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Suppose, Supantho and Mohaimen are moving to each other at a relative velocity ofNow, consider the situation in Supantho's reference frame (first figure): The distance between Supantho and Mohaimen is . Both Supantho and Mohaimen's clock show 4:00.
Again, consider the situation according to Mohaimen's reference frame (second figure): Supantho's clock shows 4:00. What will be the distance between them and what does Mohaimen's clock show?
Details and Assumptions
The speed of light is .
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Let's format the problem in a structural way. Look, in this problem, there are 3 events in the spacetime: 1. Supantho in his rocket at 4:00 according to his clock(Fig. 1) 2. Mohaimen in his rocket at 4:00 according to his clock(Fig. 1) 3. Mohaimen in his rocket at time '?' according to his clock(Fig. 2) These 3 events are denoted by P 1 , P 2 , P 3 respectively in fig. 3: The primed coordinates are of Mohaimen's reference frame, and the unprimed ones of Supantho's (I mean a referance frame which is staionary w.r.t Supantho). I took P 2 on the origin of both reference frames, so, x 2 = x 2 ′ = x 3 ′ = 0 t 2 ′ = t 2 = t 1 = 0 t 3 ′ = t 1 ′ x 1 = 1 . 4 4 × 1 0 1 2 m We have to calculate x 1 ′ & t 3 ′ ; Using Lorentz's transformation, x 1 ′ = 1 − c 2 v 2 x 1 − v t 1 = 1 . 8 × 1 0 1 2 m t 3 ′ = t 1 ′ = 1 − c 2 v 2 t 1 − c 2 v x 1 = − 3 6 0 0 s = − 1 h r So the time would be 1 hour less than 4:00, that is 3:00.