Dirac sea

The Dirac sea is an outdated theoretical model which describes the vacuum as an infinite "sea" of particles with negative energy. It was developed in 1930 by the British physicist Paul Dirac to explain the quantum states of negative energy that are predicted in the Dirac equation for relativistic electrons.

The positron, the antiparticle of the electron, was predicted by Dirac as a hole in the Dirac sea and interpreted for years even after its experimental discovery in 1932 so.

Today, the states of negative energy with the help of quantum field theory are interpreted as creation operators for antiparticles of positive energy, so that the Dirac sea has become unnecessary (see also Feynman - Stückelberg interpretation ).

Initial problem

The origin of the Dirac lake lies in the energy spectrum of the Dirac equation. This is the general form of the Schrödinger equation taking into account the special theory of relativity. It was formulated by Dirac in 1928.

Although the equation has been very successful in the description of the movement of electrons, but it has a peculiar property: for any quantum states with positive energy E , there is a corresponding state of the energy e. This is not a problem if one considers an isolated electron, because its energy is conserved and can be easily set to use no electrons of negative energy.

Problems arise when one wants to take into account the effects of the electromagnetic field. An electron with positive energy could by continuous emission of photons emit energy. This process could be continued as desired, the electron always occupying lower energy levels, and negative. Since there is no lower limit for these energy states, thus an electron could radiate an infinite amount of energy. However, real electrons behave clearly not so.


Dirac's solution to the problem was the use of the Pauli principle. Electrons are fermions and therefore have to follow this principle of exclusion. This means that two electrons can not occupy the same energy state allowed.

Dirac assumed now, that what we see as vacuum is a state in which filled all the negative energy states and all states of positive energy are empty. Therefore, we must, if we consider a single electron, bring it into a positive energy state, as all negative states are occupied. At the limit of the zero energy of the electron can not fall even if it loses energy by emitting photons.

However, if a state of negative energy unoccupied, which is interpreted in the context of Dirac's theory as a positron, the electron can fall into it, releasing the energy difference in the form of photons into this hole. Usually two photons are emitted with the typical for this process of energy per 511 keV, the electron / positron pair it disappears. This process is called annihilation.