The Strangest Man Page 15
Quantum mechanics was still only a rudimentary theory. Much remained to be clarified about the interpretation of its mathematical symbols: what did they really mean? And was it possible to say any more about the motion of subatomic particles? How could the theory be applied to atoms more complicated than hydrogen, containing more than one electron? In later life, Dirac liked to point out that quantum mechanics was the first physical theory to be discovered before anyone knew what it meant. He spent months on the problem of interpreting its symbols and came to see that the theory was mathematically less complicated than he had first thought. Born pointed out to Heisenberg that each array of numbers in his quantum theory was a matrix, which consists of numbers arranged in horizontal rows and vertical columns that behave according to simple rules spelt out in textbooks. Heisenberg had never heard of matrices when he discovered the theory, as Born often reminded his colleagues, adding that he was the one who had ensured that Heisenberg’s egg was properly hatched and that its contents were nurtured into infancy.
It seemed to many physicists that Dirac was working in a private language, and this inaccessibility made his work unpopular. In Berlin, long the global capital of theoretical physics, the consensus was that the approach of the Göttingen group – Heisenberg, Born and Jordan – was the most effective. In the United States, then way behind Europe in developing quantum mechanics, the practically minded theoretician John Slater later recalled his frustration with Dirac’s writings. In Slater’s view, there are two types of theoretical physicist. The first consists of people like himself, ‘the prosaic, pragmatic, matter-of-fact sort, who […] tries to write or speak in the most comprehensible manner possible’. The second was ‘the magical, or hand-waving type, who like a magician, waves his hands as if he were drawing a rabbit out of a hat, and who is not satisfied unless he can mystify his readers or hearers’. For Slater and many others, Dirac was a magician.5
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Dirac’s academic stock rose further in the spring of 1926, during his final term as a postgraduate. He was no longer just another of Cambridge’s many brilliant but unfulfilled loners but was recognised as an extraordinary talent. Fowler arranged for him to give two series of lectures on quantum theory for his fellow students. Fowler was also in the audience, aware that his most brilliant protégé had overtaken him.
Although Rutherford affected to scorn highfalutin theory, he kept abreast of the latest news about quantum physics. At his request, Dirac gave a presentation at the Cavendish about the welter of quantum discoveries that had been made at Göttingen, but it was a poor, hastily prepared talk.6 His audience almost certainly included Oppenheimer and also Kapitza and Blackett, who were – beneath a veneer of amity – increasingly at odds. The tensions were rooted in their relationships with Rutherford. Kapitza shamelessly flattered and courted him, who in return gave favours and even friendship, to the extent that Kapitza was sometimes described as the son Rutherford never had. None of this went down well with Blackett, who admired Rutherford’s creative running of the laboratory but had no time for his authoritarianism. Blackett, too, was an object of envy. In the early autumn of 1925, he tutored Oppenheimer at the laboratory bench, teaching him the craft of experimental physics, for which Oppenheimer had little aptitude, as he well knew. With the peculiar logic of neurosis, Oppenheimer decided to get his own back by anonymously leaving on Blackett’s desk an apple poisoned with chemicals from the laboratory.7 Blackett survived but the authorities were outraged and Oppenheimer avoided expulsion from the university only after his parents persuaded the university not to press charges but to put him on probation, on the understanding that he would have regular sessions with a psychiatrist. A few months later, he switched to theoretical physics – a much more congenial field for him – and worked in the same circle as Dirac, who was busy hammering out his vision of quantum mechanics. Oppenheimer recalled that ‘Dirac was not easily understood, not concerned with being understood. I thought he was absolutely grand.’8
