Lawrence M Krauss’, Quantum Man: Richard Feynman’s Life in Science, and Graham Farmelo’s, The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius

Paul Dirac and Richard Feynman were legends in their lifetimes and remain so to this day. Their peers thought of them as unconventional, eccentric, magical geniuses. As theoretical physicists, they had much in common – an ability to focus on difficult problems and pursue them, if necessary, for months on end. Their personalities were, however, very different: Dirac was a loner; Feynman a joker. No one could imagine Dirac wearing a beanie hat with a helicopter on top, playing bongo drums at parties, as Feynman did at Cal Tech.

In 1928 young British physicist Dirac published a mathematical equation which was to have a profound effect on particle physics. Just three years before, Erwin Schrödinger and Werner Heisenberg developed quantum mechanics to explain the peculiar behaviour of matter at atomic and sub-atomic scales, which classical physics failed to do. Some twenty years before that Albert Einstein had unveiled his theory of Special Relativity on the relationship between space and time, and between energy and mass. The problem with quantum mechanics at first was that it did not work for particles moving at speeds close to the speed of light. It was not relativistic.

Dirac’s equation ingeniously used both quantum mechanics and relativity to describe the behaviour of the electron, but it also had unexpected implications. The equation allowed for two solutions: one for an electron with positive energy and one for an electron with negative energy, the latter flying in the face of all common sense. How can anything have negative energy? This was, of course, an expedition into the realm of pure theory on Dirac’s part, but in 1932 Carl Anderson at Cal Tech when studying cosmic rays saw a track left by something positively charged with the same mass as an electron, thus confirming Dirac’s strange finding. Anderson called this anti-electron a positron.[1] In 1933 Dirac thus shared with Schrödinger the Nobel Prize in Physics for the discovery of new forms of atomic theory. In his Nobel Lecture he speculated that while the Earth contains a preponderance of negative electrons and positive protons some stars may be built up mainly of positrons and negative protons, introducing, for the first time, the possible universality of antimatter.

In 1946 Dirac coincidentally encountered one of the most exciting scientific talents in America, twenty-eight-year-old Richard Feynman. Dirac had been invited to give a paper at a bicentennial conference in Princeton on the future of nuclear science, and Feynman was to introduce Dirac to a distinguished gathering. To Feynman, Dirac was already a hero. Even as a sophomore at MIT Feynman attended advanced graduate courses in theoretical physics, becoming attracted to topics ranging from relativity to quantum mechanics, and developing a love for the classical theory of electromagnetism. He carried these interests to graduate school in Princeton, where he tried to determine the energy levels of electrons in hydrogen only to discover that Dirac had beaten him to it more than a decade before. Feynman noticed though, that while Dirac suggested a ‘vague analogy’ between a critical quantum quantity and its classical counterpart, he took it no further. So Feynman commenced to provide calculations showing that the analogy could be made exact.

For all his admiration of Dirac, Feynman had been disappointed by the manuscript note he had seen of Dirac’s conference speech. It seemed backward looking, stale and unimportant. After the applause, Feynman tried to give lay members of the audience a sense of the significance of what Dirac was saying. Always a jokester, he cracked more than his usual quota, only to be rebuked by Niels Bohr – lionized in the play ‘Copenhagen’ – for not taking the proceedings seriously. A few hours later Feynman noticed that Dirac had left the conference and was lying outside on the grass gazing into the sky. Feyman saw this as an opportunity to answer a burning question: what had Dirac meant in writing about an analogy? Here is Feynman’s recollection of the conversation:

Feynman: “Did you know that they were proportional?”

Dirac: “Are they?”

Feynman: “Yes.”

Dirac: “Oh, that’s interesting.”

This, as we shall see, was a long conversation by Dirac’s standards. It gives no answer to Feynman’s question. Feynman himself eventually would point out that even the simplest interaction of light and matter (electrons) affects all chemistry and biology, and is therefore of the greatest importance. Dirac, in combining quantum mechanics and relativity in 1928, concentrated on the ‘simple’ electron. Even so, difficulties arose with Dirac’s formulation, notably when calculating effects of interactions between electrons and the electromagnetic field. Infinite, and therefore useless results, were obtained. In the 1930s many theoretical physicists, including Feynman, worked to improve quantum electrodynamics (QED). It was not until the late 1940s that satisfactory solutions were found.

The spur came in 1947, when Willis Lamb at Columbia University completed some remarkably accurate laboratory measurements of the fine structure of hydrogen, which showed that some energy levels of hydrogen were slightly shifted relatively to one another. Sin’Itero Tomonaga, following up suggestions by Hans Bethe and others, realised that a solution might be found by using a mathematical device known as renormalisation. Almost simultaneously, experiments at Columbia showed that the magnetic moment of the electron was larger than assumed. Julian Schwinger calculated that a small anomalous addition to the theoretical value of magnetic moment would bring it into alignment with experiment. Feyman, however, used a more radical technique of space-time diagrams to solve these knottiest of problems. His unique but simple approach was readily understood by other physicists and remains an important tool to this day. In 1965 the Nobel Prize in Physics was jointly awarded to Tomonaga, Schwinger and Feynman, as a result of which “quantum electrodynamics suddenly became one of the most accurate of all the theories of physics”[2] Dirac had combined relativity with quantum mechanics; Feynman blew away the fog of infinities. These were the great achievements of two remarkable giants of physics, Feynman and Dirac.

