by H. Kragh

© Oxford University Press 2004 All rights reserved

**Dirac, Paul Adrien Maurice** (1902-1984), theoretical physicist, was born at 15 Monk Road, Bishopston, Bristol, on 8 August 1902, the son of Charles Adrien Ladislas Dirac (1866-1936), a native of Monthey in the canton of Valais, Switzerland, and a teacher of French in the Merchant Venturers' Technical College at Bristol, and his wife, Florence Hannah (1878-1941), daughter of Richard Holten, master mariner in a Bristol ship. Paul had an older brother, Reginald Charles Felix *(b.* 1900), and a younger sister, Beatrice Isabelle Marguerite *(b.* 1906). He was registered as Swiss by birth, and only in 1919 did he acquire British nationality. As a result of his father's domineering nature and dislike of social contacts, he developed early on into an introvert, without friends or a social life, and later described his childhood as unhappy.

**Quantum mechanics**

From 1914 Dirac attended the Merchant Venturers' Technical College, where he received a good education in science and modern languages. In 1918 he entered the University of Bristol, graduating as an electrical engineer in 1921. Having no employment, he accepted the Bristol mathematics department's proposal that he stay on and take its course, from which he graduated in 1923. During this period he specialized in electrodynamics and became acquainted with the theory of relativity, which profoundly influenced his later thinking about problems in physics. In the autumn of 1923 he went up to Cambridge, to become a research student in mathematics at St John's College under the supervision of the theoretical physicist Ralph Fowler. Dirac had originally wanted to do graduate work in relativity, but under the impact of Fowler he changed to statistical physics and quantum theory. Totally absorbing himself in studies and research, he quickly transformed himself into a promising physicist and before the summer of 1925 he had published six scientific papers. These were interesting, but not of striking originality, and it was only after Werner Heisenberg's introduction of quantum mechanics that Dirac turned into a pioneer of theoretical physics.

In August 1925 Fowler received a proof copy of Heisenberg's seminal paper 'Über quantentheoretischer Umdeutung' and passed it on to Dirac for study. It contained a mysterious law of multiplication according to which the product of two physical quantities '*P*' and '*Q*' (an electron's momentum and position, for example) does not commute; that is, *PQ* differs from *QP*. Dirac realized that this feature of the theory, not fully understood by Heisenberg, was essential and tried to make it the basis of a more satisfactory formulation of quantum mechanics that would conform with the theory of relativity. In October he found the solution--'the idea first came in a flash', he recalled--namely that the Heisenberg commutator *PQ*-*QP* could be related to the Poisson bracket expression used in classical dynamics. His paper on the fundamental equations of quantum mechanics led him to an independent formulation of the new theory, which enabled him to find the energy levels of the hydrogen atom. In 1926 Dirac developed his theory into an algebraic formulation in which physical quantities can be divided into two classes, being either *c*-numbers or *q*-numbers. Whereas *c*-numbers are classical quantities (ordinary numbers), *q*-numbers are dynamical variables representing observable quantities such as position, momentum, or energy. Contrary to *c*-numbers, *q*-numbers do not satisfy the commutative law, and Dirac showed that his *q*-number theory gave the same results as Heisenberg's theory but in a logically more satisfactory way.

In one of the classics of quantum mechanics ('On the theory of quantum mechanics') Dirac in August 1926 incorporated Erwin Schrödinger's new wave mechanics into his own theory and thereby created a more general and powerful formalism which he immediately applied to develop what subsequently became known as Fermi-Dirac quantum statistics. Particles obeying this form of statistics are today known as fermions, while those obeying Bose-Einstein statistics are called bosons. These names were invented by Dirac in 1945.

A still more general version of quantum mechanics was developed by Dirac during a stay at Bohr's institute in Copenhagen in the autumn of 1926. This 'extraordinarily grandiose generalization', as Heisenberg called it in a letter of November 1926, comprised Max Born's probabilistic interpretation of quantum mechanics within the more general framework of transformation functions. Dirac introduced in this paper the *'d-function',* which soon became a standard tool in physics. While at Copenhagen, Dirac was also occupied with the interaction between matter and electromagnetic fields, and in 1927 he published 'The quantum theory of the emission and absorption of radiation', which is recognized as the pioneering paper of quantum electrodynamics. It was in this work that the idea of 'second quantization'--according to which the wave function is treated as an operator--was first introduced. Following this work, Dirac applied his theory to dispersion and resonance, and he continued throughout his life to make important contributions to the theory of quantum electrodynamics.

