Lecture 24: State dependence
In this lecture, we completed our discussion of the construction of mirror operators. We described how the construction accounts for the nontrivial commutator of interior operators with the Hamiltonian. We also described how the construction accounts for near-equilibrium states and thereby avoids the "frozen vacuum" problem.
By adding mirror operators constructed in different little Hilbert spaces, one obtains operators that can be used to describe the black hole interior for any state within the direct sum of these spaces. But this process cannot be extended to obtain globally defined mirror operators.
This observation led us to the notion of "state dependence." This is the interesting idea that the observables that are appropriate to describe the experience of the infalling observer may depend on the microstate.
