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 $⟨A(t)A(0)⟩$.

arXiv comment38 pages, 2 figures; v2: minor corrections added, accepted for publication in SciPost

References in corpus (31)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A bound on chaos
• Eternal Black Holes in AdS
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Replica Wormholes and the Entropy of Hawking Radiation
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• The entropy of Hawking radiation
• Canonical Typicality
• The approach to thermal equilibrium in quantized chaotic systems
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• A semiclassical ramp in SYK and in gravity
• Random Statistics of OPE Coefficients and Euclidean Wormholes
• The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
• Scalar field quantization on the 2+1 dimensional black hole background
• Gravity/Ensemble Duality
• Bounds on chaos from the eigenstate thermalization hypothesis
• Entropies of Scalar Fields on Three Dimensional Black Holes
• Eigenstate Thermalization and Disorder Averaging in Gravity
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Late time physics of holographic quantum chaos
• On the Distribution of the Wave Function for Systems in Thermal Equilibrium
• Unitarity From a Smooth Horizon?
• More quantum noise from wormholes
• Typicality versus thermality: An analytic distinction
• Microcanonical Path Integrals and the Holography of small Black Hole Interiors
• Wormholes without averaging
• Long time scales and eternal black holes
• Geometry And Quantum Noise
• Pure state quantum statistical mechanics and black holes
• Statistical coupling constants from hidden sector entanglement
• Ensemble averages, Poisson processes and Microstates

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