New Developments in Cosmogony

J. H. Jeans1

Astronomy has always stood somewhat apart from the other sciences; it has an entirely special field of investigation, its methods belong to it alone, and, most important of all, its results have a significance quite different from the results of other sciences. These bestow upon humanity utilitarian gifts, create new methods for producing valuables, increase pleasures, or remove human suffering; astronomy, up to now, has given them only food for reflection and contemplation. This is above all and predominantly true with regard to cosmogony—that branch of astronomy which raises the question of how the heavenly bodies came into being where they are, and in the forms in which they exist.

From a practical point of view, the difference between astronomy and the other sciences lies in the difference of scale. Most sciences, in their development, approach nature in regions of the infinitely small; but the progress of astronomy and cosmogony lies in the direction of the infinitely large or, better said, the immeasurably large. For now we know with a sufficient degree of certainty that the infinitely large does not exist. A whole series of considerations leads us to the conclusion that the universe is finite, and precisely because we now know this and are beginning to ascertain the actual—

the dimensions of the world in space and its duration in time, the modern problems of astronomy and cosmogony acquire an extraordinary interest for us. These sciences are now in approximately the same position in which geography found itself when voyages around the world had been accomplished and when, for the first time, the limits of spaces that had remained unexplored became known.

In 1838 the first distances of fixed stars were determined, and thereby the scale of distances in the universe was revealed; in that year three astronomers—Bessel, Henderson, and Struve—independently of one another determined the distances to three stars. In all these cases the “parallactic method” was applied: the motion of the Earth along its orbit causes an apparent displacement of nearby stars against the general background of distant stars, so that from observations of these apparent displacements the distance of nearby stars can be obtained. But it had long since become obvious that most stars are too far from us for their distance to be measured by this method; in any case, this method could not elucidate the distances of the most remote stars in the universe, since the very possibility of its successful application is conditioned by the possibility of observing a star against a collection of still more distant stars. Only recently have other methods given us a way of measuring still greater depths of the universe.

The most fruitful of these methods is based on the special properties of one type of variable stars, which are called Cepheids after their prototype, the star δ Cephei. The brightness of these stars does not always remain the same; at definite and always constant intervals—which for different stars of this type take values from several hours to several days—it increases twofold, threefold, in comparison with its initial value. And just as a sailor recognizes a lighthouse among hundreds of other lights by the regular appearances of its light and by the character of its brilliance, so an astronomer recognizes a variable star of the Cepheid type by the regularity, period, and character of the fluctuations of its brightness. In 1912 Miss Leavitt at the Harvard Observato-

What Is New in Cosmogony

... established a simple dependence between the period and the brightness of Cepheids observed by her in the Small Magellanic Cloud: the more slowly the luminosity of a Cepheid changes, the brighter it is; generally speaking, its brightness proves to be inversely proportional, to a certain degree, to its period. Comparatively recently Dr. Shapley, now director of the Harvard Observatory, showed that this relation (now known as the “law of luminosities and periods”) proves to be valid for all Cepheids in general. Whenever an astronomer discovers a Cepheid and can measure the length of its period, he can also derive the intensity of the light emitted by this star. Comparing this intensity of light with the apparent brightness observed in the telescope, he can easily calculate the star’s distance from us. This method is, in essence, identical with the procedure used by a sailor when, in order to determine his distance from the shore, he identifies a lighthouse, finds its light-power in a handbook, and then compares it with the apparent brightness of the lighthouse at the place where he happens to observe it. Using a method analogous to the parallactic one, he could, knowing the speed of his ship, attempt to determine the distance by observing the speed with which a belfry or factory chimney on the shore appears to shift in relation to more distant hills; this method does not require the presence of a lighthouse of known light-power; but, obviously, it would be useless for a sailor on the high seas and, moreover, as we have already noted, it could in no case give the distance to the most distant visible objects.

The discovery of the “law of luminosities and periods” opened before us a new world in the matter of determining astronomical distances; Dr. Shapley himself first of all used it to determine the distances of remarkable objects known as “globular star clusters.” As the very name indicates, these are very dense groups of stars, approximately spherical in form; in a powerful telescope they have the appearance of a swarm of bees and produce the impression of places where stars are born—stellar nests. Altogether we know of only 69 such objects, and since, in essen-

