Abstract
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 AdS/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 quasi-static 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.
Highlights
Emergence of classical spacetimes from the fundamental theory of quantum gravity is an important problem
We study how bulk local operators may be realized in a holographic theory of general spacetimes, which includes AdS=CFT as a special case, and deduce its consequences
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
Summary
Emergence of classical spacetimes from the fundamental theory of quantum gravity is an important problem. [22,23] suggest that the information about the interior is somehow contained in the holographic state, since the entanglement wedges of leaf regions cover the interior We interpret these to mean that the description of a black hole provided by the holographic theory is that of a distant picture: the information about the interior is contained in the stretched horizon degrees of freedom [24] whose dynamics is not described by local field theory in the bulk. The semiclassical operators associated with these microstates must be state-dependent as argued by Papadodimas and Raju for the interior of a large AdS black hole [28,29] This is because the code subspaces relevant for these microstates have nontrivial overlaps in the holographic Hilbert space. Throughout the paper, we adopt the unit in which the length lPl—which corresponds to the bulk Planck length when the semiclassical picture is available—is set to unity
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
