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We analyze a quantum measurement $\hat{x}$ by solving the dynamics ofstochastic amplitudes that propagate both forward and backward in the timedirection. The dynamics is derived from quantum mechanics: The instantaneousjoint density of amplitudes $x$ and $p$ is proved equivalent to the positive$Q(x,p,t)$ phase-space distribution, which establishes causal consistency. Wemodel the measurement $\hat{x}$ as amplification, confirming Born's rule for asystem prepared in a superposition of eigenstates $|x_{j}\rangle$ of $\hat{x}$.The trajectories for the backward-propagating variable $x$ are governed by afuture boundary condition determined by the measurement setting, as though thesystem were prepared in a mixture of $|x_{j}\rangle$. Causal relations arededuced from the simulations. For superpositions and entangled states, weidentify causal loops for variables that are not observable. A hybrid causalstructure exists that is consistent with macroscopic realism. Further, themodel allows forward-backward simulation of Einstein-Podolsky-Rosen and Bellcorrelations, which addresses a question raised by Schr\"odinger. Thesimulations reveal consistency with a weak form of local realism defined forthe system after the unitary interactions determining the measurement settings,the Bell violations emerging due to a breakdown of a subset of Bell'slocal-realism conditions. Our results elucidate how hidden causal loops canexplain Bell nonlocality, without requiring retrocausality at a macroscopiclevel.

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