need not be the case for for type II models. The effective speed of light might then be determined dynamically, for example from the Lieb-Robinson limit on the speed of information propagation [@Marko3] or from a group structure already present in the fundamental degrees of freedom [@Girelli]. But while isotropy may be natural, the relativity principle is more problematic. The Lorentz group is noncompact, so transformations must relate inertial frames that are arbitrarily “distant” (although it is again conceivable that an emergent compact supersymmetry could help). This noncompactness also makes it difficult to achieve Lorentz invariance by averaging over noninvariant configurations, since the integral over boosts diverges, though there has been some work on defining a group average [@Marolf].

Of course, we have not experimentally tested Lorentz invariance up to infinite boost. But even violations at very high energies can feed back into quantum field theory through loop effects and lead to drastic consequences at low energies [@Collins], although there are proposals for avoiding this problem (e.g., [@Pospelov]). Small violations of Lorentz invariance also lead to problems with black hole thermodynamics: unless black holes simply do not exist in the underlying theory, such effects generically violate the generalized second law 