy discussions late into the night. Quantum physics was being forged by this generation of physicists, and they knew it. Every researcher was seeking to put their own stamp on the emerging quantum mechanics, nervous of producing trivialities, hopeful that they would come up with insights that would be of lasting value. Their research articles were news that aspired to be history.
Bohr was a national hero in Denmark, though he scarcely looked the part. An unassuming but commanding presence, he looked as if he had absconded from the captaincy of a herring trawler. His depth and versatility enormously impressed Dirac, proving to him it was possible to be a premier-division physicist while taking an active interest in the arts, the stock market, psychology and just about any other subject. Like his mentor Rutherford, Bohr had both an eerily sound intuition about the workings of nature and a real talent for getting the best out of his young colleagues. When a special visitor arrived, Bohr would take him or her on a walk among the beech trees of the Klampenborg Forest, just outside the city, to take the measure of his new colleague and give a sense of his non-mathematical approach to physics. Most of the young physicists came under the spell of Bohr, as he had come under Rutherford’s.
Bohr and his queenly wife Margrethe oversaw life at the institute like the manager and manageress of a hostel, doing their best to make their guests feel at home. Bohr spent most of the day practising the art of talking and lighting his pipe at the same time, conversing with his colleagues alone or in groups, encouraging them and putting their ideas through the mill. Polite to a fault, his refrain when he cross-examined his young charges was ‘Not to criticize, just to learn.’5 Bohr was the Socrates of atomic physics and he made Copenhagen its Athens.
Dirac was billeted in a boarding house in the heart of the city. As he had done in Bristol and Cambridge, he lived life according to a strict routine: every day except Sunday, he took the thirty-minute walk to the institute, past the ducks and swans on the row of artificial lakes on the north-western rim of the city, returning to his lodgings for lunch.6 On Sundays, he went on long strolls through the local woods or along the coast to the north of the city, usually alone but sometimes accompanied by some colleagues or just with Bohr.7 Among the new acquaintances he made there, he got on well with Heisenberg – as likeable in person as he was as a correspondent – but apparently not with Pauli. Although prodigiously talented, Pauli was not the most endearing character in physics: he liked the sound of his own voice and routinely meted out casual verbal violence even to his friends, though he was widely admired for his candour, even by his victims. ‘You are a complete fool,’ Pauli would repeatedly tell his friend Heisenberg, who later said this joshing helped him to raise his game.8 But Dirac had no taste for it, and Pauli repeatedly broke through the firewall of his self-confidence. However, Dirac showed no sign of discomfort: whether being praised or condemned, he looked straight ahead with his thousand-yard stare, his entire bearing powerfully radiating his unwillingness to speak or even to be approached.
Dirac’s behaviour was apparently not a complete surprise to Bohr. A few years later, when describing Dirac’s first visit to a journalist, Bohr echoed the gravedigger in Hamlet: ‘in Copenhagen [we] expect anything of an Englishman’.9
The most pressing problem for quantum theorists remained: what did the symbols in their equations mean? During the summer, Max Born in Göttingen had interpreted Schrödinger’s waves by abandoning the classical principle that the future state of any particle can always, in principle, be predicted. Born had pictured an electron being scattered by a target. He argued that it is impossible to predict precisely how much the electron will be deflected and that it is possible to know only the probability that the electron will be scattered around any given angle. This led him to suggest that when a particular wave describes an electron, the probability of detecting it in any tiny region follows from a simple calculation that involves, loosely speaking, multiplying the ‘size’ of the wave in that region by itself.10 According to Born, the wave is a fictitious, mathematical quantity that enables the likelihood of future behaviour to be predicted. This was a dramatic break with the mechanistic certainties of Newton’s picture of the universe, apparently putting an end to the centuries-old notion that the future is contained in the past. Others had the same idea, including Dirac, but it was Born who first published it, though at first even he does not seem to have fully recognised its importance: in the paper where he introduced the concept, he mentions it only in a footnote.
Born’s quantum probabilities seem to have been news to no one at the institute, least of all Bohr, who remarked, ‘We had never dreamt it could be otherwise,’ though it is unclear why neither he nor any of his colleagues saw fit to publish the idea.11 Whatever the origins of the probability-based interpretation of quantum mechanics, everyone in the physics community was talking about it in the autumn of 1926, and it was one of the themes of the first Bohr–Dirac ‘dialogue’. Only weeks before Dirac’s arrival, Schrödinger had been a visitor to the institute and made it clear that he found Born’s interpretation of quantum waves and the concept of quantum jumps repugnant. On one occasion, after being grilled to a crisp by Bohr, Schrödinger retired sick to his bed, but there was to be no escape. Bohr appeared at his bedside and resumed the interrogation.12
Dirac would not have responded well to such intense questioning, but he made an effective sounding board for Bohr during their autumnal walks. Dirac hardly said a word while Bohr struggled to articulate one point after another, re
solution always lying like a phantom, just beyond his grasp. It was on a Sunday hike in October that Bohr, perhaps speculating that Dirac might be interested in classic English literature, took him to the setting of Hamlet, the royal castle of Kronborg, overlooking the stretch of water between Denmark and Sweden. The Bard would have made comic hay from their verbal exchange, both from the clash of their conversational styles and their contrasting approaches to science and every other subject. Philosophy was an important, compulsory part of Bohr’s education, and he took it seriously. Whereas Bohr sought understanding through words, Dirac thought they were treacherous and believed that true clarity could be achieved only in mathematical symbols. As Oppenheimer would later remark, Bohr ‘regarded mathematics as Dirac regards words, namely as a way to make himself intelligible to other people, which he hardly needs’.13
The Strangest Man Page 16