that no new one has been found since Herschel’s time, it may be considered that there are no more clusters unknown to us. All of them are rich in Cepheids. Dr. Shapley finds that the distances of these 69 clusters lie within the limits from 21,000 to 216,000 light-years. In these and analogous measurements the light-year is adopted as the unit of distance, because it would be senseless to express it in kilometers or in other terrestrial measures of length. Light needs about 8 minutes to traverse the distance from the Sun to the Earth, so that in the course of one year it travels approximately 64,000 times the distance between the Sun and the Earth; such is the distance which the astronomer adopts as a unit of measure and calls a light-year. And we begin to understand the meaning of the expressions: a globular cluster situated at a distance of hundreds of thousands of light-years; we make clear to ourselves that what we see in the telescope is not the cluster as it exists now, but the cluster as it was when primitive man lived on the Earth. Through a long succession of prehistoric epochs, through the dim beginnings of civilization, through the greatness and fall of kingdoms, there came to us those rays which left the cluster in remote ages, approaching us at a speed of \(3 \times 10^5\) km/sec, and only now have reached the Earth.

Quite recently Dr. Hubble, at the Mount Wilson Observatory, discovered the presence of Cepheids also in some spiral nebulae and thus was able to estimate their distances. The most distant of all the nebulae studied up to the present time proved to be the well-known Andromeda nebula—at a distance of 950,000 light-years; others—at distances comparable with it. Applying a somewhat different method, Dr. Shapley determines the distance to the star cloud N.G.C. 6822 as approximately a million light-years.

Both these objects are the most distant of all known so far. Must we suppose that their distances determine the approximate boundaries of the universe, or should we expect a continuous increase in the dimensions of the world as the power of our

instruments? It is impossible to give a definitive answer to this question, but a significant amount of evidence apparently indicates that the first alternative is the correct one. Our Sun is one of the objects in a group of 2 or 3 billion stars forming a disk-shaped or biscuit-shaped system encircled by the Milky Way. It has long been evident that this group cannot occupy infinite space. Were it so, the sky would appear to us as a continuous luminous covering, and the force of attraction emanating from an infinite mass of stars would be so great that our Sun and the other stars would in fact move with infinite velocities. The stellar field cannot even have a uniform density at the depths reached by our telescopes; for, if that were so, the number of stars visible in different telescopes would be proportional to the cube of the diameters of their objectives. But in reality we do not observe this: the aperture of a two-inch tube is 10 times larger than the aperture of the unaided eye, yet we do not see in it 1,000 times more stars. Thus the density of the distribution of stars must decrease appreciably even at the distances revealed to us by a two-inch tube. It is precisely this method—in a refined form—that made it possible to assign spatial limits to the stellar field of which the Sun is a member, and to estimate the number of stars contained in it.

This stellar field may well be the most extensive formation in the universe; but in any case it does not exhaust the universe in its entirety. Outside it, or perhaps in its outer zones, there lie many other objects, in particular star clusters—which are always much smaller than it itself—spiral and other nebulae, the largest of which are comparable to it in magnitude. The theory of the “island universes,” first proposed by W. Herschel but later fallen into disfavor, is again being affirmed as a result of the latest observational work; now, in speaking of the universe, it is best for us to imagine it as consisting of suspended bodies, separated from one another like islands in an ocean. We can

find another way of estimating the enormous distances to some of these islands because of the exceptional faintness of individual stars; but variables of the Cepheid type, beacons on these islands, make it possible for the astronomer to plot their positions with comparative accuracy. Indeed, our own stellar system is a very large island, with the Sun not far from its center; the great nebula of Andromeda is likewise a large island, of smaller but comparable dimensions; star clusters and spiral nebulae—all these are islands on a smaller scale. Considerations similar to those on which we relied above, and which provide astronomers with a basis for assigning limits to our stellar field, show that we must also set boundaries for the ocean of islands of the universe; it seems probable that these boundaries lie not very far beyond those two very remote objects already mentioned, namely beyond the spiral nebula M. 31, at a distance of 950,000 light-years, and the star cloud N.G.C. 6822, at a distance of approximately 1,000,000 light-years.

For definiteness let us suppose—although this, of course, is little more than a mere guess—that the most distant formations in the entire universe are 4 times farther away than both these objects, i.e. 4 million light-years from us. We can now try to bring this conception to life by constructing a model of the whole universe on the scale of a million million miles to the foot \((1:5.3 \times 10^{15})\). The reduction of dimensions in such a model will perhaps become most vivid if we think of it in terms of speeds of motion rather than in terms of lengths. Light, which in one second can go seven times around the Earth, would move in our model at approximately the same speed with which a blade of grass grows in spring. On this scale the entire universe would be represented by a sphere the size of our Earth; the star cloud that includes the Sun—by an island the size of Yorkshire, while the great nebula of Andromeda would be somewhat larger than the Isle of Wight, though with very indistinctly outlined boundaries. The whole solar system in this model would easily be covered by a single grain of sand, and our Earth, whose size now

turns out to be less than one ten-millionth of an inch, hardly much larger than a single molecule in this grain of sand.

