I'm having trouble understanding how the lorentz transformations are posed intially.(adsbygoogle = window.adsbygoogle || []).push({});

Why can different observers agree on their relative velocity? I don't understand why this velocity is exempt from all of the other relativistic phenomena that occur.

Also, in the initial derivation, I'm told that one could make the following equations

##x'=G(x-ut)## ##x=G(x'+ut')##

I understand the reasoning behind the signs, but I think I dont see any clear reason for wanting to use different times here. Of course, the point of this is to conclude that time intervals aren't absolute, however, I don't get why, for example:

the term (x'+ut') is constructed that way because this coordinate is measured to be going away by O (unprimed frame). But why is the translation a function of the time measured by the O' frame? namely, why is it ##ut'## that is considered by the O frame. Why isn't it ##ut##? That makes more sense to me.

Thanks.

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# Why can different observers agree on their relative velocity

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