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A.T.
#30
Nov28-09, 03:50 AM
P: 3,904
Quote Quote by cfrogue View Post
This assumes the events in O will be simultaneous with the events in O' given ta = t = tb.
What do you mean by events in one frame being simultaneous with the events in a different frame? Two events can be simultaneous (or not simultaneous) within one frame, not across frames.

Two events are simultaneous in a frame if their t coordinates in that frame are equal. For example the two light sphere events

A : (xa = cT, ta = T)
B : (xb = -cT, tb = T)

are simultaneous in the frame O where they have the above coordinates, because

ta = tb

But in the frame O' where they have the coordinates

A : (xa' = ( cT-vT)*gamma, ta' = (T-vT/c)*gamma)
B : (xb' = (-cT-vT)*gamma, tb' = (T+vT/c)*gamma)

they are not simultaneous, because

ta' <> tb'

OK, I think I understand your scenario. So just do it the other way round.
You can then swap the apostrophe annotation my formulas, so the events are simultaneous in O' but not O.