Consider the following variation of the twin paradox. A, B, and C each have a clock. In
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Consider the following variation of the twin paradox. A, B, and C each have a clock. In A’s reference frame, B flies past A with speed v to the right. When B passes A, they both set their clocks to zero. Also, in A’s reference frame, C starts far to the right and moves to the left with speed v. When B and C pass each other, C sets his clock to read the same as B’s. Finally, when C passes A, they compare the readings on their clocks. At this event, let A’s clock read TA, and let C’s clock read TC.
(a) Working in A’s frame, show that TC = TA/γ, where γ = 1√1 – v2/c2.
(b) Working in B’s frame, show again that TC = TA/γ.
(c) Working in C’s frame, show again that TC = TA/γ.
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a In As reference frame the worldlines of A B C are shown in Figure Bs clock runs slow by a factor 1 Therefore if As clock reads t when B meets C then Bs clock will read t when he meets C So the time ...View the full answer
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