Old and new ideas regarding gravitation

OLD AND NEW IDEAS REGARDING GRAVITATION*,t

In this article a review is given of various ideas regarding gravitation from Aristotle to Einstein. The defective features of the earlier hypotheses are pointed out and Einstein's method of avoiding them is indicated. I t i s to be understood that the development of our ideas 0% this subject i s not to be supposed to end with Einstein but that other hypotheses may be expected to cut still more closely to the line i n the future.

. . . . . . In the history of scientific thought we may discern a certain trend which

has never wavered since man began to speculate on the why of the wonders round about him. At first he regarded all the phenomena of Nature as having no connection with each other, and assigned a separate cause for each. The wind, the rain, and the sun were each ascribed to the action of different deities, whereas we now recognize the solar heat as the ultimate cause of both wind and rain--one cause in place of three.

This process of correlation of phenomena and reduction of ultimate causes has been many times repeated in the history of science, and has characterized scientific thinking from the earliest times. It is what philosophers call monism, as its ultimate aim is the reduction of all phenomena to special cases of one broad and all-embracing law.

A long step toward this goal was taken by Newton when in his "Prin- cipia" he showed that all cases of motion, whether terrestrial or celestial, could be explained as consequences of one gene@ law, that of universal gravitation.

A still longer step, or series of steps, was taken during the nineteenth century. The physical science of the eighteenth century had been a rather loose and disjointed affair, consisting mainly of uncorrelated facts about half a dozen entities as then recognized-matter, heat, or caloric, light corpuscles, electricity, magnetism, and phlogiston. By the end of the nineteenth century these had been correlated and consolidated along with much newly discovered material into a closely woven pattern in- volving but three fundamental concepts-matter, energy, and ether.

Among the various phenomena studied by the physicist, gravitation, from Newton's day to the twentieth century, had stood in a class by itself. For the rest, the unification of physical phenomena had gone on apace. Heat had lost its individual status, and had taken its place as but one of the many forms of that protean concept, energy. Relations had been found

Publication approved by the Director of the Bureau of Standards of the U. S. Department of Commerce.

7 An address given before the Physical Sciences Section of the Twelfth Ohio State Educational Conference, held in Columbus, April 7, 8, and 9, 1932; and printed in the Proceedings.

1897

1898 JOURNAL OF CHEMICAL EDUCATION Novs~asn, 1932

between magnetism and electricity, and between electricity and light. But with all this consolidation, gravitation had held itself aloof, steadily refusing to acknowledge any kinship to what were strongly suspected of being its relatives. Much experimental work had been done in the hope of linking up gravitation to something else, but the results had all been negative. True, there is a superfcial resemblance between gravitation and the attraction of magnetic or electrified bodies, but with the law of inverse squares the resemblance ends, for magnetic attraction can be cut off by a suitable screen, and is greatly influenced by temperature, and in electrostatics we have also the effect of the intervening medium. Nothing of this kind obtains in gravitation. By the end of the nineteenth century it had been established that gravitation acts equally on all substances; that i t does not depend on temperature; that it is not influenced by the state of matter, whether solid, liquid, or gaseous; that it is independent of chemical combination or physical solution; and that there is no known screen which will diminish its action. As for positive results, our knowledge of gravitation was just where Newton had left it two centuries before. Yet optimism prevailed, and hope was maintained that gravitation would yet be brought into line with other physical phenomena.

But like Moses of old, the physicists of the nineteenth century might look ahead over the promised land, but might not enter. It was reserved for Einstein in the twentieth century to make the first positive step toward the correlation of gravitation with other phenomena of Nature.

But with all these negative reiults, speculation as to the nature of gravitation had not been idle. The Sdhsonian Annual Report for 1876 contains a summary and criticism of some twenty-five or thirty hypotheses as to the nature of gravitation which had found their way into print since the time of Newton. Since 1876 there may be added four or five more of importance. Needless to say, none of these hypotheses is today of more than historical interest.

