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

66 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 $$K'$$ be a system of co-ordinates whose $$z'$$-axis coincides with the $$z$$-axis of $$K$$, and which rotates about the latter axis with constant angular velocity. Are the configurations of rigid bodies, at rest relatively to $$K'$$, in accordance with the laws of Euclidean geometry? Since $$K'$$ is not an inertial system, we do not know directly the laws of configuration of rigid bodies with respect to $$K'$$, nor the laws of nature, in general. But we do know these laws with respect to the inertial system $$K$$, and we can therefore estimate them with respect to $$K'$$. Imagine a circle drawn about the origin in the $$x'y'$$ plane of $$K'$$, 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 $$K'$$. If $$U$$ is the number of these rods along the periphery, $$D$$ the number along the diameter, then, if $$K'$$ does not rotate relatively to $$K$$, we shall have

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