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.Comment: 12 pages. Presentation shortened and revised for letter to Nature.
New title "A strong astrophysical constraint on the violation of special
relativity by quantum gravity". Maximum observed synchrotron frequency
lowered, resulting in weakening the constraint from E_QG>4.5*10^27 GeV to
E_QG>10^26 GeV. The role of the effective field theory assumptions underlying
the analysis is highlighte
