CHAPTER VII
IS THE UNIVERSE INFINITE?
Kant and the number of the stars—Extinct stars and dark nebulæ—Extent and aspect of the astronomical universe—Different kinds of universes—Poincaré’s calculation—Physical definition of the infinite—The infinite and the unlimited—Stability and curvature of cosmic space-time—Real and virtual stars—Diameter of the Einsteinian universe—The hypothesis of globes of ether.
Is the universe infinite? It is a question that men have asked in all ages, though they have not defined its meaning very accurately. The theory of Relativity enables us to approach it from a new and subtle point of view.
Kant—the genial grumbler who found it so horribly monotonous to see the same sun shining, and the same spring blossoming, every year—took his stand on metaphysical considerations when he affirmed that space is infinite, and is sown with similar stars in all parts.
It is, perhaps, better to confine ourselves in such a matter to the results of recent observation, and close the doors of our debating-room against the fog of metaphysics. Indeed, the latter would compel us to define pure space, about which we know nothing—not even if there is such a thing.
The proof that we know little about it is the fact that the Newtonians believe in it, while the Einsteinians regard it merely as an inseparable attribute of material things. They define space by matter; and they then have to define the latter. Descartes, on the contrary, defined matter in terms of extension, which is the same thing as space. It is a vicious circle. It is therefore better to leave Kant’s metaphysical arguments out of our discussion, and adhere strictly to experience, to what is measurable.
To simplify matters, we will admit the reality of this continuum in which the stars float, which is traversed by their radiations, which common sense calls space. If there were stars everywhere—if they were infinite in number—there would also be space and matter everywhere. Newtonians might find this a triumph equally with Einsteinians. Those who believe in absolute space and those who deny it—Absolutists and Relativists—would equally rejoice.
It would be fortunate if astronomical observation were to show that the number of the stars is infinite, and thus the holders of contrary opinions could both chant a victory in their writings. But what does astronomical observation actually report?
There are those who deny a priori that the number of the stars can be infinite. That number, they said, is capable of increase; it is therefore not infinite, because nothing can be added to the infinite. The argument is specious, but unsound; although Voltaire himself was seduced by it. One need not be a great mathematician to see that it is always possible to add to an infinite number, and that there are infinite quantities which are themselves infinitely small in comparison with others. Let us get on to the facts.