The Strangest Man Page 19
Another colleague, the German theoretician Walter Elsasser, later wrote his impressions of Dirac: ‘tall, gaunt, awkward and extremely taciturn. […] of towering magnitude in one field, but with little interest and competence left for other human activities’. Elsasser remembered that although Dirac was always polite, his conversations were almost always stilted: ‘one was never sure that he would say something intelligible.’18 Another of Dirac’s traits was his inability to comprehend anyone else’s point of view if it didn’t fit into his way of looking at things: colleagues would spend hours presenting their perspective on a physics problem, only for him to walk away after making a brief comment, apparently apathetic or bored. Oppenheimer was quite different: he would listen to a colleague’s ramblings for a few minutes but would then interject with an eloquent summary of what he was probably trying to say.
Whereas Oppenheimer mixed freely with his colleagues, Dirac spent most of his time working in the library or in one of the empty classrooms. But he was not a complete loner: in Copenhagen, he had come to appreciate being with other physicists, provided they didn’t put pressure on him to speak. Most mornings, he walked with fellow boarders at the Carios’ to the Mathematics Institute, where he attended lectures that kept them abreast of the latest experimental findings. He also took the time to go to the often-combative afternoon seminars. When Ehrenfest was in town, he was their undisputed inquisitor-in-chief, deflating egos and revealing the crux of every new argument, having cut away the underbrush. In the previous June, he had brought along a Ceylonese parrot trained to say ‘But, gentlemen, that’s not physics’ and recommended that it should chair all forthcoming seminars on quantum mechanics.19
Max Delbrück, one of the young Göttingen physicists, was probably not exaggerating when he later described the experience of walking into one of their seminars: ‘you could well imagine that you were in a madhouse.’20
Word spread to Berlin that Dirac was a difficult man and that his work was impenetrable and overrated. The Hungarian theoretician Jeno (later Eugene) Wigner later said that, in the mid-1920s, his German colleagues were suspicious of ‘the queer young Englishman who resolves [questions of physics] in his own language’.21 Many Germans were put off by Dirac’s manner. The English were known for their reserve – they acted as if everyone else was either an enemy or a bore, as John Stuart Mill had pointed out – but Dirac’s frigidity was unlike anything they had ever seen.22
Born was one of the few Germans who warmed to Dirac, but even he had trouble understanding his new field theory and apparently thought it unimportant. His lack of foresight frustrated Jordan, who had begun to develop ideas on field theory very similar to Dirac’s, only to be met with indifference.23 It would have been fascinating to see what Dirac and Jordan could have achieved in quantum field theory, but Dirac had no interest in collaboration. He turned his attention to using field theory to understand what happens when light is scattered by an atom, normally visualised as being rather like a basketball bouncing off the hard rim of the basket. But, in the new field theory, things are not so straightforward. Dirac showed that, in the fleeting moment of a photon’s scattering, it appears to pass through some strange, unobserved energy states. What makes these intermediate processes so odd is that they appear to flout the sacred law of conservation of energy. Although these subatomic ‘virtual states’ cannot be seen directly, experimenters were later able to detect their subtle influences on fundamental particles.24
Dirac’s calculations also threw up a more troubling artefact. He found that his new theory kept generating bizarre predictions: for example, when he calculated the probability that a photon had been emitted after a given interval, the answer was not an ordinary number but was infinitely large. This made no sense. The probability that an atom would emit a photon must surely be a number between zero (no chance) and one (complete certainty), so it seemed obvious that the prediction of infinity was wrong. But Dirac chose to be pragmatic. ‘This difficulty is not due to any fundamental mistake in the theory,’ he wrote with more confidence than was warranted. The root of the problem, he speculated, was a simplistic assumption he had made in applying the theory; when he had identified his error and tweaked the theory, he implied, the problem would disappear. In the meantime, he dodged the difficulties using clever mathematical tricks, enabling him to use the theory to make sensible, finite predictions. But it would not be long before he saw that his optimism was misplaced: the lamb had caught its first sight of the wolf’s tail.
