A Multiple Observer Probability Analysis for Bell Scenarios in Special Relativity

Abstract

Here we present a Multiple Observer Probability Analysis (MOPA) for the purpose of clarifying topics in experimental Bell scenarios. Because Bell scenarios are interested in quantum effects between nonlocal measurement devices, we assign an observer to each device: Alice and Bob. Given that the observers are stationary and space-like separated, each observer is privy to different information along their shared equi-temporal lines due to permutations in the order they observe events. Therefore, each observer is inclined to assign different probability distributions to the same set of propositions due to these informational differences. The observers are obligated to update their probability distributions on the basis of locally observed events, and in this sense, factuality is informational locality. In this framework, only local variables or detections may be factual, but nothing prevents an observer from inquiring or making if-then inferences on the counterfactual basis of a nonlocal proposition being true. Indeed the objects pertaining to these nonlocal counterfactual propositions may be far outside an observer's light cone. The MOPA arrives at the conclusion that the CHSH inequality is only nonlocally violated "counterfactually" by each observer whereas local violations of the CHSH may be factual or counterfactual. We believe the MOPA to better gel probability theory (and thus QM) with Special Relativity than does the standard locality conditions imposed in the Bell and CHSH inequalities. The no-signaling condition is reinterpreted, and perhaps further clarified, in the MOPA and statements about counterfactuality and observer dependent QM are made.