  Quantum gravity is studied in a semiclassical approximation and it is found
that to first order in the Planck length the effect of quantum gravity is to
make the low energy effective spacetime metric energy dependent. The
diffeomorphism invariance of the semiclassical theory forbids the appearance of
a preferred frame of reference, consequently the local symmetry of this
energy-dependent effective metric is a non-linear realization of the Lorentz
transformations, which renders the Planck energy observer independent. This
gives a form of deformed or doubly special relativity (DSR), previously
explored with Magueijo, called the rainbow metric. The general argument
determines the sign, but not the exact coefficient of the effect. But it
applies in all dimensions with and without supersymmetry, and is, at least to
leading order, universal for all matter couplings.
  A consequence of DSR realized with an energy dependent effective metric is a
helicity independent energy dependence in the speed of light to first order in
the Planck length. However, thresholds for Tev photons and GZK protons are
unchanged from special relativistic predictions. These predictions of quantum
gravity are falsifiable by the upcoming AUGER and GLAST experiments.
