Shape dynamics
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In theoretical physics, shape dynamics is a theory of gravity that implements Mach's principle, developed with the specific goal to obviate the problem of time and thereby open a new path toward the resolution of incompatibilities between general relativity and quantum mechanics.
Shape dynamics is dynamically equivalent to the canonical formulation of general relativity, known as the ADM formalism. Shape dynamics is not formulated as an implementation of spacetime diffeomorphism invariance, but as an implementation of spatial relationalism based on spatial diffeomorphisms and spatial Weyl symmetry.[1] An important consequence of shape dynamics is the absence of a problem of time in canonical quantum gravity.[2] The replacement of the spacetime picture with a picture of evolving spatial conformal geometry opens the door for a number of new approaches to quantum gravity.[3]
An important development in this theory was contributed in 2010 by Henrique Gomes, Sean Gryb and Tim Koslowski, building on an approach initiated by Julian Barbour.