Quite independently of the relativity theory, in the days when space-time was unknown, astronomers had puzzled over certain difficulties dealing with the universe as a whole. Two possibilities appeared to suggest themselves. Either star-matter was present everywhere, distributed more or less homogeneously throughout infinite space, or else the stars were concentrated into a nucleus forming an island of matter in an infinite ocean of space.
The first alternative entailed certain difficulties when we considered the illumination of the heavens at night. Calculation showed that the night sky should be many times more luminous than it is. Of course this difficulty might have been overcome by assuming that as we wandered farther and farther from the earth, the percentage of dark stars increased; or, again, that vast quantities of cosmic dust intercepted the light and obscured the heavens. It might also have been assumed that light was gradually absorbed in its long journey from the distant stars.
Over and above these first difficulties, it was shown that if the stars attracted one another according to Newton’s law it would be impossible for them to be spread more or less uniformly throughout infinite space; rather would they concentrate into a nucleus. Precise calculation shows that the density of matter, hence the number of stars per unit volume, would vanish at infinity, decreasing progressively from a centre more rapidly than
, where
represents the distance from the centre. It appears, then, that a nucleus of stars cannot be avoided if Newton’s law is to hold.[108] The astronomer Seeliger attempted to realise an infinitely extended universe of matter by modifying Newton’s law in an appropriate way. But, as Einstein remarks, the attempt had neither empirical nor theoretical foundation.
Finally, then, if we accept Newton’s law, we must assume that the universe presents the form of a nucleus of stars lost in infinite space. But here, again, a new difficulty awaits us. In the first place, astronomical observation reveals no trace of any such nucleus. Of course it might be contended that this was due to the limited range of our astronomical observations. Nevertheless, this first argument against the nucleus hypothesis cannot be passed over lightly, for we must remember that in these speculations on the form of the universe, we have to make the best of the flimsiest of clues; we cannot operate as in a laboratory.
Then there is a second argument adverse to the nucleus hypothesis. Calculation shows that the cumulative Newtonian gravitational attraction of the stars would be insufficient to retain any individual star and prevent it from escaping to infinity, leaving the nucleus forever. Similar conclusions would apply to rays of light. It would follow that our universe of stars was in a state of dissolution. It is of course possible that such is indeed the case; yet, to a number of thinkers, a universe in process of dissolution appeared most unlikely. With Newton’s law of gravitation there was no escape. This was the cosmological difficulty which classical science had to face.
Inasmuch as the justification for these statements does not involve any very complicated ideas, we may proceed to explain them briefly. Consider the hypothetical case of the earth situated in infinite space, and isolated from all other bodies. If, then, a mass is abandoned at spatial infinity, it will be attracted towards the earth, gradually gathering momentum, and may finally hit the earth’s surface with a certain velocity, which calculation proves to be about seven miles a second. This particular speed