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10 January 2026

Kolmogorovian Censorship, Predictive Incompleteness, and the Locality Loophole in Bell Experiments

Laboratoire Charles Fabry, Institut d’Optique Graduate School, Centre National de la Recherche Scientifique, Université Paris Saclay, F91127 Palaiseau, France
Entropy2026, 28(1), 80;https://doi.org/10.3390/e28010080 
(registering DOI)
This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering IV

Abstract

We revisit the status of quantum probabilities in light of Kolmogorovian Censorship (KC) and the Contexts, Systems, and Modalities (CSM) framework, and we discuss KC-based ideas with respect to superdeterminism, counterfactuality, and predictive incompleteness. After briefly recalling the technical content of KC and its scope, we show that KC correctly identifies that probabilities are classical within a fixed measurement context but does not by itself remove the conceptual tension that motivates nonlocal or conspiratorial explanations of Bell inequality violations. We argue that predictive incompleteness—the view that the quantum state is operationally incomplete until the measurement context is specified—provides a simple, minimal, and explanatory framework that preserves relativistic locality while matching experimental practice. Finally we clarify logical relations among these positions, highlight the assumptions behind them, and justify the move from Kolmogorov’s to Gleason’s framework for quantum probabilities.

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