‘AND there were . . . other little ships’ An aged minister is preaching upon that inherent longing in each human soul for companionship — for someone, human or divine, who shares the experiences of life, and can understand its joys and its struggles. He paints a picture before the mind — a wide stretch of sea, a vast expanse of sky, a far-off horizon; in the foreground a ship, a small ship tossing upon the ocean billows with great forces playing all around it, and it seems an insignificant thing upon the great broad troubled waters alone — and yet not alone, for over there on the far-away horizon are other little ships.
The picture fades away, and in its place the fancy paints upon a larger canvas the vast boundless ocean of spacetime. Stately ships are sailing in all directions. No human hand upon the helm directs their courses, an unseen force propels them onward, each ship a star, each star a sun, each sun a glowing ball of gas radiating light and heat in all directions. Look well at the stately ship in the foreground of the picture, for about it are circling an attendant fleet of smaller ships, and one of them — a very little ship — is weighted down with a living cargo in myriad forms: flowers and trees, insects, birds, beasts, and man. On its prow its name is written — The Earth.
The picture alters as in a dream. We are no longer the fanciful painters upon the canvas of the imagination; we are in the picture, a part of it, and on The Earth we are sailing around our Sun and with it across the ocean of spacetime — from whence we know not, whither we know not. Steered always by an unknown hand, we play no part in the running of our ship, we go where it takes us and we know not why we are on it. We look out across vast spaces and see only other suns, and beyond them more suns, and beyond them suns and clusters of suns; and in a moment of oppressive loneliness we cry, ‘Are there no other little ships? No other little ships like The Earth? Are we alone and unique in the universe of spacetime?’ Out of the abyss of space comes no reply, only the commanding challenge, ‘Think.’
We drop the metaphor. We turn to the written page for answer to this question, to the pages written during the past few years by the men whose aim and object have been to think, to think long and deeply about these problems, and who have brought all the light of modern astronomy, physics, and mathematical analysis to converge toward a solution.
Let us begin with Laplace, whose nebular hypothesis about the year 1800 gave a vivid and plausible picture of the origin of the solar system, a picture which has only recently been abandoned, though still regarded by men of science as one of the grandest generalizations of the human mind. A large nebula, or gaseous mass, in rotation is postulated. Its equatorial portion becomes unstable and masses of gas are thrown off into space, but centrifugal force and gravitational attraction find their balance and the ejected masses become planets and gradually cool and contract. Thus stability is attained and the solar system is gradually evolved from a single nebula. This hypothesis being in the background of men’s minds, it was natural for speculation to take the form which it did — namely, that what happened automatically in the case of the sun might happen to other nebulæ. Hence the general feeling grew that a system of planets probably accompanied every celestial object like our sun. Thus there was every reason to suppose that conditions which favored the advent of life on the earth might repeat themselves with a somewhat similar result in a multitude of cases.
The development of spectroscopy by Huggins and Lockyer gave further weight to this view, for their analysis of the fight from individual stars established the fact that our sun is unexceptional among the stars in size, chemical constitution, and temperature.
With the advance in observation and calculation of the speeds and masses of the planets and rate of rotation and mass of the sun, there was given to the astronomer a means of testing the validity of the Laplacian theory. There is a great principle, first enunciated by Newton, known as the law of conservation of momentum. The product of the mass of a body multiplied by its velocity is called its momentum, and if there be a group of bodies moving about one another the momentum of any one member of the group will change with every change in its speed, but the sum of the momenta of the group taken as a whole will never change unless external influences are brought to bear upon it.1
In the light of this law the evolution of the solar system as explained by Laplace would necessitate a rate of rotation of the sun two hundred times greater than that which it now possesses. It is found that while the sun contains 744/745 of the mass of the entire system, it contributes only 2 per cent of the revolutionary momentum, whereas the planets whose combined mass is 1/745 contribute 98 per cent of the momentum. These facts are part of the evidence against the nebular hypothesis, for such an unequal partition of momentum could not arise in the way suggested by Laplace.
The next advance in theories of earth genesis was made by T. C. Chamberlin of Chicago, who with F. R. Moulton gave to the world the planetesimal theory. This for the first time suggested a biparental origin. In brief the theory is that in bygone ages, when the sun was hotter and less dense than it now is, and in a highly eruptive state, another star chanced to steer its course through space toward our sun, and, passing close around it in a great curved path, went off again into the depths of space. The effect of this close approach upon our sun — and for all we know upon the other star as well — would be that two great tides would be raised upon its surface and drawn far out into tapering spiral arms as the direction of attraction changed. Condensation would naturally take place about any portions of these tidal arms more dense than the neighboring portions. These condensations would form the nuclei of the planets and to them would be attracted the small particles of matter, called planetesimals, widely scattered around them. Thus very gradually each young planet would grow in size and importance, and as it grew more massive its power to capture neighboring planetesimals would increase until the space between the planets became almost devoid of matter.
