Separation-Dependent Bell Correlations from Prepared Coherence in Dirac Wavepackets

Abstract

We calculate separation-dependent Bell correlations for a fixed pair of Dirac electron wavepackets in a free, weakly relativistic packet model, treating the prepared joint wave as a physical wave--entity. Each station separation is sampled at the corresponding central packet arrival time. For the illustrated phase \(χ=π/4\), the magnitude of the prescribed-setting Bell--CHSH response decreases and revives; optimizing the spin measurement directions retains the modulation. It occurs already at leading spin order, including for equal prepared branch weights. Interference between direct and exchanged assignments of the electron waves to the stations changes the relative weights and phases of the sampled spin amplitudes, thereby modulating the optimized response. Representative finite spatial and timing windows reduce visibility while retaining broader suppression and revival. This wave--entity account gives a quantitative, testable correlation pattern from prepared coherence, deterministic propagation, and local sampling, without postulating transmission between detectors.

arXiv comment9 pages, 2 figures. Title revised; analysis and references updated