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I've been trying to understand the (lack of) simultaneity between events in reference frames moving wrt each other. I'd be grateful if someone could confirm that I've got things right:

If two events are simultaneous in one reference frame (S'), then they will not be simultaneous in a reference frame (S) moving with velocity v relative to S' if the events are separated by any distance (D' or D) in the direction of motion. In which case, an observer in S will observe a time difference of:

[itex]\Delta t = \frac{Dv}{(c^2 - v^2)} (*)[/itex]

And, if two events are separated by distance D' and time t' in S', then, as observed in S, they are separated by time:

[itex]\Delta t = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}(t' \pm \frac{D'v}{c^2})[/itex]

(*) The book I'm reading expressed this equation in terms of an observer in S reading the times off clocks synchronised in S' and getting:

[itex]\Delta t = \frac{D'v}{c^2}[/itex]

Which seems to me an odd way to express things and I think this confused me somewhat. Hopefully, I've now understood this simultaneity issue?

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# Simultaneity between events in reference frames

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