The emergence of global symmetry at low energies is a familiar phenomena, for example Baryon number emerges in the context of the standard model as "accidental" symmetry. Meaning at low energies it is approximately valid, but at high energies it is not.
The reason this is the case is that it so happens that the lowest dimension operator you can write, with the matter content and symmetries of the standard model, is dimension 5. The effect is then suppressed by one power of some high energy scale - it is an irrelevant operator. This is a model independent way to characterize the possibility of the emergence of global symmetries at low energies.
We can then ask about Lorentz invariance - what are the possible violations of Lorentz invariance at low energies, and what is the dimensions of the corresponding operators. This depends on the matter content and symmetries - for the system describing graphene, there is such emergence. For anything containing the matter content of the standard model, there are lots and lots of relevant operators*, whose effect is enhanced at low energies - meaning that Lorentz violating effects, even small ones at high energies, get magnified as opposed to suppressed at observable energies.
Of course, once we include gravity Lorentz invariance is now a gauge symmetry, which makes its violation not just phenomenologically unpleasant, but also theoretically unsound. It will lead to all the inconsistencies which necessitates the introduction of gauge freedom to start with, negative norm states and violations of unitarity etc. etc.
This post imported from StackExchange Physics at 2014-04-01 16:44 (UCT), posted by SE-user user566
- At least 46, which were written down by Coleman and Glashow (Phys.Rev. D59, 116008). Relaxing their assumptions you can find even more. Each one of them would correspond to a new fine-tuning problem (like the cosmological constant problem, or the hierarchy problem).