Could quantum mechanics be an approximation to another theory?

TL;DR

This paper explores the idea that quantum mechanics might be an approximation derived from a more fundamental cosmological theory, involving non-local hidden variables and noise effects, leading to Nelson's stochastic quantum formulation.

Contribution

It demonstrates conditions under which quantum mechanics emerges from a cosmological theory via averaging over external variables, connecting it to Nelson's stochastic formulation.

Findings

Quantum mechanics can be derived from a cosmological theory by averaging over non-local hidden variables.

Coupling to external degrees of freedom introduces noise but preserves energy and time reversal invariance.

Nelson's stochastic formulation of quantum mechanics is consistent with these conditions and is not purely classical.

Abstract

We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by averaging over variables which are not internal to the subsystem, which may be considered non-local hidden variables. We find conditions for arriving at quantum mechanics through such a procedure. The key lesson is that the effect of the coupling to the external degrees of freedom introduces noise into the evolution of the system degrees of freedom, while preserving a notion of averaged conserved energy and time reversal invariance. These conditions imply that the effective description of the subsystem is Nelson's stochastic formulation of quantum theory. We show that Nelson's formulation is not, by itself, a classical stochastic theory as the conserved averaged energy is not a linear function of the probability density. We also investigate an argument of Wallstrom posed against the equivalence of Nelson's stochastic mechanics and quantum mechanics and show that, at least for a simple case, it is in error.