Séminaire de Physique Théorique

Time, measurements and observables in Lorentzian (2+1)-gravity
Catherine Meusburger (University of Nottingham )
Wednesday 21 January 2009 11:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
(2+1)-dimensional gravity is equipped with a complete set of observables, the Wilson loops, which parametrise the physical phase space of the theory and play a central role in many quantisation approaches. However, it has been difficult to relate these observables to quantities that could be measured by an observer in the spacetime and, conversely, to identify functions on the physical phase space that have a clear physical interpretation. This complicated the interpretation of the theory and made it difficult to extract interesting physics from the model. In this talk, we address this problem for (classical) Lorentzian (2+1)-gravity with vanishing cosmological constant and without matter. We relate the observables which parametrise the physical phase space of the theory to quantities that could be measured by observers and have a clear physical interpretation. By considering an observer who probes the geometry of the spacetime by emitting lightrays that return to him at a later time, we derive explicit expressions for three quantities measured by the observer as functions on the physical phase space: the eigentime elapsed between the emission and return of a lightray, the angles between the directions which yield returning lightrays and the relative frequency shift between the emitted and returning lightray. This provides a concrete example in which questions about time, measurements and observables in gravity can be addressed. In particular, we discuss the role of time, and we show that the Wilson loop observables arise naturally in the measurements performed by certain observers. References: arxiv: 0811.4155v1 [gr-qc]

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