General covariance and the objectivity of space-time point-events

TL;DR

This paper explores the physical objectivity of space-time in general relativity, emphasizing the role of gravitational field degrees of freedom in individuating point-events and challenging the frozen-time view of evolution.

Contribution

It introduces a model-based approach to space-time objectivity using Dirac observables, bridging substantivalist and relationist perspectives, and demonstrating real temporal change.

Findings

Physical individuation of point-events via Dirac observables

Real temporal change in gravitational models

Counter-example to frozen-time thesis

Abstract

"The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. 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. At the end, a peculiar four-dimensional {\it holistic and structuralist} view of space-time emerges which includes elements common to the tradition of both {\it substantivalism} and {\it relationism}. The observables of our models undergo real {\it temporal change} and thereby provide a counter-example to the thesis of the {\it frozen-time} picture of evolution. Invited Contribution to the ESF 2004 Oxford Conference on Space-Time