On the first view the entire stellar universe, in so far as it is accessible to us, consists of the Milky Way and its annexes: that is to say, a local concentration of stars, beyond which we can see nothing. The stellar universe is, in other words, practically limited, or at least finite.
On the second view our Milky Way is simply one of the myriads of spiral universes we see. The spiral nebula (with its hundreds of millions of stars) plays the same part in this vaster universe that a star has in the Milky Way. We have the same problem as before, but on a vaster scale: if the Milky Way consists of a concentration of a finite number of stars, as observation proves, does the accessible universe consist of a finite number of spiral nebulæ?
Experience has as yet not pronounced on this point. But in my opinion it is probable that, when our instruments are powerful enough to tackle such a problem—in several centuries, perhaps—science will answer “yes.”
If it were otherwise, if the spiral nebulæ were fairly evenly distributed as we go outward, we can show by calculation that, attraction being in inverse proportion to the square of the distance, gravitation would have an infinite intensity in such a universe, even in the part in which we live. But this is not the case. It follows that, either the attraction of two masses decreases at great distances rather more rapidly than in inverse proportion to the square of the distance (which is not wholly impossible), or that the number of stellar systems and stars is finite. Personally I favour the second hypothesis, but it is incapable of proof. In such matters there is always an alternative, always a way of escaping in accordance with one’s bias, and there is really nothing that compels us to say that the stars are finite in number.
Starting from the mean value, as it has been observed, of the proper motions of the nearer stars, Henri Poincaré has calculated that the total number of stars in the Milky Way must be about one thousand million. The figure agrees fairly well with the results of the star-gauges effected by astronomers by means of photographic plates.
He has also shown that the proper motions of stars would be greater if there were many more stars than those which we see. Thus Poincaré’s calculations are opposed to the hypothesis of an indefinite extension of the stellar universe, as the number of stars “counted” agrees fairly closely with the number “calculated.” We should add, however, that these calculations prove nothing if the law of attraction is not quite the inverse proportion of the square at enormous distances.
On the other hand, if the universe is finite in space as it is conceived in classic science, the light of the stars, and isolated stars themselves, would gradually drift away into the infinite, and the cosmos would disappear. Our mind resents this consequence, and astronomical observation discovers no trace whatever of such a dislocation.
In a word, in the space of the “Absolutists” the stellar universe can only be infinite if the law of the square of distances is not quite exact for very remote masses; and it cannot be finite except on the condition that it is ephemeral in point of time.
For Newton, indeed, the stellar universe might be finite within an infinite universe, because in his view there can be space without matter. For Einstein, on the contrary, the universe and the material or stellar universe are one and the same thing, because there is no space without matter or energy.