Comments on Microcausality, Chaos, and Gravitational Observables
Donald Marolf
TL;DR
The paper investigates gravitational observables that respect diffeomorphism invariance while preserving a notion of locality. It identifies a class of single-integral, diffeomorphism-invariant observables that are classically microcausal when IR effects are neglected and argues this microcausality can persist order-by-order in the semiclassical expansion, subject to nonperturbative limitations. It analyzes infrared issues and their impact on microcausality in AdS/dS contexts and explores implications for black hole interiors, including how chaos manifests or is avoided for Hawking-radiation observables. The findings clarify locality structures in quantum gravity, inform black hole information considerations, and suggest avenues for future work on gauge invariance and covariant quantum constructions of these observables.
Abstract
Observables in gravitational systems must be non-local so as to be invariant under diffeomorphism gauge transformations. But at the classical level some such observables can nevertheless satisfy an exact form of microcausality. This property is conjectured to remain true at all orders in the semiclassical expansion, though with limitations at finite $\hbar$ or $\ell_{Planck}$. We also discuss related issues concerning observables in black hole spacetimes and comment on the senses in which they do and do not experience the form of chaos identified by Shenker and Stanford. In particular, in contrast to the situation in a reflecting cavity, this chaos does not afflict observables naturally associated with Hawking radiation for evaporating black holes.