1: Introduction
I. Historical Motivation
2: Newton's bucket
3: Origins of the Mach-Poincare Principle
II. Relational Particle Dynamics
4: Barbour-Bertotti best matching
5: Best matching: Technical details
6: Hamiltonian formulation
III. Relational Field Theory
7: Relativity without Relativity
8: York's solution to the initial-value problem
9: A derivation of Shape Dynamics
10: Cotton-squared theory
IV. Shape Dynamics
11: Historical interlude
12: Shape Dynamics and the Linking Theory
13: Solutions of Shape Dynamics
V. Appendices
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.
Shape Dynamics is a new theory of gravity based on fewer and
arguably more fundamental principles than the general theory of
relativity. It reproduces all of the hitherto confirmed predictions
of Einstein's theory but is much more restrictive in the solutions
that it allows. Besides being therefore a more strongly predictive
theory, it also reveals new aspects of gravity that have the
potential to transform our understanding of the Big Bang and black
holes. Flavio Mercati has been actively involved with the recent
exciting developments of Shape Dynamics. His monograph includes a
valuable account of the historical background to the theory and its
conceptual underpinnings. It is an excellent introduction suitable
for readers of a wide range of abilities: from physics and
mathematics undergraduates, to active gravitational and
cosmological researchers.
*Julian Barbour, author of The Discovery of Dynamics and The End of
Time*
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