Limits of Quantum Gravity Observation

Abstract

We apply the Yoneda Constraint on Observer Knowledge---the principle that an embedded observer accesses reality only through the representable functor---to the problem of observing quantum gravitational phenomena. We construct a quantum gravitational measurement category whose objects are observer-spacetime pairs and whose morphisms are measurement interactions compatible with both quantum mechanics and general relativity. We identify three independent Yoneda obstructions to Planck-scale observation: the gravitational backreaction obstruction, the holographic entropy obstruction, and the causal structure obstruction.

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 (33 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.