23 ‘Many patients with tuberculosis present with general symptoms, such as tiredness, malaise, loss of appetite, weakness or loss of weight’: Seaton et al. (2000: 516).
24 There are insights into the childhood of autistic children in the memoir of Gunilla Gerland (translated by Joan Tate), A Real Person: Life on the Outside. Gerland writes powerfully of her perception of the misunderstandings in her early relationship with her parents, notably with her father. ‘He had no respect for anyone’s needs […] The effect of my father’s actions was one of pure sadism, although he was not really a sadist. He didn’t enjoy my humiliation in itself – he couldn’t even imagine it’ (Gerland 1996). See also Grandin (1984).
Thirty-one
Dirac told physics students they should not worry about the meaning of equations, only about their beauty. This advice was good only for physicists whose sense of purely mathematical beauty is so keen that they can rely on it to see the way ahead. There have not been many such physicists – perhaps only Dirac himself.
STEVEN WEINBERG, Dirac Centenary Meeting, University of Bristol, 8 August 20021
All scientists, even the most eminent, are dispensable to science. Although inspired individuals influence it in the short term, the absence of any of them would be unlikely to make much difference to it in the long run. If Marie Curie and Alexander Fleming had never been born, radium and penicillin would have been discovered soon after the dates now in the textbooks.
Every scientist can hope, however, that posterity will judge him or her to have revealed more than a typical share of nature’s secrets. By this criterion, there is no doubt that Dirac was a great scientist, one of the few who deserves a place just below Einstein in the pantheon of modern physicists. Along with Heisenberg, Jordan, Pauli, Schrödinger and Born, Dirac was one of the group of theoreticians who discovered quantum mechanics. Yet his contribution was special. In his heyday, between 1925 and 1933, he brought a uniquely clear vision to the development of a new branch of science: the book of nature often seemed to be open in front of him. Freeman Dyson sums up what made Dirac’s work so unusual:
The great papers of the other quantum pioneers were more ragged, less perfectly formed than Dirac’s. His great discoveries were like exquisitely carved marble statues falling out of the sky, one after another. He seemed to be able to conjure laws of nature from pure thought – it was this purity that made him unique.2
Dirac’s book The Principles of Quantum Mechanics was one of these statues, Dyson points out: ‘He presents quantum mechanics as a work of art, finished and polished.’ Never out of print, it remains the most insightful and stylish introduction to quantum mechanics and is still a powerful source of inspiration for the most able young theoretical physicists. Of all the textbooks they use, none presents the theory with such elegance and with such relentless logic, a quality of Dirac’s highlighted by Rudolf Peierls in 1972: ‘The thing about Dirac is that he has a way of thinking logically […] in a straight line, where we’d all tend to go off in a curve. It’s this absolutely straight thinking in unexpected ways that makes his works so characteristic.’3
Most young physicists, however, are concerned not with the internal logic of quantum mechanics but with using the theory as a way of getting quick and reliable results. In effect, it gives scientists a completely dependable set of practical tools for describing the atomic and molecular world. Every day, tens of thousands of researchers in the microelectronics industry routinely employ the techniques developed by Dirac and his colleagues: ideas that took years to clarify are now used without a thought for the headaches they once caused their creators.
The modern trend to miniaturisation is making quantum mechanics even more important. In the growing field of ultra-miniature technology – usually called nanotechnology (from the Greek word for dwarf, nanos) – quantum mechanics is as indispensable as classical mechanics was to Brunel. In one branch of this new technology, spin-tronics (short for spin-based electronics), engineers are trying to develop new devices that rely not only on controlling the flow of the charge of electrons – the way conventional devices work – but also the flow of the electrons’ spins. Because these can be flipped from one state to another much more quickly than charge can be moved around, spintronic devices should operate faster than conventional ones and produce less heat. If, as engineers hope, they can produce a spin-based transistor to replace conventional transistors in memory and logic circuits, it may be possible to continue the trend towards ever-more compact computers beyond the currently feasible limits.
It could be that, just over a century after Dirac first brought electron spin into the logical structure of quantum mechanics, his equation – once seen as mathematical hieroglyphics with no relevance to everyday life – becomes the theoretical basis of a multi-billion dollar industry.
Great thinkers are always posthumously productive. By this criterion, Dirac can be counted as one of the greatest of all scientists – many of the concepts he introduced are still being developed, still instrumental in modern thinking. The Dirac equation, for example, is still a fecund source of ideas for mathematicians, who have long been fascinated by spinors, mathematical objects that first appeared in the equation. In Sir Michael Atiyah’s opinion:
No one fully understands spinors. Their algebra is formally understood but their geometrical significance is mysterious. In some sense they describe the ‘square-root’ of geometry and, just as understanding the concept of the square root of –1 took centuries, the same might be true of spinors.4
Dirac’s influence is felt most strongly by scientists studying the universe’s tiniest constituents. Experimenters can now smash particles together with energies so high that even Rutherford would have been impressed: at the Large Hadron Collider, the huge particle accelerator at CERN, they can recreate the conditions of the universe to within a millionth of a millionth of a second of the beginning of time. During the subatomic collisions produced in this and other accelerators, experimenters routinely see subatomic particles created and destroyed, processes that can be explained only using relativistic quantum field theory. Dirac’s hand is all over this theory – he was one of its co-discoverers and the author of the action–principle formulation of quantum mechanics, now a crucial part of modern thinking about fields.
