Shape Dynamics

TL;DR

Shape Dynamics is a theory equivalent to General Relativity that uniquely implements local relativity of rods and spatial covariance, aligning with Mach's principle and Barbour's formulation.

Contribution

The paper demonstrates how Shape Dynamics and a BRST formulation called Doubly General Relativity realize Barbour's principles, addressing limitations of General Relativity.

Findings

Shape Dynamics implements local relativity of rods.

Doubly General Relativity incorporates all of Barbour's principles.

Theories are locally equivalent to General Relativity.

Abstract

Barbour's formulation of Mach's principle requires a theory of gravity to implement local relativity of clocks, local relativity of rods and spatial covariance. It turns out that relativity of clocks and rods are mutually exclusive. General Relativity implements local relativity of clocks and spatial covariance, but not local relativity of rods. It is the purpose of this contribution to show how Shape Dynamics, a theory that is locally equivalent to General Relativity, implements local relativity of rods and spatial covariance and how a BRST formulation, which I call Doubly General Relativity, implements all of Barbour's principles.