The Objectivity of Spacetime: Dirac Observables and Gauge Variables for the Gravitational Field

In special relativity the chronogeometrical structure is absolute and there is no notion of instantaneous 3‐space: distant clock synchronization is based on a convention, which changes going from inertial to non‐inertial frames. On the contrary in Einstein general relativity the metric tensor has a double role: 1) it is the mediator of the gravitational interaction; 2) it determines the dynamical chronogeometrical structure of spacetime. As a consequence, it “teaches relativistic causality” to to every other field with the following implications: a) the conventions for distant clock synchronization in non‐inertial frames are dynamically determined; b) the 8 arbitrary gauge variables hidden in the metric tensor describe “inertial effects” in non‐inertial frames; c) the Dirac observables of the gravitational field describe “tidal effects” in non‐inertial frames. A Hamiltonian reading of Bergmann‐Komar intrinsic pseudo‐coordinates, in connection with Einstein’s Hole Argument, leads to a identification of the notions of “spacetime” and “gravitational field”, which must be taken into account in any approach to quantum gravity.