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

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

${\frac {U}{D}}=\pi .$

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 contrac-