[asa] Paul Dirac, a man apart

From: Alexanian, Moorad <alexanian@uncw.edu>
Date: Tue Nov 10 2009 - 14:19:40 EST


Note the following:

Dirac points out that if the universe were simply what follows from a given set of equations of motion with trivial initial conditions, it could not possibly explain the complexity of the universe down to the teeming life forms on Earth. But quantum mechanics, he argues, can explain that complexity by attributing it to quantum jumps in the very early universe. Dirac seems to have known that he had hit on an important insight as he, unusually, summarized the point in italics: “ The quantum jumps now form the uncalculable part of natural phenomena, to replace the initial conditions of the old mechanistic view. ” Nima Arkani-Hamed, Seiberg’s colleague at the IAS, remarked to me, “This is an amazing insight. Although Dirac didn’t know the details of how the universe develops, such as the modern theory of inflation, he got the overarching concept dead right. So he was a bit like Darwin, coming up with evolution by natural selection without knowing anything about the underlying ge!

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Published: November 2009

Paul Dirac, a man apart

Dirac practiced theoretical physics for almost 60 years with a unique style: a sometimes baffling combination of intuition, imagination, rectilinear logic, and steam-hammer mathematical power.

Graham Farmelo<http://ptonline.aip.org/servlet/PrintPTJ#bio>
November 2009, page 46


Often called “the theorist’s theorist,” Paul Dirac was one of science’s archetypal loners, shy and taciturn, apparently devoid of empathy. Late in his life, when physicists cold-called him to ask if he would care to chat about some idea that had appeared in his papers, he would cut them off firmly, saying “I think people should work on their own ideas,” before putting the phone down.

Dirac is most famous for contributions to the development of quantum mechanics, begun by Werner Heisenberg and Erwin Schrödinger in 1925, when Dirac was 23. Among the early papers on the theory, Dirac’s stand out, as Freeman Dyson has pointed out: “His great discoveries were like exquisitely carved marble statues falling out of the sky, one after another.”1<http://ptonline.aip.org/servlet/PrintPTJ#ref> Although Dirac was widely admired as a scientific magician, many physicists—especially ones in Berlin and in Göttingen, Germany, where many of the foundational papers on quantum mechanics were written—found his language impenetrable, his reasoning hard to fathom, and his manner cold and distant. Albert Einstein was among those who were perplexed: “I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful.” Niels Bohr, impressed by Dirac though puzzled by his indifference to philosophical questions about the new theory, said he was “the !
 strangest man who ever visited my institute.” 2<http://ptonline.aip.org/servlet/PrintPTJ#ref>

Dirac’s singular personality and his approach to theoretical physics had their origins in his upbringing in Bristol, the largest city in southwest England. By his own account, he had a tragically loveless and asocial childhood but a rich education in science, mathematics, and engineering. By the time Dirac arrived at Cambridge University eight weeks after his 21st birthday to begin his PhD, his knowledge of modern physics was patchy, but he had already taken two undergraduate degrees, in electrical engineering and in applied mathematics. He was an extremely unusual student, an outsider ready to make his unique mark on science, but few would have guessed that he was destined to be the most accomplished researcher Britain produced in the 20th century.

He never had a childhood, Dirac later said. According to his recollections of his early years—no others have survived—his life at home was miserable, largely because of his domineering father, a Swiss schoolteacher who insisted that the family receive virtually no visitors and that his children (Dirac, his elder brother, and his younger sister) speak with him only in French. At mealtimes, the Dirac family would split up: In the front room, he and his father would talk only in French, while his mother and his siblings ate in the kitchen and spoke only in English. A well-researched newspaper article written in 1933 reported that Dirac believed as a small boy that men and women spoke different languages. His disciplinarian father would punish him for the slightest grammatical error, even denying requests to go to the bathroom. As a result, Dirac recalled, he thought it best to avoid punishment by staying silent. Such was his explanation for his reluctance to speak unless there !
 was a very good reason.

At elementary school, he was successful though not exceptional (one of his fellow students was Archie Leach, later known as Cary Grant). Dirac came into his own in high school, where he studied for the duration of World War I. Many of the boys joined the armed services; the vacancies they left in higher-level classes at the school enabled bright students like Dirac to make rapid progress. The school gave him a first-class practical education that allowed him to avoid Latin and Greek and other subjects unlikely to be useful in getting a job. He excelled in almost every subject but especially in math, science, and technical drawing. By his early teens, Dirac was far ahead of the rest of his class and already reflecting on the nature of space and time, although he knew nothing of relativity. Fellow students perceived him to be odd and withdrawn; one witness described him as “a slim, tall, un-English looking boy in knickerbockers and curly hair.” A math teacher, despairing of se!
 tting Dirac homework problems that would keep him occupied, decided to invite him to study Riemannian geometry, an invitation he accepted.

