A principle of maximum ignorance for semiclassical gravity

TL;DR

This paper introduces a maximum ignorance principle in holography to model microstate ensembles, predicting semiclassical physics and matching wormhole contributions, thus linking microstructure ignorance to gravitational path integrals.

Contribution

It develops a state-averaging ansatz for microstates in holography, connecting statistical moments to wormhole configurations and microstructure ignorance.

Findings

Ensembles reproduce semiclassical physics on average

Statistical moments match wormhole contributions

Microstructure ignorance is encoded in gravitational path integrals

Abstract

The principle of maximum ignorance posits that the coarse-grained description of a system is maximally agnostic about its underlying microscopic structure. We briefly review this principle for random matrix theory and for the eigenstate thermalization hypothesis. We then apply this principle in holography to construct ensembles of random mixed states. This leads to an ensemble of microstates which models our microscopic ignorance, and which on average reproduces the effective semiclassical physics of a given bulk state. We call this ensemble the state-averaging ansatz. The output of our model is a prediction for semiclassical contributions to variances and higher statistical moments over the ensemble of microstates. The statistical moments provide coarse-grained -- yet gravitationally non-perturbative -- information about the microstructure of the individual states of the ensemble. We show that these contributions exactly match the on-shell action of known wormhole configurations of the gravitational path integral. These results strengthen the view that wormholes simply parametrize the ignorance of the microstructure of a fundamental state, given a fixed semiclassical bulk description.