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

TL;DR

This paper examines the role of Kolmogorovian Censorship in quantum probabilities, arguing that predictive incompleteness offers a local, minimal explanation for Bell-inequality violations, contrasting with nonlocal or conspiratorial views.

Contribution

It clarifies the conceptual distinctions between KC, predictive incompleteness, and other interpretations, proposing predictive incompleteness as a simple local framework consistent with experiments.

Findings

KC identifies classical probabilities within fixed contexts

Predictive incompleteness preserves locality in quantum explanations

Logical relations among interpretations are clarified

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.