Special relativity asserts that physical phenomena appear the
same to all unaccelerated observers. This is called Lorentz
symmetry and relates long wavelengths to short ones: if the
symmetry is exact it implies that space-time must look the same
at all length scales. Several approaches to quantum gravity,
however, suggest that there may be a microscopic structure of
space-time that leads to a violation of Lorentz symmetry. This
might arise because of the discreteness1 or non-commutivity2 of
space-time, or through the action of extra dimensions3. 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
limit by a factor of 40 million, ruling out this type of Lorentz
violation, and thereby providing an important constraint on
theories of quantum gravity.
