By E. Taylor, J. Wheeler [non-OCR]
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Extra resources for Spacetime Physics
Sample text
As a reassuring check that we haven’t made some mistake, notice the following. Suppose the velocity v of the train in the track frame were 0. Then the track frame would be the same as the train frame. Consequently w, the velocity of the ball in the track frame, would be the same as u, the velocity of the ball in the train frame. 4). 12) remains entirely correct if we replace the photon by anything at all that moves with the same speed in both directions, and allow that speed, c, to be any speed at all greater than w and v.
Since the Earth moves about the sun at a brisk clip of 30 km/sec in different directions, depending on the time of year, and the sun moves briskly about the center of our galaxy, it would be a remarkable coincidence if the Earth just happened to be stationary in the rest frame of the ether. One would expect there to be a kind of “ether wind” blowing past the Earth, leading to a dependence of the speed of light on Earth on the direction of that wind. The speed of light on Earth into the direction from which the ether wind was blowing ought to be a bit less than its speed along the direction of the wind.
1) At the start of the race the photon and the ball are together at the rear of the train, moving with speeds c and u. (2) The photon reaches the front of the train and bounces back toward the rear (whence the two-headed arrow). (3) At the conclusion of the race the photon reencounters the ball a fraction f of the way back from the front of the train. frame u, then, since the speed of the photon in either direction is c, 1−f u = . 3) The people on the train have thus measured the speed of the ball without using clocks and without having to know the length of the cars in their train.