Page:The Meaning of Relativity - Albert Einstein (1922).djvu/79

tion (along their lengths!).^[1] It therefore follows that

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

It therefore follows that the laws of configuration of rigid bodies with respect to $K'$ do not agree with the laws of configuration of rigid bodies that are in accordance with Euclidean geometry. If, further, we place two similar clocks (rotating with $K'$), one upon the periphery, and the other at the centre of the circle, then, judged from $K$, the clock on the periphery will go slower than the clock at the centre. The same thing must take place, judged from $K'$ if we define time with respect to $K'$ in a not wholly unnatural way, that is, in such a way that the laws with respect to $K'$ depend explicitly upon the time. Space and time, therefore, cannot be defined with respect to $K'$ as they were in the special theory of relativity with respect to inertial systems. But, according to the principle of equivalence, $K'$ is also to be considered as a system at rest, with respect to which there is a gravitational field (field of centrifugal force, and force of Coriolis). We therefore arrive at the result: the gravitational field influences and even determines the metrical laws of the space-time continuum. If the laws of configuration of ideal rigid bodies are to be expressed geometrically, then in the presence of a gravitational field the geometry is not Euclidean.

1. These considerations assume that the behaviour of rods and clocks depends only upon velocities, and not upon accelerations, or, at least, that the influence of acceleration does not counteract that of velocity.