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Special Relativity in Week One: 2) All Clocks Run Slow
1.Elisha Huggins, “Special relativity in week one: 1) The principle of relativity,” Phys. Teach. 49, 148–150 (Feb. 2011).
2.To get the formula for the rate of the astronaut's clock, consider the right triangle of Fig. 3. The vertical leg, the distance we see that our light pulse travels in one bounce, is the speed of light c times the length of our nanosecond tus. Calling t astronaut the longer length of time we see that the astronaut's light pulse takes to travel between mirrors, the hypotenuse is c times t astronaut. The horizontal leg is the distance the astronaut's clock travels at a speed v during this time, namely vt astronaut. From the Pythagorean theorem we get (ct astronaut)2 = (ctus)2 + (vt astronaut)2, which we can solve to get as the length of the astronaut's longer nanosecond.
3.That real clocks run slow is beautifully illustrated in the movie by Frisch and Smith, “Time Dilation, an Experiment with Mu‐Mesons,” that is the focus of our next article. A detailed discussion of the movie appears in David H. Frisch and James H. Smith, “Measurement of the relativistic time dilation using μ mesons,” Am. J. Phys. 31, 342–355 (May 1963).
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