A dis-solution of the Hole Argument

L.Lusanna and M.Pauri

The philosophical relevance of Einstein's Hole Argument is revisited and dis-solved for any globally hyperbolic model of GR. Furthermore, for a definite continuous family of spatially non-compact models, the "last remnant of physical objectivity" of space-time point-events is disclosed in terms of the "individuating" (or "ontic") part of the metric field, viz.by suitable functions of the Dirac observables. It is also shown that the level of gauge freedom plays a basic physical role in GR since it fixes the connections of the Dirac observables (ruling the tidal effects) to the "generalized inertial effects". Precisely, every complete gauge-fixing turns out to specify the "appearance" of the intrinsic gravitational effects in every "global, non-inertial, space-time laboratory" (called NIF). The rephrasing of general relativity in terms of generalized inertial effects, namely those effects which are necessarily met with by any experimental access to the theory (and which are described by the "epistemic part" of the metric field), discloses the real physical content of the so-called Leibniz equivalence, which is nothing else than the shift from a given NIF to another NIF. Finally, the relation between the concepts of Dirac and Bergmann observables is clarified.