With the further aspects of this beautiful theory we are not here concerned, our interest being centred upon its position as a stepping-stone to the researches of an English mathematician, astronomer, and physicist, J. H. Jeans. It is from him that mankind has within the last six years received two replies to the question, Are there other little ships?
While still a student at Cambridge, Jeans attacked the problem of determining the forms of equilibrium of a rotating fluid. Poincaré and Roche in France and Sir George Darwin in England had outlined the possibilities. Jeans carried the mathematical analysis yet further and showed that the normal mode of break-up for a huge star was not that suggested by Laplace but that suggested nearly a century later by Poincaré — namely that the equatorial section will gradually cease to be circular, becoming more and more elliptical and then unsymmetrical, like a pear on its side. The lesser lobe grows more and more distinct until a critical stage is reached when the mathematics stops short. What happens next is left to the imagination, for when mathematical equations take up the tale it is with a binary star, not a single star, that they have to deal. Thus far observation confirms theory, for nearly half the known stars are double stars revolving about their common centre of gravity.
When Jeans came to investigate the disruption of a star by the loss of matter from its equator, — the Laplacian idea developed in detail by Roche, — he came to the conclusion that this was an impossible occurrence for a single star of mass only that of our sun or even many times greater. He felt, however, that this might indeed be the true story of a vastly grander evolution, the evolution of a whole galaxy of stars.
But in vain did he look for any force within a giant sun which was in itself sufficient to account for the formation of a solar system. He was forced to turn to the biparental theory; but the probability that such an occurrence should take place, that two stars should come so close together, was ludicrously small — once in a thousand million years! Are we then justified in attributing our existence as a planet to such an absurdly improbable cause?
Harold Jeffreys, geophysicist of Cambridge, in his recent book, The Earth, answers this query with a quotation: ‘It is an old maxim that when you have excluded the impossible, whatever remains, however improbable, must be the truth.’
Professor Eddington of Cambridge Observatory summarized the conclusions of Dr. Jeans in the following paragraph: —
It has seemed a presumption, bordering almost on impiety, to deny to them (the millions of single stars) inhabitants (on planets about them) of the same order of creation as ourselves. But we forget the prodigality of Nature. How many acorns are scattered for one that grows into an oak? And need she be more careful of her stars than of her acorns? ... If, indeed, she has no grander aim than to provide a home for her pampered child Man, it would be just like her methods to scatter a million stars whereof but two or three might happily achieve the purpose.
The exact points of difference between the tidal theory of Jeans and the pioneer theory of Chamberlin need not detain us. The latter considers, in general terms, many probable factors which would influence the disruption of the ancestral sun, while the former considers only those factors which are amenable to rigorous mathematical analysis. To one type of mind rigorous conclusions from admittedly limited premises are less satisfying than the vague conclusions resulting from more comprehensive premises, while to the mathematical mind the former conclusions alone carry any weight.
We thus see that to the question, Are there other little ships? the answer of Jeans in 1919 was, Not impossible, but highly improbable.
So the matter has stood for several years. No voice was raised to question the dictum, save an occasional poetic sentimentalist who clung to the old idea of a plurality of earths and dazzled the imaginations of his hearers by proclaiming the possibility that every star in the firmament was a sun to a family of planets, on some of which — nay, perchance on many of which — there existed life. But to all such speculations the scientist merely shook his head and, following his example, we shook our heads likewise.
We were still solemnly shaking our heads when, a few months ago, a voice was raised in protest with an authoritative and familiar ring about it, for it was none other than the voice of Jeans. Will he confirm or reverse his former judgment? Are we or are we not upon a unique planet in the ocean of spacetime?
Jeans has been endeavoring to ascertain the age of our galaxy, and it is interesting to trace the ideas upon which he has based his estimate. In 1908 Einstein showed theoretically that matter may cease to exist as matter, its energy being liberated in the form of radiant energy and as light and heat. In 1918, from quite another point of view, W. D. MacMillan of Chicago came to a very similar conclusion. Both he and Jeans have suggested that the tremendous flow of energy from a star may be accounted for on the assumption that the mass of the star is actually diminishing, matter being transmuted into radiant energy and dissipated gradually into space. There being no way of testing this suggestion, it lay dormant until, last March, Eddington found that it was one of only two possible explanations of an extraordinary relation which he had discovered, a relation between the mass of a star and its absolute luminosity, a relation which holds true no matter what the density of the star. This established relation is in direct contradiction to the accepted theory of stellar evolution proposed some years ago by H. N. Russell under the name of the Giant and Dwarf Theory, unless a gradual decrease in the mass of a radiating star be postulated.
