Dirac's Cosmology and the General Theory of Relativity

An explanation is given, according to the principles of the general theory of relativity, of some results previously obtained by Dirac. It is assumed that there is a different unit of distance for electromagnetic phenomena from the unit of distance used for describing gravitational phenomena. The ratio of these units varies with the time. The former unit gives the usual “ cosmic ” distance and a Newtonian law of gravitation which is independent of the time, the latter unit leads to a Newtonian law of gravitation for which the gravitational power of matter varies inversely as the epoch. Formulae are derived which enable the age of the universe $$(\bar{t})$$ , Hubble's constant ( H ) and the mean density of matter in the universe ( ω ), to be calculated from the values of the constants of atomic theory and the present observed value of the gravitational “ constant ”. It is found that $$\bar{t}=4\cdot 1\times{10}^{9}$$ years, H = 160 km/sec/megaparsec, and $$\omega =4\cdot 8\times{10}^{-29}\,\text{gm}/\text{cm}^{3}$$ .