Geometrodynamics as Functionalism about Time

TL;DR

This paper reviews three geometrodynamical projects through the lens of spacetime functionalism, showing their reduction to a common functionalist framework and discussing implications for shape dynamics.

Contribution

It demonstrates how three different geometrodynamical approaches exemplify D. Lewis's functionalist reduction, unifying them under the Canberra Plan perspective.

Findings

All three projects are examples of spacetime functionalism.

Shape dynamics has a well-founded rationale for its Hamiltonian.

The projects exemplify the reduction of geometrodynamics to functionalist principles.

Abstract

We review three broadly geometrodynamical---and in part, Machian or relational---projects, from the perspective of spacetime functionalism. We show how all three are examples of functionalist reduction of the type that was advocated by D. Lewis, and nowadays goes by the label 'the Canberra Plan'. The projects are: (1) the recovery of geometrodynamics by Hojman et al. (1976); (2) the programme of Schuller and collaborators (Schuller 2011; Dull, Schuller et al. 2018) to deduce a metric from the physics of matter fields; (3) the deduction of the ADM Hamiltonian by Gomes and Shyam (2016). We end by drawing a positive corollary about shape dynamics: namely, it has a good rationale for the Hamiltonian it postulates.