Lecture 25: More on state dependence
In this lecture, we showed how the use of state-dependent mirror operators resolves all paradoxes associated both with large AdS black holes and the eternal black hole. All such paradoxes tacitly invoke a trace over the Hilbert space. But if the operator in the trace varies from one basis element to another, then the paradoxes disappear.
On the other hand, state-dependent gives rise to its own puzzle since it suggests that black holes are anomalously sensitive to low-energy perturbations.
We showed that this puzzle could be resolved by refining the notion of a "simple observable." If we restrict (a) allowed perturbations to those obtained by turning on a source dual to a simple local operator and (b) allowed observations to correlators within a single causal patch, then, as a result of a remarkable property of AdS correlators, the anomalous sensitivity of black holes to low-energy excitations disappears.
