A Possible Violation of the Equivalence Principle by Neutrinos

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.