In an online lecture on Special Relativity, the instructor asserts that in the space-time coordinate system, [tex](d{\tau})^{2}=(dt)^{2}-(dx)^{2}[/tex] with [tex]\tau[/tex] representing the proper time in a frame moving with velocity v, t representing a period of time measured from an inertial reference frame, and c being clearly treated as 1. It is known from the Lorentz transformations that x and t are related through hyperbolic angles, but surely this cannot be sufficient to assume that the proper time is as it is given. If there is no clear mathematical basis for [tex](d{\tau})^{2}=(dt)^{2}-(dx)^{2}[/tex], then how can it be possible to derive such an equation willy-nilly?(adsbygoogle = window.adsbygoogle || []).push({});

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# Arbitrariness in Special Relativity

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