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I learned today that it is, theoretically, impossible to prove the speed of light in a vacuum, at least in terms of any common unit of distance that we currently have. The distance light travels in a single second, in metres, is entirely arbitrary, and is in fact the basis for the metre as a unit of measurement.

It would be like me stating that a = 5, and then attempting to prove that a = 5. The only basis for it is my original assertion that the two are equal - it's only true for as long as I say it is.