Transitional Bell Correlation from Dirac Wavepackets

TL;DR

This paper derives a formula for Bell correlation in entangled Dirac electrons, showing how the Bell parameter varies with wave overlap and emphasizing the local nature of quantum correlations.

Contribution

It provides a closed-form expression for Bell correlation using realistic Dirac wavepackets, revealing the dependence on wave overlap and challenging the notion of nonlocality.

Findings

Bell parameter decreases from 2√2 to 2 as wave overlap diminishes.

Quantum violation depends on transverse wave overlap, not action at a distance.

Bell violation reflects local wave overlap, not nonlocal effects.

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.