By the time Dirac was 16, he was ready for university studies. Unsure about which subject to study, he decided to join his brother by taking a degree in engineering at Bristol University. Dirac munched his way through theoretical work but was hopelessly inept in the laboratory, where he spent most afternoons soldering circuits, operating lathes, load-testing beams, engaging in other rites of passage for the student engineer.

A mind captured by ideas

Although busy, he needed a challenge. Sure enough, one came along in late 1919, shortly after he and his family gave up their Swiss citizenship and became British, when Einstein’s general theory “burst upon the world,” as Dirac later put it. He and his fellow students were caught up in the excitement following the sensational news that data from the recent solar eclipse appeared to demonstrate that Einstein’s theory accounted better than Newton’s for the bending of starlight by the Sun. (See the article by Daniel Kennefick in PHYSICS TODAY, March 2009, page 37<http://dx.doi.org/10.1063/1.3099578>.) It was difficult for Dirac to find out what lay behind the headlines; details of the theory were scarce, and most of the catchpenny booklets on Einstein’s work were insubstantial, misleading, and often wrong.

Dirac’s appetite for more details was sated when he sat in on a course given by philosopher Charlie Broad on scientific thought, which focused on Einstein’s special and general theories of relativity. Broad had been trained in natural philosophy at Cambridge and had a gift for summarizing new ideas accurately and entertainingly (he read every sentence of his carefully prepared lecture notes twice, except for the jokes, which he read three times). Dirac’s imagination was captured by the way fundamental ideas, expressed in mathematical form, could be used to guess the laws of nature. Aged 17, he was on the road to becoming a theoretical physicist.

In July 1921 Dirac was awarded a first-class honors degree and, soon afterwards, a certificate of unemployment. The British economy was then faltering and jobs were scarce; Dirac went to several interviews but to no avail. David Robertson, one of his lecturers in the engineering department, took the initiative of arranging for him to freeload on the university’s mathematics degree program, skipping the first year. During his studies of pure mathematics, Dirac took courses given by Peter Fraser, who never wrote a research paper in his life but was a superb teacher—the best Dirac ever had, he would later say. Fraser’s passion was projective geometry, the study of geometric properties invariant under special transformations—a subject closely related to geometric drawing, which Dirac had been studying for almost a decade. Although the lectures on pure mathematics were Dirac’s favorites, he spent most of his time in a course of applied mathematics, solving hundreds of problems us!
 ing Newtonian mechanics and attending several lectures on relativity. In that course he probably knew more than his lecturer.

When Dirac arrived at Cambridge for his PhD in October 1923, the school authorities knew they had an unusual student. A report from a talent scout in Bristol said that Dirac “is a bit uncouth, and wants some sitting on hard, is rather a recluse, plays no games, [and] is very badly off financially.” His performance in the entrance examinations had impressed the authorities, and they were eager to give him a postgraduate place (he would have been ineligible to take an undergraduate course as he had neither Latin nor Greek). Although there were wide gaps in his knowledge, including Maxwell’s equations, he plainly had a special talent for mathematics and brought with him the skills and sensibilities of a well-trained engineer.

Dirac had wanted to begin his research in relativity, so he was disappointed to be told that his adviser was Ralph Fowler, an expert on statistical mechanics and quantum theory. Soon Dirac realized, however, that he had one of the best advisers in Cambridge—someone well-connected, encouraging, and capable of identifying tractable problems. Dirac established himself as a first-rate student, quickly and imaginatively solving the problems set by Fowler. He also continued to study projective geometry in his spare time and assuaged his appetite for special relativity by taking up the unusual hobby of finding relativistic versions of various classical theories.

So far as one can tell from the ultraconcise postcards he wrote home, Dirac seems to have been fairly content. But in the spring of 1925 he suffered a terrible blow when he heard that his brother—from whom he was by then estranged—had taken his own life by drinking potassium cyanide. No record of Dirac’s initial reaction to the tragedy exists, but it was a subject he found too painful to discuss in later life, even with his wife; he did remark to close friends, though, that he blamed his brother’s death on their bullying father. After Dirac heard the news, his productivity dropped sharply, and by the time he returned to Bristol that summer, he had published nothing for months. Out of the blue, toward the end of the vacation, he received an envelope whose contents would change his life.

