One of the scientists who dismissed the new photon picture of light as nonsense was the Danish theoretician Niels Bohr. He had made his name in 1913, when he built on Rutherford’s suggestion that every atom contains a tiny nucleus. Rutherford’s picture could not explain the experimental discovery that atoms emit and absorb light with certain definite wavelengths (each type of atom that gives out visible light, for example, emits only light with a particular set of colours). It is as if each atom has its own ‘song’, composed of light, not sound – instead of musical notes, each played with a characteristic loudness, every atom can give out light with its own set of colours, each colour with a characteristic brightness. Scientists had, somehow, to understand the composition of every atomic melody. Bohr came up with his idea soon after he heard that the colours of the light emitted by hydrogen – the simplest atom, containing only one electron – had an extremely simple pattern, first spotted in 1885 by Johannes Balmer, a Swiss schoolteacher. He happened on a simple but mysterious formula that accounted for the colours of the light given out by these atoms, a mathematical encapsulation of hydrogen’s signature tune. Every other atom was more complicated and much harder to understand. Bohr’s achievement was to take the cue from the hints in this pattern, to build a theory of the hydrogen atom and then to generalise it to every other kind of atom.
Bohr’s atom had a positively charged nucleus, which has most of the atom’s mass, orbited by negatively charged electrons which are tethered by the attractive force between the opposite charges. In much the same way, the planets are held in their orbits around the Sun by the attractive force of gravity. He imagined that the electron in a hydrogen atom could move around in its nucleus in only certain circular orbits – called by others ‘Bohr orbits’ – each of them associated with a particular value of energy, ‘an energy level’. Each of these orbits had its own whole number, known as a quantum number: the orbit closest to the nucleus was labelled by the number one, the next orbit by the number two, the next orbit by three, and so on. Bohr’s innovation was to imagine that the atom gives out light when it jumps (or, in other words, makes a transition) from one energy level to another of a lower energy, simultaneously emitting a quantum of radiation that has an energy equal to the difference between the energies of the two levels. Bohr was saying, in effect, that matter at the atomic level behaves very differently from everyday matter: if the apple that fell in Newton’s garden were able to lose energy by descending down a set of allowed energy values, it would not have fallen smoothly but would have made its way jerkily to the ground, as if bumping its way down an energy staircase. But the energy values of the apple are so close together that their separation is negligible and the fruit appears to slide smoothly down the staircase. Only in the atomic domain are the differences between energy values significant enough for the transitions to be jerky.
Bohr’s theory offered a simple understanding of Balmer’s mysterious formula. In just a few lines of undemanding high-school algebra, any physicist could derive the formula using Bohr’s assumptions, leaving the satisfying impression that the pattern of hydrogen’s colours was comprehensible. Yet Bohr’s theory was only a qualified success: according to the laws of electromagnetism, it was absurd. Maxwell’s theory said that the orbiting electron would shine – continuously give out electromagnetic radiation – and thus gradually radiate its energy away. So it would not take long before the orbiting electron would spiral to its doom in the nucleus, with the result that the atom would not exist at all. The only way Bohr could counter this was to assert, by fiat, that orbiting electrons do not give off such radiation, that Maxwell’s theory did not work on the subatomic scale.
With a remarkable sureness of intuition, Bohr extended his ideas to all other atoms. He suggested that each atom has energy levels and that this helped to explain why the different chemical elements behaved so differently – why, for example, argon is so inert but potassium is so reactive. Einstein admired the way Bohr’s ideas explained Balmer’s formula and the insights they gave into the differences between each type of atom, hinting at an understanding of the very foundations of chemistry. As Einstein remarked in his autobiographical notes, Bohr’s theory exemplified ‘the highest form of musicality in the sphere of thought’.48
But no one properly understood the relationship of Bohr’s atom to the great theories of Newton and Maxwell. These theories came to be described as ‘classical’, to distinguish them from their quantum successors. A fundamental question was, how, precisely, does the theory of the very small merge into the theory of the comparatively large? To answer this, Bohr developed what he called the correspondence principle: the quantum description of a particle resembles the classical theory more and more closely as the particle’s quantum number becomes larger. Similarly, if a particle vibrates rapidly and therefore has a very small quantum number, quantum theory must be used to describe it; classical theory will almost certainly fail.
