  The discovery of neutrino oscillations invites many fundamental physics
questions that have yet to be answered. Two of these questions are simple, easy
to state, and essential: What are the values of the neutrino masses? Are
neutrinos Majorana fermions? The reason we don't know the answer to those
questions is that it is difficult to measure neutrino properties outside of the
ultrarelativistic regime. We discuss the physics of $e\gamma\to e\nu\bar{\nu}$
near threshold, where one has access to nonrelativistic neutrinos and only
nonrelativistic neutrinos. Near threshold, $e\gamma\to e\nu\bar{\nu}$ is a rich
phenomenon and its cross section is sensitive to the individual values of the
neutrino masses and the nature of the neutrinos. We show that if one could scan
the threshold region, it would be simple to identify the mass of the lightest
neutrino, the neutrino mass ordering, and whether the neutrinos are Majorana
fermions. In practice, however, event rates are tiny and backgrounds are huge;
the observation of $e\gamma\to e\nu\bar{\nu}$ in the sub-eV regime appears to
be utterly inaccessible in the laboratory. Our results, nonetheless,
effectively illustrate the discriminatory power of nonrelativistic neutrino
observables.
