A Theory of Evolving Natural Constants Based on theUnification of General Theory of Relativity and Dirac's Large Number Hypothesis

Abstract

Taking Dirac's large number hypothesis as true, we haveshown [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703]the inconsistency of applying Einstein's theory of generalrelativity with fixed gravitation constant G to cosmology, anda modified theory for varying G is found, which reduces toEinstein's theory outside the gravitating body for phenomena ofshort duration in small distances, thereby agrees with all thecrucial tests formerly supporting Einstein's theory. The modifiedtheory, when applied to the usual homogeneous cosmological model,gives rise to a variable cosmological tensor term determined bythe derivatives of G, in place of the cosmological constantterm usually introduced ad hoc. Without any freeparameter the theoretical Hubble's relation obtained from themodified theory seems not in contradiction to observations, as Dr.Wang's preliminary analysis of the recent data indicates[Commun. Theor. Phys. (Beijing, China) 42 (2004) 703]. Asa complement to Commun. Theor. Phys. (Beijing, China) 42(2004) 703 we shall study in this paper the modificationof electromagnetism due to Dirac's large number hypothesis in moredetail to show that the approximation of geometric optics stillleads to null geodesics for the path of light, and that the generalrelation between the luminosity distance and the proper geometricdistance is still valid in our theory as in Einstein's theory, andgive the equations for homogeneous cosmological model involvingmatter plus electromagnetic radiation. Finally we consider theimpact of the modification to quantum mechanics and statisticalmechanics, and arrive at a systematic theory of evolving naturalconstants including Planck's ℏ as well as Boltzmann'skB by finding out their cosmologically combined counterpartswith factors of appropriate powers of G that may remain trulyconstant to cosmologically long time.