Matter creation is the process inverse to particle annihilation. It is the conversion of massless particles into one or more massive particles. This process is the time reversal of annihilation. Since all known massless particles are bosons and the most familiar massive particles are fermions, usually what is considered is the process which converts two bosons (e.g. photons) into two fermions (e.g., an electron–positron pair). This process is known as pair production.
Photon pair production
Because of momentum conservation laws, the creation of a pair of fermions (matter particles) out of a single photon cannot occur. However, matter creation is allowed by these laws when in the presence of another particle (another boson, or even a fermion) which can share the primary photon's momentum. Thus, matter can be created out of two photons.
The law of conservation of energy sets a minimum photon energy required for the creation of a pair of fermions: this threshold energy must be greater than the total rest energy of the fermions created. To create an electron-positron pair, the total energy of the photons, in the rest frame, must be at least 2mec2 = 2 × 6986818712184856999♠0.511 MeV = 6987163742436971400♠1.022 MeV (me is the mass of one electron and c is the speed of light in vacuum), an energy value that corresponds to soft gamma ray photons. The creation of a much more massive pair, like a proton and antiproton, requires photons with energy of more than 6990301209179555999♠1.88 GeV (hard gamma ray photons).
The first published calculations of the rate of e+–e− pair production in photon-photon collisions were done by Lev Landau in 1934. It was predicted that the process of e+–e− pair creation (via collisions of photons) dominates in collision of ultra-relativistic charged particles—because those photons are radiated in narrow cones along the direction of motion of the original particle, greatly increasing photon flux.
In high-energy particle colliders, matter creation events have yielded a wide variety of exotic heavy particles precipitating out of colliding photon jets (see two-photon physics). Currently, two-photon physics studies creation of various fermion pairs both theoretically and experimentally (using particle accelerators, air showers, radioactive isotopes, etc.).
As shown above, to produce ordinary baryonic matter out of a photon gas, this gas must not only have a very high photon density, but also be very hot – the energy (temperature) of photons must obviously exceed the rest mass energy of the given matter particle pair. The threshold temperature for production of electrons is about 1010 K, 1013 K for protons and neutrons, etc. According to the Big Bang theory, in the early universe, photons and fermions (massive particles of matter) would inter-convert freely. As photon gas expanded and cooled, some fermions would be left over (in extremely small amounts ~10−10) because low energy photons could no longer break them apart. Those left-over fermions would have become the matter we see today in the universe around us.