Dirac, who said he never felt love as a child, was born in 1902 at Bristol, a large industrial and commercial city in southwest England. His father, Charles, brought up in a French-speaking Swiss canton, settled in Bristol in the mid-1890s, and was Head of Modern Languages at the Merchant Venturers’ School at the time of Paul’s birth. Paul’s Cornish mother, Flo, was twelve year younger than her husband. He was a Catholic, though he kept that to himself; she a devout Methodist. It was a strange, if not estranged, marriage. The husband was a dominant personality; she was a day-dreamer. He spoke French to their children (Paul had an older brother and a younger sister), she spoke to them in English. They rarely ate together. Paul would eat with his father; his siblings with his mother. Paul found the meals with his father distressing. He had no talent for languages, and if he made any slip in pronunciation or grammar his father would refuse any requests. Unable to express himself properly in French, he thought it better to remain silent. Dirac would always be ill at ease with normal conversation.

At age five Dirac started junior school. At first he did not shine but later picked up and passed exams with flying colours. In August 1914, when war was breaking out, Dirac entered the school at which his father taught. The curriculum was slanted towards technical subjects and Dirac soon established himself as a star pupil in science and mathematics. Aged only sixteen, with war coming to an end, he began studying engineering at Bristol University and was awarded a first class degree. His father, keen that Dirac should go to Cambridge, wrote to St John College. Dirac passed the entrance examination, but the accompanying minor scholarship was not enough to support him. Fortunately the head of the mathematics department at Bristol arranged for him to take an honours mathematics degree course free of charge, allowing him to skip the first year. Dirac was in his element, but not being overstretched; he attended lectures in physics, and learned quantum theories and new ways of thinking about light. The head of the mathematics department also wrote to St John’s College, Cambridge, extolling Dirac’s prowess. He also added a caveat: ‘He is a bit uncouth, and wants some sitting on hard, is rather a recluse, plays no games, and is very badly off financially’. This time, Dirac got the award of scholarships just sufficient to cover his first year costs.

At Cambridge Dirac’s low social standing was revealed by his cheap suit, gauche manners and, on the occasions he spoke, his accent. His manner at dinner in Hall was legendary. Most students had been educated at the top fee-paying schools, knew Latin and Greek, and conversed easily on fashionable topics. Dirac sat through courses without saying a word, or even acknowledging those sitting beside him. Yet, as his biographer records, he did prefer to eat in company and to hear intelligent people talking about serious matters.

Fortunately, his supervisor, physicist Ralph Fowler, recognised Dirac’s talent and gave him carefully chosen problems to solve, and constant encouragement. Fowler had a light touch and for the most part Dirac worked on his own. Fowler, however, encouraged him to report his results, rather than filing them away, and Dirac developed a writing style characterised by ‘directness, confident reasoning, powerful mathematics, and plain English.’ By the end of 1924, he produced five papers and was recognised as an outstanding student and a natural researcher. In 1925 Dirac’s paper, ‘The Fundamental Equations of Quantum Mechanics,’ was published in the proceedings of the Royal Society, and Cambridge woke up to the fact that a star had been born. Quantum Mechanics was new, and little understood. Max Born, who had coined the phrase in 1924, was amazed to read a year later a paper ‘perfect in its way and admirable’ written by a youngster. Heisenberg was also fulsome in his praise. In 1926 Dirac was awarded a PhD for a thesis of exceptional distinction.

Dirac left Cambridge to spend a year in Europe: six months with Niels Bohr at Copenhagen and six with Max Born at Göttingen, meeting many great innovators of quantum theories. These were enjoyable and productive interludes for Dirac. It was in Copenhagen that he turned to finding a relativistic quantum theory of the electron which led to his Nobel Prize. Dirac returned to Cambridge and published his famous equation in 1928. Some four years later, in the midst of triumphs in the Cavendish laboratory, in particular Cockcroft and Walton’s ‘splitting of the atom’, Dirac was appointed Lucasion Professor of Mathematics, a Chair previously occupied by Isaac Newton and, more recently, Stephen Hawking.

In1934 Dirac began a sabbatical at the Institute of Advanced Study at Princeton, with an office next to Hungarian refugee, Eugene Wigner. He struck up a friendship with Wigner’s sister, Manci, a lively divorcee with a young son and daughter, who encouraged Dirac to take more interest in music, literature and ballet. They married in January 1937. Their first child, Mary, was born in London in 1940. A second daughter, Monica, was born in 1942. During the war Dirac turned down invitations to join teams of scientists working for the war effort, but stayed at Cambridge where he spent time advising those engaged on the development of the atomic bomb on practical ways of enriching uranium.