Such is the universe which the astronomer hands over to the cosmogonist for interpretation. The cosmogonist, accepting the universe as it is, must try to explain why it is precisely thus and not otherwise. What for the astronomer is a complex of observed facts is, for the cosmogonist, the last link in a long chain of processes, a section through the whole interweaving of effects and causes. Whereas the astronomer is satisfied if he succeeds in observing the universe as it is, the cosmogonist must have before him the aim of seeing it as it was and as it will be. Just as one of the chief tasks of the astronomer is to assign the limits of the universe in space, so the chief task of the cosmogonist is to assign to it the corresponding limits in time.

For these limits must exist. The universe cannot forever continue its existence in the forms in which it exists now, and it could not have been in its present form from all eternity. Every star continuously radiates energy into space; we have no evidence that any appreciable part of this radiation returns in any way to the stars and replenishes their stores of energy. The universe works like a clock that there is no one to wind up.

The surface of the Sun is approximately \(10^{23}\) square inches \((6.1 \times 10^{22}\ \text{cm}^2)\); each square inch of it radiates energy, and the power of this process corresponds to the work of a 50-horsepower engine \((6.2 \times 10^{10}\ \text{erg}/\text{sec. cm}^2)\). If this energy were supplied to the Sun by a power plant, it would have to burn \(10^{18}\) tons of coal per minute. Hence it is obvious that the source of solar energy cannot be, contrary to what was originally thought, the combustion of the Sun’s own mass. Somewhat later Mayer proposed that solar energy could be continuously replenished by meteorite bombardment, and then Helmholtz proposed his well-known contraction hypothesis, according to which the energy of solar radiation is obtained from the compression of its mass under the influence of its own attraction. From both of these theories there followed limits for the duration

of solar radiation; but both of these limits proved to be far smaller than those with which the totality of known phenomena could have been reconciled. Meteorites could not always have fallen into the Sun, for its mass would by now have become infinite; in fact it was shown that meteorites could not have fallen into the Sun in the required quantities for more than 20 million years, since the mass of the Sun would already have become greater than it is. The same is true of Helmholtz’s hypothesis: the Sun could not have been contracting on the required scale for significantly longer than 20 million years; otherwise its dimensions would already have become smaller than its present dimensions.

Such periods of time are disproportionately small for the life of the Sun. Geologists find evidence that the general conditions of the Earth’s existence have been approximately identical for at least the last 100 million years; analysis of the radioactive content of certain Canadian minerals determines their age as at least \(1 \tfrac{1}{2}\) billion years; analysis of other rocks confirms this result. And if, as is usually assumed, the Sun is akin to our Earth, it must be older than the oldest minerals on Earth. At one time it was thought that radioactive elements might supply the Sun with almost unlimited stores of energy for radiation, but this supposition was not justified. E. Rutherford calculated that if the Sun at the beginning of its life had been in a state of high radioactivity and had been a sphere of pure uranium, radioactivity could have maintained its radiation at its present intensity for 5 million years. After this it became evident that the true source of the Sun’s energy must be such as to ensure for it a life whose duration would be of an order entirely different from everything with which we had previously been accustomed to deal.

In 1905 Einstein’s special theory of relativity appeared. According to this theory, every increase in the energy of a material system must be accompanied by an increase in its mass. Several years before this, it had already been established as a property of electrified bodies that their mass increases

parallel with an increase in their energy; the theory of relativity has shown that this is a general property of matter, under all conditions and in all its states. The converse proposition must likewise be true, so that a body like our Sun, losing its energy through radiation, must also lose its mass. From the known power of solar radiation we can readily calculate the corresponding loss of mass, and we find that its mass must decrease at a rate of approximately 250 million tons per minute.

This assertion by no means implies that by the end of each minute there are fewer atoms or molecules in the Sun than there were at its beginning. If the Sun were merely cooling, like a cannon shell heated red-hot in space, then the thermal motion of each molecule would be weaker at the end of the minute than at its beginning, so that on average the molecules would move more slowly and would thus have less mass. The total decrease in the mass of an innumerable number of molecules would give exactly the required 250 million tons. But the whole special difficulty of our question lies in the fact that, of the entire mass of the Sun, at best only one millionth part constitutes this comparatively easily separable portion; so that, if in the process of radiation the Sun could give up only this part of its mass, its energy could not last for more than a few million years. Let us now suppose, however, that in the depths of the Sun phenomena occur as a result of which not merely a slowing of the motion of molecules can take place, but their complete annihilation as well. In that case the entire mass of the annihilated molecule will be converted into energy, and the entire mass of the Sun (\(2\times 10^{27}\) tons) becomes available for transformation into radiation; at its present intensity (\(250\times 10^{6}\) tons per minute), the mass of the Sun could serve as a source of radiation for 15 quadrillion (\(15\times 10^{12}\)) years.

