Can the present be the average of the future?

Abstract

We introduce a two state vector formalism of quantum mechanics by generalizing Bell hidden variable model to higher dimensions and by attributing a physical significance, a state evolving backward in time, to the hidden variable. A simple deterministic and time symmetric rule for measurement outcomes allows us to obtain the Born rule. It turns out that probabilistic outcomes can be derived from a deterministic assignment and averaging over future states that propagate backward to the present. The assignment rule provides an alternative statement and demonstration of the Pusey, Barrett, Rudolph theorem.