  In this essay, we introduce a new effect of gravitationally induced quantum
mechanical phases in neutrino oscillations. These phases arise from an hitherto
unexplored interplay of gravitation and the principle of the linear
superposition of quantum mechanics. In the neighborhood of a 1.4 solar-mass
neutron star, gravitationally induced quantum mechanical phases are roughly 20%
of their kinematical counterparts. When this information is coupled with the
mass square differences implied by the existing neutrino-oscillation data we
find that the new effect may have profound consequences for type-II supernova
evolution.
