The final state proposal [G. T. Horowitz and J. M. Maldacena, J. High Energy Phys. 04 (2004) 008] is an attempt to relax the apparent tension between string theory and semiclassical arguments regarding the unitarity of black hole evaporation. Authors Bousso and Stanford [Phys. Rev. D 89, 044038 (2014)] analyze thought experiments where an infalling observer first verifies the entanglement between early and late Hawking modes and then verifies the interior purification of the same Hawking particle. They claim that ``probabilities for outcomes of these measurements are not defined'' and therefore suggest that ``the final state proposal does not offer a consistent alternative to the firewall hypothesis.'' We show, in contrast, that one may define all the relevant probabilities based on the so-called ABL rule [Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz, Phys. Rev. 134, B1410 (1964)], which is better suited for this task than the decoherence functional. We thus assert that the analysis of Bousso and Stanford cannot yet rule out the final state proposal.
The black hole final state proposal reconciles the infalling vacuum with the unitarity of the Hawking radiation, but only for some experiments. We study experiments that first verify the exterior, then the interior purification of the same Hawking particle. (This is the same protocol that renders the firewall paradox operationally meaningful in standard quantum mechanics.) We show that the decoherence functional fails to be diagonal, even upon inclusion of external ``pointer'' systems. Hence, probabilities for outcomes of these measurements are not defined. We conclude that the final state proposal does not offer a consistent alternative to the firewall hypothesis.
Alice stays outside a black hole; Bob falls in. Alice never sees the interior. Bob crosses the horizon but can never signal back. Physics holds subjectively for both, yet their realities objectively contradict. This illustrating a conflict between quantum and classical mechanics. AMPS is a thought experiment about this. It asks one observer to distil a purifier of a late Hawking mode
B from early radiation
R, then compare it with the interior partner
A inside a single causal patch. The hidden cost is not just computation but control. If the correct decoder depends on the black hole microstate, the observer must carry a physical selector for the decoder family. I model that selector as a finite control register bounded by the covariant entropy bound on the patch. A covering argument shows that any fixed, state-independent decoder works on at most
2α∗SBH+cε microstates, so the observer needs at least
(1−α∗)SBH−cε control bits---requiring a patch with area fraction
ρ2≥1−α∗−cε/SBH. A time-sharing objection fails because single-observer verification requires co-instantiation, not mere sequential occurrence; serialisation creates no free room. The conclusion: a subhorizon observer generally cannot certify the AMPS contradiction. In quantum gravity, control information is physical, and single-observer certification is a capacity problem. If the contradiction can never be measured, is it real?
In an attempt to restore the unitarity of the evaporation process, Horowitz and Maldacena recently proposed a boundary-condition constraint for the final quantum state of an evaporating black hole at its singularity. Gottesman and Preskill have argued that the proposed constraint must lead to nonlinear evolution of the initial (collapsing) quantum state. Here we show that in fact this evolution allows signaling, making it detectable outside the event horizon with entangled-probe experiments of the kind we proposed recently. As a result the Horowitz-Maldacena proposal may be subject to terrestrial tests.
A bstract Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations of entanglement entropy. We show how these computations can be justified using the replica trick, from geometries with a spacetime wormhole connecting the different replicas. In a simple model, we study the Page transition in detail by summing replica geometries with different topologies. We compute related quantities in less detail in more complicated models, including JT gravity coupled to conformal matter and the SYK model. Separately, we give a direct gravitational argument for entanglement wedge reconstruction using an explicit formula known as the Petz map; again, a spacetime wormhole plays an important role. We discuss an interpretation of the wormhole geometries as part of some ensemble average implicit in the gravity description.