Any physical, monopole equation of motion structure uniquely determines a projective inertial structure and an (<i>n</i>−1)-force

Abstract

It is proved that, in the context of a conformal causal structure, (a) any acceleration field decomposes uniquely into the sum of an affine structure that is compatible with the conformal structure and an n-force, and (b) any directing field, such that the n-force of the corresponding family of acceleration fields is due to tensor fields and is orthogonal to the n-velocity, uniquely decomposes into a projective structure that is compatible with the conformal structure and an (n−1)-force. Moreover, if there are no second clock effects and variable rest masses do not exist, there exists a unique pseudo-Riemannian metric on space-time that determines the unique standard of no acceleration for all massive monopoles. It follows from this that a non-null result for the Eötvös experiment entails the existence of a fifth force rather than a violation of the universality of free fall.