Relativity and Cosmology

   

Einstein’s Clock Observation While Riding a Train

Authors: Richard Kaufman

In this note, we revisit Einstein’s thought experiment for viewing Bern’s clock tower with riding on a train. Einstein imagined observing Bern’s clock tower while travelling on a train at the speed of light away from the clock. He concluded that he would not see the clock hands move. As the story goes, this inspired Einstein’s work on Special Relativity, where he used an assumed constant speed of light, c, to show that time dilation and length contraction must occur for different observers moving at uniform velocity (greater than 0) relative to each other. This is a different interpretation of Lorentz’s equation, where the formulas still hold.Typically, time dilation is discussed in terms of considering the clocks for each of the two inertially moving observers. However, in the one-page paper that follows, we shall consider what a clock would show at different distances to the clock. Here, we will only consider the observations of the observer (us) stationary to the clock, and still show that the other observer would see a different time according to the light from the clock. We will observe that the moving observer will see the time on the clock slow down when moving away from the clock at a constant speed of 0.5c (for example) and that this observer would see time on the clock speed up when returning to the clock at the same speed. Everything works out so that both observers see the same time on the clock at the beginning and end of the trip (at the clock’s location).

Comments: 2 Pages.

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Submission history

[v1] 2023-09-02 15:40:34

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