Massless neutrinos will mix if their couplings to gravity are flavor dependent, i.e., violate the principle of equivalence. Because the gravitational interaction grows with neutrino energy, the solar neutrino problem and the recent atmospheric neutrino data may be simultaneously explained by violations at the level of ${10}^{-14\mathrm{}}$ to ${10}^{-17\mathrm{}}$ or smaller. This possibility is severely constrained by present accelerator neutrino experiments and will be preeminently tested in proposed long-base-line accelerator neutrino experiments.

• Received 5 November 1992

DOI:https://doi.org/10.1103/PhysRevD.47.R4199