Dirac's outstandingly significant achievement was his relativistic wave equation for the electron. Earlier attempts to formulate a relativistic Schrödinger wave equation had failed, but in early 1928, Dirac found a new wave equation of the same formal structure as Schrödinger's *(HY* = *EY),* but with a Hamilton function *(H)* that made the equation fit the requirements of relativity. The new equation was of the first order in both the time and space derivatives and included a new type of matrix with four rows and columns (Dirac matrices). The Dirac equation led to many empirically correct predictions and was immediately hailed as a great theoretical progress. The Dirac matrices are related to the Pauli spin matrices and Dirac proved that the correct value of the electron's spin appeared as a consequence of his theory. He also proved that it was possible to give an exact explanation of the hydrogen spectrum, including the so-called fine structure. 'The quantum theory of the electron' marked a turning-point in modern physics and the Dirac equation was received enthusiastically and created a minor industry in mathematical physics. However, some of the consequences appeared strange, especially that the theory seemed to predict the existence of electrons with positive charge and negative energy. The difficulty was solved by Dirac in 1930-31 by a brilliant and imaginative interpretation of the negative energies formally occurring in the theory. He suggested the existence of positively charged 'antielectrons' that would annihilate in collision with ordinary electrons, and at first believed that antielectrons were identical with protons. In a remarkable paper of 1931, 'Quantised singularities in the electromagnetic field', he realized that the idea did not work and instead predicted that the antielectron was a new kind of particle, with the same mass as the electron but opposite charge. The daring speculation was unexpectedly confirmed in 1932 when positive electrons (positrons) were discovered in the cosmic radiation. In his 1931 paper Dirac also suggested the existence of antiprotons--negatively charged protons--and isolated magnetic poles. Whereas the antiproton was eventually discovered (in 1955), the magnetic monopole has escaped discovery in spite of many attempts and some discovery claims.

**Honours and awards**

On 2 January 1937 Dirac married Margit Balazs *(b.* 1905), daughter of Antal Wigner, manager of a leather factory at Budapest, and sister of the physicist Eugene Wigner. His wife had a son and a daughter, Gabriel and Judith, from her previous marriage; the Diracs had two daughters, Mary Elizabeth and Florence Monica. Until his marriage Dirac had lodged at St John's College, but the family then moved to a house at 7 Cavendish Avenue, Cambridge. Dirac had taken his PhD degree at Cambridge in 1926 and was the following year invited to the Solvay Congress in Brussels, a sign of his rising international reputation. He was frequently invited to the continental centres of physics and also to the USSR and America. For example, he visited the USSR in 1928 and in 1929 he was in the United States from where he returned via Japan, China, and the Soviet Union. In 1930 he was elected a fellow of the Royal Society and in 1932 Lucasian professor of mathematics at Cambridge University. The following year he received, jointly with Schrödinger, the Nobel prize, primarily for his wave equation of the electron. Much to his dismay, this made him a public figure. A London newspaper portrayed him under the headline 'The genius who fears all women' and described him--not inaccurately--to be 'as shy as a gazelle and modest as a Victorian maid' *(Sunday Dispatch,* 19 Nov 1933). In his Nobel lecture he speculated about antimatter made up of positrons and antiprotons and suggested that entire stars might be built up in this way. From the autumn of 1927 onwards Dirac lectured on quantum mechanics at Cambridge and in 1930 he published his authoritative textbook *The Principles of Quantum Mechanics,* which became translated into many languages and deeply influenced a generation of physicists. A second edition appeared in 1935, a third in 1947, and a fourth edition in 1958.

**New directions in physics**

Although Dirac continued to do important work in physics, his main contributions dated from the period 1925-33. He spent the war years in England, where he did consultancy work on the uranium bomb project, especially dealing with the separation of isotopes and the calculation of neutron multiplication in atomic bomb models. When the bomb project was taken over by the Manhattan Project in the United States, Dirac was asked to join the project, but he refused. After about 1950 he turned away from mainstream physics and became increasingly heterodox in his views and areas of research. In particular, he objected strongly to the new renormalization quantum electrodynamics that was developed by Julian Schwinger, Richard Feynman, and others and which soon obtained a paradigmatic status. According to Dirac, the theory was illogical and could not possibly be correct, in spite of its empirical success. He never came to peace with the direction quantum theory took after the Second World War and preferred to stay away from what he called the rat race of mainstream physics. Deeply distressed by the mathematical and conceptual problems of quantum electrodynamics, he suggested alternatives to the theory until the end of his life. For example, in 1965 he published a theory of quantum electrodynamics without making use of renormalization ideas; however, the theory did not lead to new results and failed to win acceptance. Other post-war work--on magnetic monopoles, classical electron theory, quantization of constrained dynamical systems, and Hamiltonian formulations of general relativity--were important, but not of the same revolutionary nature as his early work in quantum theory. He summarized much of his later work in the semi-popular *Directions in Physics* (1978).

