Extending Bell's Theorem: Nonlocality via Measurement Dependence
G. Bacciagaluppi, R. Hermens, G. Leegwater
TL;DR
This work broadens Bell’s theorem by treating Measurement Independence (MI) as a potentially violated assumption and showing that certain MI violations yield signalling in principle, thereby enabling testable forms of nonlocality beyond standard OI/PI analyses. It formalizes signaling in principle via preparation-contexts and equiprobability theorems, and proves that Bell inequality violations coupled with MI violations imply operational signalling under Outcome Independence, while also accommodating no-signalling constraints. The authors provide a sequence of results (Lemma 1, Lemma 2, Theorems 2 and 2') linking Bell violations to signalling through sub-ensembles, and illustrate with Schulman/Wharton retrocausal models that MI-violating ensembles can be constructed to reproduce quantum-like correlations and, in principle, allow signalling. The paper thus extends Shimony’s experimental metaphysics program to a broader class of nonlocality notions, and argues for combined experimental tests that close multiple loopholes while probing the foundations of measurement dependence and preparation-context effects.
Abstract
Besides well-known conditions of locality or factorisability, deriving the Bell inequalities requires assuming that the distribution of hidden variables and Alice's and Bob's measurement settings be independent of each other. We show that (analogously to violations of locality due to action at a distance) certain violations of this Measurement Independence assumption can be associated with a notion of signalling in principle, thus making them also testable in principle, and spell out the appropriate conditions. Accordingly, we show that by imposing no-signalling one can prove a version of Bell's theorem that does not require the assumption of Measurement Independence. We discuss the "Schulman model" as an example, as well as lessons for "experimental metaphysics".