Bell's inequality with Dirac particles

TL;DR

This paper investigates Bell's inequality using relativistic Dirac spinors, demonstrating that the inequality's violation remains observer-independent under Lorentz transformations, highlighting the relativistic invariance of quantum nonlocality.

Contribution

It introduces a relativistically invariant formulation of Bell's inequality using Dirac spinors and the Pauli-Lubanski vector, showing maximal violation persists across reference frames.

Findings

Bell's inequality is maximally violated in all inertial frames.

The violation is observer-independent due to relativistic invariance.

The spin operator relates to the Pauli-Lubanski vector, ensuring Lorentz invariance.

Abstract

We study Bell's inequality using the Bell states constructed from four component Dirac spinors. Spin operator is related to the Pauli-Lubanski pseudo vector which is relativistic invariant operator. By using Lorentz transformation, in both Bell states and spin operator, we obtain an observer independent Bell's inequality, so that it is maximally violated as long as it is violated maximally in the rest frame.