Pagina 179 van 212

We already know from our previous discussion that the behaviour

of measuring-rods and clocks is influenced by gravitational

fields, i.e. by the distribution of matter. This in itself is

sufficient to exclude the possibility of the exact validity of

Euclidean geometry in our universe. But it is conceivable that

our universe differs only slightly from a Euclidean one, and this

notion seems all the more probable, since calculations show that

the metrics of surrounding space is influenced only to an

exceedingly small extent by masses even of the magnitude of our

sun. We might imagine that, as regards geometry, our universe

behaves analogously to a surface which is irregularly curved in

its individual parts, but which nowhere departs appreciably from

a plane: something like the rippled surface of a lake. Such a

universe might fittingly be called a quasi-Euclidean universe. As

regards its space it would be infinite.