On the relation of the large numbers problem to the nature of mass

Abstract

The large numbers problem is usually stated in terms of coincidences between dimensionaless numbers of order 10⁴⁰, constructed from quantities arising in local physics on the one hand and cosmology on the other hand. The problem is usually thought of in terms of explaining these coincidences. In the Introduction it is shown that the coincidences are all derivative from the same source; namely, a multiplying constant of order 10⁻³⁸ which appears in the mass-gravitational physical action formula, when the latter is expressed in its most economical form as a single term. Thus the problem can be seen to arise from the smallness of this mass-gravity coupling rather than from coincidences which have no particular significance in themselves.

A hint towards explaining the origin of this very small number arises already in the classical theory, but a proper understanding appears only in a quantum formulation. Such a formulation leads to a removal of 10⁻³⁸ from the action and to its replacement byg ², the strong coupling constant. In the outcome it turns out that the nucleon mass can be calculated to within about 15% of the experimentally-determined value of 938 MeV, a result which strongly supports the proposition that physics, even in its apparently most fundamental form, cannot be separated from cosmology. Cosmology is not simply an application of physics, as it is commonly supposed to be. Much of the great complexity of modern physics is probably due to attempting to formulate the basic laws in the absence of cosmology.