Is length an intrinsic property or is it something which is only relative to other lengths? Is an inch an inch? Or is it simply a relation between other (length) phenomena?
It is indeed an interesting question, and in fact it's more than one question. To begin with, my colleague is correct: in special relativity, length is like velocity in classical mechanics: it's a "frame-dependent" quantity. However, the theory of relativity is also a theory of absolutes; between any two points in space-time there is a quantity called the interval , and it is not frame-dependent. To put it in the jargon of relativity, the space-time of special relativity has a metric -- a generalized "distance function" -- and that metric delivers an unequivocal answer to the question of whether the interval between w and x is equal to the interval between y and z. But now we have a new question: suppose that relativity says that the interval between w and x is, in fact, the same as the interval between y and z. What kind of fact is that? Suppose that the two intervals have no overlap. Doing business as usual, so to speak, we come up with the answer that the intervals are equal, but we ...
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