Geometric Structure of Bell Correlations in Bohmian Mechanics: A Configuration-Space Analysis of EPR Experiments

Abstract

We develop an explicit configuration-space formulation of EPR-Bell experiments within the framework of de Broglie-Bohm theory, in which joint measurement outcomes arise from a deterministic mapping from initial particle configurations to outcome pairs. This construction induces a partition of the hidden-variable configuration space into domains associated with the different measurement outcomes. Using a reduced-dimensional Stern-Gerlach model, we derive the structure of these domains and identify the corresponding separatrices that define their boundaries. We show that Bell correlations emerge from the geometry of these partitions: the domain boundaries depend nonlocally on the measurement settings, while the marginal outcome distributions remain invariant, providing a direct dynamical realization of no-signaling. Analytical results are supported by numerical simulations, which exhibit quantitative agreement with the predicted domain structure as a consequence of the underlying partition of configuration space induced by the measurement dynamics. This approach provides an explicit configuration-space representation of nonlocal correlations in Bohmian mechanics, linking trajectory dynamics, measurement processes, and statistical predictions within a unified framework.