  One solution to the so-called problem of time is to construct certain Dirac
observables, sometimes called evolving constants of motion. There has been some
discussion in the literature about the interpretation of such observables, and
in particular whether single Dirac observables can be measured. Here we clarify
the situation by describing a class of interactions that can be said to
implement measurements of such observables. Along the way, we describe a useful
notion of perturbation theory for the rigging map eta of group averaging
(sometimes loosely called the physical state "projector"), which maps states
from the auxiliary Hilbert space to the physical Hilbert space.
