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*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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