SIDELIGHTS ON RELATIVITY

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Assuming that we know, let us say, the statistical distribution
of the stars in the Milky Way, as well as their masses, then by
Newton's law we can calculate the gravitational field and the mean
velocities which the stars must have, so that the Milky Way should
not collapse under the mutual attraction of its stars, but should
maintain its actual extent. Now if the actual velocities of the stars,
which can, of course, be measured, were smaller than the calculated
velocities, we should have a proof that the actual attractions
at great distances are smaller than by Newton's law. From such a
deviation it could be proved indirectly that the universe is finite.
It would even be possible to estimate its spatial magnitude.

Can we picture to ourselves a three-dimensional universe which is
finite, yet unbounded?

The usual answer to this question is "No," but that is not the right
answer. The purpose of the following remarks is to show that the