Cinsider please the invariance of the space-time interval in an one space dimension approach(adsbygoogle = window.adsbygoogle || []).push({});

(x-0)^{2}-c^{2}(t-0)^{2}=(x'-0)^{2}-c^{2}(t'-0)^{2}

My question is: does it hold for arbitrary events (x,t) in I and (x',t') in I?

Does it hold only in the case when the events are genertated in I and I' by the same light signal (x=ct,t=x/c); (x'=ct',t'=x'/c) or in the case when the events are generated by the same tardyon moving with speed u in I and u' in I' i.e. (x=ut,t=x/u) and (x'=u't', t'=x'/u')?

Are x and x' the components of a "two" vector or only x=ct, x'=ct' and x=ut, x'=u't', u amd u' being related by the addition law of parallel speeds?

Thanks for your answer.

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# Space-time interval invariance question

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