Statistical Mechanics at Extremely High Temperatures

Equilibrium conditions between elementary particles and nuclei at temperatures $T\gtrsim {10}^9$ degrees are studied. Three temperature intervals below the upper limit ∼${10}^{12}$ degrees [$\mathrm{kT}\sim {10}^8$ ev] are considered. It is found that because of the behavior of some high energy particles, known experimentally from observations on cosmic rays and nuclei, some limitations arise to the validity of the laws of quantum statistics, in accordance with the idea of the existence of a supplementary indeterminacy for high energy particles and a lower limit for measurable lengths. Some astrophysical aspects of the phenomena of pair production and of the gravitational effect of light particles are discussed. The results concerning pair production at temperatures ∼${10}^9$ degrees are summarized in Table I. General formulae for thermal equilibrium between nuclei and light particles are given.