As a scientist, but not a physicist, I've always wondered why the speed of light in a vacuum should be constant. Speed is a derived variable from distance travelled and time. Yet it's time that is the variable (OK spacetime). I understand that it all depends on the frame of reference (relativity), but it makes no sort of sense. Given that electromagnetic waves are sort of spread out anyway and are massless, why have a maximum speed?

It's not limited to electromagnetic waves. Every massless particle with non zero energy must travel at that speed.

The fact is constant (better, *invariant*. It means it doesn't depend on the frame of reference) comes from the fact that it's the maximum speed possible, and this because of spacetime properties.

You can see it in this way: because of Lorentz contraction of lenghts, a very fast moving object measures contracted distances, so if you were inside a spaceship moving at near light speed, you would travel around the entire universe in a few seconds (zero seconds, at the limit v --> c). Clearly, you can't travel faster than that. So, in a certain sense (that is, in the sense of "rapidity", but I want to make it easy for the moment) it is as if it were infinite, and if you sum infinite to a finite number you still get infinite. For this reason, if you launch a light signal from a moving object, you "sum" the finite speed of that object with the "infinite" speed of light and so you get the same result (the *speed* is not infinite, but the rapidity is and the rapidity is a better concept, at high speeds).

Light speed is a finite number just because we measure speed as space/time, but this is a good definition of speed only at low speeds, because in this case only we have that the space travelled is independent of the interval of time.

At high speeds the usual definition loses its "common sense" meaning, as I showed in the example of the spaceship.

Don't know if all this was useful.