  Recent work has proposed that the interaction between ordinary matter and a
stochastic gravitational background can lead to the decoherence of large
aggregates of ordinary matter. In this work we point out that these arguments
can be carried over to a stochastic neutrino background but with the Planck
scale of the gravitational decoherence replaced by the weak scale. This implies
that it might be possible to observe such neutrino induced decoherence on a
small, microscopic system rather than a macroscopic system as is the case for
gravitationally induced decoherence. In particular we suggest that neutrino
decoherence could be linked with observed variations in the decay rates of
certain nuclei. Finally we point out that this proposed neutrino induced
decoherence can be considered the complement of the Mikheev-Smirnov-Wolfenstein
(MSW) effect.
