I have very little to add, except that experience is only plain and simple on its uppermost level. We measure space...with other measures of space, time with other measures of time, and assume we're doing something. One of the two constants we've found is one of speed, which means that time and space can be different for different observers even as we measure that speed with time and space. Of course, the wonderful thing about light is that we can measure its speed, no matter how we may be bobbing along, and get the same answer.
UPDATE: The experiment seems to prove as well that space is not quantized, which is good for Relativity.
