  The launch of the Fermi telescope in 2008 opened up the possibility of
measuring the energy dependence of the speed of light by considering the time
delay in the arrival of gamma ray bursts emitted simultaneously from very
distant sources.The expected time delay between the arrival of gamma rays of
significantly different energies as predicted by the framework of relative
locality has already been calculated in Riemann normal coordinates. In the
following, we calculate the time delay in more generality and then specialize
to the connection normal coordinate system as a check that the results are
coordinate independent. We also show that this result does not depend on the
presence of torsion.
