User:JulianBrabour/sandbox

In theoretical physics Shape Dynamics is a theory of gravity that implements Mach's principle. Shape dynamics is dynamically equivalent to the canonical formulation of General Relativity, known as ADM formalism. Shape dynamics is not formulated as an implementation of spacetime diffeomorphism invariance, but as an implementation of spatial relationalism based spatial diffeomorphism- and spatial Weyl symmetry. An important consequence of shape dynamics the absence of a problem of time in canonical quantum gravity.

Background
Mach's principle has been an important inspiration for the construction of general relativity, but the physical interpretation of Einstein's formulation of general relativity still requires external clocks and rods and thus fails to be manifestly relational. Mach's principle would be fully implemented if the predictions of general relativity where independent of the choice of clocks and rods. Barbour and Bertotti conjectured that Jacobi's principle and a mechanism they called best matching where construction principles for a fully Machian theory. Barbour implemented these principles in collaboration with Niall O Murchadha, Edward Anderson, Brendan Foster and Bryan Kelleher to derive the ADM formalism in constant mean curvature gauge. This did not implement Mach's principle, because the predictions of general relativity in constant mean curvature gauge depend on the choice of clocks and rods. Mach's principle was successfully implemented by a group around Perimeter Institute researcher Tim Koslowski.

Construction of shape dynamics
The construction of shape dynamics requires trading refoliation invariance for spatial Weyl invariance and the identification of a parametrized dynamical system.

Relation with general relativity
Shape dynamics posses the same dynamics as general relativity, but has different gauge orbits. The link between general relativity and shape dynamics can be established using the ADM formalism.