This principle was too vague for Dirac: he preferred theoretical statements to be expressed in an equation with a single, lapidary meaning, not to be set out in words that philosophers could dispute. But he was fascinated by Bohr’s theory of the atom. He had not heard of it in Bristol, so Fowler’s lectures on the theory were an eye-opener. Dirac was impressed that Bohr had come up with the first tractable theory of what was going on inside atoms. Dirac spent long afternoons in the libraries studying his notes from Fowler’s lectures and poring over the classic textbook Atomic Structure and Spectral Lines, by the Munich theoretician Arnold Sommerfeld. Required reading for every student of quantum theory, the book set out Bohr’s picture of the atom and showed how it could be refined and improved. Sommerfeld gave a more detailed description in which the possible orbits of the electron are not circular (as Bohr had assumed) but elliptical, like the path of a planet round the Sun. He also improved on Bohr’s work by describing the motion of the orbiting electron not using Newton’s laws but using Einstein’s special theory of relativity. The result of Sommerfeld’s calculation was that the measured energy levels should differ slightly from the levels predicted by Bohr, a conclusion supported by the most sensitive experiments. Bohr knew as well as everyone else in atomic physics that his theory was fatally flawed and therefore only provisional; what was unclear was whether the theory that succeeded it would be based on a few tweaks to Bohr’s ideas or on a radically new approach.
At the same time as he was learning and applying Bohr’s theory, Dirac was immersed in geometry, which he studied privately and at weekly tea parties held on Saturdays by the mathematician Henry Baker, a close friend of Hassé’s. Now approaching his retirement, Baker was an intimidating man with the thick moustache which was, in those days, almost mandatory. His parties took place at four o’clock on Saturday afternoons in the Arts school, a grim Edwardian building only a short walk from the Cavendish. Apart from the porter and a few cleaners, the School was as lifeless as a museum at midnight until Dirac and fifteen or so other aspiring scholars of geometry arrived and knocked on the front door. Baker regarded these meetings as his opportunity to promote his love of geometry to his most able students. The subject needed him: for almost a century, it had been the most fashionable branch of mathematics in Britain, but its popularity was waning as fashion began to favour mathematical analysis and the study of numbers.49
The parties – better described as after-hours classes for devotees – were friendly but tense with formality and protocol. Each gathering began promptly at 4.15 p. m., and, in the time-honoured way at English universities, could not begin until everyone had been served a cup of tea and a biscuit. The only students allowed to be late were the sportsmen – rowers, rugby players and athletes who would arrive red-faced and settle down hurriedly after depositing their knapsacks full of sweaty kit. Each week, Baker arranged in advance for one of the students to give a talk to the party before submitting to a grilling by the audience, most of them writing with one hand and smoking with the other. Baker was a spirited teacher, a no-
nonsense mediator but a stern host – he had no compunction about berating any student whose attention showed the slightest sign of wandering. For several of the young men, the parties were a chore, but they were a highlight of Dirac’s week: ‘[they] did much to stimulate my interest in the beauty of mathematics’. He learned that it was incumbent on mathematicians to express their ideas neatly and concisely: ‘the all important thing there was to strive to express the relationships in beautiful form’.50
