  We derive the character of neutrino oscillations that results from a model of
equivalence principle violation suggested recently by Damour and Polyakov as a
plausible consequence of string theory. In this model neutrino oscillations
will take place through interaction with a long range scalar field of
gravitational origin even if the neutrinos are degenerate in mass. The energy
dependence of the oscillation length is identical to that in the conventional
mass mixing mechanism. This possibility further highlghts the independence of
and need for more exacting direct neutrino mass measurements together with a
next generation of neutrinoless double beta decay experiments.
