So I just finished reading my text book on special relativity and am a bit confused by the discussion of time dilation. We equip an observer with a light source, a mirror, and a clock and herd him onto a train moving at constant velocity relative to a second observer located at the station. If D is the distance between the source and the mirror, then the time (measured by the observer on the train) that it takes for a pulse of light to strike the mirror and reflect back to the source is given by(adsbygoogle = window.adsbygoogle || []).push({});

Δt_{0}= 2D/c.

We compare this to the time observed by the stationary observer, which will be:

Δt = Δt_{0}/√1-(v/c)^{2}.

The measured times are different and related by the Lorentz factor. Now the reason these two times are different is a consequence of the constancy of the speed of light. For the stationary observer, the light beam has to travel a longer path (a triangle of height D and base vΔt), and since it travels at the same speed it takes longer. Now here comes my question.

How would this result be applied to a tennis ball rather than a light beam? As I understand it, the idea of time dilation is supposed to apply to all phenomena, not just electromagnetic phenomena. So suppose we fire a tennis ball from a tennis-ball-souce and reflect it from a tennis-ball-mirror (i.e., wall). There is no principle of the constancy of the speed of sports equipment, so wouldn't the time measured by the observer on the train be equal to that measured by the stationary observer (I mean the time it takes for the tennis ball to leave its source and be reflected back). Because though the stationary observer watches the ball travel a longer path, the ball is moving with a greater speed due to the speed imparted to it by the movement of the train, and that greater speed is precisely enough to compensate for the extra distance, since both are caused by the movement of the train. So I guess my question is first of all, am I right that there would be no time difference measured if we used a tennis ball instead of a light beam? And second, how do we justify the application of special relativity to tennis balls if the effects are dependent upon the constancy of the speed of light?

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# Time Dilation with a Tennis Ball

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