[Paper Review] More quantum noise from wormholes

Douglas Stanford|arXiv (Cornell University)|Aug 19, 2020

Black Holes and Theoretical PhysicsPhysics and Astronomy48 references69 citations

TL;DR

The paper studies wormhole contributions in dilaton gravity that reproduce ensemble-averaged noise in Hawking radiation, connecting classical and quantum calculations to the Page curve and replica wormholes.

ABSTRACT

For black hole evaporation to be unitary, the naive density matrix of Hawking radiation needs to be corrected with a sprinkling of pseudorandom "noise." Using wormholes, semiclassical gravity appears to describe an averaged "true random" theory of this noise. We discuss the wormholes in dilaton gravity theories with matter. They are classical solutions that depend on a small amount of backreaction from matter fields, and they are closely related to the wormholes that give the Page curve.

Motivation & Objective

• Motivate how pseudorandom noise in Hawking radiation can be modeled as true randomness via gravitational wormholes.
• Analyze classical and quantum contributions of wormholes in dilaton gravity with matter to the squared inner products of black hole microstates.
• Show agreement between wormhole computations and ensemble averages for correlation functions.
• Relate wormhole results to replica wormholes and factorization discussions in gravity.

Proposed method

• Compute the squared overlap |<ψ_i|ψ_j>|^2 via wormhole geometries in two-dimensional dilaton gravity with matter.
• Use a phase-space (E, θ) formulation for the wormhole dynamics, including operator insertions as impulsive forces and geodesic lengths.
• Employ both classical approximate analysis and quantum (exact quantization) treatment of JT gravity and general dilaton gravities.
• Relate gravitational contributions to ensemble averages, showing E{<ψ_i|ψ_j>|^2} = δ_ij + e^{-S} with S as entropy.
• Match results to an ensemble interpretation where off-diagonal noise has mean zero and unit variance in appropriate scaling.
• Discuss replica wormholes and factorization through the cylinder vs disk topologies and their implications.

Experimental results

Research questions

• RQ1 What is the gravitational origin of the off-diagonal noise in the radiation density matrix?
• RQ2 How do wormholes in dilaton gravity reproduce ensemble-averaged correlations like |<ψ_i|ψ_j>|^2?
• RQ3 Can classical and quantum JT/dilaton gravity calculations reproduce the expected Page curve-like behavior for radiation entropy?
• RQ4 How do operator insertions affect the stabilization and geometry of wormholes, and what is the resulting energy and length dynamics?
• RQ5 What is the relationship between replica wormholes, factorization, and ensemble interpretation in this context?

Key findings

• The wormhole contribution to |<ψ_i|ψ_j>|^2 yields an e^{-S} term, matching the ensemble-average expectation δ_ij + e^{-S} when appropriately interpreted.
• Classical phase-space analysis shows how operator insertions act as impulsive forces that stabilize or modify wormhole lengths and energies.
• In JT gravity and dilaton gravity with matter, the computed wormhole effects align with what one expects from an ensemble average over theories, supporting a gravity-based average rather than a single fixed theory.
• For two operator insertions, the equilibrium condition fixes the relationship β = m/E in the cylinder topology, highlighting a different energy-β relation than the disk topology.
• Quantum (exact) calculations in JT gravity corroborate the classical intuition and demonstrate how the cylinder geometry contributes the expected entropy factors.
• The results connect to replica wormhole ideas and provide a framework for factorization vs ensemble interpretation in gravitational path integrals.