An Algebraic Resolution of the Firewall Paradox

TL;DR

This paper uses algebraic quantum gravity techniques to resolve the firewall paradox by showing that the interior and radiation modes cannot be independent, thus invalidating the paradox's core assumption.

Contribution

It formulates subsystem independence in operator-algebraic terms, demonstrating that interior and radiation modes are not independent, resolving the firewall paradox without new physics.

Findings

Subsystem independence assumption fails in diffeomorphism-invariant quantum gravity.

Interior Hawking modes cannot form an independent algebra from radiation modes.

Black hole evaporation is compatible with horizon smoothness without entanglement islands.

Abstract

The AMPS firewall argument relies on treating early radiation, late outgoing Hawking modes, and interior partner modes as approximately independent quantum subsystems. In diffeomorphism-invariant quantum gravity, however, gravitational dressing and asymptotic constraints obstruct such a tensor-product factorization of physical observables. In this essay, we sharpen this obstruction by formulating subsystem independence directly in operator-algebraic terms. Using modular theory, half-sided modular inclusions along null directions, and the sector-wise maximality of the dressed radiation algebra at future null infinity, we show that -- within a fixed asymptotic charge sector -- the algebra associated with the interior Hawking partner cannot form an independent commuting subalgebra, but must be contained as a (non-commuting) subalgebra of the radiation algebra itself. The subsystem-independence assumption underlying the AMPS paradox therefore fails, and the entanglement-monogamy step never becomes applicable. As a result, unitary black hole evaporation and semiclassical horizon smoothness are compatible in asymptotically flat quantum gravity, without invoking entanglement islands, replica wormholes, or modifications of semiclassical horizon physics.