Page:The Meaning of Relativity - Albert Einstein (1922).djvu/78

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THE MEANING OF RELATIVITY

we come into conflict with that physical interpretation of space and time to which we were led by the special theory of relativity. For let be a system of co-ordinates whose -axis coincides with the -axis of , and which rotates about the latter axis with constant angular velocity. Are the configurations of rigid bodies, at rest relatively to , in accordance with the laws of Euclidean geometry? Since is not an inertial system, we do not know directly the laws of configuration of rigid bodies with respect to , nor the laws of nature, in general. But we do know these laws with respect to the inertial system , and we can therefore estimate them with respect to . Imagine a circle drawn about the origin in the plane of , and a diameter of this circle. Imagine, further, that we have given a large number of rigid rods, all equal to each other. We suppose these laid in series along the periphery and the diameter of the circle, at rest relatively to . If is the number of these rods along the periphery, the number along the diameter, then, if does not rotate relatively to , we shall have

But if rotates we get a different result. Suppose that at a definite time , of we determine the ends of all the rods. With respect to all the rods upon the periphery experience the Lorentz contraction, but the rods upon the diameter do not experience this contrac-