Obviously if you could come with me that would please me more.
My fond good wishes and may God prosper you.
Father24
But Charles was to be disappointed. His son was planning another vacation in the Soviet Union, this time with Kapitza in Gaspra, a mountainous coastal resort in the Crimea. In Stalin’s time, it was a place for the scientific elite to take breaks, away from the forced migrations of peasant farmers, the food shortages and rationings and all the other disasters of the Five Year Plan and collectivisation.
Dirac had begun his trip at a conference in Leningrad, where he spoke about his field theory of electrons and photons. After Boris Podolsky – an American of Russian-Jewish blood – and Vladimir Fock told him that they were studying the same problem, Dirac agreed to work with them. During his stay in Kharkhov, Dirac collaborated with his Russian colleagues, and, after a long exchange of technical correspondence, they produced a surprisingly simple proof that Dirac’s field theory is equivalent to Heisenberg and Pauli’s and more transparently consistent with the special theory of relativity. 25 This project was another sign that Dirac was no longer quite so insular: early in the year, he had written a modest paper on atomic physics with one of Rutherford’s students and now here he was, working on quantum fields in equal harness with Soviet theoreticians. But Dirac remained wary of collaboration: visiting theoreticians who were not previously acquainted with him found him distant, utterly uninterested in sharing his ideas.26 When Dirac was visited by one of them, Leopold Infeld, the young Pole found him friendly and smiling but unwilling to respond to any statement that was not a direct question. After twice receiving a reply of just ‘No’, Infeld managed to phrase a technical query that drew from Dirac an answer consisting of five words. They took Infeld two days to digest.27
When Dirac was relaxing on the Crimean coast, he was unaware that the story of the anti-electron was approaching its conclusion more speedily than he had dared to believe possible. Many of the characters in this strange denouement, including Dirac, behaved in ways that are now barely comprehensible, even bearing in mind that hardly any physicists in 1932 took Dirac’s hole theory seriously and few were even vaguely aware of his prediction of the anti-electron.
The end of the story began shortly before Dirac’s vacation, at the end of July 1932 in Pasadena, not far from the Hollywood Bowl, where the Los Angeles Olympic Games were just beginning. It would be a welcome opportunity for the people of the city and millions of radio listeners to have some respite from the economic gloom and political manoeuvrings in advance of the coming presidential election. 28 At Caltech, many of the scientists were on vacation. But in a comfortably warm room on the third floor of the aeronautics laboratory, Carl Anderson was hard at work on the effects of cosmic rays within his cloud chamber. By the end of the first day of August, a Monday, all he had to show for his latest experiments were blank photographs, but, on the following day, he struck lucky.29
Anderson managed to take a photograph of a single track, just five centimetres long. It looked rather like a hair. The density of bubbles around the track seemed to indicate that it had been left by an electron, but the curvature of the path suggested otherwise – it had been left by a positively charged particle, so it could not possibly have been an electron. Still not quite believing his eyes, Anderson spent an hour or two checking that the poles of his magnet were correct and that they had not been switched by jokesters.30 Convinced he was not the victim of a prank, he was elated, though his euphoria was cooled by an icy trickle of panic: was this really a discovery or some stupid mistake?31 To clinch the existence of the positive electron Anderson needed more evidence, but by the end of the month he had found only two more examples of his unusual tracks, neither as cut and dried as the first. Millikan was not persuaded.
