Mathematics – Logic
Scientific paper
Dec 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aipc.1196..181m&link_type=abstract
THE PLANCK SCALE: Proceedings of the XXV Max Born Symposium. AIP Conference Proceedings, Volume 1196, pp. 181-189 (2009).
Mathematics
Logic
1
Gravitational Constant, Space-Time Configurations, Quantum Gravity, Geodesy, Observational Cosmology, Quantum Field Theory In Curved Spacetime, Phenomenology Of Quantum Gravity, Geodesy And Gravity
Scientific paper
We consider an observer in a (2+1)-spacetime without matter and cosmological constant who measures spacetime geometry by emitting lightrays which return to him at a later time. We investigate several quantities associated with such lightrays: the return time, the directions into which light needs to be emitted to return and the frequency shift between the lightray at its emission and its return. We derive explicit expressions for these quantities as functions on the reduced phase space and show how they allow the observer to reconstruct the full geometry of the spacetime in finite eigentime. We comment on conceptual issues. In particular, we clarify the relation between these quantities and Dirac observables and show that Wilson loops arise naturally in these quantities.
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