The earliest of these speculations that can be ascribed to any definite authority is that of Aristotle. The philosopher was content to explain the falling of bodies by ascribing to them a property of "heaviness," and because he observed that smoke and other vapors rose rather than fell he ascribed to them a corresponding property of "lightness," thus dividing all bodies into two classes with a sharp line of distinction between them. The idea that the rising of smoke might be a differential action, like the rising of wood in water, apparently never occurred to him.

So great was the influence of Aristotle upon human thought that this particular error lasted in the minds of some persons until the eighteenth century. It played an important part in the invention of the balloon by the Montgolfier brothers. These had observed, like Aristotle, the rising of smoke and the floating of clouds, and they reasoned that if they could

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enclose sufficient smoke in a bag the "lightness" of the smoke would carry the bag upward with it. That they had no thought of the part that hot air might play in this experiment is shown by the fact that the fuel they used for their first fire balloon was chopped straw, a material rather in- conveniently bulky, but one which produced much smoke. After the success of their first experiments the true cause of the ascent of their balloon was pointed out by the physicist, Charles, who suggested the use of hydrogen in later trials.

Another error was made by Aristotle when he stated that heavy bodies fell with speeds proportional to their weights. Though he might easily have checked this erroneous conclusion by experiment he does not appear to have done so, and so great was his authority that we have no record of any one presuming to question this statement until the appearance of Galileo, 2000 years later.

But neither Aristotle nor Galileo nor any intermediate student of Nature seems to have advanced any hypothesis as to the cause of gravitation. Newton himself, as he says in his "Principia," purposely avoided this; but though he "framed no hypotheses" in his formal writings, his letters show that he speculated freely, as every scientific man should. There is extant a letter from Newton to Boyle in which he suggests that the mutual attraction of all bodies might be due to a change in the density of the ether at different levels above the earth's surface.

Among the many suggestions made since, Newton there are a few that i t may be of interest to consider. One of the most notable of these was that put forth by Le Sage of Geneva in 1750.

Imagine two circular plates to be held parallel to each other in a hail storm. If the storm is so violent that the stones may be assumed to come from every direction it will be seen that the two plates will to a certain extent shield each other's inner faces from the impact of the hail stones, and the closer the plates are to each other the greater will be this shielding. As a result, the two plates will be pushed together by a force which will increase as the distance between the plates is lessened.

Le Sage imagined the universe to be filled with what he called "ultramundane corpuscles" flying about in all directions with high speeds, like the molecules of a gas, and pushing together any pieces of matter that happened to be close enough to each other. The obvious objection to this theory is the heating effect of these impacts, and a source of continuous supply for the energy, but i t is to be remembered that at the time this hypothesis was put forward the conservation of energy was as yet unrecognized.

Another objection to this theory is that according to i t a closed box should at least to a certain extent shield particles of matter within i t from gravitative action. Gravitational screening, however, was as completely unrecognized in the eighteenth century as was the conservation of energy.

1900 JOURNAL OF CHEMICAL EDUCATION NOVEMBER, 1932

We find in Le Sage's hypotheses a concept which has held its own in every later suggestion that has been made as to the cause of gravitation, namely that gravitation is a push rather than a pull.

Le Sage's hypothesis attracted wide attention, and its influence is to be seen in many of the hypotheses which followed. If we imagine the number of these ultramundane corpuscles increased until they pass from the state of a swarm of discrete particles to that of a stream in a fluid, we have the fundamental idea which was repeatedly set forth in one form or another during succeeding years, and which is frequently proposed today as any one of fair experience with scientific cranks can testify. The definite shaping of the concept of the luminiferous ether in the nineteenth century had much to do with the growth and spread of such ideas, but to all such suggestions the non-existence of gravitational screening is a fatal objection. I t is conceivable that snch streams might penetrate the structure of solids, but not without some reduction in velocity, else the body penetrated would not be subject to gravitation. And any reduction in the momentum of the stream must show itself in a corresponding reduction of gravitative force on the other side of the screen.