*
Meanwhile, the debates about the interpretation of quantum theory had not abated, least of all in Copenhagen, where Heisenberg was struggling to understand the theoretical limits of what can be known about a quantum. He achieved this brilliantly with his uncertainty principle, which made him into the nearest the quantum fraternity had to a household name.
The principle emerged only after anguished and protracted gestation, which apparently began with a letter from Pauli during the previous October.25 Heisenberg believed that the correct way to think about the quantum world was in terms of particles, and that the more popular wave-based ideas were merely useful supplementaries. Somehow, Heisenberg wanted to find a way of making definite statements about the measurements that could be made on quantum particles, especially about the limitations on what experimenters can know about them. Heisenberg had talked with Einstein about this, and, when Dirac was in Copenhagen developing transformation theory, he had also discussed it with him.26
The nub of what became known as Heisenberg’s uncertainty principle is that the knowledge experimenters have of a quantum’s position limits what they can know about its speed, at the same instant. The more they know about a quantum’s position, the less they can know about its speed. So, for example, if experimenters know an electron’s location with perfect precision, then it follows that they can know nothing whatsoever about its speed at the same moment; on the other hand, if they know the exact value of the electron’s speed, they will be totally ignorant of its position. There is, Heisenberg argued, no way round this: regardless of the accuracy of the measuring apparatus or the extent of the experimenters’ ingenuity, the principle puts fundamental limitations on knowledge. It turns out that even the most accurate knowledge imaginable of the location of an ordinary object puts only negligible constraints on knowledge of its speed (likewise with the location and speed reversed), so the principle is unimportant in everyday life. This is the root of the physicists’ joke about the motorist who tries to con the traffic police by pleading not guilty of speeding on the grounds ‘I knew exactly where I was, so I had no idea how fast I was travelling’: the plea would be perfectly admissible if it were made by a sentient electron.
In his paper, Heisenberg explained his principle by picturing what happens when an experimenter uses a photon of light to probe the behaviour of an electron, demonstrating that the very act of probing disturbs the electron. An analysis of this thought experiment led Heisenberg to a mathematical expression that encapsulated the principle. He also derived the expression mathematically, using two of Dirac’s innovations: transformation theory and the relationship between the non-commuting position and momentum.27
As spring set in, Dirac will probably have thought about the principle during his constitutional walks along the tree-lined path following the contours of what was once Göttingen’s outer wall.28He was not especially impressed with Heisenberg’s discovery, as he noted later: ‘People often take [the uncertainty principle] to be the cornerstone of quantum mechanics. But it is not really so, because it is not a precise equation, but only a statement about indeterminacies.’ 29 Dirac was similarly lukewarm a few months later when Bohr announced his principle of complementarity, apparently related to Heisenberg’s principle. According to Bohr’s idea, quantum physicists have to accept that a complete picture of subatomic events always involves descriptions that appear incompatible but that are actually complementary – both the wave and particle pictures are needed. In Bohr’s v
iew, this idea was part of an ancient philosophical tradition, in which truth cannot be pinned down using only one approach but needs complementary concepts: for example, a mixture of reason and feeling, analysis and intuition, innovation and tradition.
This principle was fundamental to Bohr’s thinking, to the extent that he chose it in 1947 as the basis of the design of his coat of arms.30 The design features the Chinese yin-yang symbol, which represents the two opposing but inseparable elements of nature, and the Latin motto below reads ‘Opposites are complementary’. Many physicists thought that Bohr had uncovered a great truth, but Dirac was again unimpressed: the principle ‘always seemed to me a bit vague’, he later said. ‘It wasn’t something which you could formulate by an equation.’31
Dirac’s opinion of Heisenberg’s uncertainty principle was not shared by most scientists, including Eddington. In his acclaimed book The Nature of the Physical World, published in November 1928, he gave a sparkling account of ‘the principle of indeterminacy’, describing it as ‘a fundamental general principle that seems to rank in importance with the principle of relativity’. Writing with his usual panache, Eddington introduced tens of thousands of lay readers to the new principle as one of the cornerstones of quantum mechanics.
