Relative Space-Time and Simultaneity

Review of Metaphysics 17 (4):514 - 535 (1964)
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Abstract

The picture which one naturally presents of the situation is that which would arise before an observer placed outside the earth, who could watch the light wave starting from the central mirror and pursuing the distant mirror, catching up with it at some distance beyond the point at which it was when the light wave started. In this case the observer is able to locate the points at which the parts of the apparatus were at different moments and to measure the distances between. We could simulate this situation on the earth by assuming an enclosed square car, from some point in which two balls were shot out in directions at right angles to each other to the walls of the car, bounding back to the point at which they started. We will assume that the balls move with uniform velocity going and coming, and we will assume that the car is moving. An observer outside the car who marked the point on the rail directly over the starting point and the points reached by the balls when they struck the sides of the car, and then measured the distances which the balls travelled, would find that the ball which travelled with the car covered a greater distance than that traversed by the ball which went at right angles to the direction of the train, and yet the balls would return to the starting point at the same moment, provided they travelled over both their paths at the same velocity during their entire trajects, i.e., the same velocity measured within the car. The observer would be at no difficulty to explain this, for he would see that the velocity in the direction of its motion of the car had to be added to that of balls within the car. That is not the case of the light wave. The velocity of a moving shining body is not added to that of the light wave. The wave motion being set up in ether travels with its own uniform velocity of approximately 300,000 kilometers a second. The light waves then, from the standpoint of the observer outside the earth, traverse through the stagnant ether different distances at a uniform velocity and yet the ether waves exhibit on their return none of the evidence which they should exhibit in the interferometer.

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