A new turn was given this idea that gravitation was due in some way to ether motion when Kelvin suggested his famous hypothesis of vortex atoms in 1867. When this theory was proposed the question that came a t once to the mind of every one was: "Will these atoms gravitate'" I t was not apparent a t first whether they would or would not, and a long and difficult mathematical analysis was'required before this question could be answered. Maxwell expressed the hop& and doubts of the time in the article "Atom" which he wrote for the ninth addition of the "Encyclo- paedia Britannica" in the 1870's, in which he said: "It may seem hard to say of an infant theory that it is bound to explain gravitation." Such, however, was the case. The searching mathematical examination to which the theory was subjected, largely a t the hands of J. J. Thomson, failed to indicate any possibility of mutual attraction between these atoms, and Kelvin finally admitted that his hypothesis must be abandoned.

But hope springs eternal in science as elsewhere, and in a few years a new and promising suggestion appeared. It was discovered experimentally that oscillating or pulsating bodies immersed in a fluid medium snch as air or water would under certain circumstances attract each other, and under others repel. At once the question of gravitation of vibrating atoms suggested itself. This was given serious study by Karl Pearson in 1889, but he later abandoned this line of attack for another which seemed to him more promising. This was his theory of "ether squirts."

It had been observed that a source in a fluid medium, such as the end of a hose turned on under water, would under certain circumstances attract a similar source. Pearson followed up the hydrodynamics of this problem,

VOL. 9. NO. 11 GRAVITATION 1901

and found that not only would two such sources attract each other, but two sinks, where fluid disappeared, would also attract, while a source and a sink would mutually repel each other.

Pearson suggested that an atom might be a source in the ether a t which ether was continually generated, perhaps poured in from somewhere outside in the fourth dimension, or conversely it might be a sink a t which ether disappeared. If the ether was incompressible, as was generally held, and space was full of it, it followed that matter, to exist a t all, must be found in equal and opposite quantities of the two possible kinds. To account for the fact that hut one kitid is known to us, Pearson suggested that in the course of ages the two kinds had separated by their mutual repulsion, and that somewhere in the distant reaches of space there would be found a universe of the opposite type of matter, a counterpart of our own. Whether this would be of the source or sink variety it was of course impossible to say. In support of this hypothesis he cited the instance of a certain star (1830 Grwmbridge) which possessed the greatest proper motion of any star then known, a velocity so great that it could not have been produced by the attraction of all the known matter in the universe, acting a t the distances involved. Pearson suggested that this velocity might have been produced by repulsion, the star having a t one time been much nearer our system.

Against this theory of gravitation there is to be considered the apparently omnipresent objection of gravitational screening, which would entirely vitiate the hydrodynamical reasoning upon which Pearson founded his hypothesis. It is to be said, however, that the fun force of the evidence for the absence of gravitational screening was not recognized until the twentieth century.

The next hypothesis of importance came from Osborne Reynolds. In its way it was as original as that of Pearson, for it involved a complete inversion of our ideas of the structure of the universe.

Reynolds supposed the ether to have a fine-grained structure such as might result from some process akin to the piling of shot. He further supposed there to he cracks or irregularities in the piling. These empty spaces or cracks in the substratum of the universe Reynolds regarded as the atoms of matter.

He was able to show that under pressure there would be a tendency for two such cracks to approach each other, thus satisfying the first re- quirement of an atomic model, as understood a t that time. It can be seen, however, that if two cracks were separated by a large completely empty space, corresponding to a thick and very dense piece of matter, while there might be a tendency for both cracks to approach the empty space, the latter would effectually prevent any action of one crack on the


other across it. In other words, the everlasting objection of screening again interposes itself.

Reynolds' suggestion was the last notable attempt to explain gravitation prior to Einstein. Before considering Einstein's work we may profit- ably review in some detail the character of the negative evidence which we have so frequently cited, especially that referring to gravitative screening.

Gravitation appears to a d equally on all bodies. This was shown for light and heavy bodies first by Galileo, and the experiment has since been repeated many times with a much higher degree of precision. As to its action on dierent substances, Newton by pendulum experiments showed this to he the same to about one part in 1000. Bessel carried the precision of this work to about one part in 60,000 without finding any positive result. It is noteworthy that among the substances tested by him were meteoric iron and meteoric stone.

The most precise experiments of this nature are those of Eotvos, who by an ingenious application of the torsion balance succeeded in pushing the precision to six parts in a billion (los). The substances tested by him form a considerable list, including copper sulfate both in the solid state and in solution, thus furnishing evidence as to the effect of change of state. Eotvos also tested radioactive material. To the limit of precision which he was able to reach, his results were negative in all cases.