Dirac probably did not notice the intrigues among his friends and acquaintances or their personal problems; even if he did, he would probably have ignored them. He worked all day long and took time off only for his Sunday walk and to play chess, a game he played well enough to beat most students in the college chess club, sometimes several at the same time. Nor did Dirac take much interest in politics. He was an onlooker during the General Strike that almost brought the UK to a halt for nine days in early May 1926 and led many to fear that a Bolshevik revolution was imminent. King George V urged moderation, while in the Government, Churchill demanded ‘unconditional surrender’ from the workers (‘the enemy’) who were supporting the demands of the Miners’ Union. Some students thought the strike was a national crisis, but to others it was an opportunity to drive a tram or to play at being a docker or a policeman. Almost half the university’s students took part in strike-breaking activities, so the authorities had no choice but to postpone the end-of-year examinations, prolonging the merriment.9 Dirac heard from his mother that trams and buses in Bristol were still running, a relief to his father, so weakened by grief that he could not walk the mile between his home and the Merchant Venturers’ School. Fate was about to bring Charles even more sorrow: he heard from Geneva in early March that his mother had died.10
The collapse of the General Strike was important in the development of political thought in Cambridge. The strength of opposition to the strike in the university demonstrated the unwillingness of its dons to disrupt the political status quo; even some of its socialist academics had been strike-breakers. The humiliation of May 1926 was one of the main motivations of a few Marxist scientists who were determined to establish radical politics in Cambridge and then to spread the word across the country. The most effective of the proselytisers was the young crystallographer Desmond Bernal, an energetic and charismatic polymath, who had joined the Communist Party after he graduated in 1923.11 He had a vision of a just and well-informed collectivist society, with all policy decisions taken according to scientific principles and with the benefit of expert technological knowledge. Scientists were his ideal society’s elite, to the extent that he suggested that they might be granted the freedom to form ‘almost independent states and be enabled to undertake their largest experiments without consulting the outside world’.12 The theoretical basis for Bernal’s thinking was supplied by Marxism, which seemed to him and his friends to provide a framework for the solution of every social, political and economic problem.
Bernal and his colleagues at first made slow progress in converting colleagues to Marxist thinking, partly because of resistance by moderates such as Rutherford, who despised Bernal more than anyone else in Cambridge for his activism and, apparently, for his open sexual promiscuity.13 The suspicion of card-carrying Communists was so intense that Bernal apparently decided in 1927, when he began a period of working full-time in the Cavendish, that it would be better to let his membership of the party drop. After that, it appears that none of his colleagues officially joined the party.14
Kapitza did not make the error of alienating senior colleagues: although he shared many of Bernal’s political views, he was careful not to offend Rutherford by talking politics in the laboratory. However, Kapitza will have shared his vision of society with Dirac, who had arrived in Cambridge a political innocent and so heard for the first time the claim that Marxism offered an all-embracing scientific theory that could do for society what Newton had done for science. According to this vision, every economy could be the test bed for a theory that promised a brighter future, with intelligent planning taking the place of the sometimes cruel, invisible hand of market forces. Dirac may have noted the strong support Marxists gave to education and industrialisation and the contempt they poured on religion – themes that emerged soon afterwards in his perspective on aspects of life he was discovering outside physics.
During the General Strike, Dirac was absorbed in writing his Ph. D. thesis, a compact presentation of his vision of quantum mechani
cs. Confident though he was of his understanding of the theory, he knew as he wrote his thesis that it was not the whole story, for he had recently heard that an alternative version of quantum theory had appeared, one that looked completely different from Heisenberg’s. The author of the new version was the Austrian theoretician Erwin Schrödinger, working in Zurich. He was thirty-eight years old, a generation older than Heisenberg and Dirac, with a formidable reputation in Europe as a brilliant polymath.
Schrödinger had discovered his quantum theory independently of Heisenberg and a few weeks later, by building on de Broglie’s wave theory of matter, which Dirac had admired but had not taken seriously. In the Christmas vacation of 1925, during an illicit weekend with a girlfriend in the Swiss mountains, Schrödinger discovered an equation that described the behaviour of quanta of matter in terms of their associated waves, and then applied the theory in a series of dazzling papers. His achievement was to generalise de Broglie’s idea: the young Frenchman’s theory applied only to the special case of matter with no overall force acting on it, but Schrödinger’s theory applied to all matter, in any circumstances.