The process most acceptable to us, which might entail the complete transformation of mass into radiation, consists in combinations of the positive and negative electric charges of which all matter is composed,

and in their mutual annihilation. If the two poles of a Leyden jar are connected, a spark appears and a crack is heard—a miniature thunderclap; this reveals that energy has been liberated somewhere. Here we do indeed know that the energy has arisen from the bringing together of electric charges of opposite signs, which have neutralized one another. Modern investigations have proved quite convincingly that the hydrogen atom consists of two electrically charged particles, of which one—the electron—has a negative charge, and the other—the proton—a positive charge; there is nothing else in this atom. If these two particles could actually be brought into coincidence with one another, then, as it is natural to suppose, a mutual annihilation of the charges would take place; and since we cannot admit the existence of uncharged electrons and protons, we may with some justification believe that the electron and proton would completely annihilate one another. It is even still more probable that nothing would remain here to be annihilated, since it is known that the entire mass of the electron arises from its charge, so that to speak of an “uncharged electron” is an internal contradiction; the same, one must think, is also true with respect to the proton. Thus, when the electron and proton of the hydrogen atom are brought together, its entire mass must be converted into radiation. Of course, it cannot be regarded as plausible that more complex atoms are annihilated as the result of a single process of this kind; it is more probable that here there will occur a successive coincidence of electrons with protons, each time one by one, so that the atom will gradually diminish its mass and, of course, the complexity of its structure. But the details of this process are immaterial; by whatever act the annihilation of matter is achieved, the result will be the same, as, of course, will be the total quantity of radiation liberated.

In 1914 Prof. Russell, of Princeton University, proposed a scheme of stellar evolution which, at least in its general outlines, is now accepted by everyone. According to his scheme, all stars descend along a certain evolutionary ladder. Some of them begin their course from the very bottom

above, others, probably, join somewhere along the way, but all traverse one and the same path and end in the same state. At the top of the ladder are the stars with the greatest luminous power; radiating, probably, 10,000 times more heat and light than the Sun; the lower down the ladder, the more the brightness of the stars weakens; here we encounter such stars as Sirius, radiating approximately 40 times more powerfully than the Sun; then, already considerably lower, the Sun itself and stars with the same strength of radiation; finally, on the very lowest rungs are stars whose radiation is so weak that they are almost invisible to us. Undoubtedly, there are still lower rungs as well, with stars that have already become completely dark, but we shall not touch upon them here. Since the appearance of Russell’s theory it has gradually become clear that the stars on the higher rungs have a greater mass than the stars on the lower rungs; and then also that stars on one and the same rung, i.e. all stars possessing the same brightness of radiation, have approximately equal mass, so that a gradual decrease of mass on the lower rungs of this ladder is established; and if—as there is no serious reason to doubt—all stars descend along it downward in the course of their evolution, then obviously they must all the while decrease in their mass. Having arrived at such a conclusion, it is natural to suppose that the decrease in mass is exactly matched by the emission of radiation. This hypothesis acquires the significance of something more than a mere supposition when it is found that it withstands any quantitative comparison that can be applied to it.

Since the intensity of the radiation of the stars on each of the rungs of the ladder is known, it proves not difficult to calculate at what speed their movement along these rungs must proceed, assuming only that the decrease of their mass is exactly equivalent to their radiation. Simple addition will then show what interval of time is needed for a star, under these assumptions, to pass from a given rung of the ladder to any other. In this way we find, for example, that the time from the state—

Sirius to the state of the Sun is approximately 6,400,000 years; from the brightest stars known to us to the faintest it is of the order of 200 trillion \((2 \times 10^{14})\) years, whereas from the brightest stars to the Sun it is only 7 trillion \((7 \times 10^{12})\) years. It is remarkable that these hypothetical ages of the different types of stars agree excellently with estimates that can be obtained from certain purely astronomical facts, quite independently of assumptions about the source of stellar radiation. Unfortunately, these proofs are too technical to set out here; but they leave no room for doubt that the long-standing problem of the nature of stellar radiation has now been solved, and that its solution has been found in the astonishingly simple assumption that the source of stellar heat is the mass of the star. Stars live by converting their mass into radiation; we can estimate their age by determining how much of it remains; another calculation, based on the same data, will show us how long the life still remaining before the star will be. The interval from the top to the end of the staircase—approximately 300 trillion years—limits the whole life of a star, and all stars differ only in that they are higher or lower on that same staircase, that they are young or old.

