Review of Shape Dynamics: Relativity and Relationalism by Flavio Mercati

Phillip Helbig

The Observatory, 138, 1267, 327–328 (December 2018)

This is a book review of Shape Dynamics: Relativity and Relationalism by Flavio Mercati. Shape Dynamics is an attempt to base a theory of gravity on fewer and more-fundamental first principles than General Relativity, motivated by a desire to incorporate Mach's Principle to a greater degree than does GR, even though that means giving up the relativity of simultaneity in favour of invariance under spatial conformal transformations. The name comes from the fact that only angles are fundamental, while the local scale factor plays no role. In almost all cases, predictions are the same as those of GR. There appears to be no easy test to distinguish between the two theories; the motivation, however, is more aesthetic than phenomenological. Nevertheless, a net angular momentum of the universe would rule out SD, and a spatially open universe or one with non-zero total energy would be difficult to reconcile with SD. This is a very mathematical textbook (704 equations), not an introduction, although there is a summary in one section of the introductory chapter and a couple of chapters on historical motivation. A good grounding in classical theoretical mechanics is need to follow the argument(s).

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