  We investigate the relation between measurements and the physical observables
for vacuum spacetimes with compact spatial surfaces in (2+1)-gravity with
vanishing cosmological constant. By considering an observer who emits lightrays
that return to him at a later time, we obtain explicit expressions for several
measurable quantities as functions on the physical phase space of the theory:
the eigentime elapsed between the emission of a lightray and its return to the
observer, the angles between the directions into which the light has to be
emitted to return to the observer and the relative frequencies of the lightrays
at their emission and return. This provides a framework in which conceptual
questions about time, observables and measurements can be addressed. We analyse
the properties of these measurements and their geometrical interpretation and
show how they allow an observer to determine the values of the Wilson loop
observables that parametrise the physical phase space of (2+1)-gravity. We
discuss the role of time in the theory and demonstrate that the specification
of an observer with respect to the spacetime's geometry amounts to a gauge
fixing procedure yielding Dirac observables.
