Fractal gravity and symmetry breaking in a hierarchical Cantorian space

In this paper we determine the exact expectation value and standard deviation for the dimensionality of a Cantorian spacetime. We show further that the symmetry of the universe is a precondition and the origin of its asymmetry. Connections to time symmetry breaking and the generalization of complex numbers are considered. Finally, a link between general relativity and Cantorian spacetime is proposed which amounts to the claim that the Bethe lattice-like fractalization of microspace is the origin of gravity. (C) 1997 Elsevier Science Ltd.