Relativistic Einstein-Podolsky-Rosen Correlations in curved spacetime via Fermi-Walker Transport

TL;DR

This paper introduces a geometric method using Fermi-Walker transport to analyze relativistic EPR correlations in curved spacetime, linking it to Lorentz boosts and Bell inequality violations, with implications for quantum entanglement in general relativity.

Contribution

It presents a novel geometric framework employing Fermi-Walker transport to study relativistic EPR correlations in curved spacetime, unifying Bell inequality analysis with spacetime geometry.

Findings

Fermi-Walker transport mimics successive Lorentz boosts in EPR states.

Bell inequality violation depends on the Wigner rotation angle.

The approach offers a promising way to explore quantum correlations in general relativity.

Abstract

We present a geometric description to study the relativistic EPR correlations in curved spacetime background given by the application of the Fermi-Walker transport in the relativistic EPR states and we show that its result has the same effect as the applications of successive infinitesimal Lorentz boosts in the relativistic EPR states. We also show that the expression for the Bell inequality due to the Fermi-Walker transport is equivalent to the expression demonstrated by Terashima and Ueda \cite{TU2}, where the degree of violation of the Bell inequality is dependent of the angle of the Wigner rotation. This geometrical approach to study the relativistic EPR correlations is a promissing formulation to investigate the EPR correlations in the general relativity background.