Relativistic entanglement and Bell's inequality

Abstract

In this paper, the Lorentz transformation of entangled Bell states seen by a moving observer is studied. The calculated Bell observable for 4 joint measurements turns out to give a universal value, $<\hat{a}\otimes\vec{b}>+<\hat{a}\otimes\vec{b}&#39;>+\lang le\hat{a}&#39;\otimes\vec{b}> -<\hat{a}&#39;\otimes\vec{b}&#39;>=\frac{2}{\sqrt{2-β^2}}(1+\sqrt{1-\be ta^2})$, where $\hat{a}, \hat{b}$ are the relativistic spin observables derived from the Pauli-Lubanski pseudo vector and $β=\frac{v}{c}$. We found that the degree of violation of the Bell&#39;s inequality is decreasing with increasing velocity of the observer and the Bell&#39;s inequality is satisfied in the ultra-relativistic limit where the boost speed reaches the speed of light.