After the Olympic pageant had folded and the Caltech staff had returned after the summer break, Anderson wrote a short description of his experiment for the journal Science. Like Chadwick’s presentation of his apparent discovery of the neutron, Anderson’s account was cautious: he examined every conceivable reason why the track might not be a new particle. Even more circumspect than Chadwick had been, Anderson couched his claim to a discovery in a paper that he entitled ‘The Apparent Existence of Easily Deflectable Positives’, hardly an eye-catching phrase. Readers who reached the end of the article were rewarded with a sentence that qualifies as a masterpiece of scientific conservatism: ‘It seems necessary to call upon a positively charged particle having a mass comparable with that of an electron.’ According to one report, Anderson was so worried by his failure to find more good examples of the track that he thought of writing to Science to withdraw his paper. But it was too late: the article was at the printers.32
Here, under Anderson’s nose, was clear evidence for Dirac’s anti-electron – a particle with the same mass as the electron but with the opposite charge. Anderson had earlier spent several evenings a week struggling through Oppenheimer’s evening lectures on Dirac’s hole theory, so it is practically certain that he knew about the part played by the anti-electron within it.33 Yet he did not make the connection, probably because he was directing his attention almost exclusively to the cosmic-ray theory of his boss.34
Anderson sent off his paper on 1 September, and it appeared in the libraries of American physics departments about eight days later, to be greeted with indifference and disbelief. His finding was ‘nonsense’, one of his Caltech friends told him. Millikan still believed that something was wrong with Anderson’s experiment and so did almost nothing to promote it. Anderson, worried that he had not found another track like the one he detected in early August, spoke publicly about the need to be cautious.35 Oppenheimer was almost certainly among the thousands of physicists who read the article, and he wrote soon after to his brother that he ‘was worrying about […] Anderson’s positive electrons’.36 But Oppenheimer failed to put two and two together. Perhaps he was blinkered by a narrow interpretation of Dirac’s sea of negative-energy electrons: Dirac had always believed that this sea would contain some holes, whereas Oppenheimer assumed that the electron sea was always completely full, so that the concept of the hole was redundant. It beggars belief that Oppenheimer never pointed out the connection between Dirac’s theory and Anderson’s experiment to Dirac, to Anderson or to anyone else. Yet that appears to be what happened.
One of Anderson’s colleagues did, however, take his result seriously. Rudolph Langer – a Harvard-trained mathematician, talented but not noteworthy – had read Dirac’s work on the anti-electron and talked with Anderson and Millikan about the new cosmic-ray photographs. The day after Science published Anderson’s paper, Langer sent a short paper to the journal, making connections between the new observations and Dirac’s theories. Showing none of Anderson’s restraint, Langer concluded that Anderson had observed Dirac’s anti-electron. He did not stop there; he went on to build an imaginative new picture of matter, suggesting that the photon is a combination of an ordinary electron and a negative-energy electron, that the monopole is built from a positive and negative monopole and that the proton ‘of course’ comprises a neutron and a positive electron. The paper looks impressively imaginative today, but it made no impact in 1932, probably because Langer was not sufficiently respected to command attention and because it was simply not done to speculate with such abandon. His insight left no trace in Anderson’s memory and was soon forgotten.
By early autumn, Anderson’s ‘easily deflected positive’ appears to have been a minor query in the minds of most Caltech physicists, a rogue result to be refuted or possibly a puzzle to be solved. In Cambridge, no one seems to have been aware of Anderson’s experiment or of Langer’s article. The journal Science arrived in the Cambridge libraries by early November, but neither Dirac nor any of his colleagues appear to have read it. But, by then, Blackett was hot on Anderson’s trail.
