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TimeDilation

# TimeDilation - T c(T T cT = D B T T(second detector goes...

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t = 0 (starting point) x = 0 DISTANCE TIME L A WHEN PLATFORM IS VIEWED AS STATIONARY (Frame A) c c T A At T A , both detectors register flashes simultaneously ! T = 0

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t = 0 (starting point) x = 0 DISTANCE TIME L B WHEN PLATFORM IS VIEWED AS BY OBSERVER MOVING AT -V WITH RESPECT TO PLATFORM (Frame B) c c T A v
t = 0 (starting point) x = 0 DISTANCE TIME L B c c T 0 (first detector goes off) v c v vT 0 cT 0 L B /2 = vT 0 + cT 0

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t = 0 (starting point) x = 0 DISTANCE TIME L B c c T 0 (first detector goes off) v c v vT 0 cT 0 L B /2 = vT 0 + cT 0 v v(T 0 + ! T) L B /2 c(T 0 + ! T) c(T 0 + ! T) = L B /2 + v(T 0 + ! T) subtracting : c ! T = v(2T 0 + ! T) D B : distance between flashes T 0 + ! T (second detector goes off)
t = 0 (starting point) x = 0 DISTANCE TIME L B c c T 0 (first detector goes off) v c v vT 0 cT 0 v v(T 0 + ! T) L B /2 D B : distance between flashes c(T 0 + ! T) c(T 0 + ! T) = L B /2 + v(T

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Unformatted text preview: + ! T) c(T + ! T) + cT = D B T + ! T (second detector goes off) subtracting : c ! T = v(2T + ! T) ! T = v D B c 2 L B /2 = vT + cT 0 From the perspective of Frame A (platform is moving) v L A 0 -T B all clocks read 0 From the perspective of Frame A (platform is moving) v L A 0 -T B all clocks read 0 v L A +T B all clocks read T A D A From the perspective of Frame A (platform is moving) From the perspective of Frame B (ground is moving) v L B 0 0 T A D B from before : T A = v D A / c 2 T B = v D B / c 2 From the perspective of Frame A (platform is moving) From the perspective of Frame B (ground is moving) v L B 0 0 T A D B from before : T A = v D A / c 2 T B = v D B / c 2 v L B +T B 2T A +T B T A...
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