A Shape Dynamics Tutorial

TL;DR

Shape Dynamics is an alternative gravity theory emphasizing spatial conformal invariance, offering a simpler gauge symmetry compared to General Relativity, with a comprehensive tutorial suitable for students and researchers.

Contribution

This paper provides a detailed, self-contained tutorial on Shape Dynamics, including its motivations, development, and current status, serving as an accessible resource for newcomers and experts.

Findings

Shape Dynamics replaces GR's relativity of simultaneity with conformal invariance.

The theory is based on fewer fundamental principles than GR.

The tutorial is suitable for undergraduates and researchers interested in SD.

Abstract

Shape Dynamics (SD) is a new theory of gravity that is based on fewer and more fundamental first principles than General Relativity (GR). The most important feature of SD is the replacement of GR's relativity of simultaneity with a more tractable gauge symmetry, namely invariance under spatial conformal transformations. This Tutorial contains both a quick introduction for readers curious about SD and a detailed walk-through of the historical and conceptual motivations for the theory, its logical development from first principles and an in-depth description of its present status. The Tutorial is sufficiently self-contained for an undergrad student with some basic background in GR and Lagrangian/Hamiltonian mechanics. It is intended both as a reference text for students approaching the subject and as a review for researchers interested in the theory.