  We ask the question of how angular momentum is conserved in weak interaction
processes, beginning with inverse beta decay for massless neutrinos and
electrons, in which both the incident neutrino and final electron are in
helicity eigenstates with respect, however, to {\em different} directions. To
elucidate the problem we recast the final electron state in terms of a
spherical Dirac wave. We then generalize these results to massive neutrinos and
electrons, and finally examine electron-positron annihilation processes through
the same lens. In all these processes, the apparent non-conservation of angular
momentum is a result of the quantum measurement process in which the measuring
apparatus is not in an initially well-defined quantum state, but is coupled to
the outside world; the measuring process, being outside the rules of elementary
quantum mechanics, does not allow a satisfactory accounting of the angular
momentum transfer.
