Quantum error correction has given us a natural language for the emergence of
spacetime, but the black hole interior poses a challenge for this framework: at
late times the apparent number of interior degrees of freedom in effective
field theory can vastly exceed the true number of fundamental degrees of
freedom, so there can be no isometric (i.e. inner-product preserving) encoding
of the former into the latter. In this paper we explain how quantum error
correction nonetheless can be used to explain the emergence of the black hole
interior, via the idea of “non-isometric codes protected by computational
complexity”. We show that many previous ideas, such as the existence of a large
number of “null states”, a breakdown of effective field theory for operations
of exponential complexity, the quantum extremal surface calculation of the Page
curve, post-selection, “state-dependent/state-specific” operator
reconstruction, and the “simple entropy” approach to complexity
coarse-graining, all fit naturally into this framework, and we illustrate all
of these phenomena simultaneously in a soluble model.
