Observer-Dependent Entropy and Operational Information: An Observer-Algebra View of the Black Hole Information Puzzle

This preprint argues that much of the black hole information puzzle comes from comparing entropies defined on different observer algebras of observables. In standard QFT examples (Unruh/Rindler and moving-mirror radiation), a globally pure state induces a thermal state once restricted to an accessible subalgebra. We also state an operational no-go: if late-time exterior restrictions of candidate microstates are all within trace distance ε, then no exterior measurement can decode the microstate label beyond O(ε) (Helstrom/Holevo bounds). Hayden–Preskill decoding and island Page curves naturally correspond to algebra enlargement (additional degrees of freedom and/or nonlocal operators), not to new information available to a strictly semiclassical exterior observer.