Hidden causal loops, macroscopic realism and Einstein-Podolsky-Rosen-Bell correlations: forward-backward stochastic phase-space simulations

• URL: http://arxiv.org/abs/2303.02373v1
• Date: Sat, 4 Mar 2023 10:21:03 GMT
• Title: Hidden causal loops, macroscopic realism and Einstein-Podolsky-Rosen-Bell correlations: forward-backward stochastic phase-space simulations
• Authors: M. D. Reid and P. D. Drummond
• Abstract summary: We analyze a quantum measurement $hatx$ by solving the dynamics of amplitudes that propagate both forward and backward in the time direction. For superpositions and entangled states, we identify causal loops for variables that are not observable. Our results elucidate how hidden causal loops can explain Bell nonlocality, without requiring retrocausality at a macroscopic level.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze a quantum measurement $\hat{x}$ by solving the dynamics of stochastic amplitudes that propagate both forward and backward in the time direction. The dynamics is derived from quantum mechanics: The instantaneous joint density of amplitudes $x$ and $p$ is proved equivalent to the positive $Q(x,p,t)$ phase-space distribution, which establishes causal consistency. We model the measurement $\hat{x}$ as amplification, confirming Born's rule for a system prepared in a superposition of eigenstates $|x_{j}\rangle$ of $\hat{x}$. The trajectories for the backward-propagating variable $x$ are governed by a future boundary condition determined by the measurement setting, as though the system were prepared in a mixture of $|x_{j}\rangle$. Causal relations are deduced from the simulations. For superpositions and entangled states, we identify causal loops for variables that are not observable. A hybrid causal structure exists that is consistent with macroscopic realism. Further, the model allows forward-backward simulation of Einstein-Podolsky-Rosen and Bell correlations, which addresses a question raised by Schr\"odinger. The simulations reveal consistency with a weak form of local realism defined for the system after the unitary interactions determining the measurement settings, the Bell violations emerging due to a breakdown of a subset of Bell's local-realism conditions. Our results elucidate how hidden causal loops can explain Bell nonlocality, without requiring retrocausality at a macroscopic level.

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