and
is no coincidence at all; according to him, there exists a causal connection between these two magnitudes. The density of matter creates
, or, again, the total amount of matter in the universe creates the universe of space. Were more matter to be created, the universe would expand; were matter to be annihilated in part, the universe would contract. Indeed, were no matter to be in existence, there would be no space; hence, a totally empty universe would be quite impossible. Thus there is a marked difference between Einstein’s universe and de Sitter’s universe, which can exist without matter.
We may also mention another reason which directed Einstein to the cylindrical universe. We remember that when discussing the boundary values of the
’s we saw that de Sitter considered it necessary to obtain boundary values which would remain invariant to a change of mesh-system. In accordance with this requirement, he assumed that all the
’s vanished at the boundary. As a result he obtained his hyperbolical universe. Similar considerations prompted Einstein. Here, however, it must be noted that in Einstein’s model, while all the space-