In the post war years Dirac spent much time travelling, making many returns to his favourite haunt, Princeton. In 1963, Oppenheimer told him that he had arranged for a framed photo of him to hang on a wall at the Institute, next to one of Einstein: ‘You two are alone on that wall.’ In 1969 Dirac relinquished his Cambridge post. Two years later he became Visiting Eminent Professor at the University of Florida.  On 20 October 1984, aged 82, Dirac died. He had turned down a knighthood and honorary degrees, but accepted membership of the Order of Merit, which did not oblige him to call himself anything other than ‘Mr Dirac.’ He is commemorated in the science corner of Westminster Abbey.

Richard Feynman was born in 1918 in Manhattan and brought up in Far Rockaway, a small town on the outskirts of New York.  His father was the son of Lithuanian Jews who migrated to the United States when he was five, and settled in Long Island. He tried various occupations before establishing himself in a business making uniforms. Richard’s mother, Lucille, the daughter of a prosperous businessman, was of Polish Jewish descent. Their house was shared with Lucille’s sister and her family, so Richard and his younger sister were not lacking in company, their cousins in the house being thought of as siblings.[3]  Richard got on very well with his parents. His father stimulated his interest in science. His mother’s sense of humour, warmth and compassion greatly influenced his character.

When Richard was about ten, the Feynmans moved to Cedarhurst, and he attended the local elementary school where he was taught little he did not already know, except in the last two years when he studied algebra, and surprised his teachers with his mastery of it. After two years or so the family went back to Far Rockaway and Richard entered High School. Avidly reading popular books on science, he again found that he knew everything that was being taught, except for advanced mathematics, in which he was pushed hard and learned a lot. The head of the department told Lucille to ensure that her son went to college after high school.  Feynman prepared for college by working as a waiter to raise money. He was accepted by Massachusetts Institute of Technology, with a small scholarship, in 1935. In his first year he studied engineering and then switched to physics. By the end of his final year he had covered not only the undergraduate but also the graduate physics curricular and was looking forward to another four years in graduate research. He was offered a scholarship to Havard but chose Princeton, where Einstein was. Here he had the good fortune to be supervised by John Wheeler, a young scientist who had worked with Niels Bohr in Copenhagen. As Wheeler wrote later: “I am eternally grateful for the fortune that brought us together on more one fascinating enterprise…Discussions turned into laughter, laughter into jokes, and jokes into more to-and-fro, and more ideas.” Feynman brought mathematical brilliance and insight, Wheeler brought experience and perspective. In his Nobel acceptance speech in 1965, Feynman emphasises the part played by Wheeler in his development of quantum mechanics.

From their high school days, Feynman and Arline Greenbaum had been in love. From MIT and from Princeton Feynman returned home on vacations to see her. They became engaged. Arline became seriously ill and was diagnosed with a fatal disease. After receiving his PhD Feynman and Arline were married in a registry office in 1942. At that time Feynman was beginning to work on aspects of the Manhattan Project at Princeton, and in the spring of 1943 he moved to Los Alamos, where Oppenheimer helped in making arrangements for Arline to stay in a hospital in Albuquerque. She died on 16 June 1945.

At Los Alamos, he joined Hans Bethe’s Theoretical Division and ultimately was put in charge of the Theoretical Computations Group. He greatly admired Bethe, and the sentiment was reciprocated. After the war, Bethe returned to Cornell and used his influence to secure an assistant professorship for Feynman. It was at Cornell that he developed his space-time approach to quantum electrodynamics that led to a Nobel Prize. After wrestling with QED from 1946 to 1950, Feynman was searching for new challenges and new environments. He settled on Cal Tech in sunny Pasadena where he teamed up with a twenty-five year old wonder boy called Murrey Gell-Mann, a combination that was to attract many students to Cal Tech. Feynman’s lectures to undergraduates at Caltech, in turn funny and serious, and sometimes over the heads of students, were published to great acclaim. In 1952, Feynman began an unhappy marriage with platinum blond Mary Louise Bell. They parted four years later. In Geneva in 1958 he met a young English woman Gweneth Howarth and invited her to Pasadena to be his maid. They married in 1960, had a son two years later and later adopted another child, Michelle. They remained happily married until Feynman died, after a long illness on 15 February 1988, at the age of sixty-nine. Eugene Wigner once described Feynman as ‘a second Dirac, only this time human.’ Unlike Feynman, Dirac was, in conversation, an extremely poor communicator, especially of his feelings, but in other situations he was a normal human being. On the evidence of the two biographies under review I would recast Wigner’s epigram to read: ”Feynman was a second Dirac, only this time one who could talk as well as listen.’

Notes