Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior

TL;DR

This paper argues that state-dependence in the black hole interior is essential for the boundary CFT to accurately describe physics behind the horizon, and it clarifies how this does not violate quantum mechanics for infalling observers.

Contribution

It refines the understanding of state-dependence in black hole holography, showing its necessity and how it aligns with quantum mechanics and the ER=EPR conjecture.

Findings

State-dependence is necessary for describing the black hole interior in the CFT.

Infalling observers cannot detect violations of quantum mechanics due to state-dependence.

The ER=EPR conjecture naturally emerges from the construction.

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.