The envelope, sent by Fowler, contained a proof copy of an article—now recognized as the first published on quantum mechanics—by Werner Heisenberg.3<http://ptonline.aip.org/servlet/PrintPTJ#ref> At first, Dirac thought it too complicated and put it aside. But about two weeks later, his attention was caught by a few lines in which Heisenberg noted parenthetically that one apparent flaw with his theory was that its position and momentum variables did not commute, though he implied that the problem was not insuperable. In the following weeks, Dirac focused on the phrase and realized that it contained the key to quantum mechanics. He constructed his own version of quantum mechanics, in close analogy to the classical theory of the Poisson bracket, which is important in determining the time development of a dynamical system. His first paper on the subject, “The Fundamental Equations of Quantum Mechanics,” 4<http://ptonline.aip.org/servlet/PrintPTJ#ref> deeply impressed Heisenberg,!
  Max Born, and their colleagues in Göttingen. Forty years later Heisenberg remarked in a BBC interview that none of them had heard of Dirac but had guessed that he was a leading mathematician.

Dirac’s early papers on quantum mechanics are remarkable for their insightfulness and elegance. Many of them still look fresh and remarkably modern. In the mid-to-late 1920s, the book of nature seemed open in front of him: He produced one great paper after another, codiscovering quantum transformation theory and quantum field theory, dispersion theory, the density matrix, and hole theory, and he made several other groundbreaking contributions. Scholars puzzled over the insights that underpinned his stream of papers, but they did not receive much help from Dirac until the 1960s, when he began to talk about his early work. In one telling remark, he said that he had used projective geometry in his earliest papers; he had neglected to mention the mathematics in the papers themselves partly because he thought it was unfamiliar to other physicists. In 1971, when asked by Roger Penrose at a lecture at Boston University to explain how he had used that geometry in those papers, Dirac!
  refused, gently shaking his head. He did, however, shed light on the inspiration for the delta function in a 1963 interview, when he traced it back to his studies in engineering:

When you think of . . . engineering structures, sometimes you have a distributed load and sometimes you have a concentrated load at the point. Well, it is essentially the same . . . but you use somewhat different equations in the two cases. Essentially it’s only to unify these two things which sort of led to the delta function.

Perhaps the highlight of Dirac’s creative streak was the 1928 publication of his equation for the electron.5<http://ptonline.aip.org/servlet/PrintPTJ#ref> Consistent with both quantum mechanics and special relativity, the equation accounted, at a stroke, for the particle’s spin and magnetic moment. Three years later he used the equation to foresee the existence of the antielectron, in a comment he made almost in passing in his pathbreaking paper on magnetic monopoles.6<http://ptonline.aip.org/servlet/PrintPTJ#ref> The nearest Dirac came to a forthright prediction of the antielectron was at the end of a series of lectures at Princeton University in the fall of 1931, though there is no evidence that he actually encouraged experimenters to hunt for the new particle. The first experimenter to publish evidence for a particle with the same mass as the electron but with opposite charge was Carl Anderson at Caltech in August 1932. But he did not mention Dirac’s work, and it wasn’t u!
 ntil several months later that the community realized that Anderson had discovered Dirac’s antielectron. Thirty years later Dirac remarked, with an Olympian detachment that became his trademark, that he derived greatest satisfaction not from the discovery of antielectrons but from getting the equations right.

The successful prediction impressed the Nobel Prize committee, which had been reluctant to award a prize for quantum mechanics until it had garnered sufficient experimental support. In November 1933, just over a year after Dirac became Lucasian Professor at Cambridge, the Nobel committee announced that he would receive a half share of that year’s prize with Erwin Schrödinger and retroactively awarded Heisenberg the 1932 prize. Dirac had become the youngest theoretician ever to win the Nobel Prize in Physics, a record that stood until 1957, when it was broken (by a margin of a few months) by T. D. Lee.

Opposition to QED



After Dirac won the prize, a few weeks after he presented his ideas on the vacuum polarization, his golden streak came to an end. He was becoming disenchanted with quantum electrodynamics (QED) and was deeply perturbed that the theory’s prediction of infinities for many of the observables rendered the calculations meaningless. In late 1936 he briefly turned his attention to cosmology and set out his controversial large-numbers hypothesis, according to which simple, linear equations link the vast numbers that occur in cosmology.

