# Dirac, Paul

# DIRAC, PAUL

Paul Adrien Maurice Dirac (1902–1984) became a member of the Royal Society in 1930, professor at Cambridge University in 1932, and the following year he shared with Erwin Schrödinger the Nobel Prize in Physics for his contributions to the theory of quantum mechanics. Throughout his life, he was occupied with fundamental questions of physics, which he approached in an original and often unorthodox way. Although not himself a particle physicist, his contributions to theoretical physics were of crucial importance to the science of elementary particles that emerged in the 1930s.

## Pioneer of Quantum Mechanics

In 1921 Dirac graduated in electrical engineering at Bristol University, England, but was unable to find a job as an engineer. Two years later, he entered Cambridge University as a research student under Ralph Fowler. At that time he knew very little about the quantum theory of atoms, but under Fowler's guidance he quickly mastered the subject. After having become acquainted with Werner Heisenberg's new quantum mechanics, in 1925 he developed his own algebraic formulation of quantum mechanics.

During 1925–1927, Dirac further developed and refined the theory of quantum mechanics, which he presented in a general and logical way. In one of his important papers from 1926, he examined the quantum properties of two or more particles of the same kind, and thereby introduced the distinction between Fermi-Dirac statistics and Bose-Einstein statistics.

(Unknown to Dirac, Fermi-Dirac statistics had been considered by Enrico Fermi half a year earlier.) Many years later, in 1945, Dirac invented the names fermion and boson.

Among the most important of Dirac's early works were his transformation theory and his quantum theory of electromagnetic radiation, both of which were published in 1927. The transformation theory was a general theory of quantum mechanics that comprised both particle and wave aspects, including Max Born's probabilistic interpretation of wave mechanics. His radiation theory treated the emission and absorption of electromagnetic radiation and introduced the notion of second quantization that became of fundamental significance in quantum field theory. Dirac's theory served as the foundation of quantum electrodynamics. It initiated a new field of research that would soon occupy center stage in theoretical physics, to which Dirac made important contributions.

The original quantum mechanics of Heisenberg, Schrödinger, and Dirac did not satisfy the principle of relativity and, for this reason, was not considered completely satisfactory. In 1926–1927, several physicists sought in vain to develop a relativistic wave equation that agreed with experiments. The problem was solved in January 1928, when Dirac found a relativistically invariant equation that had the same formal structure as the Schrödinger equation. Moreover, he found that the equation led to the correct spin magnetic moment of the electron. Dirac's equation of the relativistic and spinning electron took the physics community by surprise. Whereas the ordinary Schrödinger equation is of the second order in the space derivatives, the Dirac equation is of the first order. And the wave function does not include two components (one for each spin value), but four components. Although the equation made sense mathematically, it was harder to understand it physically.

## Antiparticles

Dirac realized that, in a formal sense, his linear wave equation included solutions that corresponded to particles with negative energy. However, real particles must have positive energy, and he was therefore led to search for a physically valid interpretation of the solutions. In 1929 he came up with a remarkable solution to the puzzle, namely, that the proton is an electron in disguise. Dirac assumed an infinite, unobservable "sea" of negative-energy electrons and suggested that protons were vacancies or "holes" in the sea, hence they had positive energy. He wrote to Niels Bohr: "I think one can understand in this way why all things one actually observes in nature have a positive energy. One might also hope to be able to account for the dissymmetry between electrons and protons; one could regard the protons as the real particles and electrons as the holes in the distribution of protons of [negative] energy" (Kragh 1990,p. 91). He predicted that protons might annihilate with electrons and turn into gamma rays. In spite of Bohr's and most other physicists' rejection of the electron-proton theory, Dirac kept to it for more than a year. By 1930 matter was thought to consist of electrons and protons only, and Dirac felt greatly attracted to the idea—"the dream of philosophers," as he called it—because it promised a reduction to just one fundamental entity.

However, the dream of philosophers remained a dream. It could not account for the difference in mass between the two particles, and Dirac was forced to abandon what he considered a most beautiful idea. Yet he kept to his general picture and deftly turned the defeat into a victory by postulating in 1931 that the hole was an antielectron, "a new kind of particle, unknown to experimental physics, having the same mass and opposite charge to an electron" (Kragh 1990, p. 103). In this remarkable paper, the notion of antiparticles was introduced in quantum physics. However, although the hypothesis agreed with the principles of relativity and quantum theory, in 1931 it had no experimental support. Dirac further suggested that the proton would have its own antiparticle, a negatively charged antiproton, and a few years later he speculated that the symmetry between particles and antiparticles would probably imply the existence of antimatter made up purely by antielectrons and antiprotons.

