|MadSci Network: Physics|
The only proper way of measuring the relative speed of two objects is to find the speed of object A in a reference frame in which object B is at rest (or vice versa). Now, there is no way that we can do this for two photons. All real photons in vacuum travel at the speed of light in any inertial reference frame. If we change reference frames, the energy and momentum of each photon will change, but its speed remains the speed of light. There is no allowed inertial reference frame in vacuum such that a real photon is at rest. So there is no proper way to perform this measurement. Therefore, the relative speed of two photons is not a measurable quantity. Or, as we say in quantum mechanics, there is no observable which measures this quantity. I think you probably will not like this answer, but it is the correct one.
Try the links in the MadSci Library for more information on Physics.