We argue that classical spacetimes represent amplified information in the holographic theory of quantum gravity. In general, classicalization of a quantum system involves amplification of information at the cost of exponentially reducing the number of observables. In quantum gravity, the geometry of spacetime must be the analogously amplified information. Bulk local semiclassical operators probe this information without disturbing it; these correspond to logical operators acting on code subspaces of the holographic theory. From this viewpoint, we study how bulk local operators may be realized in a holographic theory of general spacetimes, which includes $\mathrm{AdS}/\mathrm{CFT}$ as a special case, and deduce its consequences. In the first half of the paper, we ask what description of the bulk physics is provided by a holographic state dual to a semiclassical spacetime. In particular, we analyze what portion of the bulk can be reconstructed as spacetime in the holographic theory. The analysis indicates that when a spacetime contains a quasistatic black hole inside a holographic screen, the theory provides a description of physics as viewed from the exterior (though the interior information is not absent). In the second half, we study how and when a semiclassical description emerges in the holographic theory. We find that states representing semiclassical spacetimes are non-generic in the holographic Hilbert space. If there are a maximal number of independent microstates, semiclassical operators must be given state-dependently; we elucidate this point using the stabilizer formalism and tensor network models. We also discuss possible implications of the present picture for the black hole interior.

• Received 23 May 2017

DOI:https://doi.org/10.1103/PhysRevD.97.106025

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Published by the American Physical Society