Sprecher
Beschreibung
Authors: Lorenzo Catani,1 Nesta Van Der Schaaf,2 and Rui Soares Barbosa,3
1 INESC TEC, Rua da Universidade, 4710-057 Braga, Portugal
2 Université Paris-Saclay, CNRS, CentraleSupélec, ENS Paris-Saclay,
Inria, Laboratoire Méthodes Formelles, 91190, Gif-sur-Yvette, France
3 International Iberian Nanotechnology Laboratory,
Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal
Abstract: Bell's theorem is popularly stated as the inconsistency of quantum theory with local realism. More precisely, realism here is mathematically described by the ontological models framework, where the elements of reality are represented by points in a measurable space, and probabilities obey the Kolmogorov axioms. In the Bell scenario, such models amount to a common cause supporting a global valuation— a joint assignment of outcomes to all measurements at once, across mutually incompatible contexts. Within this notion of realism, Bell's theorem implies that any realist explanation of the quantum predictions must be conspiratorial: any underlying mechanism, whether superluminal, superdeterministic, or retrocausal, must be finely tuned so as never to manifest at the operational level.
In this work, we redefine realism by developing a new ontological framework that generalizes the standard one and takes the incompatibility of measurement contexts seriously. The elements of reality are no longer points but regions of a point-free topological space (sublocales of a locale). These regions are primitive and inherently relational: they act as records that establish the sameness of a measurement across two incompatible contexts without fixing a joint assignment of outcomes across them. The common cause becomes a network of such records rather than a global valuation. Within this framework, Bell's no-go theorem becomes a go theorem: local causality is no longer at odds with the statistics of quantum theory. This is possible because, with no global valuation to preserve, the underlying probability theory generalizes Kolmogorov's, modularity being no longer required across incompatible contexts. We exhibit an explicit family of models in the new framework, reproducing several quantum strategies, including the optimal CHSH violation. More broadly, locally causal models of this kind attain every Bell--CHSH value up to the algebraic maximum.