 The breaking of rotation and boost invariance causes direction dependence in the theory as well as unconventional energy dependence that introduces novel effects, including Lorentz-violating neutrino oscillations and modifications to the dispersion relations of different particle species, which naturally could make particles move faster than light.In some models of broken Lorentz symmetry, it is postulated that the symmetry is still built into the most fundamental laws of physics, but that spontaneous symmetry breaking of Lorentz invariance shortly after the Big Bang could have left a "relic field" throughout the universe which causes particles to behave differently depending on their velocity relative to the field; however, there are also some models where Lorentz symmetry is broken in a more fundamental way.If Lorentz symmetry can cease to be a fundamental symmetry at the Planck scale or at some other fundamental scale, it is conceivable that particles with a critical speed different from the speed of light be the ultimate constituents of matter.