Observables, gravitational dressing, and obstructions to locality and subsystems

TL;DR

This work shows that diffeomorphism invariance in gravity mandates gravitational dressing of any operator with nonzero Poincaré charges, introducing nonlocal dependence on the asymptotic metric at leading order and undermining the standard locality structure of local quantum field theory. The authors prove a dressing theorem constraining the asymptotic tails of gauge-invariant dressings, argue that positive energy prevents screening, and conclude that local commuting subalgebras—and hence clean quantum subsystems—do not exist in perturbative gravity. They explore alternative observable constructions, including diffeomorphism-invariant single-integral (relational) observables and extended phase-space frameworks, as potential routes to approximate locality or new notions of subsystems, though a universal solution remains elusive. The results bear on foundational questions about locality, entanglement, and information in quantum gravity and may inform holographic and black hole information scenarios by clarifying the limits of subsystem factorization. Overall, locality in gravity appears to be state-dependent and approximate, rather than an exact structural staple of the theory.

Abstract

Quantum field theory - our basic framework for describing all non-gravitational physics - conflicts with general relativity: the latter precludes the standard definition of the former's essential principle of locality, in terms of commuting local observables. We examine this conflict more carefully, by investigating implications of gauge (diffeomorphism) invariance for observables in gravity. We prove a dressing theorem, showing that any operator with nonzero Poincare charges, and in particular any compactly-supported operator, in flat-spacetime quantum field theory must be gravitationally dressed once coupled to gravity, i.e. it must depend on the metric at arbitrarily long distances, and we put lower bounds on this nonlocal dependence. This departure from standard locality occurs in the most severe way possible: in perturbation theory about flat spacetime, at leading order in Newton's constant. The physical observables in a gravitational theory therefore do not organize themselves into local commuting subalgebras: the principle of locality must apparently be reformulated or abandoned, and in fact we lack a clear definition of the coarser and more basic notion of a quantum subsystem of the Universe. We discuss relational approaches to locality based on diffeomorphism-invariant nonlocal operators, and reinforce arguments that any such locality is state-dependent and approximate. We also find limitations to the utility of bilocal diffeomorphism-invariant operators that are considered in cosmological contexts. An appendix provides a concise review of the canonical covariant formalism for gravity, instrumental in the discussion of Poincare charges and their associated long-range fields.