A restricted proof that the weak equivalence principle implies the Einstein equivalence principle
Schiff has conjectured that the weak equivalence principle (WEP) implies the Einstein equivalence principle (EEP). A proof is presented of Schiff's conjecture, restricted to: (1) test bodies made of electromagnetically interacting point particles, that fall from rest in a static, spherically symmetric gravitational field; (2) theories of gravity within a certain broad class - a class that includes almost all complete relativistic theories that have been found in the literature, but with each theory truncated to contain only point particles plus electromagnetic and gravitational fields. The proof shows that every nonmentric theory in the class (every theory that violates EEP) must violate WEP. A formula is derived for the magnitude of the violation. 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.