A Local $$\psi $$ ψ -Epistemic Retrocausal Hidden-Variable Model of Bell Correlations with Wavefunctions in Physical Space

Abstract

We construct a local $\psi$-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state $|\psi_e(t)\rangle$ as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state $|\psi_o(t)\rangle$ which is different from the prepared quantum state $|\psi_e(t)\rangle$ and has an ontic status. The ontic state of a single particle consists of two parts. First, a single particle ontic quantum state $\chi(\vec{x},t)|i\rangle$, where $\chi(\vec{x},t)$ is a 3-space wavepacket and $|i\rangle$ is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space $\vec{x}(t)$, which evolves via a de Broglie-Bohm type guidance equation with the 3-space wavepacket $\chi(\vec{x},t)$ acting as a local pilot wave. The joint ontic quantum state $|\psi_o(t)\rangle$ fixes the measurement outcomes deterministically whereas the prepared quantum state $|\psi_e(t)\rangle$ determines the distribution of the $|\psi_o(t)\rangle$'s over an ensemble. Both $|\psi_o(t)\rangle$ and $|\psi_e(t)\rangle$ evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider `non-equilibrium' extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics.