  Measurements of the beta decay rates of nuclei have revealed annual
periodicities with approximately the same relative amplitude even though the
half-lives range over nine orders of magnitude. Here we show that this can be
explained if the emitted neutrinos behave as if they propagate in a medium with
a refractive index which varies as the Earth orbits the sun. This refractive
index may be due to fundamental Lorentz non-invariance (LNI), or apparent LNI
arising from interactions with solar or relic neutrinos, or dark matter.
Additionally, this medium could have consequences for experiments attempting to
measure the neutrino mass.
