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With the passing of Paul Dirac, OM, FRS, the world has lost one of the greatest physicists of all time. His contributions to quantum mechanics and to elementary particle physics have been of dominating importance for those subjects and also of great significance for astronomy and cosmology. The general principles of quantum mechanics, quantum electrodynamics, the relativistic theory of the spinning electron, electron statistics, and the discovery of anti-matter are all due to him. In addition his proposals concerning magnetic monopoles and a time-dependent gravitational constant, while still speculative, have given rise to a large literature both theoretical and experimental. His personality was as famous as his physics and indeed was closely related to it, for both manifested a logical directness and economy of a singularly pure kind. This directness and economy led to his being a superb lecturer, whose cogent exposition of subtle theory had a commanding clarity and authority. Allied to his great reserve, it also led to the circulation of numerous Dirac stories, many of them entirely legendary.
Dirac was born on 1902 August 8 in Bristol, the second of three children of a Swiss father and an English mother. He went to Merchant Venturer's School, where his father taught French, and entered Bristol University at the age of 16 to read electrical engineering. He graduated three years later, to find no job openings available for a beginning engineer. Bristol University came to the rescue by offering him a free place in their mathematics course. Dirac completed this course in two years and then in 1923 entered Cambridge University as a research student, supported by an 1851 Exhibition Studentship and a grant from the Department of Scientific and Industrial Research.
At Cambridge Dirac was supervised by R.H.Fowler, a centrai figure in statistical mechanics who at that time was also working on its astronomical applications, partly in collaboration with E.A.Milne. Milne himself supervised Dirac when Fowler spent a term in Copenhagen, and communicated an early paper of Dirac's to the Monthly Notices of the Royal Astronomical Society. This paper appeared in June 1925 and was entitled 'The effect of Compton scattering by free electrons in a stellar atmosphere'. At the end Dirac thanks Milne for his assistance. A year earlier Dirac had published a note on the relativity dynamics of a particle. This note was communicated to the Philosophical Magazine by A.S.Eddington. In later years these two great men exerted a considerable influence on each other.
Dirac's fundamental work on quantum mechanics also began as early as 1925, only a few months after Heisenberg's introduction of non-commuting quantities into physics. In later years Dirac credited Heisenberg with taking the essential step, the rest being 'mere commentary'. This is not how other physicists judge the matter. Once Dirac took up the subject, his deep insight, powerful technique and creative originality made him the acknow-ledged master. This phase of his work is summed up in his masterpiece The Principles of Quantum Mechanics, the first edition of which was published in 1930, and rapidly became the bible of modern physics. In later editions he modified the presentation, but many connoisseurs prefer the greater abstractness of the first edition. In this work also the Dirac delta function was born, later to be applied in diverse fields of mathematical physics and to provoke the development of L.Schwarz's rigorous theory of distri-butions.
For astronomical applications the most important part of this work was Dirac's introduction in 1926 of Fermi-Dirac statistics for particles like electrons which obey the Pauli exclusion principle (Fermi's contribution being made independently), and his 1928 relativistic theory of the spinning electron. The Fermi-Dirac statistics were applied in the same year of 1926 to white dwarfs by Fowler, who showed how these statistics for electrons play the key rôle in the structure of those otherwise anomalous objects. Later it was realized that the same analysis applies to the neutrons in neutron stars, and that considerations of relativistic degeneracy lead to an upper mass limit for equilibrium configurations of cold matter (the Chandrasekhar limit).
Dirac's theory of the electron is undoubtedly his greatest single contribu-tion to physics. It showed how special relativity could be united with quantum mechanics, how the spin of the electron could be a natural dynamical variable, and that its value of 1½ was also natural, and how 'exotic' representations of the Lorentz group (spinors) played an essential rôle in physics. Most important of all, the negative energy states apparently required by the Dirac equation led, on re-interpretation, to the necessary existence of the anti-particle to the electron, that is, the positron, which was discovered experimentally in 1932. Today the electron-positron system and its annihilation into, and production by, photons, is a staple ingredient of high-energy astrophysics. All other types of particle also have anti-particles, some of which again play a key rôle in high energy astrophysics and in processes occurring in the early Universe.
Much of Dirac's remaining work after 1930 involved important technical studies in quantum field theory, or in classical theory with an eye on the transition to the quantum theory. Particularly noteworthy was his 1938 theory of classical radiating electrons in which the explicit introduction of advanced potentials clarified the origin of the radiation damping force, and led to the remarkable phenomenon of pre-acceleration. On the quantum side it was a remark of Dirac's which led Feynman to devise his path integral procedure which has transformed our understanding of quantum field theory. For the astronomer and cosmologist great interest attaches to Dirac's 1931 hypothesis that single magnetic poles might exist, a proposal which has again excited physicists recently because such poles would arise naturally in Grand Unified Theories and might be produced in profusion in the early Universe. Despite great efforts, and some false alarms, no magnetic poles have yet been detected in the laboratory.
