Paul Dirac

• 1. Introduction

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  Paul Adrien Maurice Dirac was born on the 8th of August 1902 in Bristol, England, and died on the 20th of October 1984 in Tallahassee, Florida. In the eighty-two years between those dates, he wrote an equation that predicted the existence of antimatter before anyone had seen it. He built the theoretical scaffolding for quantum field theory, the framework that underlies every description of subatomic forces we have today. And he did much of it in near silence, earning a Cambridge unit of measurement named in his honour: one "dirac", equal to one word per hour.

  Who was this man that Albert Einstein said gave physics "the most logically perfect presentation" of quantum mechanics? How did a boy trained in electrical engineering become the founder of quantum electrodynamics? And what drove him to keep searching, right to the last paper he ever published, for a mathematical structure he never quite found?

• 2. Bristol Beginnings

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  Charles Adrien Ladislas Dirac arrived in Bristol from Saint-Maurice, Switzerland, as a French teacher, and he ran his household with a strict linguistic rule: his children were to speak to him only in French. For Paul, the effect was unexpected. When he could not find the right French words, he simply said nothing. That habit of silence, imposed in childhood, stayed with him for the rest of his life.

  Paul's mother, Florence Hannah Holten, came from a Cornish Methodist family in Liskeard, Cornwall. Her father, a ship's captain, had named her after Florence Nightingale after meeting Nightingale during the Crimean War. Florence worked as a librarian at the Bristol Central Library, though she always thought of herself as Cornish rather than English.

  Paul's older brother, Reginald Charles Felix, known as Felix, died by suicide in March 1925. Dirac later recalled: "My parents were terribly distressed. I didn't know they cared so much... I never knew that parents were supposed to care for their children, but from then on I knew." The family had not been naturalised British subjects until the 22nd of October 1919; before that date, Charles and his children were officially Swiss nationals.

  One of Paul's classmates at Bishop Road Primary School was Archibald Leach, later known to the world as Cary Grant. At the Merchant Venturers' Technical College, Paul absorbed subjects unusual for British secondary education at the time: bricklaying, shoemaking, metalwork, modern languages. He would later express gratitude for an education that trained him in practical making rather than the classics.

• 3. The Road to Cambridge

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  Dirac passed the entrance examination for St John's College, Cambridge, shortly before completing his engineering degree in 1921, and was awarded a scholarship of seventy pounds. The sum was not enough to live on. The post-war economic depression meant he could not find work as an engineer either, despite graduating with first-class honours. He returned instead to the University of Bristol to study mathematics free of charge, skipping his first year on the strength of his engineering background.

  Under the influence of a teacher named Peter Fraser, whom Dirac called the best mathematics teacher he had, his interest moved toward projective geometry and then to Hermann Minkowski's geometrical treatment of special relativity. By 1923 he graduated with first-class honours again and received a scholarship of one hundred and forty pounds from the Department of Scientific and Industrial Research. Combined with his seventy-pound scholarship from St John's College, it was finally enough.

  At Cambridge, he worked under Ralph Fowler, pursuing the theory of general relativity and the new field of quantum physics. From 1925 to 1928 he held an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851. He completed his doctorate in June 1926, with the first thesis on quantum mechanics to be submitted anywhere in the world. He then continued his research in Copenhagen and Gottingen before visiting the University of Wisconsin-Madison as a visiting professor in the spring of 1929.

• 4. The Quantum Breakthrough

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  Late in September 1925, Ralph Fowler sent Dirac a proof copy of a new paper by Werner Heisenberg, asking him to look into it carefully. Dirac was on vacation in Bristol at the time. In the paper, Heisenberg was working in the framework of Bohr and Sommerfeld's old quantum theory, and he had changed the equations to involve only directly observable quantities. The result was a mysterious mathematical relationship that Dirac initially found unintelligible.

  Weeks later, back in Cambridge, Dirac recognised that the mathematical form in Heisenberg's paper had exactly the same structure as the Poisson brackets from classical particle dynamics. His memory of Poisson brackets was vague, so he turned to E. T. Whittaker's book Analytical Dynamics of Particles and Rigid Bodies for guidance. From that recognition, Dirac built a quantum theory based on non-commuting dynamical variables. The formulation was more general than anything before it, and it allowed him to derive the quantisation rules in a new and more transparent way. The work earned him his Cambridge PhD in 1926.

  Shortly after Wolfgang Pauli proposed his exclusion principle, stating that two electrons cannot occupy the same quantum energy level, Enrico Fermi and Dirac independently recognised that the principle would fundamentally alter the statistical mechanics of electron systems. Their joint insight became what is now called Fermi-Dirac statistics. It applies to any system of many identical particles with half-integer spin, a category that includes electrons in solids and liquids, and it is essential to understanding how electrical conduction works in semiconductors.

• 5. The Equation That Predicted Antimatter

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  In 1928, Dirac proposed what became known as the Dirac equation: a relativistic equation of motion for the wave function of the electron. He built it using spin matrices he believed he had discovered independently of Pauli's earlier work on non-relativistic spin. He told the physicist Abraham Pais: "I believe I got these matrices independently of Pauli and possibly Pauli got these independently of me."

  The equation fused special relativity with quantum mechanics. Among its consequences was a mathematical prediction that every fermion particle must have an antiparticle of equal mass and opposite charge. For the electron, that partner would be positively charged. Carl Anderson observed this positron experimentally in 1932, confirming the prediction four years after the equation was written down. The equation also explained quantum spin as a consequence of relativity rather than an additional assumption. Werner Heisenberg later reinterpreted the Dirac equation in 1934 as a field equation accurately describing all elementary matter particles, a category that today encompasses quarks and leptons.