The great virtue of Schrödinger’s theory was that it was easy to use. For the many scientists intimidated by the abstract mathematics in Heisenberg’s approach, Schrödinger offered the balm of familiarity: his theory was based on an equation that closely resembled those most physicists had mastered as undergraduates, when they were studying water and sound waves. Better still, in Schrödinger’s theory, the atom could be, at least to some extent, visualised. Roughly speaking, the energy levels of an atom correspond to the waves that can be set up on a piece of rope, held fixed at one end and shaken up and down at the other. The shaker can set up a single half-wavelength (like a crest, moving up and down) on the rope, or, by shaking more vigorously, two half-wavelengths, or three half-wavelengths, or four, or five, and so on. Each of these wave patterns corresponds to a definite energy of the rope, just as each possible Schrödinger wave of an atom corresponds to an atomic energy level. The meaning of these Schrödinger waves was unclear: their discoverer suggested unconvincingly that they were a measure of the spread of the electron’s charge around the nucleus. Whatever the true nature of these waves, they were more intuitively appealing than Heisenberg’s matrices to those who lacked mathematical confidence. They, along with everyone else, were relieved when Schrödinger gave a preliminary proof (completed two years later by others) that his theory gave the same results as Heisenberg’s. The frightened sceptics could then ignore those intimidating matrices.
At first, Dirac was annoyed by Schrödinger’s theory, as he resented even the thought of suspending work on the new quantum mechanics and starting afresh. But in late May, as he was finishing the writing of his Ph. D. thesis, he received a persuasive letter from Heisenberg urging him to take Schrödinger’s work seriously. This wise advice was ironic coming from Heisenberg, an opponent of the rival theory, who had written to Wolfgang Pauli in early June, ‘The more I reflect on the physical portion of Schrödinger’s theory the more disgusting I find it. What Schrödinger writes on the visualizability of his theory is probably not quite right. In other words, it’s crap.’ Schrödinger gave as good as he got, dismissing the mathematical arcana of Heisenberg’s theory and the idea of quantum jumps. The two theorists clashed unpleasantly when they first met a month later at a packed seminar in Munich, the first skirmish in what was to be a long and acrimonious dispute.15
Dirac ignored Schrödinger’s theory in his Ph. D. thesis, ‘Quantum Mechanics’, the first to be submitted anywhere on the subject. The thesis was a great success with his examiners, including Eddington, who took the unusual step on 19 June of sending him a short handwritten letter on behalf of the Degree Committee of the Mathematical Board, congratulating him on ‘the exceptional distinction’ of his work.16 Dirac disliked celebrations and formality, so he was almost certainly not looking forward to the ceremony. He could have taken the degree without attending it but decided to be there in person for the sake of his proud parents, especially his father, who had given him the money that enabled him to begin his Cambridge studies.
Dirac’s parents and his sister Betty set off at four in the morning, in good time to take the train to Cambridge via Paddington to see Paul be awarded his degree in the setting of the university’s grand Senate House. Every detail of the proceedings harked back to the University’s monastic origins. The ermine-collared Vice Chancellor presided and, like the other officials, spoke only in Latin, ensuring that Dirac understood scarcely a word. Wearing evening dress with a white bow tie, a small black cap and red silk gown, he knelt on a velvet cushion, placed his hands together and held them out to be grasped by the Vice Chancellor, who delivered a prayer-like oration. Dirac arose, a doctor.17
It was the wettest June in Cambridge for five years, but on that day the rain held off. The town was at its most relaxed, teeming with students and their families. Dirac had not learned the local practice of punting, so he and his family could only watch as others steered their flat-bottomed boats along the Cam, through the lawns and fields, past the gorgeous colleges and chapels.