The age of stars is by no means the same thing as the age of the whole universe, and there is not even any necessity for them to be comparable with one another. Stars may be compared with icebergs drifting down from the north and melting as they enter warmer seas. We can determine the age of the icebergs that are before us, but we cannot say how long this motion of theirs from the pole to the equator has already been going on, nor how long the formation of icebergs and their appearance to replace those drifting southward toward their end will continue. Over the polar regions where icebergs are born there lies a curtain of fog, and we do not know how to see what is hidden behind it. But the problem of the age of those stars that are now already in existence is comparatively simple; in practice they constitute the universe for the cosmogonist, just as for the astronomer. Each

NEW IN COSMOGONY

we may assign to the star a lifetime on the order of 100 trillion \((10^{14})\) years, after which there follows a period of darkness and, perhaps, complete extinction; for the Sun, life in the past is measured by a number on the order of 7 billion years, so that in respect of time, though not in respect of brightness and brilliance, the greater part of its life still lies ahead.

The ages which we must now assign to the Sun and to other stars are many times greater than those which were considered probable, or even merely possible, up to the very recent past. This expansion of the time scale will require a transformation of our views in many branches of cosmogony and astronomy. Many of the questions belonging here are exceedingly complex, but one of them is relatively simple and at the same time very curious. Among the great number of theories proposed to explain the origin of the Earth and the other planets, the so-called tidal theory, at least in the opinion of the author of these lines, has enormous advantages over the others and apparently encounters far fewer objections than all the rest. According to this theory, the Sun, in remote epochs of its wanderings through space, must have met a star more massive than itself; this star moved in a direction so close to its path that tidal waves were formed on the surface of the Sun—waves of such enormous height that their crests lost all connection with the lower layers and began their independent motion as separate planets. This theory, developed mathematically, proves capable of explaining in a very satisfactory way the principal features of the structure of the solar system. But, until the very recent past, it had to reckon with one very serious objection. The distances separating stars from one another are enormous in comparison with their own dimensions. If we take six billion spheres and place one each in Europe, Asia, Africa, Australia, North America, and South America, we shall obtain a model of the spatial arrangement of the six stars nearest to the Sun and of their mutual distances in relation to their sizes. Since all the stars are distant

from one another, generally speaking, by a large number of their diameters, the convergence of their paths to within a few diameters must be an extremely rare phenomenon; meanwhile the tidal theory requires a mutual approach of no less than two diameters as a condition for the formation of planets. Under the former views on the age of the stars, it seemed exceedingly improbable that any particular star, such as, for example, our Sun, could in the course of its whole life have experienced so close an encounter; and this was a serious objection to the tidal theory. The necessity, now established, of greatly increasing the age of the stars removes this objection; we must suppose that stars which move among other stars over the course of billions of years have had several sufficiently close encounters with their neighbors. But even now we must regard approaches to the extreme closeness required for the birth of planets as rather rare events; only a small fraction of stars, apparently, can be surrounded by families of planetary satellites and thus serve as possible centers of life.

At one time it seemed possible that the cosmogonist would descend from his lofty pedestal and, in justification of his former impotence in the creation of material goods, would bring the most precious of all these goods in general—the secret of obtaining free energy. For if in the stars matter is continuously transformed into energy, then the question arises why mankind should not discover their secret and obtain mechanical energy by destroying small quantities of matter, instead of the painful extraction, transportation, and burning of millions of tons of coal; the entire amount of coal consumed in England produces less heat, light, and energy than could be obtained by destroying 30 g of matter per day. But, so far as can now be judged, these dreams are not destined to be realized. The analysis of astronomical phenomena shows that in the stars all kinds and forms of matter must be mixed; and only some, but by no means all, of its types are transformed into energy to any appreciable extent, and precisely these types—whether for good or ill—are absent on Earth. They may be

to suppose, consist of elements heavier than uranium—the heaviest of all the elements known on Earth; it is even possible that the capacity for spontaneous disintegration, which is exhibited by uranium and other radioactive substances, i.e., the heaviest terrestrial substances, represents the surviving remnants of the ability their atoms once possessed to diminish their mass by means of the radiation they emitted.

1. J. H. Jeans, The New Outlook in Cosmogony. — Smithsonian Report for 1926, pp. 151–166. Washington, 1927. ↩