The Black Hole Information Paradox
Abstract
We analyze the black hole information paradox through the lens of the Yoneda Constraint on Observer Knowledge, a category-theoretic principle establishing that an embedded observer accesses reality only through the representable functor. We argue that the information paradox---the apparent conflict between unitarity and the thermal nature of Hawking radiation---is not a physical paradox but a structural consequence of the Yoneda Constraint: the representable presheaf of an observer embedded in a black hole spacetime cannot access the full unitary structure of the quantum gravity theory. We construct a quantum gravitational measurement category, define the relevant Kan extensions, and prove that the Page curve emerges naturally as the image of a left Kan extension along the inclusion of the exterior observer subcategory.
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 (26 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.