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Unformatted text preview: . Imagine a measuring rod at rest in the moving frame S ± , where its proper length is L . An observer, stationary in S , calculates the length of the rod using the time interval between the passing of the two end of the rod at his origin O in S . From this he measures L = u Δ t (19) in the stationary frame S . The observer in S ± , notices the passing of the two end of the rod at the origin to happen at L ± = L = u Δ t ± (20) 3 Thus L L ± = L L = Δ t Δ t ± (21) But, from our result of time dilation, Δ t ± Δ t = 1 ± 1( u/c ) 2 (22) therefore L = Δ t Δ t ± L = ± 1( u/c ) 2 L (23) therefore, the length of the rod is shorter when measured in a frame moving with respect to its stationary frame, with proper length L . 4...
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 Spring '10
 RogerMelko
 Special Relativity, Light, Speed of light, Time Dilation

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