[Paper Review] Incompatible Statistics and Bell-KS Theorem

Ángel Rivas|arXiv (Cornell University)|Jan 20, 2015

Quantum Mechanics and Applications3 citations

TL;DR

This paper challenges the Bell-KS theorem by identifying a loophole: models that assign non-trivial joint statistics to quantum-incompatible observables are ruled out by Bell-KS arguments, yet such models could, in principle, support a realistic, noncontextual, or local interpretation of quantum mechanics. The key contribution is showing that rejecting these models does not preclude a realist framework, as they are not physically viable under quantum theory's constraints.

ABSTRACT

We analyze a possible loophole to the conclusion of the Bell-KS theorem that quantum mechanics is not compatible with any realistic and noncontextual or local theory. We emphasize that the models discarded by Bell-KS-like arguments possess a property not shared by quantum mechanics, i.e. the capability to make non-trivial statements about the joint statistics of quantum incompatible observables. By ruling out this possibility, apparently nothing seems to prevent from a realistic, noncontextual or local view of quantum mechanics.

Motivation & Objective

• To investigate whether the Bell-KS theorem truly rules out realistic, noncontextual, or local theories in quantum mechanics.
• To identify and analyze a potential loophole in Bell-KS-type arguments based on the assumption of non-trivial joint statistics for incompatible observables.
• To assess whether models assigning such joint statistics are physically viable within quantum mechanics.
• To determine whether rejecting these models allows for a consistent, realistic, noncontextual, or local interpretation of quantum theory.
• To clarify the physical and conceptual boundaries of compatibility between realism and quantum mechanics.

Proposed method

• Analyzing the logical structure of Bell-KS-type theorems to isolate assumptions about joint statistics of incompatible observables.
• Identifying models that assign non-trivial joint probabilities to quantum-incompatible observables as candidates for realistic, noncontextual theories.
• Demonstrating that such models are incompatible with quantum mechanics due to the non-physical nature of their statistical assignments.
• Ruling out these models based on their violation of quantum mechanical constraints on joint measurements.
• Establishing that the exclusion of such models does not invalidate the possibility of a realistic, noncontextual, or local theory.
• Using logical and foundational analysis to show that the Bell-KS conclusion relies on rejecting physically implausible models.

Experimental results

Research questions

• RQ1 Can realistic, noncontextual, or local models of quantum mechanics be constructed if they assign non-trivial joint statistics to incompatible observables?
• RQ2 Are models that assign joint statistics to incompatible observables physically consistent with quantum mechanics?
• RQ3 Does the Bell-KS theorem genuinely rule out all realistic, noncontextual, or local theories, or is there a loophole?
• RQ4 What physical constraints prevent the viability of models assigning joint statistics to incompatible observables?
• RQ5 Can a realist interpretation of quantum mechanics be maintained if such models are excluded?

Key findings

• Models that assign non-trivial joint statistics to quantum-incompatible observables are incompatible with quantum mechanics due to foundational constraints.
• The Bell-KS theorem relies on rejecting such models, which are not physically viable, to conclude that quantum mechanics is incompatible with realism.
• Excluding these non-viable models does not rule out the possibility of a realistic, noncontextual, or local theory of quantum mechanics.
• The assumption of joint statistics for incompatible observables introduces a physical inconsistency not present in quantum mechanics.
• The paper identifies a loophole in Bell-KS-style arguments by showing that the excluded models are not physically realizable, thus preserving the possibility of realism.
• The conclusion that quantum mechanics is incompatible with realism depends on rejecting models that are already ruled out by quantum theory itself.