General interest also attaches to Dirac's 1937 Large Numbers Hypothesis. In this work he was again influenced by Milne, although the resulting theory is quite different from Milne's cosmology. According to the hypothesis 'any two of the very large dimensionless numbers occurring in Nature are connected by a simple mathematical relation, in which the coefficients are of the order of magnitude unity'. Dirac included the age of the Universe in the construction of large dimensionless numbers and so was led to conclude that some of the supposed constants of Nature, such as the gravitational constant G, actually change with time. This would then require altering general relativity, a question to which he often returned in his last years. The most refined experiments have not yet revealed any change in fundamental constants with time, although laser ranging to the Moon and the radio tracking of spacecraft have now reached an accuracy for relevant to Dirac's hypothesis.
Dirac also carried out important work in classical general relativity. In particular he showed in 1958 how to put Einstein's field equations into Hamiltonian form. This technical step has played a key rôle in attempts to quantize the gravitational field and also in studies of the initial value problem in general relativity. His earlier work on Hamiltonian dynamics in the presence of constraints here came into its own.
During these later years Dirac wrote a number of short books based on his lecture courses: Lectures on Quantum Mechanics (1964), Lectures on Quantum Field Theory (1966), The Development of Quantum Theory (1971), Spinors in Hilbert Space (1974) and The General Theory of Relativity (1975). His seventieth birthday was celebrated in 1972 by a Symposium in his honour held at the International Centre for Theoretical Physics in Trieste, the lectures being subsequently published as The Physicist's Conception of Nature, edited by J.Mehra. Also in 1972 the Cambridge University Press published a celebratory volume, Aspects of Quantum Theory, edited by A.Salam and E.P.Wigner.
Dirac was elected to the Fellowship of the Royal Society in 1930. In 1932 he succeeded Sir Joseph Larmor as Lucasian Professor of Mathematics at Cambridge University, the chair once occupied by Newton. He was then only 30 years old, and when he retired in 1969 he was by far the senior professor in Cambridge. After his retirement he went to the United States and in 1971 became Professor of Physics at Florida State University in Tallahassee. In 1933 Dirac shared the Nobel prize with Schrödinger. The Royal Society awarded him its Royal Medal in 1939 and the Copley Medal in 1952. In 1973 he was appointed to the Order of Merit. He died on 1984 October 20, one of the immortals of physics, leaving a wife (Margit Wigner), and two daughters.
D.W.SCIAMA
Dirac was born on 1902 August 8 in Bristol, the second of three children of a Swiss father and an English mother. He went to Merchant Venturer's School, where his father taught French, and entered Bristol University at the age of 16 to read electrical engineering. He graduated three years later, to find no job openings available for a beginning engineer. Bristol University came to the rescue by offering him a free place in their mathematics course. Dirac completed this course in two years and then in 1923 entered Cambridge University as a research student, supported by an 1851 Exhibition Studentship and a grant from the Department of Scientific and Industrial Research.
At Cambridge Dirac was supervised by R.H.Fowler, a centrai figure in statistical mechanics who at that time was also working on its astronomical applications, partly in collaboration with E.A.Milne. Milne himself supervised Dirac when Fowler spent a term in Copenhagen, and communicated an early paper of Dirac's to the Monthly Notices of the Royal Astronomical Society. This paper appeared in June 1925 and was entitled 'The effect of Compton scattering by free electrons in a stellar atmosphere'. At the end Dirac thanks Milne for his assistance. A year earlier Dirac had published a note on the relativity dynamics of a particle. This note was communicated to the Philosophical Magazine by A.S.Eddington. In later years these two great men exerted a considerable influence on each other.
Dirac's fundamental work on quantum mechanics also began as early as 1925, only a few months after Heisenberg's introduction of non-commuting quantities into physics. In later years Dirac credited Heisenberg with taking the essential step, the rest being 'mere commentary'. This is not how other physicists judge the matter. Once Dirac took up the subject, his deep insight, powerful technique and creative originality made him the acknow-ledged master. This phase of his work is summed up in his masterpiece The Principles of Quantum Mechanics, the first edition of which was published in 1930, and rapidly became the bible of modern physics. In later editions he modified the presentation, but many connoisseurs prefer the greater abstractness of the first edition. In this work also the Dirac delta function was born, later to be applied in diverse fields of mathematical physics and to provoke the development of L.Schwarz's rigorous theory of distri-butions.
