Entanglement, Space–Time Coordinates, and Bell's Inequalities in Photon–Polarization Experiments

Abstract

This work presents a revised analysis and corresponding perspective of Bell-type inequalities and their connection to entanglement in polarization experiments with single-photon resolution. It is argued that standard derivations of Bell-type inequalities implicitly rely on additional assumptions beyond those originally stated, specifically concerning the cardinalities of the sets of measurements and the sets of photon-pair properties (Einstein's elements of physical reality, Bell's $\lambda$). Any model-based averages must depend on these cardinalities and violations of Bell-type inequalities become possible for certain ranges of them. In addition, we argue that for Aspect-type experiments, the statistical properties associated with Bell's (hidden variable) λ can be different before and after actual photon-transmission through the polarizers. This distinction is particularly necessary for the actual equipment used in the Aspect-type experiments. Building on these observations, we construct a model based on a consistent evaluation of the measurement events relative to each other. The model reproduces all quantum-mechanical expectation values for polarization correlations without invoking instantaneous influences at a distance, and additionally yields explicit outcomes for individual photon-pair measurements. Within this framework, our Einstein-type Global Space-Time Model (GSTM) accounts also for polarization correlations in Malus-type experiments and addresses all commonly discussed paradoxes associated with single-photon measurements.