PAP111_Lecture17 - PAP111 Lecture17 TimeDilation...

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PAP 111  Mechanics and Relativity Lecture 17 Consequences of Special Relativity Time Dilation The Twin Paradox Length Contraction
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Time Dilation – Verification Time dilation is a very real  phenomenon that has been verified by  various experiments. These experiments include: Airplane flights Muon decay
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Time Dilation Verification –  Airplanes Flight In 1971, Hafele and Keating conducted an experiment, in which four  cesium atomic beam clocks were flown on commercial jet flights  around the world twice, once eastward and once westward, to test  Einstein’s theory of relativity with macroscopic clocks. “From the actual flight paths of each trip, the theory predicted that the  flying clocks, compared with reference clocks at the U.S. Naval  Observatory, should have lost 40 ± 23 ns during the eastward trip and  should have gained 275 ± 21 ns during the westward trip.” “Relative to the atomic time scale of the U.S. Naval Observatory, the  flying clocks lost 59 ± 10 ns during the eastward trip and gained 273 ± ns during the westward trip, where the errors are the corresponding  standard deviations. These results provide an unambiguous empirical  resolution of the famous clock paradox with macroscopic clock.” 
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Time Dilation Verification –  Muon Decays Muons are unstable particles that have  a lifetime given by the proper time  interval of  Δ t p  = 2.2  µ s . Since these  particles travel close to the speed of  light, we expect them to decay after  traveling  Δ t p  = 6.6x10 m. But we  observe them on the surface of Earth?? Time dilation explains the observation.  Relative to an observer on the Earth,  muons should have a lifetime of  γ   Δ t 16 µ s  for  =0.99 c . Hence, the muons  travel  v   γ   Δ t =4.8x10 m before decay  and reach the surface of Earth.
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Time Dilation – Muons Decay  Curve
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