Sprecher
Beschreibung
Lorenzo Catani,1,2 Nesta Van Der Schaaf,3 and Rui Soares Barbosa,2
1 INESC TEC, Rua da Universidade, 4710-057 Braga, Portugal
2 International Iberian Nanotechnology Laboratory,
Av. Mestre José Veiga s/n, 4715-330 Braga, Portugal
3 Université Paris-Saclay, CNRS, CentraleSupélec, ENS Paris-Saclay,
Inria, Laboratoire Méthodes Formelles, 91190, Gif-sur-Yvette, France
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, locally causal ontological models posit 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. The elements of reality are no longer points, but regions of
a point-free generalization of a topological space (sublocales of a locale). These parts, which we
call records, are primitive and inherently relational. A record shared by two incompatible contexts
establishes the sameness of a measurement across them, without such pairwise identities composing
into a global valuation. The common cause is then a web 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 each context is
normalized on its own, so that modularity, the inclusion-exclusion law of classical probability, fails
across incompatible contexts and the underlying probability theory generalizes Kolmogorov’s. 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. A realist explanation of the quantum predictions
need not be conspiratorial; every causal influence posited by these explicit models is reflected in the
operational predictions.
This work is funded by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the support UID/50014/2025 (https://doi.org/10.54499/UID/50014/2025).