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Let's say we are in a frame of reference S and we see a clock moving at velocity $c/2$. Let's say that a clock in our frame of reference reads $t=0$ when the moving clock reads $t'=0$. I want to then find out what time our clock will read when the moving clock reads $t=100$.

Here's what I did: We have $$t=\gamma\left(t'+\frac{vx'}{c^2} \right)$$ and we know that $t'=100$, $v=c/2$ and I suppose that $x'=vt'=ct'/2$ and so to give $$t=\gamma\left(t'+\frac{c^2t'}{4c^2} \right)=\frac{5}{4}\gamma t'$$ so here's the problem: shouldn't it be simply $$t=\gamma t'$$ what did I overlook? Thank you.

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$x'$ and $t'$ is the value measured in $S'$-frame.(i.e. frame moving at velocity $c/2$ in $S$-frame) So, $x' = 0$ in $S'$-frame.

More precisely, we should assume that $x'=0$ when $t'$ is 0

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  • $\begingroup$ Oh! Because in the clock's frame its position never changed, even after t'? $\endgroup$
    – Racconn
    Mar 12, 2018 at 2:33
  • $\begingroup$ @Racconn Yes. That's right. $\endgroup$
    – ChoMedit
    Mar 12, 2018 at 2:34

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