Coupling Shape Dynamics to Matter Gives Spacetime

TL;DR

This paper extends Shape Dynamics, a gravity theory equivalent to General Relativity, to include matter, enabling a spacetime interpretation and providing a clock and rod model within this framework.

Contribution

It demonstrates the coupling of matter to Shape Dynamics without obstruction and constructs a model for spacetime interpretation.

Findings

Gravity can be coupled to standard matter in Shape Dynamics.

A clock and rod model for Shape Dynamics is constructed.

Spacetime trajectories are recovered within the Shape Dynamics framework.

Abstract

Shape Dynamics is a metric theory of pure gravity, equivalent to General Relativity, but formulated as a gauge theory of spatial diffeomporphisms and local spatial conformal transformations. In this paper we extend the construction of Shape Dynamics form pure gravity to gravity-matter systems and find that there is no obstruction for the coupling of gravity to standard matter. We use the matter gravity system to construct a clock and rod model for Shape Dynamics which allows us to recover a spacetime interpretation of Shape Dynamics trajectories.