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The Lorentz transformation for time along the x-axis is

[tex]t'=\frac{t-\frac{ux}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}}[/tex], where u is the relative velocity of S'.

Why is there a dependence on x there? I'm interpreting x to be the distance between the origin of S and some event. At t=0, the origins of S' and S cross and their clocks are synced. S' is moving to the right at velocity u relative to S. When an event occurs at (x,t) according to S, it occurs at (x', t') for S'.

i) Let's say t=2s in the frame of S.

**Is t' the time that S' sees the event according to S? So in her frame, S' really sees it happening at 2 seconds but when she alerts S, t' has passed for S (t'>t)?**

ii) And the dependence on x - why should the distance of S to the event affect how time is affected in S' frame? This distance dependence doesn't appear in the time dilation formulas I see in all the textbooks I've flipped through!