Does Loop Quantum Gravity predict that high-energy photons or light waves will travel faster or slower than low-energy (longer-wavelength) ones? Matthew O'Dowd, the Australian-born host of PBS Space-Time, insists that high-energy (short-wavelength) photons (or waves) of light will travel slightly more slowly through space than lower-energy, longer-wavelength ones; while Don Lincoln of Fermilab says the exact opposite....
Does anyone know the correct answer?
Do photons in the 'ultraviolet regime' travel slightly faster or slower than ones in the 'infrared' regime? .....
 A: In standard general relativity, spacetime is considered to be smooth and continuous. That is, you can in theory divide it into smaller and smaller volumes without limit. Loop quantum gravity, LQG on the other hand (because it is a quantum theory after all), breaks this smoothness into a discrete structure where spacetime is a spin network of lines and nodes.
Loop quantum gravity predicts that the speed of light is not constant which violates one of the fundamental concepts of relativity. Specifically, higher energy photons would travel slower than lower energy photons.
Low frequency light, for example radio waves, have long wavelengths. For such a wavelength, travelling through spacetime will be fairly "smooth" since there is no microscopic structure of spacetime to contend with, since the scale for a radio wave is so much bigger than any loop quantum gravity scale.  But on the opposite side, for example a gamma ray photon, has a very high frequency and a very small wavelength, one which exists on a scale somewhat closer to the scale where LQG  (or any quantum theory of gravity) effects will become more noticeable.
So one could conclude that light of high energy and frequency, as it travels through spacetime interacts with these microscopic points in the spin network, so that the effect is a slowed down light ray, and as stated above, the converse is true for low energy long wavelength light, who's interaction with the same is negligible.
I'm inclined to think, that although there is this description of changing light-speed at different scales, one could still say that the local speed of light still remains unchanged. But there are various physicists that actually think that if LQG were accurate, and such spin networks existed, this would break the notion of the constant nature of the speed of light.
