  We discuss the inverse $\beta$-decay of accelerated protons in the context of
neutrino oscillations. The process $p\rightarrow n \ell^+ \nu_\ell$ is
kinematically allowed because the accelerating field provides the rest energy
difference between initial and final states. The rate of $p\to n$ conversions
can be evaluated in either the laboratory frame (where the proton is
accelerating) or the co-moving frame (where the proton is at rest and interacts
with an effective thermal bath of $\ell$ and $\nu_\ell$ due to the Unruh
effect). By explicit calculation, we show the rates in the two frames disagree
when taking into account neutrino oscillations, because the weak interaction
couples to charge eigenstates whereas gravity couples to neutrino mass
eigenstates. The contradiction could be resolved experimentally, potentially
yielding new information on the origins of neutrino masses.