Eddington writes that he is giving an outline of the theory only against his better judgement: ‘It would probably be wiser to nail up over the door of the new quantum theory a notice “Structural alterations in progress – No admittance except on business”, and particularly to warn the doorkeeper to keep out prying philosophers.’32 Eddington’s account of the theory was the clearest account of quantum mechanics for English-speaking lay readers and was the first widespread publicity for the new theory. If Bohr or another influential figure had taken a leaf out of Eddington’s book and been savvy enough to provide a dramatic presentation of the uncertainty principle’s discovery to well-briefed journalists, then quantum mechanics may well have become much better known, along with its creators.
With a hint of nostalgia, Eddington pointed out that modern physicists no longer thought about the universe as a giant mechanism, as Victorian physicists such as James Clerk Maxwell had done, but framed their accounts of the fundamental nature of things in the language of mathematics. The images of cogs and gearwheels were now passé, but Eddington believed there were dangers inherent in the new, mathematical way of thinking of fundamental physics:
Doubtless the mathematician is a loftier being than the engineer, but perhaps even he ought not to be entrusted with the Creation unreservedly. We are dealing in physics with a symbolic world, and we can scarcely avoid employing the mathematician who is a professional wielder of symbols; but he must rise to the full opportunities of the responsible task entrusted to him and not indulge too freely his own bias for symbols with arithmetical interpretations.33
Eddington had put his finger on the central conceptual challenge that made quantum mechanics so difficult for most professional physicists. The great majority of them still thought like engineers and were mathematically weak by the standards of Dirac and his peers. So, most physicists were still trying to visualise the atom as if it were a mechanical device.
The metaphor of nature as a colossal clockwork mechanism, popular since Newton’s day, had long been apt for most purposes. But no longer. Quantum mechanics was based fundamentally on mathematical abstractions and could not be visualised using concrete images – that is why Dirac refused to discuss quantum mechanics in everyday terms, except in later life, when he began to use analogies between the behaviour of quanta and the way ordinary matter behaves. Yet Dirac often remarked that he did not think about nature in terms of algebra, but by using visual images. Since he was a boy, he had been encouraged to develop visual imagination in his art and technical-drawing classes, which were an ideal grounding for his studies of projective geometry. None of the other pioneers of quantum mechanics had been given an education in which geometric visualisation played such a prominent part. Five decades later, when he looked back on his early work in quantum mechanics, Dirac declared that he had used the ideas of projective geometry, unfamiliar to most of his physicist colleagues:
[Projective geometry] was most useful for research, but I did not mention it in my published work […] because I felt that most physicists were not familiar with it. When I had obtained a particular result, I translated it into an analytic form and put down the argument in terms of equations.34
Dirac had a perfect opportunity to explain the influence of projective geometry on his early thinking about quantum mechanics at a talk he gave in the autumn of 1972 at Boston University.35 Its philosophy department had invited him to give the talk to clarify this influence and had recruited the urbane Roger Penrose, an eminent mathematician and scientist who knew Dirac well, to chair the seminar. If anyone could prise the story out of Dirac, it was he. In the event, Dirac gave a short, clear presentation on basic projective geometry but stopped short of connecting it to quantum behaviour. After Dirac had batted away a few simple questions, the disappointed Penrose gently turned to him and asked him point-blank how this geometry had influenced his early quantum work. Dirac firmly shook his head and declined to speak. Realising that it was pointless to continue, Penrose filled in the time by extemporising a short talk on a different subject. For those who wanted to demystify Dirac’s magic, his silence had never been so exasperating.
Note - Chapter nine
1 Bird and Sherwin (2005: 62).
2Bernstein (2004: 23).
3 Bird and Sherwin (2005: 65).
4 The address of the Carios’ home was Giesmarlandstrasse 1. See interview with
Oppenheimer, AHQP, 20 November 1963, p. 4.
