Abstract
We revisit the "state-dependence" of the map that we proposed recently between bulk operators in the interior of a large AdS black hole and operators in the boundary CFT. By refining recent versions of the information paradox, we show that this feature is necessary for the CFT to successfully describe local physics behind the horizon --- not only for single-sided black holes but even in the eternal black hole. We show that state-dependence is invisible to an infalling observer who cannot differentiate these operators from those of ordinary quantum effective field theory. Therefore the infalling observer does not observe any violations of quantum mechanics. We successfully resolve a large class of potential ambiguities in our construction. We analyze states where the CFT is entangled with another system and show that the ER=EPR conjecture emerges from our construction in a natural and precise form. We comment on the possible semi-classical origins of state-dependence.
Highlights
Recent work by Mathur [1], Almheiri et al [2,3] and by Marolf and Polchinski [4] has sharpened the information paradox [5,6] and highlighted some of the difficulties in analyzing questions about local bulk physics in the anti–de Sitter (AdS)/CFT correspondence
By refining recent versions of the information paradox, we show that this feature is necessary for the CFT to successfully describe local physics behind the horizon— for single-sided black holes but even in the eternal black hole
Reconstructing the bulk and state-dependence: Section III is partly devoted to clarifying some conceptual issues related to bulk to boundary maps
Summary
Recent work by Mathur [1], Almheiri et al [2,3] and by Marolf and Polchinski [4] has sharpened the information paradox [5,6] and highlighted some of the difficulties in analyzing questions about local bulk physics in the AdS/CFT correspondence. Almheiri et al argued that even large black holes in anti–de Sitter (AdS) should contain firewalls To make this argument they had to make a second tacit assumption, which was that local bulk observables like the metric are represented by fixed linear operators in the CFT. Is it acceptable at all, within quantum mechanics, to use state-dependent bulk to boundary maps so that the metric at a given point in space may be represented by different operators in different microstates and backgrounds? III we present a discussion of relational observables in AdS quantum gravity This concept is important throughout this paper to understand the geometric properties of operators behind the horizon, but we believe that it may be of broader significance. For a precursor of the firewall paradox, see [21] and for approaches using complexity see [22]
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