Lorentz invariance and quantum gravity: An additional fine-tuning problem?

The elementary particle interactions with a Planck-scale preferred frame, which gives rise to Lorentz violation and are unnaturally strongly fine tuned, were investigated. It was found that direct investigations of Planck-scale phenomena need short-wavelength probes with elementary-particle energies of order the Planck energy E_p = (hc⁵/G)^1/2 = 1.2 x 10¹⁹ GeV. The preferred frame and the consequent Lorentz violation occurred even though the fundamental classical equations of both of the theories were locally Lorentz invariant. The results show that the Lorentz violation can be removed by explicit Lorentz-violating counterterms that are fine tuned to give the observed low-energy Lorentz invariance.