Dirac's large numbers hypothesis in Einstein's theory of gravitation

Abstract

A method is given for incorporating Dirac's Large Numbers hypothesis into Einstein's standard theory of general relativity. The method involves the assumption that at each point in space there exist two types of clocks, a cosmological clock measuring ephemeris timeτ and an atomic clock measuring atomic timet A . Newton's law of universal gravitation is formulated relativistically in terms of these two times and the proper distance determined by measuring rods between simultaneous events, and a method is given for operationally identifyingG. The Large Numbers hypothesis requirement thatG A ∝1/t A is then used to establish the relationship between the two times. Alternative derivations of the time relationship not involving a time-varying gravitational “constant” are obtained by intercomparison of various large numbers. It is shown that the resulting relationship betweent A andτ gives agreement with the observed natural microwave radiations. Also, the Large Numbers hypothesis leads to a time formed from the fundamental constants of Nature that is comparable to the age of the Universe.