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arXiv:1403.3706

Experimental Test of the Final State Hypothesis

Michael Devin

Published Mar 13, 2014• 0 citations
arXivHTMLPDF

Abstract

The black hole final state projection model, also known as the Horowitz-Maldacena model has garnished new interest due to the current debate over black hole firewalls. The nonlinear quantum mechanics of post-selection preserves information and avoids the AMPS argument by relaxing monogamy of entanglement. While these are promising features there are also potentially observable predictions to be made.

DOI
10.48550/arxiv.1403.3706

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The black hole final state projection model, also known as the Horowitz-Maldacena model has garnished new interest due to the current debate over black hole firewalls. The nonlinear quantum mechanics of post-selection preserves information and avoids the AMPS argument by relaxing monogamy of entanglement. While these are promising features there are also potentially observable predictions to be made.
Almheiri et al. have emphasized that otherwise reasonable beliefs about black hole evaporation are incompatible with the monogamy of quantum entanglement, a general property of quantum mechanics. We investigate the final-state projection model of black hole evaporation proposed by Horowitz and Maldacena, pointing out that this model admits cloning of quantum states and polygamous entanglement, allowing unitarity of the evaporation process to be reconciled with smoothness of the black hole event horizon. Though the model seems to require carefully tuned dynamics to ensure exact unitarity of the black hole S-matrix, for a generic final-state boundary condition the deviations from unitarity are exponentially small in the black hole entropy; furthermore observers inside black holes need not detect any deviations from standard quantum mechanics. Though measurements performed inside old black holes could potentially produce causality-violating phenomena, the computational complexity of decoding the Hawking radiation may render the causality violation unobservable. Final-state projection models illustrate how inviolable principles of standard quantum mechanics might be circumvented in a theory of quantum gravity.
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.
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.
Black holes offer an exciting area to explore the nature of quantum gravity. The classic work on Hawking radiation indicates that black holes should decay via quantum effects, but our ideas about how this might work at a technical level are incomplete. Recently Almheiri-Marolf-Polchinski-Sully (AMPS) have noted an apparent paradox in reconciling fundamental properties of quantum mechanics with standard beliefs about black holes. One way to resolve the paradox is to postulate the existence of a ``firewall'' inside the black hole horizon which prevents objects from falling smoothly toward the singularity. A fundamental limitation on the behavior of quantum entanglement known as ``monogamy'' plays a key role in the AMPS argument. Our goal is to study and apply many-body entanglement theory to consider the entanglement among different parts of Hawking radiation and black holes. Using the multipartite entanglement measure called negativity, we identify an example which could change the AMPS accounting of quantum entanglement and perhaps eliminate the need for a firewall. Specifically, we constructed a toy model for black hole decay which has different entanglement behavior than that assumed by AMPS. We discuss the additional steps that would be needed to bring lessons from our toy model to our understanding of realistic black holes.
Recent models of the black-hole final state suggest that quantum information can escape from a black hole by a process akin to teleportation. These models rely on a controversial process called final-state projection. This Letter discusses the self-consistency of the final-state projection hypothesis and investigates escape from black holes for arbitrary final states and for generic interactions between matter and Hawking radiation. Quantum information escapes with fidelity approximately = (8/3pi)2: only half a bit of quantum information is lost on average, independent of the number of bits that escape from the hole.
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.