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Can the metric of special relativity be derived from requiring the infinitesimal line segment, dτ, to be invariant in space and time? If we parameterize a line segment by the variable τ marked off along the line (that exists in space and time dimensions) is the length in τ of that line segment only invariant with respect to the Lorentz transformations? Or are there other coordinate Xformations for which dτ would also be invariant? Thank you.

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