One description of relativistic effects that I've heard/read goes something like this:
Everything moves through spacetime at a constant speed. An object's direction of travel through spacetime can change, though. For instance, if you are at rest, all of your motion through spacetime is through time. If you are walking, though, some of your motion through spacetime will be allocated to traveling through space. Since less of your motion through spacetime will be allocated to traveling through time, your local time will be slower than the local time of your surroundings.
I don't know if this description is a good model or not. It could just be an imperfect analogy as far as I know. If it is a good model, though, it seems to me like light might only be devoting some of its total motion through spacetime to moving through space: it seems that light also travels through time. (This might be incorrect because of the relativity of simultaneity. I don't really know.) If nothing can go through space faster than light but light isn't devoting all of its motion through spacetime to traveling through space, could that mean that spacetime is quantized?