It was at one of these parties that Dirac gave his very first seminar, about projective geometry. From his fellow students and Baker, he also became acquainted with a branch of mathematics known as Grassmann algebra, named after a nineteenth-century German mathematician. This type of algebra resembled Hamilton’s quaternions, as they are both non-commuting: one element multiplied by another gives a different result if the two are multiplied in a different order. Some applied mathematicians jeered that Grassmann’s ideas were of little practical use, but such concerns did not trouble Baker. He warned his students to expect no public recognition for anything they achieved in pure mathematics, whereas ‘if you discover a comet you can go and write a letter to “The Times” about it’.51
Baker was the type of don Cambridge academics called ‘deeply civilised’ – a subject specialist whose enthusiasms were grounded in high culture. One of his hobbies was the culture of ancient Greece, and he was fascinated by the Greeks’ love of beauty, which he believed was as good a stimulus to a scientific life as any. This may be one reason why Dirac drew attention to the aesthetic appeal of Einstein’s theory of gravity in a talk he gave at one of Baker’s gatherings, having pointed out that its predecessor, Newton’s law of gravity, ‘is of no more interest – (beauty?) – to the pure mathematician than any other inverse power of distance’.52 This is Dirac’s first recorded mention of ‘beauty’. In Bristol, he had been encouraged to take an aesthetic view of mathematics; now, in Cambridge, he had found again that the concept of beauty was in vogue. The popularity of the concept was at least partly due to the enduring success of Principia ethica, published in 1903 by the philosopher George Moore, one of Charlie Broad’s colleagues in Trinity College. Writing with a refreshing absence of jargon, Moore made the incisive suggestion that ‘the beautiful should be defined as that of which the admiring contemplation is good in itself’.53 Soon the talk of intellectuals, Principia ethica was admired by Virginia Woolf and her colleagues in the Bloomsbury Group and declared by Maynard Keynes to be ‘better than Plato’. Over a century before, Immanuel Kant had rendered the subject of beauty too complex and intimidating for most philosophers, but Moore made it accessible again in a way that commanded respect.54 Although Principia ethica did not consider the aesthetics of science, Moore’s common-sense approach to beauty probably influenced his scientific colleagues at Trinity, including Rutherford and the college’s most eminent pure mathematician, G. H. Hardy: both often talked about the beauties of their subject. Kapitza, too, looked on experimental physics not as ‘business’, as it was to several of his colleagues, but as a kind of ‘aesthetic enjoyment’.55
Although Dirac was not interested in philosophy, this fascination with the nature of beauty had powerful resonances for him. Like many theoreticians, he had been moved by the sheer sensual pleasure of working with Einstein’s theories of relativity and Maxwell’s theory. For him and his colleagues, the theories were just as beautiful as Mozart’s Jupiter Symphony, a Rembrandt self-portrait or a Milton sonnet. The beauty of a fundamental theory in physics has several characteristics in common with a great work of art: fundamental simplicity, inevitability, power and grandeur. Like every great work of art, a beautiful theory in physics is always ambitious, never trifling. Einstein’s general theory of relativity, for example, seeks to describe all matter in the universe, throughout all time, past and present. From a few clearly stated principles, Einstein had built a mathematical structure whose explanatory power would be ruined if any of its principles were changed. Abandoning his usual modesty, he described his theory as ‘incomparably beautiful’.56
Dirac was extremely hard to read. Usually, he looked blank or wore a thin smile, whether he was making headway with one of his scientific problems or depressed by his lack of progress. He seemed to live in a world in which there was no need to emote, no need to share experiences – it was as if he believed he was put on Earth just to do science.
