Kolmogorovian Censorship, Predictive Incompleteness, and the locality loophole in Bell experiments

TL;DR

The paper compares Kolmogorovian Censorship (KC) with the Contexts, Systems and Modalities (CSM) framework in Bell-test contexts, contrasting KC’s context-specific classical probabilities with alternatives like superdeterminism, nonlocality, and predictive incompleteness. It argues that KC alone cannot resolve Bell-type nonlocal or conspiratorial explanations, and promotes predictive incompleteness as a locality-preserving approach that aligns with experimental practice and leads to Gleason's Born-rule structure via context-gluing. The discussion links KC to Gleason's theorem, using the projection-lattice formalism and extravalence to justify a single quantum probability law across contexts while maintaining contextuality. The work offers a clear map of assumptions and shows that predictive incompleteness provides a minimal, explanatory framework compatible with relativistic locality and quantum phenomenology.

Abstract

We revisit the status of quantum probabilities in light of Kolmogorovian Censorship (KC) and the Contexts, Systems and Modalities (CSM) framework, and we compare KC-based frameworks with alternatives such as superdeterminism, supermeasurements, 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.