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Illustration Two Inertial Systems Move Relative to Each Other

Two Inertial Systems Move Relative to Each Other
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Two inertial systems \(S\) and \(S'\) with coordinates \((c\,t, x,y,z)\) and \((c\,t', x',y',z')\) move relative to each other with a constant velocity \(\boldsymbol{v} \) in \(x\) direction. A point \(P\) has the position vector \(\boldsymbol{r} \) in the \(S\) system and the position vector \(\boldsymbol{r}' \) in the \(S'\) system.

The transformation of the coordinates from \((c\,t, x,y,z)\) to \((c\,t', x',y',z')\) is given by the Lorentz transformation (here: Lorentz boost).