  One of the most common expectations of a quantum theory of gravity is that
space-time is uncertain or fluctuating at microscopic scales, making it a
stochastic medium for particle propagation. Particles traversing this
space-time may experience fluctuations in travel times or velocities, together
referred to as lightcone fluctuations, with even very small effects potentially
accumulating into observable signals over large distances. In this work we
present a heuristic model of lightcone fluctuations and study the resulting
modifications to neutrino propagation, including neutrino decoherence and
arrival time spread. We show the expected scale of such effects due to
`natural' Planck scale physics and consider how they may be observed in
neutrino detectors, and compare the potential of neutrinos to $\gamma$-ray
astronomy. Using simulations of neutrino mass states propagating in a
fluctuating environment, we determine an analytic decoherence operator in the
framework of open quantum systems to quantitatively evaluate neutrino
decoherence resulting from lightcone fluctuations, allowing experimental
constraints on neutrino decoherence to be connected to Planck scale
fluctuations in space-time and $\gamma$-ray results.
