Imagine a theoretical universe which contained only two photons with the same energy. Imagine that each photon began at approximately the same point and traveled in exactly opposite directions. I believe that general relativity predicts that photons exert a gravitational force on each other. In this case, what happens to these two photons? Will they simply redshift to some slightly lower energy level due to the gravitational effect, however small? Or will the gravitational effects ever even reach the other photon? I would hypothesize that the photons would never feel the influence of each other's gravitational force because from the point of view of one photon, it's gravity would be traveling at C, chasing after the other photon also traveling at C, unless they were not traveling at exactly opposite directions. Does anyone have any theories that explain how this system would behave from a relativistic perspective from the point of view of an observer at the origin? I'd love to know how this looks from the point of view of one of the photons, but I'm afraid that might not possible to predict. I have a little trouble with a redshift occurring because it seems to me that in this system the relativistic conservation of energy would not hold in that case.