  We show by direct calculation that the common Equivalence Principle
explanation for why gravity must deflect light is quantitatively incorrect by a
factor of three in Schwarzschild geometry. It is therefore possible, at least
as a matter of principle, to tell the difference between local acceleration and
a true gravitational field by measuring the local deflection of light. We
calculate as well the deflection of test particles of arbitrary energy, and
construct a leading-order coordinate transformation from Schwarzschild to local
inertial coordinates, which shows explicitly how the effects of spatial
curvature manifest locally for relativistic trajectories of both finite and
vanishing rest mass particles.