The question of a possible effect of temperature on gravitation was investigated by P. E. Shaw. he investigator at first believed that he had obtained a small positive result, b6t afterward found that this was due to a certain error in experiment. His final conclusion was that gravitation is independent of temperature to one part in 10,000.

Astronomical evidence on this point is furnished by certain short-period comets. As these bodies approach the sun they must rise considerably in temperature, and if this has any effect on gravitation, the orbit should be altered considerably. But since these comets return time after time with no displacement other than can he accounted for by the influence of the planets near which they pass, the temperature effect must be non-existent. Because of the great rise in temperature involved in such cases, many times that which can be applied in laboratory experiments of this character, the precision of the negative result must greatly exceed that obtained by Shaw.

As to gravitational screening, the best evidence is also astronomical, though laboratory work on this point has been carried out. That which has attracted the greatest attention has been that of Majorana, published about twelve years ago. He reported a small positive result which, however, seemed to grow smaller a t every repetition of his experiment. The practical difficulties of such work are so great that a result of the order

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of magnitude reported by Majorana might easily be accounted for by experimental error.

Astronomical evidence on this point is not lacking, and because of the large scale of the experiment and the length of time available for comparison the precision of such evidence is high. For example, we may use the whole earth as a screen, and consider what should happen a t every eclipse of the moon if there were any gravitational screening. If at such times the solar gravitation should be cut off from the moon by an amount as small as that reported by Majorana, the moon would retreat slightly from the earth and the sun, and the cumulative effect of the millions of eclipses that have happened since the moon separated from the earth would long ago have removed the moon to such a distance that we would never know that we had had such a satellite.

If it be argued that the gravitational shadow of the earth may not reach as far as the light shadow, we may consider the evidence furnished by the tides. The gravitational pull of the moon produces a tide on the side of the earth opposite to the moon as well as on that facing it, and it has been shown by Russell that an absorption of a thousandth part of that an- nounced by Majorana would show itself as a perceptible irregularity in the tidal motion.

In this case we have also the evidence of astronomical clocks. A few years ago the Lick Observatory claimed to have found a small diierence in the rates of their clocks as between noon and midnight. The records of the U. S. Naval Observatory do not confirm this. Results over a period of fifteen years show that there can he no &e& as great as one-tenth of that which was claimed by the Lick astronomers. The precision of the Naval Observatory results would limit gravitational absorption to about one-hundredth of the amount claimed by Majorana. It may therefore be concluded that there is no substance on or in the earth in quantity sufficient to exercise any perceptible gravitative screening.

All these facts concerning gravitation were well known to Einstein, who pondered over them, set them in perspective, and by his genius was able t o evolve from them a suggestion as to the nature of gravitation, which, while not perfect, is the first positive advance that has been made in the subject since the time of Newton.

Every hypothesis as to the cause of things, no matter how flawless in logic and sound in mathematics, must stand the test of experiment before final acceptance. In the case of the Newtonian law of gravitation this test required many years and involved long-continued observations of the planets. For decade after decade the motions of these bodies were observed to follow with exquisite accuracy the paths prescribed for them. With the passage of time instruments became more perfect and with the lapse of years the cumulative accuracy of the measurements increased;

1904 JOURNAL OF CHEMICAL EDUCATION NOVEMBSR, 1932

yet so closely had Newton cut to the line that over a century elapsed before any serious divergence of observation from theory became noticeable. Finally, in 1845 Leverrier called attention to the fact that the planet Mercury showed a slight irregularity in its motion, inconsistent with the law of inverse squares, and too large to be explained as an error of observation. This discrepancy has been confirmed by later astronomers, and the seriousness with which i t has been generally regarded is shown by the many attempts to explain it on the basis of Newton's law.

All such attempts were failures. I t is true, the assumption of a belt of diffuse and very finely divided attracting matter surrounding the sun would account for this irregularity on the part of Mercury, but such matter, in quantity sufficient to produce this effect, would undoubtedly be visible.

