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

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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.