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

Rh (along their lengths!). It therefore follows that

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.