 Our third and final point is this. Although it is possible to couple shape dynamics to matter (see e.g. (Gomes 2012)), in this theory, just as in GTR as discussed in the previous section, one also has vacuum solutions, with primitive conformal structure on the 3-geometries. Given the existence of these vacuum solutions, as with GTR, it is far from clear that the theory makes good on the ambitions of Mach and the early Einstein to construct a theory in which all spatiotemporal notions are reduced to facts about matter. That said, it is worth noting that, unlike in GTR, in shape dynamics one cannot have a solution consisting of a single rotating body: the overall angular momentum of the universe must vanish.