The shape dynamics description of gravity

Classical gravity can be described as a relational dynamical system without ever appealing to space–time or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the shape dynamics description of gravity can be derived is a motivation to consider shape dynamics (rather than general relativity) as the fundamental description of gravity. Adopting this point of view leads to the question: What is the role of space–time in the shape dynamics description of gravity? This question contains many aspects: Compatibility of shape dynamics with the description of gravity in terms of space–time geometry, the role of local Minkowski space, universality of space–time geometry and the nature of quantum particles, which can no longer be assumed to be irreducible representations of the Poincaré group. In this contribution I derive effective space–time structures by considering how matter fluctuations evolve along with shape dynamics. This evolution reveals an “experienced space–time geometry.” This leads (in an idealized approximation) to local Minkowski space and causal relations. The small-scale structure of the emergent geometric picture depends on the specific probes used to experience space–time, which limits the applicability of effective space–time to describe shape dynamics. I conclude with discussing the nature of quantum fluctuations (particles) in shape dynamics and how local Minkowski space–time emerges from the evolution of quantum particles.