Holism and Structuralism in Classical and Quantum General Relativity

Dorato, Mauro and Pauri, Massimo (2004) Holism and Structuralism in Classical and Quantum General Relativity.

Abstract

The main aim of our paper is to show that interpretative issues
belonging to classical General Relativity (GR) might be
preliminary to a deeper understanding of conceptual problems
stemming from on-going attempts at constructing a quantum theory
of gravity. Among such interpretative issues, we focus on the
meaning of general covariance and the related question of the
identity of points, by basing our investigation on the Hamiltonian
formulation of GR. In particular, we argue that the adoption of a
peculiar gauge-fixing within the canonical reduction of ADM metric
gravity may yield a new solution to the debate between
substantivalists and relationists, by suggesting a \emph{tertium
quid} between these two age-old positions. Such a third position
enables us to evaluate the controversial relationship between
entity realism and structural realism in a well-defined case
study. After having indicated the possible developments of this
approach in Quantum Gravity, we discuss the structuralist and
holistic features of the class of spacetime models that are used
in the above mentioned canonical reduction.