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

Area of Science:

• Quantum mechanics
• Foundations of probability theory
• Quantum information theory

Background:

• The interpretation of quantum probabilities remains a subject of debate.
• Bell inequality violations challenge local realism, suggesting nonlocality or conspiracy.
• Existing frameworks struggle to reconcile quantum probabilities with relativistic locality.

Purpose of the Study:

• To analyze quantum probabilities using Kolmogorovian Censorship (KC) and the Contexts, Systems, and Modalities (CSM) framework.
• To investigate the implications of KC for superdeterminism, counterfactuality, and predictive incompleteness.
• To propose predictive incompleteness as a framework that preserves relativistic locality and matches experimental practice.

Main Methods:

• Revisiting the technical content and scope of Kolmogorovian Censorship (KC).
• Analyzing the relationship between KC, Bell inequality violations, and explanations like nonlocality.
• Developing the concept of predictive incompleteness for quantum states.

Main Results:

• KC confirms probabilities are classical within a fixed measurement context.
• KC alone does not resolve the conceptual tension behind Bell inequality violations.
• Predictive incompleteness provides a minimal, explanatory framework preserving relativistic locality.

Conclusions:

• Predictive incompleteness offers a resolution to the conceptual tension in quantum probabilities.
• This framework aligns with experimental practices and upholds relativistic locality.
• A shift from Kolmogorov's to Gleason's framework is justified for quantum probabilities.