Walking Across the Train

Walking Across the Train - dilation factor, just as is...

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Walking Across the Train Imagine now a rather wide train, of width w , and the walker begins the walk across the train, which is now equipped with clocks on both sides, when the clock where he begins reads t = 0. For walking speed u y' (relative to the train, and across the train is the y -direction) when he reaches the clock at the other side it will read w / u y' . How is this seen from the ground? The width of the train w will be the same, there is no Lorentz contraction in the y -direction for motion in the x -direction. The beginning and ending clocks will also be synchronized as seen from the ground, since they are separated in the y -direction but not the x -direction. However, they are clocks moving at relativistic speed, so they will exhibit the familiar time dilation factor. That is, when they read w / u y' , a clock on the ground will read Thus, as observed from the ground, walking directly across the train is slowed down by the time
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Unformatted text preview: dilation factor, just as is every other activity on the train as seen from the ground. However, for steady motion on the train in an arbitrary direction, velocity components ( u x' , u y' ) the cross-train velocity transforms in a more complicated way, because the train clocks at the beginning and end of the walk are now separated in the x-direction, so if they register an elapsed time of w / u y a ground observer would add a lack of synchronicity term Thus the time for the walk as observed from the ground From this we find the general formula for transformation of transverse velocities: For the special case of walking directly across the train, u x' = 0, we recover the earlier result, that transverse velocity is simply slowed by the time dilation effect....
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