On the Unitarity of the Stueckelberg Wave Equation and Measurement as Bayesian Update from Maximum Entropy Prior Distribution

The Stueckelberg wave equation is transformed into a quantum telegraph equation and a set of stationary states is obtained as unitary solutions. As it has been shown previously that this PDE relates to the Dirac operator, and on the other hand it is a linearized Hamilton–Jacobi–Bellman PDE, from which the Schrödinger equation can be deduced in a nonrelativistic limit, it is clear that it is the key equation in relativistic quantum mechanics. We give a Bayesian interpretation for the measurement problem. The stationary solution is understood as a maximum entropy prior distribution and measurement is understood as a Bayesian update. We discuss the interpretation of the single electron experiments in the light of finite speed propagation of the transition probability field and how it relates to the interpretation of quantum mechanics more broadly.