Hidden variables with nonlocal time

TL;DR

This paper introduces a nonlocal time rescaling in relativistic hidden variable theories to reconcile nonlocal quantum correlations with relativity, supported by toy models and a comprehensive theory matching quantum predictions.

Contribution

It proposes a novel nonlocal time framework that allows local relativistic particle trajectories to produce quantum correlations, addressing a key tension in hidden variable theories.

Findings

Toy models reproduce nonlocal quantum phenomena.

The realistic theory matches all quantum predictions.

Nonlocal time rescaling maintains relativistic consistency.

Abstract

To relax the apparent tension between nonlocal hidden variables and relativity, we propose that the observable proper time is not the same quantity as the usual proper-time parameter appearing in local relativistic equations. Instead, the two proper times are related by a nonlocal rescaling parameter proportional to |psi|^2, so that they coincide in the classical limit. In this way particle trajectories may obey local relativistic equations of motion in a manner consistent with the appearance of nonlocal quantum correlations. To illustrate the main idea, we first present two simple toy models of local particle trajectories with nonlocal time, which reproduce some nonlocal quantum phenomena. After that, we present a realistic theory with a capacity to reproduce all predictions of quantum theory.