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

TL;DR

This paper uses the Hamiltonian approach to general relativity to reinterpret symmetries, analyze gauge fixing effects, and explore the dynamical nature of simultaneity and clock synchronization in curved spacetime.

Contribution

It provides new insights into the role of gauge symmetries and the dynamical aspects of synchronization in general relativity using Hamiltonian methods.

Findings

Active diffeomorphisms reinterpreted as dynamical symmetries

Canonical reduction clarifies gauge fixing effects

Distant simultaneity has a dynamical, gauge-related nature

Abstract

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 \emph{new} results concerning specific issues, and for new insights about \emph{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 {\it active} diffeomorphisms as {\it 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 {\it 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 \emph{global (non-inertial) space-time laboratory}. This analysis discloses the peculiar \emph{dynamical nature} that the traditional definition of distant simultaneity and clock-synchronization assume in general relativity, as well as the {\it gauge relatedness} of the "conventions" which generalize the classical Einstein's convention.