As seen from AB's reference frame: A'B' is moving from left to right with a speed v and so has a length of
. AB is at rest has a length of l0.The distance traveled by A'B' when A and A' align is
and so the time taken is
The distance traveled by A'B' when B and B' align is l0 and so the time taken is l0/v.
As seen from A'B''s reference frame: AB is moving from right to left at a speed v and so has a length of
. A'B' is at rest and has a length of l0.The distance traveled by AB when B and B' align is
and hence the time required is .The distance traveled by AB when A and A' align is lo and so the time required is lo/v.
Isn't it interesting that according to AB, A and A' align first and then B and B' while according to A'B', B and B' align first and then A and A'. This demonstrates that in relativistic mechanics sequence of events as seen by different observers may in fact be different!
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