Restricted Proof that the Weak Equivalence Principle Implies the Einstein Equivalence Principle

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Abstract
Schiff has conjectured that the weak equivalence principle (WEP: free-fall trajectories independent of test-body composition) implies the Einstein equivalence principle (EEP: all nongravitational laws of physics the same in every freely falling frame). This paper presents a proof of Schiff's conjecture, restricted to (i) test bodies, made of electromagnetically interacting point particles, that fall from rest in a static, spherically symmetric gravitational field; and (ii) theories of gravity within a certain broad class—a class that includes almost all complete relativistic theories that we have found in the literature, but with each theory truncated to contain only point particles plus electromagnetic and gravitational fields. The proof shows that every "nonmetric" theory in the class (every theory that violates EEP) must violate WEP. A formula is derived for the magnitude of the violation. Comparison with the results of Eötvös-Dicke-type experiments rules out various nonmetric theories, including those of Belinfante and Swihart and of Naida and Capella—theories that previously were believed to agree with all current experiments. It is shown that WEP is a powerful theoretical and experimental tool for constraining the manner in which gravity couples to electromagnetism in gravitation theories.

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