5 Michalka and Niedhart (1980: 118).
6 Frenkel (1966: 93).
7 Interview with Gustav Born, 6 April 2005.
8Frenkel (1966: 93).
9 Weisskopf (1990: 40).
10 Bird and Sherwin (2005: 56, 58).
11 See Frenkel (1966: 94) for a reference to the practice of Mensur in Göttingen. See
also Peierls (1985: 148).
12Interview with Oppenheimer, AHQP, 20 November 1963, p. 6.
13 Interview with Oppenheimer, AHQP, 20 November 1963, p. 11.
14 Delbrück, M. (1972) ‘Homo Scientificus According to Beckett’, available at http://www.ini.unizh.ch/~tobi/fun/max/delbruckHomoScientificusBecket1972.pdf,
p. 135 (accessed 13 May 2008).
15 Greenspan (2005: 144–6).
16 Elsasser (1978: 71–2).
17 Letter from Raymond Birge to John Van Vleck, 10 March 1927, APS.
18 Elsasser (1978: 51).
19Frenkel (1966: 96).
20 Delbrück (1972: 135).
21Wigner (1992: 88).
22 Mill’s comment is in Mill (1873: Chapter 2).
23Interview with Oppenheimer, AHQP, 20 November 1963, p. 11.
24 During his time in Göttingen, Dirac successfully applied his theory to the light emitted
by atoms when they make quantum jumps, apparently after discussions with
Bohr. See Weisskopf (1990: 42–4).
25 Letter from Pauli to Heisenberg, 19 October 1926, reprinted in Hermann et al. (1979). See also Beller (1999: 65–6); Cassidy (1992: 226–46).
26 Heisenberg (1971: 62–3).
27 Heisenberg demonstrated that the principle also applied to energy and time and to
other pairs of quantities known technically as ‘canonically conjugate variables’.
28 This was a popular walk with students. See, for example, Frenkel (1966: 92). On 5
April 1927, Dirac referred to the walk in a postcard of the path to his parents
(DDOCS).
29 Lecture by Dirac, 20 October 1976, ‘Heisenberg’s Influence on Physics’: Dirac
Papers, 2/29/19 (FSU); see also the interview with Dirac, AHQP, 14 May 1963, p. 10.
30 See the article on complementarity in French and Kennedy (1985), e.g. Jones, R.V.
‘Complemen
tarity as a Way of Life’, pp. 320–4; see also the illustration of Bohr’s
coat of arms, p. 224.
31 Interview with Dirac, AHQP, 10 May 1969, p. 9.
32 Eddington (1928: 211). This book is an overview of the latest ideas in physics based
on a series of lectures he gave between January and March 1927.
33 Eddington (1928: 209–10).
34 Dirac (1977: 114).
35Dirac Papers, 2/28/35 (FSU). The seminar took place on 30 October 1972. See
Farmelo (2005: 323).
Ten
Hitler is our Führer, he doesn’t take the golden fee
That rolls before his feet from the Jew’s throne
The day of revenge is coming, one day we will be free […]
From an early Nazi marching song, c. 1927
As a Jew, Max Born had every reason to be alarmed and frightened by the rise of anti-Semitism in Göttingen. The atmosphere was ‘bitter, sullen […] discontent [ed] and angry and loaded with all those ingredients which were later to produce a major disaster’, Oppenheimer remembered, a few years before he died.1 The Nazis had set up one of their first branches in the town in May 1922. Three years later, the chemistry student Achim Gercke secretly began to compile a list of Jewish-born professors, to provide ‘a weapon in hand that should enable the German Reich to exclude the last Hebrew and all mixed race from the German population in the future and expel them from the country’.2
Life among the Göttingen researchers did have its lighter side, however. Many of them gloated that their profession was for the young, and they mocked the sclerotic imaginations of their elderly professors, paid and revered much more for doing much less. As his later comments confirm, Dirac shared this dismissiveness, and, if an improbable Göttingen legend is to be believed, he wrote a quatrain about this for a student review: