dimensions of a triangle (two-simplex) and a tetrahedron (three-simplex). An individual building block is a piece of flat four-dimensional Euclidean space and therefore does not carry any curvature. However, numerical investigations of the nonperturbative dynamics of DT quantum gravity found that it has neither a large-scale limit compatible with general relativity [@Ambjorn:1991pq; @Agishtein:1992xx; @Catterall:1994pg], nor a second-order phase transition allowing for a continuum limit in the sense of lattice quantum field theory [@Bialas:1996wu; @deBakker:1996zx]. Despite the negative nature of this result, the fact that the model contains criteria which could be used for its falsification should be appreciated. For many other candidate theories of quantum gravity this is not obviously the case.

Causal Dynamical Triangulations (CDT) were introduced in [@al] in an attempt to overcome these problems. The key new idea of CDT is to incorporate aspects of the [*causal structure*]{} of classical general relativity at a more fundamental level into the nonperturbative gravitational path integral.[^1] The elementary building blocks of CDT quantum gravity are flat four-simplices of [*Lorentzian*]{} signature, that is, pieces of Minkowski space. The carrier space of the corresponding path integral consists of piecewise flat simplicial manifolds assembled from these building blocks. In addition, each path integral 