Lec28 - two clocks Assume the other clock has a dierent...

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two clocks. Assume the other clock has a di ff erent rate for the passage of time. Using two di ff erent clock designs and getting di ff erent readings of time, we could tell these clocks are in motion, in violation of the Principle of Relativity. (We of course assume both clocks are good clock, because real clocks often show just that...) Length (Lorentz–Fitzgerald) contraction We have already seen that contraction of the length of a moving object (or of moving empty space: in the Michelson–Morley experiment there is no matter along the arm of the interferometer!) can explain the null result of the Michelson–Morley experiment, but we want more than just that: we want to show that it is an inevitable conclusion from the Principle of Relativity. Also, for Lorentz it was a property of electromagnetism and the structure of matter, not of spacetime itself (and therefore an e ff ect that applies equally to all material regardless of what they are made of, which detailed force law holds them together, etc. Consider a platform in the train station, of length L 0 in its rest frame, and a passing train is moving with speed v . How is the length of the platform L , as measured by an observer on board the train, related to the proper length L 0 of the platform? An observer on the train makes a measurement of the length of the platform by taking a time measurement when she passes by one side of the platform, and another time measurement when she passes by the other side of the platform. She is co–moving with the clock, and therefore measures the proper time Δ t 0 , because both measurements happen in the same place (in the train frame). Therefore, the length of the platform is L = v Δ t 0 . This is perhaps an unusual operation to measure distance, but it has to be equivalent to the operation of measuring distance between two simultaneous events using a meter stick. Normally, we accept that the distance between two points equals the product of the traveling speed and time. In addition, the operational

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