Dirac lake
The Dirac lake is a theoretical model that describes the vacuum as an infinite "lake" of particles with negative energy . It was developed by British physicist Paul Dirac in 1930 to explain the quantum states of negative energy predicted in the Dirac equation for relativistic electrons . The term hole theory was also used for this theory .
The positron , the antiparticle to the electron , was predicted by Dirac as a hole in the Dirac Sea, and was interpreted as this for years after its experimental discovery in 1932.
Today the states of negative energy are interpreted with the help of quantum field theory as generation operators for antiparticles of positive energy, see Feynman-Stückelberg interpretation .
Initial problem
The origin of the Dirac lake lies in the energy spectrum of the Dirac equation. This generalizes the Schrödinger equation taking into account the special theory of relativity . It was formulated by Dirac in 1928.
Although the equation was very successful in describing the movement of electrons, it has a peculiar property: for every quantum state with positive energy there is a corresponding state with the energy . This is not a problem as long as one is looking at an isolated electron, since its energy is retained and one can simply specify not to use any electrons with negative energy.
It becomes problematic if you want to take the effects of the electromagnetic field into account. An electron with positive energy could be achieved by continuous emission of photons transfer energy. This process could be continued at will, with the electron taking ever lower energy states , including negative ones . Since there is no lower limit for these energy states, an electron could emit an infinite amount of energy. However, real electrons clearly do not behave that way.
solution
Dirac's solution to the problem was to use the Pauli principle . Electrons are fermions and therefore have to follow this exclusion principle. This means that two electrons must not occupy the same energy state.
Dirac now assumed that what we consider vacuum to be a state in which all states of negative energy are filled and all states of positive energy are empty. Therefore, when we look at a single electron, we have to bring it into a positive energy state, since all negative states are occupied. The electron cannot get below the limit of energy zero , even if it loses energy by emitting photons .
If, however, a state of negative energy is unoccupied, which is interpreted as a positron in the context of Dirac's theory , the electron can fall into this hole, releasing the energy difference in the form of photons. Usually two photons with the typical energy of 511 keV each are emitted, the electron / positron pair disappears. This process is known as annihilation .
Individual evidence
- ↑ Luis Alvarez-Gaume, Miguel A. Vazquez-Mozo: Introductory Lectures on Quantum Field Theory