If we observe the original and the double star, the reality and the mirage, simultaneously from some remote part of the stellar system, such as our planet, we shall see a great difference between them, since the “copy” will show us the original as it was thousands of centuries before. It may, in fact, happen that the second star is more brilliant than the first, because in the meantime the first has gradually cooled, and may even be extinct.
It is improbable that we should find many of these phantom-stars, or virtual stars, luminous and unreal daughters of heavy suns. The reason is that the rays in their passage through the universe will generally be diverted by the stars near which they pass. Concentration or convergence of them at the antipodes of the real star must be rare. Moreover, the rays are to some extent absorbed by the cosmic stuff they meet in space. It is, however, not impossible that the astronomers of the future may discover such phenomena. It is, in fact, not impossible that we have already observed such things without knowing it.
In any case, what observers have not done in the past they may very well do in the future, thanks to the suggestions of the new science. Possibly it is going to have a great effect on observational astronomy and induce it to furnish brilliant new verifications of theory. There may be astonishing results, unforeseen by our folly, of the new conceptions, surpassing in their fantastic poetry the most romantic constructions of the imagination. Reality, or at least the possible, is rising to giddy heights that were far beyond the reach of the golden wings of fantasy.
I spoke on a previous page of the millions of years which light takes to travel round our curved universe. Starting from the fairly well-ascertained value of the quantity of matter comprised in the Milky Way, it is possible to calculate the curvature of the world and its radius. We find that the radius has a value equal to at least 150,000,000 light-years.
It therefore takes light at least 900,000,000 years, at a speed of 186,000 miles a second, to travel round the universe, assuming that it consists only of the Milky Way and its annexes. The figure is quite consistent with the figures we get from astronomical observation for the dimensions of the galactic system, and also with the much larger figures which we find if we regard the spiral nebulæ as Milky Ways.
Thus for the Relativist the universe may be unlimited without being infinite. As to the Pragmatist, who goes straight ahead—who follows what he calls a straight line, or the path of light—he will get back in the end to the body from which he started, provided that he has time enough at his disposal. He will then say that, if that is the nature of things, the universe is not infinite.
Hence the question of the infinity or finiteness of the universe can be controlled by experience, and some day it will be possible to prove whether the whole cosmos and space are Newtonian or Einsteinian. Unfortunately, it will have to be a very long experience, with various little practical difficulties to overcome.
We may therefore prefer not to commit ourselves without further instructions. We may not feel ourselves obliged to choose between the two conceptions, and we may leave the benefit of the doubt to whichever of the two is false.