Forward-Time Equivalent of a "Retrocausal" Diffusion Hidden Variable Model for Quantum Mechanics

TL;DR

This paper reformulates a retrocausal quantum hidden variable model into a forward-time framework with initial conditions, linking it to particle interactions and mean-field limits.

Contribution

It provides a forward-time equivalent of a retrocausal model, connecting quantum guidance to particle interactions and mean-field theory.

Findings

Equivalent forward-time equations reproduce the same trajectories.

Guidance term derived as mean-field limit of particle interactions.

Links between retrocausal models and particle ensemble dynamics.

Abstract

A recently proposed stochastic hidden variable model for quantum mechanics has been claimed to involve "retrocausality" due to the appearance of equations of motion with future-time boundary conditions. We formulate an equivalent system of forward-time equations of motion that gives rise to the same trajectories as solutions, but involves only initial-time boundary conditions. The forward-time dynamics involves a guidance term for the dynamical variables, determined by the phase-space distribution corresponding to a quantum wavefunction. We show, however, that this particular guidance term can be recovered as the mean-field limit of averaged pairwise interactions among an ensemble of finitely many particles.