All such attempts having failed, the radical proposal was made to alter slightly the Newtonian law by changing the exponent 2 to 2.000,000,161,2. This suggestion was made by Asaph Hall, the discoverer of the satellites of Mars, and for a time it received the favorable consideration of no less an authority than Newcomb, who abandoned it only after E. W. Brown showed that the motion of the moon would not allow of even this slight de- parture from the whole number 2. The anomalous behavior of Mercury thus remained an unexplained puzzle.

Such was the state of affairs when Einstein appeared on the scene with his now famous law of gravitation. This law had little in the way of in- trinsic attractiveness to re'commend it. As opposed to the simplicity of Newton's law, that of Einstein is complfkated in the extreme. Theories far less formidable have fallen of their own weight, but that of Einstein has gradually compelled recognition despite its repelling appearance, solely upon performance, by reason of its ability to furnish results; for it not only explained everything which the Newtonian law explained, and equally well, but it also, without forcing, explained the great puzzle of the irregu-. larity of Mercury. Nay, more: i t undertook the always precarious busi- ness of prediction, for it indicated the existence of a phenomenon hitherto unobserved-the deflection of a ray of light under the intense gravitational force of the sun. This prediction has now received the stamp of verifica- tion in the results of several solar eclipse expeditions. Such a record of performance on the part of a new theory demands for it the serious atteu- tion of all who profess and call themselves physicists.

I have said that gravitation stood for a long time in a class by itself among physical phenomena. In so far as this is true, it was due to the short sight of the observers, for Einstein pointed out that there was another phenomenon of very much the same kind, namely inertia, in the form known as centrifugal force. Centrifugal force is independent of the material, is not a function of the temperature and cannot be cut off by any

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form of screen. In fact, centrifugal force, like gravitation, seems to be a function of nothing but the mass involved and its space and time coordinates.

Einstein illustrates this by means of a revolving disk. Imagine such a disk capable of carrying an observer, such as may be seen in amusement parks. Let the disk be covered by a dome which revolves with it, so that the observer within cannot tell by direct observation of other bodies whether or not the disk is in rotation. Suppose the disk is a t first sta- tionary. The observer, in walking from one point to another of his little world, would perceive no differenceas between one point and any other. But let the disk be set in rotation, and though the observer could not directly perceive the motion he would become aware of a certain difference. At every point of his space except the center he would experience a force repelling him radically outward, and the greater the distance from the center the greater the force of repulsion. He would, in fact, be in a sort of turned-inside-out gravitational field of force.

With our superior knowledge we recognize this "force" of repulsion to be purely inertial in its nature. As such, it does not originate a t the center of the disk, but in the observer himself, and consequently no screen erected between him and the center can diminish the force he feels. Here we have an illustration of how the motion of a system may give rise to something remotely simulating a gravitational field which disappears when the motion of the system stops.

Another illustration that may help us in this connection is that of an elevator. Imagine an elevator, with closed warns, containing an observer. Suppose the elevator a t first a t rest. Let a bullet be fired through it hori- zontally. The path of the bullet, to the observer within, will appear as a straight line from wall to wall. If the elevator be moving upward with uniform velocity, the path will appear again as a straight line, but slanting downward. But if the upward motion of the elevator be accelerated, the path of the bullet will no longer appear straight, but as a curved trajec- tory, convex upward.

The observer might account for this curved path by saying that the bullet moved according to the resultant of two forces: its original impulse, causing by itself a straight path from wall to wall, compounded with another force of attraction of some unknown nature, drawing the bullet downward toward the floor of the elevator. This is again assuming the existence of a force which does not really exist, and which in consequence may be expected to be rather difficult to explain. What has actually happened is that the observer has changed from fixed to moving coordinates.

Imperfect as are these attempts to represent the actual gravitational field of a body, they may nevertheless help us to understand what Einstein means when he says that a gravitational field is equivalent to an inertial


field produced by a suitable change of coordinates; yet neither of these illustrations furnishes us with a change of coiirdinates adequate to the representation of the actual three-dimensional field of a material particle. The task of finding such a coordinate system, if indeed any should exist, might well appal the best equipped of mathematicians; yet, with sublime confidence in his intuition, it was to this task that Einstein set himself.

