When beta-decay occurs an electron or a positron is emitted along a neutrino or an antineutrino. The energy spectrum of the beta particles is continuous because, as I read, the energy is shared between the two emitted bodies.
My question is: what determines the distribution of energy here? That is, what determines with how much energy each particle is emitted? And for that matter: why is this sharing of the energy continuous?
The process must conserve all of energy, momentum and angular momentum. Within the possible final states that obey those limits it appears to be entirely random (or to be controlled by some inaccessible, non-local hidden variable if you prefer those kinds of QM interpretations).
In any case, the energy distribution of any particular decay can not be predicted, though the distributions of a large number is both predictable (on the basis of available phase space) and well measured.
