Transitional Bell Correlation from Dirac Wavepackets

Abstract

We derive a closed-form expression for the Bell--CHSH correlation of entangled, counter-propagating electrons using realistic Dirac wavepackets and localized detection. In contrast to the conventional distance-independent result, the Bell parameter evolves continuously from the quantum bound $2\sqrt{2}$ to the classical limit $2$ as the spatial overlap of the two waves decreases. The quantum enhancement arises entirely from transverse overlap, showing that the Bell violation reflects the local overlap of propagating Dirac waves rather than any action at a distance.