The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - I: Dynamical Synchronization and Generalized Inertial Effects

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This is the first of a couple of papers in which, by exploiting the capabilities of the Hamiltonian approach to general relativity, we get a number of technical achievements that are instrumental both for a disclosure of new results concerning specific issues, and for new insights about old foundational problems of the theory. The first paper includes: 1) a critical analysis of the various concepts of symmetry related to the Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian viewpoint, on the other. This analysis leads, in particular, to a re-interpretation of active diffeomorphisms as passive and metric-dependent dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose the (nearly unknown) connection of a subgroup of them to Hamiltonian gauge transformations on-shell; 2) a re-visitation of the canonical reduction of the ADM formulation of general relativity, with particular emphasis on the geometro-dynamical effects of the gauge-fixing procedure, which amounts to the definition of a global (non-inertial) space-time laboratory. This analysis discloses the peculiar dynamical nature that the traditional definition of distant simultaneity and clock-synchronization assume in general relativity, as well as the gauge relatedness of the "conventions" which generalize the classical Einstein's convention.