Complementarity Endures: No Firewall for an Infalling Observer

TL;DR

The paper analyzes the firewall paradox by treating complementarity as a frame-dependent, unitary relation in the quantum-gravitational Hilbert space ${\cal H}_{\rm QG}$. It shows that information about infalling matter is conserved and emitted via Hawking radiation in a distant frame, while the infalling frame experiences no horizon firewall due to the emergent classicality arising from dynamical quantum processes; projections onto a $b^\dagger b$ eigenstate yield states that are typically superpositions of classical worlds, not a single classical geometry. By invoking a framework where ${\cal H}_{\rm QG} = {\cal H} \oplus {\cal H}_{\rm sing}$ and interpreting complementarity as a frame change, the authors argue that the AMPS firewall is avoided and the equivalence principle persists in the appropriate semi-classical limit. They also show that the probability of obtaining a true classical world from such projections is exponentially suppressed for old black holes, reinforcing the consistency of unitarity with semiclassical gravity and guiding future explorations of quantum-gravitational reference frames.

Abstract

We argue that the complementarity picture, as interpreted as a reference frame change represented in quantum gravitational Hilbert space, does not suffer from the "firewall paradox" recently discussed by Almheiri, Marolf, Polchinski, and Sully. A quantum state described by a distant observer evolves unitarily, with the evolution law well approximated by semi-classical field equations in the region away from the (stretched) horizon. And yet, a classical infalling observer does not see a violation of the equivalence principle, and thus a firewall, at the horizon. The resolution of the paradox lies in careful considerations on how a (semi-)classical world arises in unitary quantum mechanics describing the whole universe/multiverse.

Figures (1)

• Figure 1: A Penrose diagram showing the trajectories of the reference point $p$ for two reference frames---distant (right curve) and infalling (left curve)---in a black hole background. The two frames can be related by a boost acted at some time, represented by the dot on which the two curves merge. The dashed hats attached to the left curve illustrate (null) hypersurfaces on which states, as viewed from the infalling frame, are defined. Here, we represented the setup in a fixed classical geometry for presentation purposes, but a full quantum state is in general a superposition of terms representing well-defined classical geometries.