We ask the question of how angular momentum is conserved in a number of related processes, from elastic scattering of a circularly polarized photon by an atom, where the scattered photon has a different spin direction than the original photon; to scattering of a fully relativistic spin-1/2 particle by a central potential; to inverse beta decay in which an electron is emitted following the capture of a neutrino on a nucleus, where the final spin is in a different direction than that of the neutrino – an apparent change of angular momentum.

The seeming non-conservation of angular momentum arises, in fact, in the quantum measurement process in which the measuring apparatus does not have an initially well-defined angular momentum, but is localized in direction in the outside world. We generalize the discussion to massive neutrinos and electrons, and examine nuclear beta decay and electron-positron annihilation processes through the same lens, enabling physical insights into angular and helicity distributions in these reactions.