Quantum stochastic phase-space theorems lead to hidden causal loops in a model for measurement consistent with macroscopic realism, Bell nonlocality and no-signaling (2205.06070v4)

Abstract: In this paper, we show how quantum measurement and nonlocality can be explained consistently with macroscopic realism and no-signaling. We analyze a measurement of $\hat{x}$ on a system prepared in a superposition of eigenstates, with measurement modeled as amplification, realized by interacting the system with an amplifier. Deriving quantum stochastic path-integral theorems, we prove an equivalence between a phase-space probability distribution $Q(x,p)$ (which uniquely represents the quantum state) and stochastic trajectories for the amplified and attenuated variables, $x$ and $p$, that propagate backwards and forwards in time, respectively. For the superposition, but not the mixture, the backward and forward-propagating trajectories are connected by the initial-time conditional distribution $Q(p|x)$, leading to a causal loop. The joint densities for $x(t)$ and $p(t)$ yield $Q(x,p,t)$, confirming causal consistency. A feature is hidden noise associated with an eigenstate. Unlike the eigenvalue, this noise is not amplified. This motivates an ontological model for measurement, where the amplified amplitude x(t) gives the detected outcome, from which Born's rule follows. For macroscopic superpositions, we demonstrate consistency with macroscopic realism: Further, we evaluate the initial-time distribution $Q_{loop}(x,p)$ for the coupled trajectories conditioned on a given outcome, showing that this cannot correspond to a quantum state. Finally, we analyze Einstein-Podolsky-Rosen and Bell nonlocality. Our conclusion is a model for the collapse of the wave-function and nonlocality, consistent with three weak local realistic premises. We deduce a hybrid causal structure involving causal relations for amplified variables, demonstrating through explicit simulation how microscopic retrocausality can explain measurement and entanglement, without leading to retrocausality at a macroscopic level.