  We address the construction and interpretation of diffeomorphism-invariant
observables in a low-energy effective theory of quantum gravity. The
observables we consider are constructed as integrals over the space of
coordinates, in analogy to the construction of gauge-invariant observables in
Yang-Mills theory via traces. As such, they are explicitly non-local.
Nevertheless we describe how, in suitable quantum states and in a suitable
limit, the familiar physics of local quantum field theory can be recovered from
appropriate such observables, which we term `pseudo-local.' We consider
measurement of pseudo-local observables, and describe how such measurements are
limited by both quantum effects and gravitational interactions. These
limitations support suggestions that theories of quantum gravity associated
with finite regions of spacetime contain far fewer degrees of freedom than do
local field theories.
