Frequently asked questions about Shape Dynamics

TL;DR

This paper explains the new Shape Dynamics theory, a reformulation of gravity emphasizing spatial conformal geometry, clarifying its relation to General Relativity and other symmetries, with insights from simple models.

Contribution

It clarifies the conceptual and technical relations between Shape Dynamics and General Relativity, highlighting local conformal invariance as a gauge symmetry.

Findings

Shape Dynamics implements local spatial conformal invariance.

It replaces refoliation invariance in General Relativity.

Simple models illustrate symmetry trading in gauge theories.

Abstract

Barbour's interpretation of Mach's principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, "shapes." Recently, it was shown that the dynamics of General Relativity can indeed be formulated as the dynamics of shapes. This new Shape Dynamics theory, unlike earlier proposals by Barbour and his collaborators, implements local spatial conformal invariance as a gauge symmetry that replaces refoliation invariance in General Relativity. It is the purpose of this paper to answer frequent questions about (new) Shape Dynamics, such as its relation to Poincar\'e invariance, General Relativity, Constant Mean (extrinsic) Curvature gauge, earlier Shape Dynamics, and finally the conformal approach to the initial value problem of General Relativity. Some of these relations can be clarified by considering a simple model: free electrodynamics and its dual shift symmetric formulation. This model also serves as an example where symmetry trading is used for usual gauge theories.