And then a wonderful thing happened, for with but the slenderest of clues and guided principally by what we may fairly call the intuition of genius, he succeeded! He found a transformation of coijrdinates which represents a little more accurately than Newton's law the physical phenomena concerned in gravitation.

Imagine a surface of still water of indefinite extent. On such a water surface a floating particle, if set in motion and freedfrom the action of all forces, accelerating or retarding, would travel in a straight line. If the surface was curved slightly, the particle would follow the shortest, "straightest" path it could find, obeying Newton's first law of motion with the added condition of being confined to the curved surface. For a spheri- cal surface, this path would be an arc of a great circle; for a surface of any kind of curvature, the path would be a more or less twisted line, called in general a geodesic.

Let us imagine a flat surface. By careful manipulation it is possible to lay upon this surface a small particle of a heavy body, such as lead or even gold, so that it will float. The only thing necessary is to avoid breaking through the surface. The particle then lies supported by the un- broken water surface bent into a cnsp or Gepression. The geodesic of this cusp will be a curved line, but if this geodesic be continued on either side of the cnsp i t soon straightens out.

Suppose now a comparatively heavy particle thus floating and forming a rather deep and widely extended cusp. At some distance from it, where the surface is again flat, suppose a light particle, which makes hardly any cusp, is moving in such a direction as will carry it past the heavy particle at a short distance from it, but well within the latter's cusp. The path of the moving particle, a t first a straight line, will, as it enters the cusp, gradually assume the curved or geodesic form proper to the space in which it finds itself. Assuming no attraction to exist between the particles, the small particle will pass on and out of the cusp, its path again becoming straight; but on account of the brief twist to which i t was subjected in passing through the cusp, the latter portion of the path will not in general be a continuation of the first. The particle will have suffered a ddection.

An observer watching the motion of the particle through what we may call Newtonian spectacles, which do not show him the curvature of the cusp, will say: "Yes; on passing the large particle the smaller one seems to have suffered a force of some kind, and to have been deflected from its

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straight path." But let him replace these glasses by others of Einsteinian make, and he will say: "No; I see now that there was no force of attraction at all. I t was purely the inertia of the moving particle combined with the peculiar curvature of the surface which it had to traverse that produced the change in its path."

So much for a two-dimensional surface curved in a third dimension. Einstein's explanation of gravitation contemplates an analogous phenomenon in a space of four dimensions, curved slightly in a fifth. A ray of light coming from a star traverses for millions of miles a region of space remote from material bodies, and .consequently "flat." Through this region the path of the ray is a straight line. But if it eventually passes close by the sun, whose great mass causes a considerable cusp or warp in space, the path becomes twisted, and when i t again becomes straight it has been permanently deflected from its original course.

.

If the small particle passed very close to the large one i t might not be able to get out of the cusp at all, but would circulate round and round, describing a curve whose shape would depend on that of the cusp and on the plane of motion of the small particle. If the cusp be shaped somewhat like that around the stem of an apple, the path of the small particle might be an ellipse that failed to close, and would resemble the actual orbit of Mercury.

Concepts such as these are apt by their strangeness and transcendental character to cause us to lose the true perspective of the situation. The theory of relativity is but a working mathematical hypothesis, designed to cut a little more closely to the line than that gf Newton. But it is still artificial in its nature, and is by no means to be regarded as the ultimate representation of the truth of Nature.

Einstein himself regards this child of his brain quite sanely. Being a mathematician, he naturally recognizes an empirical equation fitted to a curve as something totally different from the real equation of the curve, and bound to diverge from it if carried out far enough. "No amount of ex- perimentation," Einstein is reported to have said, "can ever prove me right. A single experiment may at any time prove me wrong." Not that any one has at present a better theory to suggest than that of Ein- stein; but such a thing may and doubtless will come to pass when the hour and the man arrive. Newton cut so closely to the line that over two centuries elapsed before an Einstein could better his formula; and how long i t will be before the next corrective term is added to the empirical equation for the great curve of Nature is a matter a t present on the knees of the gods.

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Old and new ideas regarding gravitation