Collection: Dirac’s Equation

The equation was discovered in the late 1920s by physicist Paul Dirac. It remains highly influential. It brought together two of the most important ideas in science: quantum mechanics, which describes the behaviour of tiny objects; and Einstein’s special theory of relativity, which describes the behaviour of fast-moving objects.

As a result, Dirac’s equation describes how particles like electrons behave when they travel close to the speed of light. It was the first step towards what’s called quantum field theory, which has given us the standard model of particle physics and the Higgs boson. The equation also implied the existence of a new form of matter, antimatter previously unsuspected and unobserved and which was experimentally confirmed several years later.

It also provided a theoretical justification for the introduction of several component wave functions in Pauli's phenomenological theory of spin. The wave functions in the Dirac theory are vectors of four complex numbers (known as bispinors), two of which resemble the Pauli wavefunction in the non-relativistic limit, in contrast to the Schrödinger equation which described wave functions of only one complex value. Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation.

Although Dirac did not at first fully appreciate the importance of his results, the entailed explanation of spin as a consequence of the union of quantum mechanics and relativity—and the eventual discovery of the positron—represents one of the great triumphs of theoretical physics. This accomplishment has been described as fully on a par with the works of Newton, Maxwell, and Einstein before him.