The Dirac family arrived home at 4 a.m. on Sunday. It had been a happy trip, though its cost had upset Charles. Flo wrote to her son: ‘Pa said it cost him £8, so that will be our summer holiday.’18 It was to be the highlight of her summer, though she was worried that her son was looking drawn and emaciated: ‘I wish you would have a nice rest & feed up & get strong. Do try!’ As usual, he took no notice. Like his father, he had no need of holidays – the long vacations were not for relaxing but for hard work. The university was about to hibernate for the summer and would be virtually devoid of social distractions for the few scholars who remained. It was the perfect environment for Dirac to concentrate even more intensively on his work. Heisenberg and Schrödinger had knifed a sack of gemstones, and the race was on to pick out the diamonds.
Dirac moved out of his lodgings and into a college room, where he worked at his desk through a sweltering July, producing what would prove to be one of his most enduring insights into nature.19 He realised that he had been wrong to be wary of Schrödinger’s work. Dirac saw that he could have derived Schrödinger’s equation using his theory if only he had not been quite so fixated on the links between classical and quantum mechanics. Now, having set aside his prejudice, he could proceed with new gusto. He explained how to generalise Schrödinger’s first version of his equation, which applied only to cases that stayed the same as time progressed, to situations that did change with time, such as an atom in a fluctuating magnetic field. Quite independently, Schrödinger wrote down the same general equation, which is now named – not entirely fairly – only after him.
Within a few weeks of mastering Schrödinger’s equation, Dirac used it to make one of his most famous contributions to science. It concerned the most basic particles that exist in nature, usually described as ‘fundamental’ because they are believed to have no constituents at all. Classic examples are photons and electrons. Today, two established experimental facts form the bedrock of studies about fundamental particles. First, for each type of fundamental particle, every single one of them in the universe is the same and identical to all other particles of the same type – every electron in every atom on Earth is indistinguishable from every electron in galaxies millions of light years away, just as all the trillions of photons given out each second from a light bulb are the same as the photons given out by the most distant star. For electrons and photons, if you have seen one, you have seen them all. Second, the types of fundamental particles fall into one of two classes, much as almost all human beings can be classified as males or females. The first class is exemplified by the photon, the second by the electron. In 1926, no one knew that there were two such classes.
The differences between the behaviours of electrons and photons exemplify the sharp contrast in behaviour between the two known classes of particle. For a collection of electrons, say in an atom, each availabl
e energy state can usually accommodate no more than two electrons. The situation is quite different for photons: each energy state can host any number of them. One way to visualise this difference is to imagine a pair of bookcases with horizontal shelves arranged vertically above one another in ascending order of energy – the higher the shelf, the higher the energy to which it corresponds. The shelves of the ‘electron bookcase’ represent the energy states available to electrons, while the shelves of the ‘photon bookcase’ correspond to the states available to photons. For the ‘electron bookcase’, each shelf can accommodate at most two books: once the shelf is occupied, it is full and no others can join it. The ‘photon bookcase’ is different because its shelves can each house any number of books. It is as if electrons are unsociable, whereas photons are gregarious.
Pauli first realised the aversion of electrons to their own company in 1925 when he suggested his exclusion principle. This explained the puzzle of why all the electrons in an atom do not all orbit the nucleus in the same, lowest-energy orbit: it is because the electrons simply are not allowed to fit into the same state – they are forced by the exclusion principle to occupy higher-energy states. This is why the different types of atom – manifest as different chemical elements – behave so differently. In common experience, neon is a gas and sodium is a metal, yet the atoms of neon gas are very similar to the sodium atoms: outside their nuclei, they differ only in that a sodium atom contains one more electron than a neon atom. That additional electron determines the differences between the two elements, and the Pauli exclusion principle explains why sodium’s extra electron does not simply join the others and form an almost identical type of atom; rather, it occupies a higher-energy quantum state that is responsible for the differences between the behaviour of the two elements. For the same reason, if there were no exclusion principle, the world around us would have none of the huge variety of forms, textures and colours that we take for granted. Not only would our senses have nothing to perceive, they would not exist. Nor, indeed, would human beings or even life itself.