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We know that in lorentz transformation , x'= lorentz factor*(x-vt) Suppose, that in unprimed frame , x=0 ; and the primed frame moves with velocity c wrt unprimed one. Then accor to the transformation, x'=-(infinite), as lorentz factor is infinite. But how can infinite distance be traversed by the primed frame with respect to the unprimed frame at a finite time?

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First of all, the Lorentz transformation $x'=\gamma (x-vt)$ is not for distances, but for single events. Here $x'$ represents the position where some event occurs in the moving frame and approaches $\infty$. This isn't really possible because it would take an infinite amount of energy to accelerate an object with mass to $c$ which is why the $v=c$ frame does not exist.

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  • $\begingroup$ But what if we take the primed frame as light itself? $\endgroup$ – Syed Jaffri Jun 13 '17 at 18:47
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    $\begingroup$ @Syed, according to SR, there is no inertial reference frame for light, light has speed c in all inertial reference frames, there is no rest frame for light, there is no inertial reference frame with relative speed c. $\endgroup$ – Alfred Centauri Jun 14 '17 at 1:20

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