Over the past twenty-five years or so, the gap between the energies accessible by particle accelerators and the energies needed to test the latest theories has widened alarmingly. The building of the accelerators is increasingly difficult and expensive for the international collaborations needed to fund and operate them, so new devices come on stream only slowly. One consequence has been that the theory of subatomic particles has run ahead of the supply of data from experiment, producing a scenario of the type Dirac envisaged in his landmark paper of 1931 where he set out an agenda for theoretical physics led by mathematics rather than experiment. One physicist who believed this was prescient was C. N. Yang: at a Princeton meeting they both attended in 1979, Yang suggested that when Dirac set out this idea, he had hit on a ‘great truth’.5 In the same 1931 paper, Dirac suggested the existence of the anti-electron and the anti-proton and developed a quantum theory of magnetic monopoles using a geometric approach that has influenced generations of theoreticians. As experimenters were unable to detect monopoles, Dirac regarded this project as another disappointment, and he died believing it unlikely that monopoles occur in nature.6 But, today, many physicists disagree, as monopoles are predicted by some simple generalisations of the Standard Model (the ‘modern’ monopole is a mathematically better-defined relative of Dirac’s).7 Moreover, according to cosmologists, monopoles should have been created during the Big Bang in vast quantities and should now be detectable; that they are not is known as ‘the monopole problem’.
The detection of Dirac’s monopole would raise a question in virtual history: what would have been the effect on his reputation if the monopole had been detected around the time the positron was first observed? Such a pair of suc
cesses would have further bolstered his reputation among his colleagues and may well have made him much better known to the public. But there was never any chance that he would become a media celebrity like his most recent Lucasian successor, Stephen Hawking: it seemed not to have occurred to Dirac to write a popular book, nor would he have contemplated making the kind of forays into the media spotlight undertaken by Hawking, such as his appearances on Star Trek, The Simpsons and on the dance floor of a London nightclub.8 Yet Dirac admired such boldness more than most of his colleagues knew.
Dirac left his mark on several other fields besides quantum mechanics. One of his least typical contributions was his invention of a new way of separating different isotopes of a chemical element. He developed the method during the Second World War but it seemed that the idea was impracticable; it was soon forgotten, only to be independently rediscovered thirty years later by engineers in Germany and South Africa.9 His method still does not appear to be economically viable, but the development of new, ultra-strong materials still leaves open the possibility that the method could be used in the nuclear industry.
Another of Dirac’s less characteristic pieces of work was his exploration of the wave and particle nature of electrons with Kapitza in 1933. Modern improvements in laser technology provided fresh opportunities to verify the existence of the Kapitza–Dirac effect, the diffraction (bending) of a thin beam of electrons by a standing wave of light. Kapitza and Dirac had themselves discussed the new possibilities at the final meeting of the Kapitza Club in 1966. Several groups attempted to demonstrate the effect, but none was successful until, in the early spring of 2001, a team at the University of Nebraska observed it with a high-powered laser and a fine beam of electrons, using apparatus that would have fitted on a dining-room table.10 The Kapitza–Dirac effect is now used as a subtle probe of the wave-like and particle-like behaviours of both electrons and light.
Dirac also left a legacy in general relativity, if one not quite equal to his talent. It is a mystery that he showed so little interest in following up the discovery – made by Oppenheimer and his colleagues in 1939 – that Einstein’s theory predicted the existence of black holes, objects with such a strong gravitational field that not even light can escape them. In Dirac’s most important contribution to the theory of relativity, he set it out in analogy to his favourite Hamiltonian version of quantum mechanics and devised a set of complementary mathematical techniques (other physicists did similar work at about the same time).11 These methods have proved useful to astronomers studying closely spaced pairs of rotating neutron stars (usually called pulsars), orbiting each other, slowly losing energy. This gradual loss of energy can easily be explained by Einstein’s general theory of relativity, especially if it is interpreted using the methods Dirac co-invented: the pulsars emit gravitational radiation, in much the same way as accelerating electrons emit electromagnetic radiation. The study of gravitational waves is now one of the most promising areas of astronomy.