A few years later Dirac accepted an invitation to give the James Scott Lecture on his philosophy of physics. His acceptance was quite a surprise, as Dirac openly disdained the philosophy of science; in 1963 he would describe the subject as “just a way of talking about discoveries that have already been made.” But Dirac did not disappoint his audience in Edinburgh when he spoke in February 1939 about “the relation between mathematics and physics”; he gave an insightful lecture in plain language, without using a single abstract mathematical symbol. 7<http://ptonline.aip.org/servlet/PrintPTJ#ref> Even his introductory comments were pleasingly direct: “The mathematician plays a game in which he himself invents the rules, while the physicist plays a game in which the rules are provided by Nature.”

He suggested that theoretical physicists should seek fundamental physical laws with the greatest possible mathematical beauty. He had no patience with the obvious question of what, objectively, constitutes that kind of aesthetic quality: “This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating.” Dirac later said that his belief in what he called the principle of mathematical beauty became “like a religion” to him and his friend Schrödinger.

The change in direction of Dirac’s research coincided with important events in his personal life. His father, who had Dirac under his thumb until the end of his life, died in June 1936. After the funeral, Dirac was relieved: “I feel much more free now; I feel I am now my own master.” He wrote those words to his close friend Margit Balázs, the divorced sister of his Hungarian friend and colleague Eugene Wigner. Within six months she and Dirac were married. It was an improbable union, as she was in many ways his opposite—talkative, gregarious, and opinionated. Yet the marriage worked, yielded two daughters, and lasted almost five decades. Dirac became a self-styled family man, keen on tending his garden and lawn, still dedicated to theoretical physics but increasingly detached from the mainstream. During World War II, he was a consultant to the secret British group working on the nuclear bomb, spending part of the time developing an idea he had conceived for separating isotope!
 s using an apparatus with no moving parts. Yet he did not entirely give up theoretical physics. He was one of the few theoreticians who continued to work on QED during the war, and he kept in touch with his refugee colleagues Schrödinger and Wolfgang Pauli.

By the early 1950s, the next generation of theoreticians—notably Dyson, Richard Feynman, Julian Schwinger, and Sin-itiro Tomonaga—had developed a completely robust theory of QED that had its troublesome infinities systematically removed by the process of renormalization. The theory’s agreement with experiment was excellent, but Dirac was unimpressed. When Dyson asked him what he thought of the new theoretical developments, Dirac did not mince his words: “I might have thought that the new ideas were correct if they had not been so ugly.”

Dirac thought it foolish to try to advance particle physics until the interaction between the photon and the electron was better understood. Virtually ignoring new work on the weak and strong interactions, he became somewhat detached from his research community and his productivity dropped sharply. In the late 1950s and early 1960s, when he was trying to set out a quantum theory of gravity, he did important work on a Hamiltonian formulation of the general theory of relativity and on the quantum theory of constrained systems. Those were weighty contributions, but the majority of Dirac’s colleagues saw him as working in the backwaters of his subject, someone to be honored rather than listened to. Two years after retirement from his Lucasian professorship at Cambridge in 1969, he joined the physics department at Florida State University in Tallahassee and traveled the world giving lectures mainly about his philosophical approach to physics; he never tired of pointing out what h!
 e saw as the crippling shortcomings of QED and urged younger colleagues to develop a revolutionary theory to replace the one he had codiscovered.

In his 1980 lecture “The Engineer and the Physicist,” Dirac shed light on his adamantine opposition to QED by suggesting that his view originated in his training as an engineer. Renormalization entails a practice that no self-respecting engineer would countenance, Dirac said: the neglect of infinite terms in a series that approximates to a real, measurable quantity. To neglect infinitely large quantities in such an equation was, in his estimation, absurd. Other engineers might take a more practical approach and accept a theory on the ground that it works, giving excellent agreement with experiment. Yet Dirac could not accept that, for he was an unusual engineer—one with the sensibilities of an accomplished pure mathematician.

“The main problem of the engineer is to decide which approximations to make,” he said. A good engineer makes wise, often intuitive choices about the mathematical terms one can ignore in equations: “The terms neglected must be small and their neglect must not have a big influence on the result. He must not neglect terms that are not small.”

Principled but cranky

Like great poems, Dirac’s papers reward repeated reading. Over and over again, researchers have found ideas and insights in papers that made little impact when they were first published. A case in point is his 1939 paper on the relation between mathematics and physics, which is still being passed around among the theoretical physicists at the Institute for Advanced Study (IAS) in Princeton, New Jersey. Among them, Nathan Seiberg recently told me, “This paper would look just as impressive if the date on the front were not 1939 but 2009.”

