Apologies if this is a really stupid question, but what is the exact argument for why one can use proper time to parametrise timelike curves? Is it simply that the arclength of a timelike curve is its elapsed proper time and hence we are simply parametrising the curve by its arclength? Also, is the reason that we cannot parametrise lightlike and spacelike curves by proper time because, for the former, the proper time is zero, and for the latter, the proper time is not defined?(adsbygoogle = window.adsbygoogle || []).push({});

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# I Parametrisation of timelike curves using proper time

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