Dirac’s intuition for the workings of the universe on the largest scale was not nearly as strong as it was when he was focusing on atoms. There is, however, no denying the far-sightedness he showed when he reviewed the state of cosmology in the Scott Lecture he delivered shortly before the outbreak of the Second World War, when the subject was in its infancy. In one of a string of astute remarks he makes in passing, he hazarded an inspired guess that the complex structure of everything around us has its seeds in a quantum fluctuation in the initial state of the universe. ‘The new cosmology’, Dirac suggested, ‘will probably turn out to be philosophically even more revolutionary than relativity or the quantum theory,’ perhaps looking forward to the current bonanza in cosmology, where precise observations on some of the most distant objects in the universe verse are shedding light on the nature of reality, on the nature of matter and on the most advanced quantum theories. In the view of Nathan Seiberg, Dyson’s colleague at the Institute for Advanced Study, ‘The lecture would look just as impressive if the date on the front were not 1939 but 1999.’12
Although Dirac was, towards the end of his life, often defensive about his large numbers hypothesis, he always had faith in its truth.13 The modern view about the large numbers that fascinated him for decades is that only one of them is a mystery: the ratio between the strength of the electrical force and that of the gravitational force between an electron and a proton (1039). The fundamental problem is to understand why the gravitational force is so feeble compared with the other fundamental forces.14 All the other huge numbers that puzzled Dirac now follow from the standard theory of cosmology, so there is no need to guess links between them – the coincidences he spotted are illusory.15
Dirac was convinced that the strength of the gravitational force had fallen since the beginning of time, and he invested many of his later years in trying to prove it, though observations made by astronomers on nearby planets in the solar system have now all but ruled it out. Although it is still just possible that Dirac’s intuition was correct, the subject is currently low on today’s research agenda. One scientist who always believed in his bones that Dirac was right was Leopold Halpern, who left Florida State University in 2004 and became a resident theoretician with a satellite-based experimental programme run by NASA and Stanford University, aiming to check some of the unverified predictions of Einstein’s general theory of relativity.16 Halpern hoped to compare the predictions of his theory with the satellite’s observations but he was unable to complete his work before he died of cancer in June 2006.17
Regardless of how Dirac’s predictions about the gravitational force fare in the future, his name will always be associated with the role of anti-matter at the beginning of the universe. According to modern Big Bang theory, matter and anti-matter were created in exactly equal amounts, at the very beginning of the universe, about 13.7 billion years ago. Soon afterwards, the decay of some of the heavy particles formed from the quarks and anti-quarks led to a small but crucial surfeit of matter over anti-matter, by just one part in a billion. The first scientist to analyse this difference in detail was Tamm’s student Andrei Sakharov – later a courageous human-rights activist in the Soviet Union – who discussed in 1967 how this excess came about and why the universe was left with an overwhelming preponderance of matter. Without that imbalance, the matter and anti-matter formed at the beginning of time would have annihilated each other immediately, so that the entire universe would only ever have amounted to a brief bath of high-energy light. Matter would, in that case, never have had the opportunity to discover anti-matter.18
The surplus of matter over anti-matter at the beginning of the universe is still not understood, and thousands of physicists are working to understand it. Their main sources of experimental information are particle accelerators, where anti-matter is produced by smashing ordinary particles into each other and then quickly ‘separating off’ the anti-matter, before it is annihilated by matter. By comparing the decays of particles with those of their anti-particles, experimenters hope to get to the bottom of the matter–antimatter imbalance.
Every day, particle accelerators now generate about a hundred thousand billion positrons and five thousand billion anti-protons – a total of roughly a billionth of a gram. Although this quantity is only tiny, the ability to produce it at will demonstrates that Homo sapiens now – a million years after our species evolved – uses anti-matter as a tool. Today, positrons are routinely generated in mass-produced equipment all over the world: doctors use positron emission tomography (PET) to see inside their patients’ brains and hearts, without the need for surgery. It is a simple technique: the patient is injected with a tiny amount of a special radioactive chemical that spontaneously emits positrons, which interact with electrons in the tissue where the chemical settles. The photograph is a record of the radiation given off in the electron–positron annihilations.
Within just a few decades, positrons changed in the eyes of scientists from appearing outlandish novelties to being just another type of
subatomic quantum; the public has become more familiar with anti-matter, too, from the fictional treatments of it in, for example, Star Trek and Dan Brown’s Angels and Demons. But what is most remarkable about the story of anti-matter is that human beings first understood and perceived it not through sight, smell, taste and touch but through purely theoretical reasoning inside Dirac’s head.
*
Like Einstein, Dirac was fundamentally in search of generalisations – theories that explain more and more about the universe, in terms of fewer and fewer principles. Both men believed, too, that the best way of achieving this was through theories expressed in terms of beautiful equations.19 As a physicist, Dirac had been well served by mathematics, as he wrote in an unusually candid passage in 1975:
If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until [this happened]. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.20
Although he never acknowledged it in public, the guiding hand of beauty had led Dirac not only to some rich new pastures of research but also into the deserts that yielded no fruit at all. In his talks, he was an ambassador of mathematical beauty, repeatedly underlining the triumphs of theories with this quality but not mentioning the years he had spent trying in vain to use sensually appealing mathematics to describe nature. It is striking that he put forward the principle of mathematical beauty several years after he had done his best work, and we have to suspect that some of his accounts of his greatest discoveries – usually portrayed as successes for his type of aestheticism – were reinterpreted in the light of his faith in the principle. In his pioneering papers on quantum mechanics, he never explicitly says that beauty was his guide; he recalled its value only in the tranquillity of his least productive years.21
The Strangest Man Page 63