Hidden Variable Debates Reconsidered

Abstract

We revisit the century-long debate over hidden variables in quantum mechanics through the lens of the Yoneda Constraint on Observer Knowledge. We argue that the hidden variable question---whether quantum indeterminacy reflects genuine ontological structure or mere epistemic limitation---is resolved by recognizing that all no-go theorems (Bell, Kochen-Specker, PBR) are instances of a single category-theoretic phenomenon: the non-representability of certain presheaves on measurement categories. The Yoneda Constraint establishes that observers access physical reality only through representable presheaves, and hidden variable models correspond precisely to attempts to extend non-representable presheaves to representable ones.

Key Results

This paper applies the Yoneda Constraint on Observer Knowledge to provide a rigorous category-theoretic analysis of one of the deepest open problems in quantum foundations and gravitational physics.

The central mathematical framework involves:

• Measurement Categories: Observer-system interactions formalized as morphisms in structured categories
• Representable Presheaves: The Yoneda embedding maps each observer to their complete relational profile
• Kan Extension Deficits: Information loss at epistemic horizons quantified as failures of exactness
• Cohomological Obstructions: No-go theorems arising as non-vanishing cohomology classes

Full Paper

The complete paper is available as a PDF (27 pages) with all proofs, constructions, and detailed mathematical development.

The companion Haskell codebase implementing all categorical constructions is available on GitHub.

Series 1 Context

This paper is part of Series 1: Foundational Problems, a collection of six papers applying the Yoneda Constraint to the deepest open questions in quantum foundations, black hole physics, and quantum gravity. The full series is available in the yoneda-ai repository.