The other day my son (13) asked me whether it was possible that light went very slightly slower than our best measured $c$, and at the same time had a very tiny mass, but we aren't able to measure these because they are so small. Although I told him that I didn't think that that was possible or made sense, it got me to thinking along a related trajectory:
We think of $c$ as the speed of light but really it's the speed of universal causality/information (I'll just say "causality", but you can read both). In fact, $c$ isn't just for light; it's the speed of any massless wave, right? So what if the actual limit of causality isn't $c$, but that's just the fastest speed that we know of things happening causally in the known universe. Maybe the actual speed limit of causality is significantly faster than $c$, and we just don't know of anything that goes faster than $c$ (maybe disentanglement?)
Best Answer
The $c$ that appears in the equations of relativity (including the famous $E = m c^2$ is the speed of causality. This is the special, unique speed that is the same for all observers regardless of their relative motions. Because it is the same for all observers, it acts as a scale factor linking space and time.
Only one such unique speed can exist, and there have been many measurements of it. It is certainly possible that this is not the speed of light; as your son suggested, it's conceivable that light has a tiny mass and hence moves slightly slower than $c$. But the relativistic $c$ (speed of causality/maximum speed) can't be significantly different from the speed of light or we would have noticed it, e.g. in particle accelerators (where things are moving very close to the maximum possible speed). And as other commentators have pointed out, there are very good theoretical reasons to suppose that light is massless and hence the speed of light is the speed of causality.