There is an interesting preprint on the arxiv by T.P. Sotiriou et al.
called "Quantum Gravity Without Lorentz Invariance" about a
modification of Horava's model:

http://arxiv.org/abs/0905.2798

However, this brief experimental paper by Dolev and Elitzur which was
also published in an edited book establishes the non-sequential
behavior of the wavefunction in QM. The overall result of this paper
*is* Lorentz-invariant, but still with Bell-like correlations and, as
the authors conclude, this result appears to transcend ordinary
concepts of probability theory, causality, space and time:

http://arxiv.org/abs/quant-ph/0102109

(I have previously suggested that this non-sequential behavior of the
wavefunction might have something to do with the speed-up of quantum
computation over classical computation.)