Paul Dirac: The Laconic Genius of Quantum Theory

April 1, 2010


P.A.M. Dirac and Richard Feynman, Warsaw, 1962. From The Strangest Man.
Book Review
Philip J. Davis


The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom. By Graham Farmelo, Basic Books, New York, 2009, 539 pages, $29.95.

Biographers of the famous have a tendency to produce lengthy books. There is a 500-page biography of Norman Mailer, a 750-page biography of Marilyn Monroe. There is a six-volume biography of Benjamin Disraeli, a three-volume biography of Henry James. Robert Caro has written three volumes on Lyndon Johnson, with a fourth yet to come. But even this is not the whole story: For every major biography there may be dozens of shorter works, often concentrating on some particular aspect of the subject's life.

Why so much? I can think of many reasons. These books provide a permanent memorial of archival value for persons of extraordinary accomplishment. They reveal the texture of time and place, the play and the clash of personality. Biographers raise and possibly satisfy the hope that by detailing the micro-events and the thoughts of their subjects, they can reveal the sources of genius. Biographies satisfy the curiosity of a prurient public, who feel superior when heroes of superior achievements are displayed with warts and clay feet. There is yet another reason: Biographers often "fall in love" with their subjects; they can't find out enough, or write enough, about them.

But now to the biography of Paul Adrien Maurice Dirac. Born in Bristol, England, in 1902, he died in Tallahassee, Florida, in 1984. In a work that is plainly a labor of love, Graham Farmelo, a professor of physics at Northeastern University, has described what came in between, in painstaking detail and with full bibliographical references. He has really combined two books into one.

Dirac arrived in Cambridge as a student in 1923 and remained there essentially until 1971, when, laden with honors, bearing an international reputation as a giant in the scientific world, wooed by innumerable universities, having shaken hands warmly with Pope John Paul II in the Vatican, he settled in at Florida State University in Tallahassee as "Visiting Eminent Professor."

The first of the books embedded in The Strangest Man is about Dirac the theoretician's theoretician, the man responsible for a crucial piece of the explanation of fundamental particles and forces. It is about quantum mechanics and about Dirac's "equation," which he proposed in 1928 at the age of 26, thereby marrying the quantum physics of Schrödinger and Heisenberg with Einstein's special relativity. That book is about Dirac the Nobelist (1933).

As a young man, Dirac had come across and admired the descriptive geometry of Gaspard Monge (1746–1818), and he reacted strongly to the great beauty inherent in mathematics. He began to think of mathematics as a game in which we invent the rules (an early variety of social constructivism?). Farmelo points out that there are two modes of theorizing in the physical sciences: bottom-up and top-down. A scientist working in the bottom-up mode proceeds from experiment to theory (often expressed mathematically); a top-down scientist does the reverse. In practice, of course, scientific research moves back and forth between these modes.

Dirac was a top-down thinker. He believed that he could describe the world by pure and beautiful mathematical ideas, culled, as it were, from pure cogitation. His genius (and his luck?) was that he was able to derive physical consequences from his equations, rather than the reverse. Thus, he predicted the existence of antiparticles, subsequently discovered in detailed studies of cosmic rays, and this led to a shared Nobel Prize for physics with Schrödinger in 1933. Niels Bohr once famously rapped Einstein's knuckles: "Albert: Don't tell God what to do"; Dirac, who was an atheist, seems in retrospect to have done just that.

Although he is known primarily for his contributions to quantum physics, Dirac's ideas (or perhaps his formalisms) have left a residue in mathematics substantial enough that there is every reason for his biography to be considered in these pages. The Dirac delta function may have origins as far back as 1822, in the work of Fourier, yet it now bears Dirac's name. By classical standards of mathematical rigor, such a function is illegitimate, i.e., it ought not to exist. The later "legitimization" of the Dirac delta function and its reformulation as a measure, as a distribution, as the limit of approximations have been a minor industry within pure mathematics. What might now be called the special function theory of the Dirac delta function is enshrined in 25 equations in DLMF, the new Digital Library of Mathematical Functions of the National Institute of Standards and Technology.

As the years pass, as major ideas and developments enter the intellectual mainstream, their originators tend to recede in public memory; they sometimes become adjectives, possibly even losing their capitalizations. Thus, I can write without eyebrows raised too high about platonic philosophies, or refer to degrees fahrenheit, ohms of resistance, amps of current, even newtons of force, with hardly a thought of the men behind the units. Dirac is not there yet, but presumably he will be admitted shortly to the lower-case Valhalla.

The second of the books embedded within The Strangest Man might be read as an Edwardian novel written by John Galsworthy. It is engaging; it flows along nicely and could very well be made into a BBC TV series. Farmelo describes Dirac's family in great detail: his grandparents, parents, siblings, children; the family's origins in Switzerland, its mental health, its social position, its animosities, its tragedies; and the tedious particulars of our protagonist's frequent comings and goings.

In this second book, you can learn of Dirac's marriage to Margit Wigner, the sister of Eugene Wigner, and of its ups and downs. Here also are described Dirac's aloofness, his defensiveness, his obsessions, his sharp, terse, laconic statements. "What would you say if I told you I was leaving?" his wife once asked him. "I'd say good-bye" was Dirac's response.

Dirac is described here as a man with an obsession for taking long walks and a fondness for mountain climbing; a man who eschewed pickles but loved Mickey Mouse films, especially those featuring Horace Horsecollar. You can even learn that his father was remiss in his tax payments and that late in life Dirac reacted with virulent outbursts to his treatment by this rigid parent. Here also is the story of his older brother Felix, who turned Buddhist and dabbled in astrology and who ultimately committed suicide. Much more significantly, you can read that some observers have seen in Dirac's genius, and in his tendency to plow through life as though no one else in the world was of any consequence, the significant influence of autism or Asperger's syndrome.

After Dirac's death, the question arose as to whether he might be memorialized in the science corner of Westminster Abbey. The dean of Westminster objected that Dirac was a "militant atheist" and even quoted the prickly Wolfgang Pauli: "There is no God and Dirac is his prophet."

Years passed. A new dean was reminded that Dirac had been a member of the Papal Academy. Objections withered, and in Nov-ember 1995, in the presence of Stephen Hawking (one of Dirac's grandstudents), of Sir Michael Atiyah, of Dirac's daughter and his grandchildren, a memorial stone was unveiled in the nave of the Abbey. It bears Dirac's name, his dates, and his equation.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at philip_davis@brown.edu.



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