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## Main Question or Discussion Point

Hi,

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?

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?