Dirac Sea

The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons. The positron, the antimatter counterpart of the electron, was originally conceived of as a hole in the Dirac sea, well before its experimental discovery in 1932.

The equation relating energy, mass and momentum in special relativity is:

,

In the special case of a particle at rest (i.e. p = 0), the above equation reduces to, which is usually quoted as the familiar . However, this is a simplification because, while, we can also see that . Therefore, the correct equation to use to relate energy and mass in the Hamiltonian of the Dirac equation is:

Here the negative solution was used to predict the existence of antimatter, discovered by Carl Anderson as the positron. The interpretation of this result requires a Dirac sea, showing that the Dirac equation is not merely a combination of special relativity and quantum field theory, but it also implies that the number of particles cannot be conserved.