OBSERVERS IN QUANTUM GRAVITY
Perimeter Institute for Theoretical Physics
Monday 22 talk
Observers, gauge symmetries, and best-matching.
One problem of gauge theories in general, but general relativity in particular, is determining a local basis of observables. E.g. a Wilson loop is not gauge-invariant within a region whose boundary intersects it. Recently, interest in defining boundary degrees of freedom which restore gauge-invariance for such types of observables has resurged. Donnelly and Freidel have related such degrees of freedom (edge-modes) to choices of local frames, which can in their turn be related to choices of local observers. In this talk, I will provide a relation between these modes, BRST ghosts, and a generalization of Barbour and Bertotti's 'best-matching'.
Tuesday 23 talk
What is an observer in quantum geometrodynamics?
General relativity has a notorious problem: parametrizing its physical configuration space, even at an abstract level, is beyond our current knowledge. Replacing refoliation invariance with conformal transformations as a local gauge-symmetry allows one to parametrize the physical configuration space. Nonetheless, each point in this reduced configuration space contains non-local information about the fields throughout physical space. It is essentially a ‘space of relations’. I will argue for a notion of "instantaneous states of observers" as consistent subsets of these relations. Such subsets define not points, but submanifolds in configuration space, corresponding to the configurations of the entire universe compatible with that instantaneous state of the observer. Relative quantum volumes of such regions define relative probabilities for different outcomes as perceived by observers. According to such outcomes, observers update their proposal for the wavefunction.