Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises

TL;DR

This paper introduces a Q-based stochastic model for quantum measurement and nonlocality that aligns with macroscopic realism and no-signaling, explaining wave function collapse and entanglement through forward-backward simulations.

Contribution

It develops a novel Q-based model with forward-backward stochastic simulations that reconcile quantum phenomena with macroscopic realism and causal structures.

Findings

Demonstrates equivalence between Q distribution and stochastic trajectories.

Shows how amplification leads to observable eigenstates and wave function collapse.

Extends the model to EPR and Bell nonlocality, maintaining consistency with local realistic premises.

Abstract

We show how measurement and nonlocality can be explained consistently with macroscopic realism and no-signaling, and causal relations for macroscopic quantities. Considering measurement of a field amplitude $\hat{x}$, we derive theorems that lead to an equivalence between a quantum phase-space probability distribution Q(x,p,t) and stochastic trajectories for real amplitudes x and p propagating backwards and forwards in time, respectively. We present forward-backward stochastic simulations that motivate a Q-based model of reality. Amplification plays a key role in measurement. With amplification, contributions due to interference become unobservable, leading to branches that correspond to distinct eigenvalues. This elucidates how the system evolves from a superposition to an eigenstate, from which Born's rule follows. We deduce a hybrid causal structure involving causal deterministic relations for amplified variables, along with microscopic noise inputs and hidden loops for unobservable quantities. Causal consistency is confirmed. The simulations allow evaluation of a state inferred for the system, conditioned on a particular branch, from which we deduce a model for projection and collapse of the wave function. The theory is extended to Einstein-Podolsky-Rosen and Bell nonlocality. We demonstrate consistency with three weak local realistic premises: the existence of real properties (defined after operations that fix measurement settings); a partial locality implying no-signaling; elements of reality that apply to the predictions of a system by a meter, once meter-settings are fixed. A mechanism for non-locality is identified. Our work shows how forward-backward stochastic simulations lead to a hybrid causal structure, involving both deterministic causal relations and hidden stochastic loops, explaining measurement and entanglement, with paradoxes associated with retrocausality avoided.