Foundations for a Theory of Gravitation Theories

Abstract

A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (i) a glossary of fundamental concepts; (ii) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (iii) a conjecture (due to Schiff) that the weak equivalence principle implies the Einstein equivalence principle; and (iv) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.