Rutherford had agreed that Blackett could begin a new programme of research into cosmic rays. But Blacket
t’s patience with his boss’s despotic style had worn thin, as a graduate student saw when Blackett returned from Rutherford’s office white-faced with rage and said, ‘If physics laboratories have to be run dictatorially […] I would rather be my own dictator.’37 Blackett carved out a niche in the Cavendish, working with an Italian visitor, Giuseppe Occhialini, a light-hearted Bohemian commonly known by his nickname ‘Beppo’.38 Ten years younger than Blackett, Occhialini was an expert experimenter who tended to rely on his intuition, rarely pausing to write down an equation, preferring to spell out the steps in his reasoning with an impressive range of accompanying gesticulations. When Occhialini arrived in Cambridge the year before, in July 1931, he had already been involved in experiments to detect cosmic rays and brought to the Cavendish years of experience working with Geiger counters, only recently introduced to Cambridge. These counters were delicate and unreliable, Blackett later remembered: ‘In order to make it work you had to spit on the wire on some Friday evening in Lent.’39 For Occhialini, Blackett was a jack of all trades in the laboratory:
I remember his hands, skilfully designing the cloud chamber, drawing each piece in the smallest detail, without an error, lovingly shaping some delicate parts on his schoolboy’s lathe. They were the sensitive yet powerful hands of an artisan, of an artist, and what he built had beauty. Some of my efforts produced what he called ‘very ugly bits’.40
Occhialini often visited Blackett at home in the evening. The two of them would relax in the front room and review their day’s work over glasses of lemonade and a plate of biscuits, while Blackett fondled the ears of his sheepdog. During their conversations at home and in the Cavendish, they came up with a clever way of getting cosmic rays to take photographs of themselves: the trick was to place one Geiger counter above their cloud chamber and another counter below it, so that the chamber was triggered when a burst of cosmic rays entered both the upper and lower counters. By the autumn of 1932, Blackett and Occhialini had used this technique to take the art of photographing cosmic rays from a time-wasting matter of pot luck to a new era of automation. Soon, word circulated round the Cavendish corridors that something special was emerging from the Anglo-Italian duo. Even the reserved Blackett, the quintessence of the upper-crust Englishman, was excited.
Soon Blackett and Occhialini were ready to treat their colleagues to the clearest batch of cosmic-ray photographs ever taken. At their seminar, Dirac was in the audience. This was surely his moment: he could quite reasonably have suggested that Blackett and Occhialini had discovered the anti-electron and, therefore, vindicated his hole theory. But he stayed silent. The mention of the possible presence of positive electrons drew Kapitza to turn to the new Lucasian Professor, sitting in the front row, exclaiming, ‘Now, Dirac, put that into your theory! Positive electrons, eh! Positive electrons!’ Kapitza had spent hours talking with Dirac but had evidently not even heard of the anti-electron. Dirac replied, ‘Oh, but positive electrons have been in the theory for a very long time.’41 Here, unless electrons really were shooting upwards from the Cavendish basement, the anti-electron seemed to be showing its face. Yet Dirac’s colleagues so mistrusted his theory that none of them was prepared to believe that it could predict new particles. Nor, it seems, did Dirac try hard to persuade them, perhaps because he believed that there was still a chance that every positive electron in his colleagues’ photographs was in some way a mirage. This was reticence taken to the point of perversity.
At that time, Dirac was not concentrating on his hole theory but on one of his favourite subjects: how quantum mechanics can be developed by analogy with classical mechanics. In the autumn of 1932, he found another way of doing this, by generalising the property of classical physics that enables the path of any object to be calculated, regardless of the nature of the forces acting on it. Newton’s laws could also do this job, and gave the same answer, but this technique – named after the French-Italian mathematician Joseph Louis Lagrange – was more convenient in practice. Dirac had first heard about this method when he was a graduate student, from lectures given by Fowler: it had taken some six years for the penny to drop.42
Although the technique is usually easy to use, it sounds complicated. At its heart are two quantities. The first, known as the Lagrangian, is the difference between an object’s energy of motion and the energy it has by virtue of its location. The second, the so-called ‘action’ associated with the object’s path, is calculated by adding the values of the Lagrangian from the beginning of the path to its end. In classical physics, the path taken by any object between two points in any specified time interval turns out, regardless of the forces acting on it, to be the one corresponding to the smallest value of the ‘action’ – in other words, nature takes the path of least action. The method enables physicists to calculate the path taken by any object – a football kicked across the park, a moon in orbit around Saturn, a dust particle ascending a chimney – and, in every case, the result is exactly the same as the one predicted by Newton’s laws.
