# Special relativity of two clocks

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## Main Question or Discussion Point

Why is it that for two clocks that are synchronised in one frame, S, but not in another, S', is there an offset in the time by a factor of $\frac{Lv}{c}$, as measured in S'. Where L is the proper length of the body, as measured in S. I'm confused as to why there is not a factor of $\gamma$ here

Many thanks

## Answers and Replies

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Orodruin
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Why do you think there should be a factor $\gamma$? Have you looked at how the relation is derived?

Why is it that for two clocks that are synchronised in one frame, S, but not in another, S', is there an offset in the time by a factor of $\frac{Lv}{c}$, as measured in S'. Where L is the proper length of the body, as measured in S. I'm confused as to why there is not a factor of $\gamma$ here

Many thanks
I'm pretty sure the offset in time is Lv/c2, not Lv/c (since obviously Lv/c is in units of length).

Also section 11.3 of this link has a problem that comes up with your Lv/c involving synchronized clocks on a train. It has a nice picture too showing the distance the photon must travel, which gives those two factors.

http://www.people.fas.harvard.edu/~djmorin/chap11.pdf

I'm pretty sure the offset in time is Lv/c2, not Lv/c (since obviously Lv/c is in units of length).

Also section 11.3 of this link has a problem that comes up with your Lv/c involving synchronized clocks on a train. It has a nice picture too showing the distance the photon must travel, which gives those two factors.

http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
How careless of me- I did mean over $c^2$. Funnily enough, this was the book that caused my confusion. I don't feel like he explains it very well. However, I have since worked it out- so all it good.

Thank you for replying though- it's very appreciated :)

How careless of me- I did mean over $c^2$. Funnily enough, this was the book that caused my confusion. I don't feel like he explains it very well. However, I have since worked it out- so all it good.

Thank you for replying though- it's very appreciated :)
Haha no it definitely could be clearer, but it does have a good picture I think.