  Dirac's 1930 book The Principles of Quantum Mechanics gathered the preceding work of Heisenberg on matrix mechanics and of Erwin Schrodinger on wave mechanics into a single mathematical framework. The book introduced the Dirac delta function and, in its third edition, the bra-ket notation that physicists still use daily. Subrahmanyan Chandrasekhar, who attended Dirac's lectures on quantum mechanics four times in 1930, described them as "just like a piece of music you want to hear over and over again."

• 6. The Man Behind the Silence

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  Albert Einstein, writing to Paul Ehrenfest in 1926 about a Dirac paper, said: "I am toiling over Dirac. This balancing on the dizzying path between genius and madness is awful." In a separate letter about the Compton effect, Einstein added: "I don't understand the details of Dirac at all."

  Niels Bohr called Dirac "a complete logical genius" and also the "strangest man" who had ever visited his Institute. Bohr's colleagues in Cambridge took the measure of Dirac's verbal economy and jokingly defined a unit called the "dirac" as one word per hour. When Bohr once told him he did not know how to finish a sentence in a scientific article he was writing, Dirac replied: "I was taught at school never to start a sentence without knowing the end of it."

  On a voyage to a conference in Japan in August 1929, the biographer Graham Farmelo described Dirac as an "Edwardian geek" who "suffered agonies if forced into any kind of socializing or small talk." His travel companion Heisenberg danced and flirted with other passengers. Dirac watched, then asked: "Why do you dance?" Heisenberg answered that when there are nice girls, it is a pleasure. Dirac considered this, then said: "But, Heisenberg, how do you know beforehand that the girls are nice?"

  Dirac married Margit Wigner in 1937, the sister of physicist Eugene Wigner. He introduced her to visitors with the formulation: "Allow me to present Wigner's sister, who is now my wife." Margit, who went by Manci, told the physicists George Gamow and Anton Capri in the 1960s that it was she who managed everything domestic, noting that Dirac published eleven papers during the difficult years of 1939-46 because she freed him entirely from household responsibility.

  Dirac's personal modesty was a consistent trait. He named the equation for the time evolution of a quantum-mechanical operator the "Heisenberg equation of motion", even though he was the first to write it down. And when lecturing in later life, he insisted on calling Fermi-Dirac statistics simply "Fermi statistics", explaining that he called the Bose-Einstein equivalent "Bose statistics" for reasons of "symmetry".

• 7. Beauty as Method

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  During a visit to Moscow State University in 1956, Dirac was asked to summarise his philosophy of physics. He walked to a blackboard and wrote: "Physical laws should have mathematical beauty." As is traditional with inscriptions left by distinguished visitors there, the phrase has never been erased.

  For Dirac, mathematical beauty was not ornamental. Peter Goddard stated that "Dirac cited mathematical beauty as the ultimate criterion for selecting the way forward in theoretical physics." In a 1939 lecture, Dirac argued that the beauty of the mathematical form of general relativity was itself one of the reasons it deserved acceptance. He extended this view to questions of faith. In the May 1963 edition of Scientific American, Dirac wrote that fundamental physical laws are described in terms of mathematical theories of great beauty and power, suggesting that "God is a mathematician of a very high order" who used very advanced mathematics in constructing the universe.

  At the 1927 Solvay Conference, a conversation among young participants about Einstein and Max Planck's views on religion drew a sharp critical response from Dirac. Wolfgang Pauli, after some silence, offered a wry summary: "Well, our friend Dirac has got a religion and its guiding principle is 'There is no God, and Paul Dirac is His prophet.'" Everybody, including Dirac, burst into laughter.

  Dirac was equally unmoved by debates over the interpretation of quantum mechanics. In a paper published in a book honouring him, he wrote plainly: "The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here. I want to deal with more fundamental things."

• 8. Final Years and Legacy

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  In 1969 Dirac reached the mandatory retirement age of sixty-seven and left his position as Lucasian Professor of Mathematics at Cambridge. He accepted a visiting position at the University of Miami's newly formed Center for Theoretical Studies and then, in September 1970, a visiting professorship at Florida State University in Tallahassee. He became a full professor at FSU in 1972 and remained there for the rest of his life.

  Contemporary accounts describe his Tallahassee years as happy. He walked about a mile to work each day, swam in Silver Lake or Lost Lake nearby, and was notably more sociable than he had been at Cambridge. He published over sixty papers at FSU during those final twelve years, including a short book on general relativity.

  His last paper, completed in 1984 and titled "The inadequacies of quantum field theory," closed with words that read like a research vow: "I have spent many years searching for a Hamiltonian to bring into the theory and have not yet found it. I shall continue to work on it as long as I can and other people, I hope, will follow along such lines." He died on the 20th of October 1984 in Tallahassee and was buried at Roselawn Cemetery.

  On the 13th of November 1995, a commemorative marker made from Burlington green slate and inscribed with the Dirac equation was unveiled in Westminster Abbey. The Dean of Westminster had initially refused permission, believing Dirac to be anti-Christian, but was persuaded over a period of five years. The International Centre for Theoretical Physics has awarded the Dirac Medal every year on Dirac's birthday, the 8th of August, since 1985. The first three recipients of the Institute of Physics's Paul Dirac Medal were Stephen Hawking in 1987, John Stewart Bell in 1988, and Roger Penrose in 1989. John Polkinghorne, one of his students, wrote that Dirac's "purity of spirit and modesty of demeanour" made him "an inspiring figure and a kind of scientific saint."