But when we ask whether the hypothesis of a finite universe _must_
be true, the answer is different. It is obvious, on general grounds,
that we cannot, from what we know, draw conclusive inferences as to
the totality of things. A very slight change in the Newtonian formula
for gravitation would prevent masses beyond the limits of the visible
universe from having appreciable effects if they existed, and would
therefore destroy our reason for supposing that they do not exist.
All arguments as to regions which are too distant to be observed
depend upon extending to them the laws which hold in our part of
the world, and upon assuming that there is not, in these laws, some
inaccuracy which is inappreciable for observable distances, but fatal
to inferences in which very much greater distances are involved. We
cannot, therefore, say that the universe _must_ be finite. We can say
that it may be, and we can even say a little more than this. We can say
that a finite universe fits in better with the laws that hold in the
part we know, and that awkward adjustments of the laws have to be made
in order to allow the universe to be infinite. From the point of view
of choosing the best framework into which to fit what we know—best, I
mean, from a logico-æsthetic point of view—there is no doubt that the
hypothesis of a finite universe is preferable. This, I think, is the
extent of what can be said in its favor.
Let us now see what the two finite universes are like. The difference
between them is that in Einstein’s world it is only space that
is queer, whereas in De Sitter’s time is queer too. Consequently
Einstein’s world is less puzzling, and we will describe it first.
Public-domain text, read in full here on John Shaqi.
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