Now Jeans considers this sufficient proof of the plausibility of the postulate, and from the known amount of energy radiated into space by our sun he calculates how many tons of matter it is losing per year to maintain this flow of energy.2 He next compares its present mass with that of a giant star like Sirius, two and a half times as heavy, and reaches the amazing conclusion that if our sun began its career as a star of the size of Sirius, no less than a million million years would have had to elapse for it to have been reduced to its present size.
This figure is about one thousand times greater than any previous estimate of the age of the sun, and Jeans seeks to find some means of confirming it. His mind turns to another observed fact, known but unexplained for many years — namely, that on the whole the most massive stars are moving more slowdy through space than the less massive stars.
Suppose that all the stars of our galaxy began their careers with haphazard velocities. The mutual gravitational influences would tend in the course of time to produce the state known as equipartition of energy3 — that is to say, there would be a retarding effect upon the massive stars and a speeding-up of the smaller stars. Now Jeans undertook to calculate the probable time since the haphazard velocity stage to the present stage of partial equipartition, and the result is of the order of a million million years — one confirmation of his first calculation!
A second confirmation always brings a thrill of excitement, and this he looked for, and not in vain, in a study of the orbits of binary stars. On the PoincaréJeans theory of the fissure of a large star into two, forming a binary system, there is no force involved to produce wide separation of the two components. Attention was drawn to this some time ago by Russell, who pointed out that observation has shown many of the binaries to be moving about their mutual centres of gravity in very large eccentric orbits. It is evident that only the influence of other stars could produce this result, and once again calculation gives a million million years as the probable time which would have to elapse before the interstellar influence could produce so marked a change on the orbits of these double stars.
There is an effect of this postulated loss of mass due to radiation, which has really been involved in the results of the last two paragraphs — namely, that the stars of our galaxy are slowly but surely drawing farther and farther apart. As mass diminishes, distance from the common centre of gravity must of necessity increase in obedience to the universal law of conservation of momentum.4 This implies that in bygone ages there was closer packing of the stars than at present, hence more frequent collisions or close approaches of two stars than is now possible.
The conclusion of all this follows unambiguously, and we listen to Jeans’s own words: —
‘Finally, it may be remarked that the extension of the time-scale that is now proposed increases enormously the chance of solar systems being formed by tidal action. . . . With the longer time-scale and the recognition that our system of stars must have been more closely packed in the past than now, we can think of planetary systems as being, if not quite the normal accompaniment of a sun, at least fairly freely distributed in space.’
‘A result of the first order,’ says Professor Turner of Oxford, and truly it is a result which will set in motion many wheels of thought. No longer is our system to be thought of as unique and alone in the vastness of space and time. There are many other suns shedding their radiance and life-sustaining rays of light and heat upon a family of planets. Just as life came into being upon this planet and developed in countless forms, so probably on many another planet the spark of life may have fallen and countless forms of life may have resulted — very different perchance, very similar perchance, to the life upon this earth. The cosmologist has sketched for us the outline of a vast picture, but it is left for each onlooker to paint in the details according to the dictates of his own fancy.
‘I am affrighted,’ wrote Pascal, ‘at the thought that I am abandoned to myself, shut in and alone amid the myriads of the universe’ — the cry of the individual from the solitude of his own spirit.
Are there other little ships? It is the cry of man looking out across the vast ocean of spacetime, and to him the mathematician makes reply: Though you may never dip your flag to a passing ship, nor ever exchange a signal with one far distant, yet you may know that it is highly probable that just over the horizon there are other little ships.
- If a dancer were spinning on one toe, his hands would be moving faster through the air if his arms were outstretched than if they were close to his sides. Thus the momentum of his hands would be greater in the former position. To increase the effect, suppose him to spin with arms outstretched and a ten-pound weight in each hand, and suddenly, while spinning, to lower his arms to his side. At once he would be seen to spin faster than before. This is because the momentum of hands and weights has been suddenly reduced, since their velocity is less than formerly, and so the whole body tends to spin faster in order to conserve the total momentum. This may easily be verified by anyone, though the effect is only momentary, due to the friction of air and floor, which quickly reduces the spin.↩
- Jeans finds that the sun is losing mass at the rate of four million tons per second to supply the energy which it is radiating into space.↩
- The equipartition of energy among the stars would be complete if the product of the mass by the square of the velocity for any one star was equal to that for every other star.↩
- Suppose the dancer above referred to were suddenly to drop a heavy cloak, thereby decreasing his mass, his total momentum could be conserved only if velocity were increased. Thus he would spin faster and his arms would tend to fly out so that their contribution to the total momentum would be increased.↩