On the Absence of Bell-CHSH Inequality Violations at Large Distances

The standard derivation of Bell-type inequality violations is typically applied only to scenarios involving short distances between detectors. This conventional approach often overlooks the dependence of quantum mechanical wave functions on space-time variables. In this study, we examine the behavior of entangled photons produced in spontaneous parametric downconversion (SPDC) experiments and demonstrate that Bell-CHSH inequalities are not violated at large distances. We analyze the propagation of entangled photon wave packets and show that these initially entangled states tend to disentangle over large spacelike separations. This finding aligns with the observed violations of Bell inequalities at shorter detector separations. To further explore this phenomenon, we propose an experiment to investigate how the quantum correlation function and Bell values change with increasing detector distance, predicting that these quantities will decrease inversely with distance. On the absence of violation of Bell-CHSH inequalities at large distances.