In one especially striking passage, Dirac speculates on the conditions at the very beginning of the universe (even in 1939, he accepted that it began in what his student Fred Hoyle later called the Big Bang). Dirac points out that if the universe were simply what follows from a given set of equations of motion with trivial initial conditions, it could not possibly explain the complexity of the universe down to the teeming life forms on Earth. But quantum mechanics, he argues, can explain that complexity by attributing it to quantum jumps in the very early universe. Dirac seems to have known that he had hit on an important insight as he, unusually, summarized the point in italics: “ The quantum jumps now form the uncalculable part of natural phenomena, to replace the initial conditions of the old mechanistic view. ” Nima Arkani-Hamed, Seiberg’s colleague at the IAS, remarked to me, “This is an amazing insight. Although Dirac didn’t know the details of how the universe develop!
 s, such as the modern theory of inflation, he got the overarching concept dead right. So he was a bit like Darwin, coming up with evolution by natural selection without knowing anything about the underlying genetics.”

Arkani-Hamed also underlined the value of Dirac’s technical papers to modern physicists, including string theorists. At the beginning of the 1970s, a young generation of physicists developing string theory realized that they were following in Dirac’s footsteps. Not only had he proposed extended objects as models for elementary particles, but in his theory of the quantization of mechanical systems subject to constraints, he also had developed the techniques the theorists needed to understand the quantum dynamics of a relativistic string. As physicists in the mid-1970s sought to understand the properties of magnetic monopoles, which occur naturally in many modern theories of fundamental particles, they found the path had been set again by Dirac in 1931 and in a later paper written in 1948.8<http://ptonline.aip.org/servlet/PrintPTJ#ref>

Dirac appears to have paid little or no attention to early papers on string theory or to the more mainstream work in the 1970s done by physicists who were putting together the standard model. Disillusioned with QED, Dirac concentrated on trying to link general relativity with his large-numbers hypothesis. And he knew that many physicists regarded him as principled but cranky. Although Dirac had a thick skin, his morale was sometimes low. No doubt mindful of that, Princeton physicist John Wheeler wrote him a characteristically sensitive note on his 80th birthday:

I write to tell you what I am not sure you divine, how many of the younger generation as well as older ones look up to you as a hero, as a model of how to do things right, of passion for rectitude as well as beauty.9<http://ptonline.aip.org/servlet/PrintPTJ#ref>

Dirac kept the note in his desk. Less than two years later, on 20 October 1984, he died of heart failure at home in Tallahassee, his wife and nurse at his bedside. He worked until the end, but his contributions to physics did not end with his passing. Like all truly great thinkers, he has proved to be posthumously productive.

Graham Farmelo, an adjunct professor of physics at Northeastern University, in Boston, is author of The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom (Basic Books, 2009).


 1. 1. Unless otherwise noted, the sources of quotations in this article are available in G. Farmelo, The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom, Basic Books, New York (2009).
 2. 2. K. Gottfried, [LINK]<http://arxiv.org/abs/quant-ph/0302041v1>, p. 9.
 3. 3. W. Heisenberg, Z. Phys. 33, 879 (1925)<http://dx.doi.org/10.1007/BF01328377> .
 4. 4. P. A. M. Dirac, Proc. R. Soc. London, Ser. A 109, 642 (1925)<http://dx.doi.org/10.1098/rspa.1925.0150> .
 5. 5. P. A. M. Dirac, Proc. R. Soc. London, Ser. A 117, 610 (1928)<http://dx.doi.org/10.1098/rspa.1928.0023> .
 6. 6. P. A. M. Dirac, Proc. R. Soc. London, Ser. A 133, 60 (1931)<http://dx.doi.org/10.1098/rspa.1931.0130> .
 7. 7. P. A. M. Dirac, Proc. R. Soc. Edinburgh, Sect. A: Math. Phys. Sci. 59, 122 (1938–39).
 8. 8. P. A. M. Dirac, Phys. Rev. 74, 817 (1948)<http://dx.doi.org/10.1103/PhysRev.74.817> [SPIN]<http://scitation.aip.org/getabs/servlet/GetabsServlet?key=PHTOAD&prog=spinref&id=PHRVAO000074000007000817000001&idtype=cvips&linksmith=yes>.
 9. 9. J. Wheeler to P. A. M. Dirac, 8 August 1982, General Correspondence, Paul A. M. Dirac Collection, Paul A. M. Dirac Library, Florida State University, Tallahassee.

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