Shape Dynamics Relativity and Relationalism

This textbook on the nature of space and time explains the new theory of Space Dynamics, which describes the dynamics of gravity as the evolution of conformal 3-dimensional geometry. Shape Dynamics is equivalent to Einstein's General Relativity in those situations in which the latter has been tested experimentally, but the theory is based on different first principles. It differs from General Relativity in certain extreme conditions. Shape Dynamics allows us to describe situations in which the spacetime picture is no longer adequate, such as in the presence of singularities, when the idealization of infinitesimal rods measuring scales and infinitesimal clocks measuring proper time fails. This tutorial book contains both a quick introduction for readers curious about Shape Dynamics, and a detailed walk-through of the historical and conceptual motivations for the theory, its logical development from first principles and a description of its present status. It includes an explanation of the origin of the theory, starting from problems posed first by Newton more than 300 years ago. The book will interest scientists from a large community including all foundational fields of physics, from quantum gravity to cosmology and quantum foundations, as well as researchers interested in foundations. The tutorial is sufficiently self-contained for students with some basic background in Lagrangian/Hamiltonian mechanics and General Relativity.

1 - Introduction
2 - Newton's bucket
3 - Origins of the Mach-Poincare Principle
4 - Barbour-Bertotti best matching
5 - Best matching: Technical details
6 - Hamiltonian formulation
7 - Relativity without Relativity
8 - York's solution to the initial-value problem
9 - A derivation of Shape Dynamics
10 - Cotton-squared theory
11 - Historical interlude
12 - Shape Dynamics and the Linking Theory
13 - Solutions of Shape Dynamics
A - Arnowitt-Deser-Misner Gravity
B - Other appendices

Flavio Mercati completed his Ph.D. at the University of Rome `La Sapienza' in 2011 with a thesis on experimental tests of quantum gravity and on effective models of quantum gravity based on noncommutative field theory. He spent one year at the University of Zaragoza in Spain as a postdoctoral fellow, and another 7 months visiting the University of Nottingham in the UK. Since 2012 he has been a postdoctoral fellow at the Perimeter Institute in Ontario, Canada. Mercati has published around 30 scientific articles and three essays. In 2015 he won the Buchalter Prize for Cosmology for his research on the arrow of time. This work has received considerable attention by the media, leading to interviews by popular science journals like Wired, Scientific American, Le Scienze and Discovery News.