1 PHY3221 Detweiler Lecture #3 Relativity A surprising consequence of length contraction: Simultaneity is relative In the search for a logical contradiction to the special relativity idea that the speed of light c is always measured to be the same value, we look at the consequences of length contraction. The train that Alice rides on is 200 m long. Bob’s platform is actually inside the train station, and is 175 m long. The station also has doors that lower over the tracks at either end. Here is a description of the experiment that Alice and Bob try. Alice’s train moves with a speed v = 0 . 6 c = 3 c/ 5 so p 1-v 2 /c 2 = 4 / 5 = 0 . 8 . Bob knows that the proper length of the train is L train0 = 200 m, so at that speed if Bob measures the length of the train it will only be L train B = L train0 p 1-v 2 /c 2 = 4 / 5 × 200 m = 160 m . So Bob arranges to have two of his assistants put themselves at the doors at either end of the station. The assistants are instructed to lower the doors when the train is inside
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