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

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.