Firewalls From Double Purity

TL;DR

The paper reframes the firewall paradox as a double-purity issue: near-horizon modes are purified by the interior in the infalling vacuum, which clashes with unitarity if the out-state is pure, independent of Page time. It argues that traditional complementarity cannot resolve this when the horizon zone is in a pure or near-pure state, and that pure-zone states span the microcanonical ensemble, making the horizon a special place. Through a donkey-map framework and a simple two-qubit model, it shows that state-dependent, nonunitary complementarity cannot universally recover the vacuum without violating either causality or the equivalence principle. The work concludes that firewalls arise from the structure of the Hilbert space and thermodynamics, implying that horizon detectability is the true criterion for firewall pathology, and that a dynamically consistent horizon theory may avoid firewall-like violations of the equivalence principle.

Abstract

The firewall paradox is often presented as arising from double entanglement, but I argue that more generally the paradox is double purity. Near-horizon modes are purified by the interior, in the infalling vacuum. Hence they cannot also be pure alone, or in combination with any third system, as demanded by unitarity. This conflict arises independently of the Page time, for entangled and for pure states. It implies that identifications of Hilbert spaces cannot resolve the paradox. Traditional complementarity requires the unitary identification of infalling matter with a scrambled subsystem of the Hawking radiation. Extending this map to the infalling vacuum overdetermines the out-state. More general complementarity maps ("A=R_B", "ER=EPR") founder when the near-horizon zone is pure. I argue that pure-zone states span the microcanonical ensemble, and that this suffices to make the horizon a special place. I advocate that the ability to detect the horizon locally, rather than the degree or probability of violence, is what makes firewalls problematic. Conversely, if the production of matter at the horizon can be dynamically understood and shown to be consistent, then firewalls do not constitute a violation of the equivalence principle.