Shape Dynamics

Dear Colleagues,

Shape dynamics is the modern incarnation of ‘relationalism’: in essence, the idea that all geometric, kinematical, and dynamical structures in physics should be determined by the internal state of the universe, rather than by something external to it. This leads to the need to systematically remove all ‘absolute’ structures from physics, such as, for example, special coordinate systems (diffeomorphism symmetry), asymptotic boundary conditions, absolute scales (conformal symmetry), and special time parameters (reparametrization invariance).

More specifically, shape dynamics is a formulation of general relativity in terms of a dynamical three-dimensional conformal field theory, which is time-reparametrization-invariant. This theory was born in the 1970s, from some important results in mathematical relativity with relationalist ideas developed by J. Barbour and B. Bertotti. The former led to the proof, due to A. Lichnerowicz, Y. Choquet-Bruhat and J. York, of the well-posedness of the initial value problem of general relativity, which indicates that the physical degrees of freedom of general relativity can be written as 3D conformal geometries (on certain hypersurfaces of simultaneity of ‘constant mean extrinsic curvature’). Combining this with relationalist ideas led to a proposal to describe gravity (and all other known field theories) as a theory describing the relative change of conformally-invariant degrees of freedom.

Revisiting well-known solutions of general relativity in shape-dynamical terms has shed some new light on classical gravity, in particular on the nature of singularities, on the problem of the arrow of time, and black holes and gravitational collapse.

This Special Issue will cover current research in shape dynamics and closely-related areas (e.g., N-body toy models), with a particular focus on the consequences of the distinctive symmetries of the theory: scale/conformal invariance and time reparametrization invariance.

Dr. Flavio Mercati
Guest Editor

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