His belief that he was working solely for himself led to one of his rare spats with Fowler. Soon after Dirac began in Cambridge, Fowler gauged the ability of his new student by asking him to tackle a nontrivial but tractable problem: to find a theoretical description of the breaking up of the molecules of gas in a closed tube whose temperature gradually changes from one end to the other.57 Some five months later, when Dirac found the solution, he wanted to file it away and forget it, a suggestion that dismayed Fowler: ‘if you’re not going to write your work up, you might as well shut up shop!’58 Dirac succumbed and forced himself to learn the art of writing academic articles. Words did not come easily to him, but he gradually developed the style for which he was to become famous, a style characterised by directness, confident reasoning, powerful mathematics, and plain English. All his life, Dirac had the same attitude to the written word as his contemporary George Orwell: ‘Good prose is like a window pane.’59
That first paper was a piece of academic throat-clearing, of little consequence and unrelated to the fundamental theories of physics that Dirac loved. In his next three papers, however, he was on the more congenial ground of relativity. In his first paper on the subject, he clarified a point in Eddington’s mathematical textbook on Einstein’s general theory of relativity, and in the next two applied the special version of the theory first to atoms jumping between energy levels and then to soups of atoms, electrons and radiation. It was not until the end of 1924 that he produced an outstanding piece of work, an exploration – using Bohr’s atomic theory – of what happens to the energy levels of an atom when the forces acting on it change slowly. Although Dirac came to no startling conclusions, his paper attested to his mastery of Bohr’s theory and of Hamilton’s mathematical methods. Yet Dirac was starting to believe that such exercises were hollow. The more he thought about the Bohr theory, the more dissatisfied he was with its weaknesses. Others shared this dissatisfaction: physicists all over Europe feared that a logical theory of the atom might simply be beyond the human mind.
Notes - Chapter five
1 Gray (1925: 184–5).
2 Boys Smith (1983: 10).
3 See contemporary issues of the Cambridge students’ magazine The Granta; for example, the poem ‘The Proctor on the Granta’, 19 October 1923.
4 Boys Smith (1983: 20).
5 Dirac kept the lodging accounts for the digs where he stayed as a student. See Dirac Papers, 1/9/10 (FSU). Dirac’s landlady at 7 Victoria Road was Miss Josephine Brown, and he resided with her from October 1923 to March 1924. From April to June
1924, he stayed at 1 Milton Road. In his final postgraduate year, he lived at 55 Alpha
Road.
6 College records attest that he took his meals there: his bill for food in college during his first term was £8 17s 0d, about the same as other students who ate there
(STJOHN). The bill from Miss Brown includes no charges at all for either ‘cooking’
or ‘food supplied’.
7 From documents in STJOHN. A typical example of a menu that Dirac would have been offered is the following, served on 18 December 1920: ‘Hare soup / Boiled mutton / Potatoes, mashed turnips, carrots au beurre / Pancakes / Ginger mould / Hot
and cold pie / Anchovy eggs’. He will not have gone hungry.
8 Interview with Monica Dirac, 7 February 2003.
9 Interview with Mary Dirac, 21 February 2003. Dirac’s words were ‘give myself courage’.
10 Interview with John Crook, 1 May 2003.
11 Boys Smith (1983: 7).
12 See contemporary issues of the Cambridge students’
magazine The Granta.
13 Werskey (1978: 23).
14 Snow (1960: 245). See also Dirac (1977: 117).
15 Needham (1976: 34).
16 Stanley (2007: Chapter 3), especially pp. 121–3; Earman and Glymour (1980: 84–5).
17 Hoyle (1994: 146).
18 de Bruyne, N. in Hendry (1984: 87).
19 This description is taken mainly from Snow (1960), and from Cathcart (2004: 223).
20 Wilson (1983: 573).
21 Oliphant (1972: 38).
22 Mott (1986: 20–2); Hendry (1984: 126).
23 Oliphant (1972: 52–3).
24 Carl Gustav Jung introduced the words ‘extrovert’ and ‘introvert’ into the English language in 1923.
25 ‘Naval diary, 1914–18. Midshipman’, by Patrick Blackett, pp. 80–1. Text kindly supplied by Giovanna Blackett.
26 Nye (2004: 18, 24–5).
27 Boag et al. (1990: 36–7); Shoenberg (1985: 328–9).
28 Boag et al. (1990: 34).
29 Chukovsky’s first book, Crocodile, was published in 1917. I am indebted to Alexei Kojevnikov for this information. Chadwick later recalled Kapitza’s first explanation
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