For astronomical applications the most important part of this work was Dirac's introduction in 1926 of Fermi-Dirac statistics for particles like electrons which obey the Pauli exclusion principle (Fermi's contribution being made independently), and his 1928 relativistic theory of the spinning electron. The Fermi-Dirac statistics were applied in the same year of 1926 to white dwarfs by Fowler, who showed how these statistics for electrons play the key rôle in the structure of those otherwise anomalous objects. Later it was realized that the same analysis applies to the neutrons in neutron stars, and that considerations of relativistic degeneracy lead to an upper mass limit for equilibrium configurations of cold matter (the Chandrasekhar limit).
Dirac's theory of the electron is undoubtedly his greatest single contribu-tion to physics. It showed how special relativity could be united with quantum mechanics, how the spin of the electron could be a natural dynamical variable, and that its value of 1½ was also natural, and how 'exotic' representations of the Lorentz group (spinors) played an essential rôle in physics. Most important of all, the negative energy states apparently required by the Dirac equation led, on re-interpretation, to the necessary existence of the anti-particle to the electron, that is, the positron, which was discovered experimentally in 1932. Today the electron-positron system and its annihilation into, and production by, photons, is a staple ingredient of high-energy astrophysics. All other types of particle also have anti-particles, some of which again play a key rôle in high energy astrophysics and in processes occurring in the early Universe.
Much of Dirac's remaining work after 1930 involved important technical studies in quantum field theory, or in classical theory with an eye on the transition to the quantum theory. Particularly noteworthy was his 1938 theory of classical radiating electrons in which the explicit introduction of advanced potentials clarified the origin of the radiation damping force, and led to the remarkable phenomenon of pre-acceleration. On the quantum side it was a remark of Dirac's which led Feynman to devise his path integral procedure which has transformed our understanding of quantum field theory. For the astronomer and cosmologist great interest attaches to Dirac's 1931 hypothesis that single magnetic poles might exist, a proposal which has again excited physicists recently because such poles would arise naturally in Grand Unified Theories and might be produced in profusion in the early Universe. Despite great efforts, and some false alarms, no magnetic poles have yet been detected in the laboratory.
General interest also attaches to Dirac's 1937 Large Numbers Hypothesis. In this work he was again influenced by Milne, although the resulting theory is quite different from Milne's cosmology. According to the hypothesis 'any two of the very large dimensionless numbers occurring in Nature are connected by a simple mathematical relation, in which the coefficients are of the order of magnitude unity'. Dirac included the age of the Universe in the construction of large dimensionless numbers and so was led to conclude that some of the supposed constants of Nature, such as the gravitational constant G, actually change with time. This would then require altering general relativity, a question to which he often returned in his last years. The most refined experiments have not yet revealed any change in fundamental constants with time, although laser ranging to the Moon and the radio tracking of spacecraft have now reached an accuracy for relevant to Dirac's hypothesis.
Dirac also carried out important work in classical general relativity. In particular he showed in 1958 how to put Einstein's field equations into Hamiltonian form. This technical step has played a key rôle in attempts to quantize the gravitational field and also in studies of the initial value problem in general relativity. His earlier work on Hamiltonian dynamics in the presence of constraints here came into its own.
During these later years Dirac wrote a number of short books based on his lecture courses: Lectures on Quantum Mechanics (1964), Lectures on Quantum Field Theory (1966), The Development of Quantum Theory (1971), Spinors in Hilbert Space (1974) and The General Theory of Relativity (1975). His seventieth birthday was celebrated in 1972 by a Symposium in his honour held at the International Centre for Theoretical Physics in Trieste, the lectures being subsequently published as The Physicist's Conception of Nature, edited by J.Mehra. Also in 1972 the Cambridge University Press published a celebratory volume, Aspects of Quantum Theory, edited by A.Salam and E.P.Wigner.
Dirac was elected to the Fellowship of the Royal Society in 1930. In 1932 he succeeded Sir Joseph Larmor as Lucasian Professor of Mathematics at Cambridge University, the chair once occupied by Newton. He was then only 30 years old, and when he retired in 1969 he was by far the senior professor in Cambridge. After his retirement he went to the United States and in 1971 became Professor of Physics at Florida State University in Tallahassee. In 1933 Dirac shared the Nobel prize with Schrödinger. The Royal Society awarded him its Royal Medal in 1939 and the Copley Medal in 1952. In 1973 he was appointed to the Order of Merit. He died on 1984 October 20, one of the immortals of physics, leaving a wife (Margit Wigner), and two daughters.
D.W.SCIAMA
Paul Dirac's obituary appeared in Journal of the Royal Astronomical Society 27:1 (1986), 124-126.