Can the present be the average of the future?

TL;DR

This paper proposes a two-state vector formalism in quantum mechanics, deriving the Born rule through a time-symmetric approach involving backward-evolving hidden variables.

Contribution

It generalizes Bell's hidden variable model to higher dimensions and introduces a deterministic, time-symmetric rule for measurement outcomes.

Findings

Probabilistic outcomes derived from deterministic backward-evolving states.

Provides an alternative proof of the Pusey, Barrett, Rudolph theorem.

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.