existence of a conformal class of metrics, and one must explain why these are not already dynamical. Models such as [@Wetterich2] in which the background has no metric avoid this problem, and Lorentz invariance may be inserted by hand as a gauge symmetry. Relating this symmetry to spacetime Lorentz invariance requires a fairly elaborate scenario, though: one must ensure the emergence of a nondegenerate soldering form, a tetrad whose two-index structure “solders” the fibers in which the gauge group acts to the spacetime [@Percacci].

If the background is discrete, one must work harder. As Dowker has emphasized [@Dowker], Lorentz invariance requires a radical nonlocality on a lattice, in the sense that each point has infinitely many nearest neighbors [@Moore; @Bombelli]. Causal set theories [@Sorkin; @Dowker; @Bombelli2] can achieve statistical Lorentz invariance with a suitable “sprinkling” of spacetime points, but this becomes much harder if one starts with a more complex discrete structure. Causal dynamical triangulations [@Loll] may recover Lorentz invariance as an average over noninvariant simplicial complexes, but this is not certain; the continuum limit of this model may be a Ho[ř]{}ava-Lifshitz theory with a preferred time slicing [@HLCDT; @HLCDT2].

One may look instead for models in which Lorentz invariance 