  We discuss the theoretical possibility that the neutrino mass differences
have part of their origin in the quantum-decoherence-inducing medium of
space-time foam, which characterises some models of quantum gravity, in much
the same way as the celebrated MSW effect, responsible for the contribution to
mass differences when neutrinos pass through ordinary material media. We
briefly describe consequences of such decoherent media in inducing CPT
violation at a fundamental level, which would affect the neutrino oscillation
probability; we speculate on the connection of such phenomena with the role of
neutrinos for providing one possible source of a cosmological constant in the
Universe, of the phenomenologically right order of magnitude. Finally we
discuss possible experimental constraints on the amount of neutrino mass
differences induced by quantum gravity, which are based on fits of a simple
decoherence model with all the currently available neutrino data.
