  This article concerns the fate of local Lorentz invariance in quantum
gravity, particularly for approaches in which a discrete structure replaces
continuum spacetime. Some features of standard quantum mechanics, presented in
a sum-over-histories formulation, are reviewed, and their consequences for such
theories are discussed. It is argued that, if the individual histories of a
theory give bad approximations to macroscopic continuum properties in some
frames, then it is inevitable that the theory violates Lorentz symmetry.
