Explaining Leibniz-equivalence as difference of non-inertial appearances: dis-solution of the Hole Argument and physical individuation of point-events

TL;DR

This paper argues that the physical identity of space-time points in general relativity is rooted in gravitational degrees of freedom, dissolving the Hole Argument and supporting a structuralist view of space-time.

Contribution

It provides a novel interpretation of space-time point individuation through Dirac observables, weakening the Hole Argument and proposing a holistic, structuralist perspective.

Findings

Physical individuation of points is given by gravitational Dirac observables.

The Hole Argument is substantially weakened and effectively dissolved.

Models show real temporal change, challenging the frozen-time view.

Abstract

"The last remnant of physical objectivity of space-time" is disclosed in the case of a continuous family of spatially non-compact models of general relativity (GR). The {\it physical individuation} of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the {\it Dirac observables}) that represent - as it were - the {\it ontic} part of the metric field. The physical role of the {\it epistemic} part (viz. the {\it gauge} variables) is likewise clarified as emboding the unavoidable non-inertial aspects of GR. At the end the philosophical import of the {\it Hole Argument} is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional {\it holistic and structuralist} view of space-time, (called {\it point-structuralism}), emerges, including elements common to the tradition of both {\it substantivalism} and {\it relationism}. The observables of our models undergo real {\it temporal change}: this gives new evidence to the fact that statements like the {\it frozen-time} character of evolution, as other ontological claims about GR, are {\it model dependent}. \medskip Forthcoming in Studies in History and Philosophy of Modern Physics