Initially, the theory of antiparticles was met with skepticism. After all, the only elementary particles known in 1931 were the negative electron and the positive proton. It was only in 1932–1933, when the positron was discovered in the cosmic radiation (by Carl D. Anderson) and identified with Dirac's antielectron (by Patrick Blackett and Guiseppe Occhialini), that the status of the theory changed. In 1933, Dirac subjected the theory of the positron to a detailed mathematical analysis in which he introduced ideas (such as vacuum polarization) that were to become important in the later development of quantum field theory. The theory of antiparticles and the discovery of the positron were among the most important events in the creation of elementary particle physics.

Whereas Dirac's theory of the antielectron was vindicated by Anderson's discovery, it took longer to confirm his prediction of the antiproton. This particle played only a marginal role in the 1930s, and it was detected only in 1955, when it was produced in accelerator experiments. Forty-one years later, in 1996, the first detection of antihydrogen was reported.

## Magnetic Monopoles

In his 1931 paper, Dirac predicted yet another elementary particle, the magnetic analogue of an electron, that is, a monopole or single magnetic pole. Such particles cannot exist according to classical electrodynamics, but Dirac showed that they were allowed by the laws of quantum mechanics. He believed that since there were no theoretical reasons barring the existence of monopoles, they would exist somewhere in nature.

The suggestion did not attract much attention, and, contrary to the antielectron, the particle remained elusive. Yet Dirac found the theory compelling, and in 1948 he developed it further. The theory of magnetic monopoles became widely known only in the 1970s, in particular after Paul B. Price in 1975 claimed to have detected a monopole in the cosmic radiation. Neither this claim nor a couple of later claims have been confirmed, and so it is believed that monopoles do not exist or are exceedingly rare. Toward the end of his life, Dirac was "inclined to believe . . . that monopoles do not exist" (Kragh 1990, p. 221). Yet, for him, the actual existence of magnetic monopoles was not what counted most. He considered it more important that the particle, real or not, could be described within the framework of quantum theory.

## Attitude to Particle Physics

Although Dirac's 1931 paper was of crucial importance to elementary particle physics, he preferred to occupy himself with fundamental quantum theory rather than follow up the development that the new particles generated. About 1936, he came to doubt quantum field theory, including Fermi's theory of beta decay. Consequently he rejected the neutrino and sought to build up an alternative theory without strict energy conservation. (He soon abandoned the idea.) In 1936 Dirac generalized his wave equation to also cover particles with spin different from that of the electron; for, as he wrote, "It is desirable to have the equations ready for a possible future discovery of an elementary particle with a spin greater than a half" (Kragh 1990, p. 169).

Dirac continued to think of the electron as more elementary than other particles and was reluctant to engage in the physics of other elementary particles. He thought that the electron first had to be understood on a classical basis, and the theory subsequently turned over into quantum theory. He developed this idea in the 1950s in the hope of reconstructing quantum electrodynamics. However, at that time he was estranged from the fast-growing development in particle physics, and his work was considered unorthodox.

*See also:*Anderson, Carl D.; Fermi, Enrico; Positron, Discovery of; Quantum Electrodynamics; Quantum Field Theory; Quantum Statistics

## Bibliography

Brown, L. M., and Hoddeson, L., eds. *The Birth of Particle Physics* (Cambridge University Press, Cambridge, England, 1990).

Dirac, P. A. M. *Directions in Physics* (Wiley, New York , 1978).

Hovis, R. C., and Kragh, H. "P. A. M. Dirac and the Beauty of Physics." *Scientific American***268** , 104–12 (1993).

Kragh, H. *Dirac: A Scientific Biography* (Cambridge University Press, Cambridge, England, 1990).

Monti, D. "Dirac's Hole Model: From Proton to Positron." *Nuncius***10** , 99–130 (1995).

Pais, A. *Inward Bound: Of Matter and Forces in the Physical World* (Clarendon Press, Oxford, 1986).

Pais, A., et al. *Paul Dirac: The Man and his Work* (Cambridge University Press, Cambridge, England, 1998).

Taylor, J. G., ed. *Tributes to Paul Dirac* (Adam Hilger, Bristol, England, 1987).

*Helge Kragh*

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