Wormholes from Averaging over States

Abstract

An important question about black holes is to what extent a typical pure state differs from the ensemble average. We show that this question can be answered within semi-classical gravity. We focus on the quantum deviation, which measures the fluctuations in the expectation value of an operator in an ensemble of pure states. For a large class of ensembles and observables, these fluctuations are calculated by a correlation function in the eternal black hole background, which can be reliably calculated within semi-classical gravity. This implements the idea of [arXiv:2002.02971] that wormholes can arise from averages over states rather than theories. As an application, we calculate the size of the long-time correlation function $⟨A(t)A(0)⟩$.

38 pages, 2 figures; v2: minor corrections added, accepted for publication in SciPost

References in corpus (6)

• Gravity/Ensemble Duality
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• More quantum noise from wormholes
• Typicality versus thermality: An analytic distinction
• Wormholes without averaging
• Statistical coupling constants from hidden sector entanglement

Cited by in corpus (7)

• Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes
• A principle of maximum ignorance for semiclassical gravity
• Multiboundary wormholes and OPE statistics
• Wormhole calculus without averaging from $O(N{)}^{q-1}$ tensor model
• Worldsheet traversable wormholes
• The entanglement entropy of typical pure states and replica wormholes
• Geometric Quantum Discord Signals Non-Factorization