  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.
