Why is High Energy Physics Lorentz Invariant?

Abstract

Despite the tremendous empirical success of equivalence principle, there are several theoretical motivations for existence of a preferred reference frame (or aether) in a consistent theory of quantum gravity. However, if quantum gravity had a preferred reference frame, why would high energy processes enjoy such a high degree of Lorentz symmetry? While this is often considered as an argument against aether, here I provide three independent arguments for why perturbative unitarity (or weak coupling) of the Lorentz-violating effective field theories put stringent constraints on possible observable violations of Lorentz symmetry at high energies. In particular, the interaction with the scalar graviton in a consistent low-energy theory of gravity and a (radiatively and dynamically) stable cosmological framework, leads to these constraints. The violation (quantified by the relative difference in maximum speed of propagation) is limited to $\lesssim 10^{-10} E({\rm eV})^{-4}$ (superseding all current empirical bounds), or the theory will be strongly coupled beyond meV scale. The latter happens in extended Horava-Lifshitz gravities, as a result of a previously ignored quantum anomaly. Finally, given that all cosmologically viable theories with significant Lorentz violation appear to be strongly coupled beyond meV scale, we conjecture that, similar to color confinement in QCD, or Vainshetin screening for massive gravity, high energy theories (that interact with gravity) are shielded from Lorentz violation (at least, up to the scale where gravity is UV-completed). In contrast, microwave or radio photons, cosmic background neutrinos, or gravitational waves may provide more promising candidates for discovery of violations of Lorentz symmetry.