CHAPTER VIIIS THE UNIVERSE INFINITE?
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 denya priorithat 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.
If the stellar universe has no limits, there is no visual line drawn from the earth to the heavens which will not encounter one of the stars. The astronomer Olbers has said that the whole nocturnal skywould in that case shine with the brilliance of the sun. But the total brilliance of all the stars put together is only three thousand times greater than that of a star of the first magnitude, or thirty million times less than the light of the sun.
But that proves nothing, as Olbers’ argument is wrong, for two reasons. On the one hand, there are necessarily a good many extinct or dark stars in the heavens. Some of them have been closely studied, even weighed. They betray their existence by periodically eclipsing brighter stars, with which they revolve. On the other hand, it was discovered some time ago that celestial space is occupied over large stretches by dark gaseous masses and clouds of cosmic dust, which absorb the light of more distant stars. We thus see that the existence of an infinite number of stars is quite compatible with the poorness of the light of the heavens at night.
Now let us put on our spectacles—our telescopes, I mean—and turn from the province of possibility to that of reality, and we shall see that recent astronomical observation has yielded a number of remarkable facts which lead irresistibly to the following conclusions.
The number of the stars is not, as was long supposed, limited by the range of our telescopes alone. As we get further away from the sun, the number of stars contained in a unity of space, the frequence of the stars, the density of the stellar population, do not remain uniform, but decrease in proportion as we approach the limits of the Milky Way.
The Milky Way is a vast archipelago of stars, our sun lying in its central region. This mass of stars, to which we belong, has, roughly, the shape of a watch-case, the thickness being only about half the widthof the structure. Light, which travels from the earth to the moon in little over a second, from the earth to the sun in eight minutes, and from the earth to the nearest star in three years, needs at least 30,000 years—three hundred centuries—to pass from end to end of the Milky Way.
The number of stars in the Milky Way is something between 500 and 1,500 millions. It is a small number: scarcely equal to the human population of the earth, much smaller than the number of molecules of iron in a pin’s head.
In addition to these we have discovered dense masses of stars, such as the Magellanic Clouds, the cluster in Hercules, and so on, which seem to belong to the fringes of our Milky Way—to be suburbs of it, so to say. These suburbs seem to stretch a considerable distance, particularly on one side of the Milky Way. The furthest away is, perhaps, not less than 200,000 light-years from us.
Beyond these, space seems to be deserted, devoid of stars over expanses which are enormous in comparison with the dimensions of our galactic universe as we have described it. What is beyond this?
Well, beyond this we find those strange bodies, the spiral nebulæ, lying like silver snails in the garden of the stars. We have discovered several hundred thousand of them. Some astronomers believe that these spiral masses of stars may be annexes of the Milky Way, reduced models of it. Most astronomers incline to think, for very good reason, that the spiral nebulæ are systems like the Milky Way, and comparable to it in their dimensions. If the former view is correct, the entire system of stars accessible to our telescopes could be traversed by light insome hundreds of thousands of years. On the second hypothesis the dimensions of the stellar universe to which we belong must be multiplied by ten, and light would take at least millions of years to traverse it.
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 stellarsystems 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 quiteexact for very remote masses; and it cannot be finite except on the condition that it is ephemeral in point of time.
For Newton, indeed, thestellaruniverse 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.
These difficulties and obscurities disappear in great part when we consider space, or space-time, from the Einsteinian standpoint of General Relativity.
What is the meaning of the sentence, “The universe is infinite”? From either the Einsteinian, the Newtonian, or the Pragmatist point of view it means: If I go straight ahead, going on eternally, I shall never get back to my starting-point.
Is it possible? Newton is compelled to say yes, because in his view space stretches out indefinitely, independent of the bodies that occupy part of it, whether the number of the stars is or is not limited.
But Einstein says no. For the Relativist the universe is not necessarily infinite. Is it therefore limited, fenced in by some sort of railings? No. It is not limited.
A thing may be unlimited without being infinite. For instance, a man who moves on the surface of the earth may travel over it indefinitely in every direction without ever reaching a limit. The surface of the earth, thus regarded, or the surface of any sphere whatsoever, is therefore both finite and unlimited. Well, we have only to apply to space of three dimensions what we find in two-dimensional space(a spherical surface), to see how the universe may be at one and the same time finite and unlimited.
We saw that, in consequence of gravitation, the Einsteinian universe is not Euclidean, but curved. It is, as we said, difficult, if not impossible, to visualise a curvature of space. But the difficulty exists only for our imagination, which is restricted by our life of sense, not for our reason, which goes farther and higher. It is one of the commonest of errors to suppose that the wings of the imagination are more powerful than those of reason. If one wants proof of the contrary, one has only to compare what the most poetic of ancient thinkers made of the starry heavens with what modern science tells about the universe.
Here is the way to approach our problem. Let us not notice for the moment the rather irregular distribution of stars in our stellar system, and take it as fairly homogeneous. What is the condition required for this distribution of the stars under the influence of gravitation to remain stable? Calculation gives us this reply: The curvature of space must be constant, and such that space is bent like a spherical surface.
Rays of light from the stars may travel eternally, indefinitely, round this unlimited, yet finite, universe. If the cosmos is spherical in this way, we can even imagine the rays which emanate from a star—the sun, for instance—crossing the universe and converging at the diametrically opposite point of it.
In such case we might expect to see stars at opposite points in the heavens, of which one would be the image, the spectre, the “double” of the other—in the sense which the ancient Egyptians gave to the word. Properly speaking, this “double” would represent, not the generatingstar as it is, but as it was at the time when it emitted the rays which form the double, or millions of years earlier.
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, isrising 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 thetwo conceptions, and we may leave the benefit of the doubt to whichever of the two is false.
Moreover, there is perhaps a third issue: if not for the Pragmatist, at least for the philosopher—I mean, seeing that in England physics comes under the head of “Natural Philosophy,” for the physicist.
Here it is. If all the heavenly bodies we know belong to the Milky Way, other and very remote universes may be inaccessible to us because they are optically isolated from us; possibly by the phenomena of the cosmic absorption of light, to which we have already referred.
But this might also be due to something else which will, perhaps, shock Relativists, but will seem to Newtonians quite possible. The ether, the medium that transmits the luminous waves, and which Einstein has ended by admitting once more (refusing, however, to give it its familiar kinematic properties), and matter seem more and more to be merely modalities. We explained this, on the strength of the most recent physical discoveries, in a previous chapter. There is nothing to prove that these two forms of substance are not always associated.
Does this not give me the right to think that perhaps our whole visible universe, our local concentration of matter, is only an isolated clump or sphere of ether? If there is such a thing as absolute space (which does not mean that it is accessible to us), it is independent of ether as well as matter. In that case there would be vast empty spaces, devoid of ether, all round our universe. Possibly other universes palpitate beyond these; and for us such worlds would be for ever as ifthey did not exist. No ray of knowledge would ever reach us from them. Nothing could cross the black, dumb abysses which environ our stellar island. Our glances are confined for ever within this giant—yet too small—monad.
“Are there, then,” some will cry in astonishment, “things which exist, yet we will never know them?” Naive pretension—to want to embrace everything in a few cubic centimetres of grey brain-stuff!