De Sitter presents another argument in defence of his solution. It deals with the relativity of mass or inertia, but as I have been unable to reconcile his views on this subject with the characteristics of his universe, I may have misunderstood his idea; hence I cannot discuss it. At all events, the relativity of inertia is a most important argument in favour of Einstein’s cylindrical universe, so we shall consider it when dealing with Einstein’s solution.
Now when we accept de Sitter’s vanishing values for the
’s or potentials at infinity, the direct outcome is a finite space-time universe. We see, then, that in this way the boundary conditions have been obviated entirely, since in a finite universe, closed round on itself, there is no longer a boundary. The precise form of de Sitter’s universe is a spherical four-dimensional space-time. When empty of matter, it is given by the equation
. In other words, it is the type of universe to which we are led when the
term is included in the gravitational equations; hence, as we have seen, it is a type which is theoretically possible.
The characteristics of de Sitter’s universe are thus those of a spherical four-dimensional space-time of radius
