That’s exactly what often troubles students of special relativity - why should a physical quantity be defined by the way you are trying to measure it. (The mass

That’s exactly what often troubles students of special relativity - why should a physical quantity be defined by the way you are trying to measure it. (The mass is the mass, for example, no matter what device you construct to measure it. In special relativity, on the other hand, the very notion of time interval seems to be tied to observing how light travels between mirrors.)