  We consider the effect of a long range, flavor changing tensor interaction of
possible gravitational origin. Neutrino mixing experiments provide the most
sensitive probe to date for such forces---testing the equivalence principle at
levels below $10^{-20}$. Here we justify and generalize a formalism for
describing such effects. The constraints from neutrino mixing experiments on
gravitationally induced mixing are calculated. Our detailed analysis of the
atmospheric neutrino data confirms a remarkable result: the atmospheric
neutrino data implies the same size force as does the solar neutrino data.
Additional tests of this suggestive result are discussed.
