# Paul Dirac

### From Wikipedia, the free encyclopedia.

**Paul Adrien Maurice Dirac**, OM (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics.

Note: "Dirac" is pronounced [dɪ'ræk].

## Contents |

## Biography

### Early years

Paul Dirac was born in Monk Road, Bishopston, in the English city of Bristol. His father, Charles Dirac, was an immigrant from the Valais Canton in Switzerland who taught French for a living. His mother was originally from Cornwall and the daughter of a mariner. Paul had an elder brother and a younger sister. His early family life appears to have been unhappy on account of his father's unusually strict and authoritarian nature, but he never publicly expressed his feelings on the subject. He was educated first at Bishop Road Primary School and later at Merchant Venturers Technical College. The latter was an institution, attached to the University of Bristol, that emphasized scientific subjects and modern languages. This was an unusual arrangement at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express gratitude.

Dirac studied electrical engineering at the University of Bristol, completing his degree in 1921. After working briefly as an engineer, Dirac decided that his true calling lay in the mathematical sciences. He completed a degree in mathematics at Bristol in 1923 and then received a grant to conduct research at St. John's College, Cambridge, where he would remain for most of his career. At Cambridge he became interested in the general theory of relativity and in the nascent field of quantum physics, and worked under the supervision of Ralph Fowler.

### Middle years

In 1926 he developed a version of quantum mechanics that incorporated the previous work of Werner Heisenberg on “Matrix Mechanics” and of Erwin Schrödinger on “Wave Mechanics” into a single mathematical formalism that associates measurable quantities with operators acting on the Hilbert space of vectors that describe the state of a physical system. For this seminal work he was awarded a Ph.D. from Cambridge.

In 1928, building on Pauli's work on nonrelativistic spin systems, he derived the Dirac equation, a relativistic equation describing the electron. This work led Dirac to predict the existence of the positron, the electron's antiparticle, which he interpreted in terms of what came to be called the Dirac sea. The positron was subsequently observed by Carl Anderson in 1932. Dirac also contributed to explaining the origin of quantum spin as a relativistic phenomenon.

Dirac's *Principles of Quantum Mechanics*, published in 1930, became one of the standard textbooks on the subject and is still used today. It introduced the Bra-ket notation, in which |ψ>, ket, denotes a state vector in the Hilbert space of a system and <ψ|, bra, its dual vector. <ψ|ψ> denotes an inner product. Dirac also introduced Dirac's delta function.

In 1931 Dirac showed that the existence of a single magnetic monopole in the universe would suffice to explain the observed quantization of electrical charge. This proposal received much attention, but there is to date no convincing evidence for the existence of magnetic monopoles.

Paul Dirac shared the Nobel Prize for physics in 1933 with Erwin Schrödinger "for the discovery of new productive forms of atomic theory." He married Eugene Wigner's sister, Margit, in 1937.

### Later years

Dirac was Lucasian professor of mathematics at Cambridge from 1932 to 1969. The Dirac Prize is awarded in his honor. After having relocated to Florida in order to be near his married daughter, Dirac spent his last years at Florida State University (FSU) in Tallahassee, Florida. The Dirac-Hellman Award at FSU was endowed by Dr. Bruce Hellman (Dirac's last Ph.D. student) in 1997 to reward outstanding work in theoretical physics by FSU researchers.

### Death and afterwards

He died in Tallahassee, where he is buried. In 1995, a plaque in his honor was unveiled at Westminster Abbey in London.

## Views

Dirac was a committed atheist. After being asked about his thoughts on Dirac's views, Pauli remarked, "If I understand Dirac correctly, his meaning is this: there is no God, and Dirac is his Prophet".

Dirac was known among his colleagues for his precise and taciturn nature. When Niels Bohr complained that he didn't know how to finish a sentence in a scientific article he was writing, Dirac famously replied, "I was taught at school never to start a sentence without knowing the end of it." While visiting the U.S.S.R., he was invited to lecture on his philosophy of physics. He merely stood up and wrote on the board, "Physical laws should have mathematical beauty and simplicity."

When asked on some occasion about his views on poetry, he replied, "In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite."

Dirac was also noted for his personal modesty. He called the equation for the time-evolution of a quantum-mechanical operator, which Dirac was in fact the first to write down, the "Heisenberg equation of motion". Most physicists speak of Fermi-Dirac statistics for half-integer spin particles and Bose-Einstein statistics for integer spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Einstein statistics" for reasons, he explained, of "symmetry".

## Books by Dirac

*Principles of Quantum Mechanics*(1930): This book was a highly original work that summarizes the ideas of quantum mechanics using the modern formalism that was largely developed by the author himself. Towards the end of the book, Dirac also discusses the relativistic theory of the electron (*see*Dirac equation) which was also pioneered by him. Interestingly, this work does not refer to any other writings then available on quantum mechanics. This is one of the landmarks in the history of science.

*Lectures on Quantum Mechanics*(1966): A good portion of this book deals with quantum mechanics in curved space-time.

*General Theory of Relativity*(1975): This short work (only 68 pages!) elegantly summarizes Einstein's general theory of relativity.

## See also

- Dirac sea
- Dirac equation
- Dirac delta function, Dirac comb
- Dirac large numbers hypothesis
- Dirac Prize
- Fermi-Dirac statistics

## External links

- Paul Dirac at the Notable Names Database
- Dirac Medal of the International Centre for Theoretical Physics
- Biography at the MacTutor archive
- Paul Adrien Maurice Dirac Biography
- Dirac Medal of the World Association of Theoretically Oriented Chemists (WATOC)
- Photographs of Dirac
- The Paul Dirac Collection at Florida State University
- The Paul A. M. Dirac Collection Finding Aid at Florida State University
- discovery of new productive forms of atomic theory.