- What are the causality properties of the Dirac equation, and how do they relate to Born's rule?
[Moderator's note: Spin off from a previous thread due to topic change.]
Actually, the form of the Hamiltonian does matter. Hegerfeldt admits that his results are not correct for the Dirac Hamiltonian unless one considers only positive energy solutions. And why should we do that? It is clear that a solution of the Dirac equation that vanishes beyond a limited volume (at some time point) hints at the existence of electron-positron pairs, which is something that does seem to happen in nature, so solutions with a superposition of states with positive and negative energies should not be arbitrarily excluded. If you say that this means the Dirac equation is deficient as a one-particle theory, I will agree, but again, why is this the Born rule's fault?Actually, the form of the Hamiltonian does not matter. See Hegerfeldt's paper
Instantaneous spreading and Einstein causality in quantum theory,
Annalen der Physik 7 (1998), 716--725.