Dirac thought that the concept of ‘action’ might be just as important in the quantum world of electrons and atomic nuclei as it is in the large-scale domain. When he generalised the idea to quantum mechanics, he found that a quantum particle has not just one path available to it but an infinite number, and they are – loosely speaking – centred around the path predicted by classical mechanics. He also found a way of taking into account all the paths available to the particle to calculate the probability that the quantum particle moves from one place to another. This approach should be useful in relativistic theories of quantum mechanics, he noticed, because it treats space and time on an equal footing, just as relativity demands. He sketched out applications of the idea in field theory but, as usual, gave no specific examples; his concern was principles, not calculations.
Normally, he would submit a paper like this to a British journal, such as the Proceedings of the Royal Society, but this time he chose to demonstrate his support for Soviet physics by sending the paper to a new Soviet journal about to publish his collaborative paper on his field theory. Dirac was quietly pleased with his ‘little paper’ and wrote in early November to one of his colleagues in Russia: ‘It appears that all the important things in the classical […] treatment can be taken over, perhaps in a rather disguised form, into the quantum theory.’43
Even if Crowther had wanted to publicise this idea, he would have found it hard to get his article published in the Manchester Guardian: it was too technical, too abstract. The ‘little paper’ appears to have been too abstruse even for most physicists and so remained on library shelves for years, a rarely read curiosity. It was not until almost a decade later that a few young theoreticians in the next generation cottoned on to the significance of the paper and realised that it contained one of Dirac’s most enduring insights into nature.
In the closing months of 1932, the news from Germany was that Hitler stood a fair chance of being elected chancellor in the impending elections: if Dirac’s later comments on the Führer are anything to go by, he will have been uneasy at the prospect. Einstein, sick of the political climate and the violent anti-Semitism, fled to the USA and agreed to join Abraham Flexner’s Institute for Advanced Study in Princeton, while Born hung on in Göttingen, where the Nazis were the largest single party: half its voters now supported them.44 In the USSR, Stalin was showing ever-greater intolerance of academic freedom. In the USA, Franklin D. Roosevelt had been elected by a landslide, but the country remained in desperate economic straits. In the UK, unemployment rose to unprecedented levels, and there were mass demonstrations about unemployment benefits all over the country.
In the normally calm centre of Bristol, near the Merchant Venturers’ College, hundreds of protestors were baton-charged by the police.45 A mile away, the Dirac household was again a battlefield. With Betty spending most of her time at university, her parents were left to explore every crevasse of their fractured marriage. Flo told Dirac that his father, becoming more aggressive, wa
s still trying to throw her out of the house. Charles was incensed when he heard that she had given a pupil wrong information about his tuition fees and threw a glass of hot cocoa at her, she reported to Dirac. Yet, to most of the people he knew, Charles looked like a model of the contented retiree. At the Cotham School prize-giving, the Headmaster praised him for his son’s success, and they talked over tea and cakes about Dirac’s recent trip to Russia. Flo wrote to her son, ‘Really, he is quite a gossip outside his own home, where he only condescends to scold.’46
The Dirac family was together for what promised to be a torrid Christmas. But Charles and Flo ceased hostilities, and the family had what Flo described as ‘quite the best Xmas we have had for years’.47 Part of the reason for this may have been that Dirac was in a good mood, as news he had wanted to hear for eighteen months had just arrived.
Notes - Chapter sixteen
1 Eddington made this remark in Leicester, at the annual meeting of the British Association for the Advancement of Science: ‘Star Birth Sudden Lemaître Asserts’, New York Times, 12 September 1933.
2 An English translation of the play, by Gamow’s wife Barbara, is given in Gamow (1966: 165–218). For comments on the production: von Meyenn (1985: 308–13).
3 Wheeler (1985: 224).
4 Crowther (1970: 100).
5 Letter from Darwin to Goudsmit, 12 December 1932, APS.
6 Interview with Beck, AHQP, 22 April 1967, p. 23.
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