A Shape Dynamics Tutorial

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.

v2.0 (greatly extended and updated), 133 pages, two columns in landscape format, for optimal reading on a computer screen or on a short-sided binding printout

References in corpus (8)

• Effective approach to the problem of time: general features and examples
• Constraints and gauge transformations: Dirac's theorem is not always valid
• Conformal Superspace: the configuration space of general relativity
• 2+1 gravity on the conformal sphere
• Scale Anomaly as the Origin of Time
• Symmetry Doubling: Doubly General Relativity
• Observable Equivalence between General Relativity and Shape Dynamics
• A first-principles derivation of York scaling and the Lichnerowicz-York equation

Cited by in corpus (31)

• Identification of a gravitational arrow of time
• A Class of Minimally Modified Gravity Theories
• The Observer's Ghost: a field-space connection-form and its application to gauge theories and general relativity
• Hamiltonian analysis of the cuscuton
• Problem of Time and Background Independence: the Individual Facets
• The constraints of post-quantum classical gravity
• The Smallest Shape Spaces. I. Shape Theory Posed, with Example of 3 Points on the Line
• Dynamics of the cosmological and Newton's constant
• Time asymmetric extensions of general relativity
• Entropy and the Typicality of Universes
• Configuration Spaces in Fundamental Physics
• Introduction to Hamiltonian Formulation of General Relativity and Homogeneous Cosmologies
• Chaos, Dirac observables and constraint quantization
• On the Conceptual Issues Surrounding the Notion of Relational Bohmian Dynamics
• Cosmological signatures of time-asymmetric gravity
• Gravitational collapse of thin shells of dust in asymptotically flat Shape Dynamics
• Relational Mechanics as a gauge theory
• Where to Apply Relationalism
• Quantum mechanics on York slices
• Self-gravitating fluid solutions of Shape Dynamics
• Thin shells of dust in a compact universe
• Intrinsic Time in Geometrodynamics of Closed Manifolds
• Gravitational collapse of thin shell of dust in shape dynamics
• Reduced Conformal Geometrodynamics of Closed Manifolds
• Gravitation and cosmology with York time
• Local(ish) gravity theories in conformal superspace
• Cosmological perturbation theory with York time
• Scale Invariance in Gravity On The Light-Front
• 'Shape Dynamics': Foundations Reassessed
• Quantum Shape Kinematics
• The frame of fixed stars in Relational Mechanics