Paul Dirac

Paul Dirac the British theoretical physicist (1902-1984) who formulated the relativistic equation for the electron and predicted the existence of antimatter, and who shared the 1933 Nobel Prize in Physics with Erwin Schroedinger. He was one of the principal architects of quantum mechanics and of quantum field theory.

Early Life and Education

Paul Adrien Maurice Dirac was born on 8 August 1902 in Bristol, the son of a Swiss-born teacher of French and a British mother. He grew up in a strict and emotionally reserved household, and he remained throughout his life a man of few words and great inward concentration. He studied electrical engineering at the University of Bristol and then mathematics at Cambridge, where he completed a doctorate in 1926.

At Cambridge Dirac came under the influence of the quantum theory being developed by Heisenberg, Born and others. He was among the first to appreciate the new mechanics and to reformulate it in a form that satisfied his own demand for mathematical beauty and rigour. His early papers established him as one of the most original thinkers of his generation. He was elected a fellow of St John's College and later became a fellow of the Royal Society at the unusually early age of thirty-one.

Quantum Mechanics and the Transformation Theory

In 1925 and 1926 Dirac developed a general formulation of quantum mechanics in which observable quantities are represented by non-commuting operators and states by vectors in a complex vector space. His transformation theory, published in 1927, unified the apparently different approaches of Heisenberg and Schroedinger and provided the abstract framework that physicists still use today. The formalism introduced the bra and ket notation that appears in every modern textbook of the subject.

The approach introduced the delta function, a mathematical device that Dirac improvised and justified on physical grounds and that was later given a rigorous foundation. He also worked out the quantum theory of radiation, showing how the emission and absorption of light could be treated as the creation and annihilation of photons, and he applied the methods of quantum statistics to systems of identical particles, arriving independently at the statistics now shared with Fermi. These papers helped to create the discipline of quantum field theory.

The Dirac Equation and Antimatter

In 1928 Dirac sought an equation for the electron consistent with both quantum mechanics and special relativity. The result, the Dirac equation, required that the wave function have four components, which corresponded naturally to the spin of the electron and led to a correct prediction of its magnetic moment. It was a triumph of theoretical reasoning, achieving in a single stroke what others had tried to reach by patching together separate ideas.

The equation, however, also had solutions of negative energy, which seemed physically absurd. Dirac interpreted these in 1931 as describing a new kind of particle, identical to the electron in mass but with the opposite electric charge. This was the first prediction of antimatter. The positron was discovered by Carl Anderson in 1932, vindicating the theory, and Dirac shared the 1933 Nobel Prize in Physics with Schroedinger for the work.

Magnetic Monopoles, Cosmology and Later Concerns

Dirac continued to make contributions across theoretical physics. He showed that the existence of a single magnetic monopole would explain the observed quantisation of electric charge, a result now called the Dirac quantisation condition. He also developed the large numbers hypothesis, speculating on a possible connection between the enormous dimensionless ratios that appear in cosmology and atomic physics. In addition he made important contributions to the theory of the magnetic moment of the electron and to the quantum theory of gravitation.

He held the Lucasian Chair of Mathematics at Cambridge from 1932 to 1969 and spent his later years at Florida State University in Tallahassee. A famously silent and solitary figure, he disliked publicity, and his few remarks recorded by colleagues became celebrated. He was a committed opponent of the pursuit of fame and regarded physics as a search for mathematical beauty above all else. His lectures were models of economy, and he is said to have spoken only when he had something worth saying.

Influence and Legacy

Dirac's equation is one of the central equations of modern physics, underlying the understanding of electrons, of atomic spectra and of the behaviour of matter in strong fields. Its prediction of antiparticles opened a new branch of physics and foreshadowed the whole development of quantum field theory, in which particles are understood as excitations of underlying fields. Every calculation in quantum electrodynamics begins from the principles he set out.

Together with Heisenberg, Schroedinger, Born and others, Dirac established the mathematical language of quantum mechanics, and his insistence that a theory should be beautiful as well as accurate influenced generations of theoretical physicists. He held chairs at Cambridge and later at Florida State University, and he received the Order of Merit in 1973. Toward the end of his life he turned to questions about the foundations of the theory and to the puzzle of why the constants of nature take the values they do, concerns that remain unresolved. He died in Tallahassee on 20 October 1984, and his equation remains engraved on the wall of Westminster Abbey among the memorials to the great physicists of Britain.

See also

• Dirac equation
• Positron
• Antimatter
• Quantum electrodynamics