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We consider an observer in a (2+1)-spacetime without matter and cosmologicalconstant who measures spacetime geometry by emitting lightrays which return tohim at a later time. We investigate several quantities associated with suchlightrays: the return time, the directions into which light needs to be emittedto return and the frequency shift between the lightray at its emission and itsreturn. We derive explicit expressions for these quantities as functions on thereduced phase space and show how they allow the observer to reconstruct thefull geometry of the spacetime in finite eigentime. We comment on conceptualissues. In particular, we clarify the relation between these quantities andDirac observables and show that Wilson loops arise naturally in thesequantities.

Spacetime Geometry in (2+1)-gravity via Measurements with Returning Lightrays