bcrowell said:
This is a separate question from why light travels at c. c is not properly defined as the speed of light, so this is not just a matter of definition. c is defined as the invariant speed in relativity, i.e., the speed that all observers agree on. The reason that light travels at the invariant speed is that light is massless, and one can prove that massless particles travel at the invariant speed (e.g., by considering the equation m^2=E^2-p^2, solving it for the v that implicitly appears in E and p, and substituting m=0).
[No disagreement below, just elaboration that the original poster may find interesting]
The historical path to this understanding was less tidy.
By the second half of the nineteenth century classical electricity and magnetism were well understood. These predicted (via Maxwell's equations) electromagnetic radiation, aka light, that would propagate at a particular speed. Of course this speed was called "the speed of light". There was nothing in the theory that suggested that the speed of light should vary with the observer's motion. Thus, nature was already giving us a subtle hint that there might be an invariant speed.
However, the idea of an invariant speed is sufficiently weird that this hint was generally missed. Instead, much effort went into theories that tried to reconcile the convincingly proven laws of electricity and magnetism with the (very very intuitive) classical notions of time and space, in which observers mving relative to each other observe different speeds for moving objects. Most of these hypothesized some sort of "luminiferous ether" that filled even empty space and in which light could propagate at the expected constant speed.
None of the ether theories were really satisfactory, and Michelson-Morley experiments (
http://en.wikipedia.org/wiki/Michelson–Morley_experiment) performed with ever greater precision made them ever less tenable. Thus, by the about the turn of the century it was clear that there was a fairly basic conflict between E&M on the one hand and classical notions of time and space on the other.
This is the background against which Einstein proposed the theory of special relativity: Accept as a postulate that there is a universal constant speed and see where the math takes us. It takes us many places, and one of them is the equation that bcrowell cites above, m
2=E
2-p
2 from which we conclude that massless particles travel at the speed of light. It's worth noting that there is only room for one invariant speed in the theory, so it's easy to see that the invariant speed must be c, the invariant speed also predicted by Maxwell's equations.