In 1937-8 Dirac suggested a new cosmological model based on the hypothesis that the dimensionless large numbers constructed from fundamental constants of nature are inter-related. Based on the 'large number hypothesis' he suggested a non-relativistic version of Big Bang cosmology which he only developed much later, in the 1970s. According to Dirac's theory the gravitational constant decreases with time and he sought to avoid the conclusion from experimental evidence that this is not the case. In spite of the failure of Dirac's cosmological theory, the large number hypothesis has been a source of inspiration for many cosmologists.

Dirac produced more than 200 publications, the first in 1924 and the last in 1984. Of these, his 1928 paper on the relativistic wave equation was the most important and the one most often cited. After retirement in 1969 he was invited to the University of Miami and in 1971 he took up a research professorship at Florida State University, Tallahassee, where he stayed for the rest of his life. He received many honours apart from the Nobel prize, among them the James Scott prize (1939), the Copley medal (1952), the Max Planck medal (1952), the Helmholtz medal (1964), and the Oppenheimer prize (1969); he was an honorary member of many scientific societies and in 1973 he was admitted to the Order of Merit.

Dirac was a legendary figure, not only because of his exceptional contributions to physics but also because of his personality. He was taciturn and seldom spoke spontaneously. As a rationalist who insisted on logic and intellectual economy in both science and life, he had little appreciation for emotions and what most people would call the human aspects of life. He was not a religious man and in his younger days he favoured an atheistic view. Neither was he interested in politics, although in the 1930s he had a brief flirtation with Marxism and expressed some sympathy with the new economic order of the Soviet Union. This, and his many travels to the country, was probably the reason why he was denied a visa to the United States in 1954 (the decision was later retracted). He was never a member of any church or political party. Dirac was fascinated by the concept of mathematical beauty, which he made his lodestar for most of his work after the early 1930s. He believed that there is a deep connection between the fundamental laws of nature and the theoretical formulations that can be expressed in mathematically beautiful ways and that physicists should strive for mathematical beauty rather than experimentally verified theories. 'A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data' he declared in 1970 (Dirac, 'Equations', 29). Dirac kept to this philosophy until his death in Tallahassee, Florida, on 20 October 1984. He was buried in Tallahassee cemetery. In 1995 Cambridge University Press began publication of his collected works, edited by R. H. Dalitz.

H. KRAGH

**Sources **

P. A. M. Dirac, 'Recollections of an exciting era', *History of twentieth century physics,* ed. C. Weiner (1977), 109-46

*The collected works of P. A. M. Dirac, 1924-1948,* ed. R. H. Dalitz (1995)

R. H. Dalitz and R. E. Peierls, *Memoirs FRS,* 32 (1986), 139-85

H. Kragh, *Dirac: a scientific biography* (1990)

J. G. Taylor, ed., *Tributes to Paul Dirac* (1985)

B. Kursunoglu and E. P. Wigner, eds., *Paul Adrien Maurice Dirac: reminiscences about a great physicist* (1987)

J. Mehra and H. Rechenberg, *The historical development of quantum theory,* 4 (1982)

H. Kragh, 'Cosmonumerology and empiricism: the Dirac-Gamow dialogue', *Astronomy Quarterly,* 8 (1991), 109-26

R. C. Hovis and H. Kragh, 'P. A. M. Dirac and the beauty of physics', *Scientific American,* 268 (May 1993), 104-9

O. Darrigol, *From c-numbers to q-numbers* (1992)

J. W. McAlister, 'Dirac and the aesthetic evaluation of theories', *Methodology and Science,* 23 (1990), 87-102

P. A. M. Dirac, 'Can equations of motion be used in high-energy physics?', *Physics Today,* 23 (April 1970), 29-31

**Archives **

Archive for History of Quantum Physics, Cambridge

CAC Cam., corresp. and papers

Florida State University, Tallahassee

L. Cong. | Royal Swedish Academy of Science, Stockholm, Nobel archive

U. Sussex, letters to J. G. Crowther

University of Copenhagen, Copenhagen, Denmark, Niels Bohr Institute for Astronomy, Physics and Geophysics, corresp. with Niels Bohr

**Likenesses **

Ramsey & Muspratt, photograph, 1934, NPG *[see illus.]*

R. Tollast, pencil sketch, 1963, St John Cam.

G. Bollobás, cold cast bronze sculpture, 1973, RS

M. Noakes, oils, 1978, St John Cam.

photographs, Hult. Arch.

**Wealth at death **

£75,548: probate, 3 May 1985, *CGPLA Eng. & Wales*

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