  Special relativity asserts that physical phenomena appear the same for all
inertially moving observers. This symmetry, called Lorentz symmetry, relates
long wavelengths to short ones: if the symmetry is exact it implies that
spacetime must look the same at all length scales. Several approaches to
quantum gravity, however, suggest that there may be a Lorentz violating
microscopic structure of spacetime, for example discreteness,
non-commutativity, or extra dimensions. Here we determine a very strong
constraint on a type of Lorentz violation that produces a maximum electron
speed less than the speed of light. We use the observation of 100 MeV
synchrotron radiation from the Crab nebula to improve the previous limits by a
factor of 40 million, ruling out this type of Lorentz violation, and thereby
providing an important constraint on theories of quantum gravity.
