Quantum Foundations: Bell Inequalities and Causality

While Bell nonlocality may be explained by superluminal influences or retrocausal effects, it is often asked why such effects would not manifest macroscopically. We present a resolution, by analyzing a model of reality based on a phase-space simulation, which explains Bell nonlocality consistently with no-signalling and macroscopic realism.

 

We consider the measurement of the entanglement of two field modes. The dynamics is solved via a Fokker-Planck equation for the Q function, Q(x₁,p₁,x₂,p₂) where x_i and p_i are amplitudes for mode i. Deriving theorems, we arrive at stochastic equations, where amplitudes propagate forward or backwards in time, subject to past and future boundary conditions. We model the measurement of a field quadrature X_θ as a phase shift followed by amplification H_amp. In a Bell experiment, the measurement of spin σ_θ is modelled by first coupling to a meter. The solutions provide a way to resolve the measurement problem, the density of the final amplitudes leading to Born’s rule.

 

Our simulations reveal hidden causal loops. Further, by analysing EPR and Bell experiments, we show how with amplification H_amp, after the setting θ is fixed, “elements of reality” appear, that predetermine the outcomes of the measurements. Thus, retrocausality manifests microscopically to explain nonlocality, but there is no retrocausality macroscopically. Finally, the simulations reveal how Bell violations can be consistent with weak forms of both locality and realism.