1. The universal repulsion which is totally foreign to matter;
2. The gravitational attraction between matter and matter.
Thus, it would be impossible to escape a duality in our conception of gravitation, if by gravitation we imply the cumulative action of both effects, yielding the one observable attraction of matter for matter.
We may summarise the chief characteristics of de Sitter’s universe as follows: First, this universe can exist in the absence of all matter. It then possesses a definite spherical structure and a radius of curvature
, where
, which is proportional to the universal curvature, is some constant which bears no palpable relation to anything else in the universe.[107] We must conceive of it as a constant of nature posited once and for all by the Creator. Secondly, if matter is introduced into this empty universe, it will produce local space-time puckers or curvatures around it; and to these local curvatures the phenomenon of attraction between matter and matter will be due. In the presence of matter, de Sitter’s universe will not be stable, for the universal repulsion will tend to cause matter to scatter if the mutual attractions are too feeble to oppose it.
In the opinion of a number of thinkers, de Sitter’s universe presents certain aspects which are most unsatisfactory. We shall discuss these later. At all events, Einstein rejects it and is led, by following a somewhat different line of attack, to a very different type of finite universe, the cylindrical universe.
We shall now proceed to a more detailed study of Einstein’s universe. First of all, we must mention certain general cosmological considerations that directed Einstein to the formulation of a finite-universe hypothesis.