the idea of violating Lorentz invariance has been around even in the late 1990s
https://arxiv.org/abs/hep-ph/9809521
any1 out there who wants to know how is rest mass distinguished from "relativistic" mass this wiki entry helps... i must point out that i am usually inclined to call rest mass as invariant mass
https://en.wikipedia.org/wiki/Mass_in_special_relativity
loosely call m the rest mass of the particle and Lorentz symmetry says that this property of the particle is invariant as we apply lorentz group of transformations on the components of the four-momentum. that is, this mass stays as it is for an observer regardless of his motion relative to the particle he is watching. the thing i’m a little curious about is that what happens if lorentz symmetry breaks for as far as i am concerned, lorentz symmetry keeps the kinematics simple and my belief is that this kind of simplicity is unbreakable!