  Shape Dynamics is a metric theory of pure gravity, equivalent to General
Relativity, but formulated as a gauge theory of spatial diffeomporphisms and
local spatial conformal transformations. In this paper we extend the
construction of Shape Dynamics form pure gravity to gravity-matter systems and
find that there is no obstruction for the coupling of gravity to standard
matter. We use the matter gravity system to construct a clock and rod model for
Shape Dynamics which allows us to recover a spacetime interpretation of Shape
Dynamics trajectories.
