The notion that gravitation might lead to a breakdown of standard space-time
structure at small distances, and that this might affect the propagation of
ordinary particles has led to a program to search for violations of Lorentz
invariance as a probe of quantum gravity. Initially it was expected that
observable macroscopic effects caused by microscopic violations of Lorentz
invariance would necessarily be suppressed by at least one power of the small
ratio between the Planck length and macroscopic lengths. Here we discuss the
implications of the fact that this expectation is in contradiction with
standard properties of radiative corrections in quantum field theories. In
normal field theories, radiative corrections in the presence of microscopic
Lorentz violation give macroscopic Lorentz violation that is suppressed only by
the size of Standard Model couplings, in clear conflict with observation. In
general, this conclusion can only be avoided by extreme fine tuning of the
parameters of the theory.Comment: Draft chapter contributed to the book "Towards quantum gravity",
being prepared by Daniele Oriti for Cambridge University Pres