Dirac , Paul Adrien Maurice

(1902–1984) British mathematician and physicist

Dirac, whose father was Swiss, was born in Bristol. After graduating in 1921 in electrical engineering at Bristol University, Dirac went on to study mathematics at Cambridge University, where he obtained his PhD in 1926. After several years spent lecturing in America, he was appointed (1932) to the Lucasian Professorship of Mathematics at Cambridge, a post he held until his retirement in 1969. In 1971 he became professor of physics at Florida State University.

Dirac is acknowledged as one of the most creative of the theoreticians of the early 20th century. In 1926, slightly later than Max Born and Pascual Jordan in Germany, he developed a general formalism for quantum mechanics. In 1928 he produced his relativistic theory to describe the properties of the electron. The wave equations developed by Erwin Schrödinger to describe the behavior of electrons were nonrelativistic. A significant deficiency in the Schrödinger equation was its failure to account for the electron spin discovered in 1925 by Samuel Goudsmit and George Uhlenbeck. Dirac's rewriting of the equations to incorporate relativity had considerable value for it not only predicted the correct energy levels of the hydrogen atom but also revealed that some of those levels were no longer single but could be split into two. It is just such a splitting of spectral lines that is characteristic of a spinning electron.

Dirac also predicted from these equations that there must be states of negative energy for the electron. In 1930 he proposed a theory to account for this that was soon to receive dramatic confirmation. He began by taking negative energy states to refer to those energy states below the lowest positive energy state, the ground state. If there were a lower energy state for the electron below the ground state then, the question arises, why do some electrons not fall into it? Dirac's answer was that such states have already been filled with other electrons and he conjured up a picture in which space is not really empty but full of particles of negative energy. If one of these particles were to collide with a sufficiently energetic photon it would acquire positive energy and be observable as a normal electron, apparently appearing from nowhere. But it would not appear alone for it would leave behind an empty hole, which was really an absence of a negatively charged particle or, in other words, the presence of a positively charged particle. Further, if the electron were to fall back into the empty hole it would once more disappear, appearing to be annihilated together with the positively charged particle, or positron as it was later called.

Out of this theory there emerged three predictions. Firstly, that there was a positively charged electron, secondly, that it could only appear in conjunction with a normal electron, and, finally, that a collision between them resulted in their total common annihilation. Such predictions were soon confirmed following the discovery of the positron by Carl Anderson in 1932. Dirac had in fact added a new dimension of matter to the universe, namely antimatter. It was soon appreciated that Dirac's argument was sufficiently general to apply to all particles.

In 1937 Dirac published a paper entitled The Cosmological Constants in which he considered large-number coincidences, i.e. certain relationships that appear to exist between the numerical properties of some natural constants. An example is to compare the force of electrostatic attraction between an electron and a proton with the gravitational attraction due to their masses. The ratio of these is about 10⁴⁰:1. Similarly, it is also found that the characteristic ‘radius’ of the universe is 10⁴⁰ times as large as the characteristic radius of an electron. Moreover, 10⁴⁰ is approximately the square root of the number of particles in the universe.

These coincidences are remarkable and many physicists have speculated that these apparently unrelated things may be connected in some way. The ratios were first considered in the 1930s by Arthur Eddington, who believed that he could calculate such constants and that they arose from the way in which physics observes and interprets nature. Dirac used the 10⁴⁰ number above in a model of the universe. He argued that there was a connection between the force ratio and the radius ratio. Since the radius of the universe increased with age the gravitational constant, on which the force ratio depends, may decrease with time (i.e. it may not actually be a constant).

Above all else however Dirac was a quantum theorist. In 1930 he published the first edition of his classic work The Principles of Quantum Mechanics. In 1933 he shared the Nobel Prize for physics with Schrödinger.