Popular Science Monthly/Volume 79/September 1911/Attempts to Explain Gravitation
| ATTEMPTS TO EXPLAIN GRAVITATION |
By WILSON C. MORRIS
STATE NORMAL SCHOOL, WARRENSBURG, MO.
TO the casual observer the heavenly bodies may seem isolated; but careful study will show how closely connected they are. Not only are they much alike in composition, but across the vast gulfs separating them they hold constant intercourse. Before the time of Newton the only influence known to pass from one heavenly body to another was what we now call radiant energy. To this Newton added a second influence, the force of gravitation. To this list we may also add a third, electrical attraction. The one with which this paper deals is gravitational attraction.
To the student who has at least an elementary knowledge of physics or astronomy gravitational attraction is one of the best known properties of matter; and it can just as truly be said that it is one of the least understood properties of matter, not only by elementary students but by mature physicists and astronomers. So often has the problem of gravitation evaded solution that some in despair have doubted the ability of the human intellect to grapple successfully with it. This feeling may have been strengthened by Newton's references to himself.
At present we can't tell how one body attracts another; and the science-producing value of the efforts made to explain the mechanism of attraction is not to be judged by the prospects afforded of ultimately obtaining a solution but by the stimulus afforded in furthering thorough investigation. What we want is a hypothesis that will conform to well-known phenomena and that will stimulate further investigation. It is needless to say that final solution finds no place in our attempt.
Most of the conjectures concerning gravitation have not reached the dignity of a hypothesis. Some of them seem even too wild for a romance. I think it is Schuster who has referred to his conjectures regarding gravitation as a-holiday-dream. I like this word in this connection. However since they are the best we have let us make the most of them or supplant them with better ones.
Before reciting some of the attempts to explain gravitation it might be well to refer briefly to its discovery, magnitude, peculiarities, etc. Kepler had stated in his first law that the earth revolves in an elliptical orbit with the sun at one focus. With this knowledge at hand, by strictly dynamical reasoning Newton showed that bodies attracted according to a definite law (the attraction between two bodies being directly proportional to the product of the masses and inversely as the square of the distance, if the dimensions of the bodies are small compared with the distance between them). Having enunciated this law he proceeded to verify it by studying the motion of the moon. The moon revolves in an orbit that is nearly circular and to keep it in this orbit there must be an acceleration toward the earth equal to where is the moon's orbital velocity and is the distance from the earth to the moon (approximately 240,000 miles). In place of we may put , where is the time of one revolution (27.3 days). Hence the acceleration toward the earth equals
The acceleration the earth should exert, if Newton's law be true, at a distance of 240,000 miles (60 times the earth's radius) where 32.16 is the acceleration at the surface of the earth. The verification in the case of the moon is complete. Hence we have the mathematical statement of the law: (the force) where is a constant depending upon units only. We say nothing about the quality of the matter but only the quantity, and the distance. Notice also that there is no factor in the equation referring to the nature of the intervening medium.
It may not be out of place to call attention to the universality of the law. There are a few slight discrepancies between observed and calculated values, but as a whole it is fully attested by observation.
In referring to the magnitude of gravitational force consider first small bodies and later astronomical bodies. We know to-day that the radiation from the sun exerts a pressure. Kepler suggested this three centuries ago and one hundred and fifty years later the great mathematician Euler adopted his suggestion in accounting for the repulsion of comets' tails. So delicate is this pressure that it was not discovered until recently (1900). Albeit this pressure is very small as bodies diminish in size, we reach a limit at which it predominates over gravitation. This is due to the fact that gravitation is proportional to the mass (the cube of the linear dimension) while radiation-pressure is proportional to the surface (the square of the linear dimension).
When we consider electrons we find that the gravitational attraction between two electrons is insignificant compared with electrical attraction. The electrical force in air between two negative electrons one centimeter apart is equal to dynes, if we take the charge on an electron to be c.g.s. electrostatic units.
The gravitational attraction between two electrons at a distance of one centimeter dynes, where is the mass of a negative electron and is the gravitational constant in the c.g.s. system. Comparing the two results, we see that the former is times the latter.
In astronomical bodies gravitation is the predominant force. An idea of its magnitude can be gained by calculating the attraction between the earth and the moon, which are small bodies astronomically speaking. The earth's mass is about 6 times tons, which is 80 times the moon's mass, and the distance between the two is about sixty times the earth's radius; hence the attraction tons of force. To hold this system while it rotates about a common center would require about five million-million steel bars each one foot square and of tensile strength of thirty tons per square inch. Knowing the distance between the earth and the sun (23,000 times the earth's radius) and that the sun is about 330,000 times as massive as the earth, in like manner we can show that the force between the earth and the sun is greater than that of the earth and the moon. What must it be for double stars! Surely the origin of such gigantic forces ought to be worth careful study.
When Priestley and later Coulomb enunciated the law of electrical attraction (inversely as the square of the distance) they ignored the intervening medium. It was shown by Henry Cavendish, although not published, and discovered independently by Faraday that the electrical attraction depends upon the nature of the medium. If we take a piece of glass having a specific inductive capacity of six and separate two charges by this glass the force between them is only one sixth of what it is when they are separated by the same thickness of air. Strange to say gravitation is not affected by the intervening medium. This may be due to the gossamery nature of matter; that is, that the size of the molecules is very small compared with the distance between them.
So far as we are aware, chemical action, temperature and change of state are without effect on gravitation. No one has succeeded in demonstrating that it takes time for its propagation. If it is propagated in time the rapidity far exceeds that of light.
If we have two bodies electrically charged in a field and introduce a third body there is a redistribution. There is nothing analogous to this in gravitation, for the introduction of a third body in no way lessens the attraction between the other two. The earth's attraction is the same for me whether alone or in a crowd.
Thus when we compare gravitation with other phenomena about which at least we know a little, so great are the dissimilarities that it seems almost to fall outside the bounds of the physical realm.
Having briefly touched the discovery, law, magnitude, characteristics and peculiarities, we are ready to review the attempted explanations of the mechanism.
One familiar with modern electrical theories knows that the present tendency is to include everything in the electromagnetic scheme. Maxwell started this when he promulgated the electromagnetic theory of light. Experiment by Kauffman on the beta rays of radium lead us to regard mass as electromagnetic. Hence it is very natural to try to explain gravitation as an ether-phenomenon. This would require that the ether be capable of supporting enormous pressure or tension. In the older views the ether was regarded as a very attenuated medium. Such an ether can hardly meet the demands. Many modern physicists regard the ether as very rigid and dense when compared with ordinary matter. See Lodge's "The Ether of Space." If we follow Sir J. J. Thomson, who regards all mass as mass of the ether[1] we can calculate the density of the ether, for the mass of an electron is about grams and the volume is of the order of cubic centimeters; hence the density of the ether is or a million million times that of water. When we consider the rapidity with which an ether disturbance is transmitted we see that the rigidity should be very great compared with ordinary matter. Taking the density of ether as and the velocity of ether waves as cms. per sec. the rigidity will be of the order of dynes per sq. cm., since The intrinsic energy if due to rotational motion will be of the order of ergs per cubic centimeter, if we assume the velocity of rotation is of the order of that of light; since the energy mass times , where the mass of a cubic centimeter is grams and the velocity is cms. per sec. Hence the intrinsic energy and rigidity of the ether will probably meet the demands if we accept the views of ether and matter held by some of the greatest modern physicists.
If a falling body does not gather its energy from the ether where does it get it? Lift a ton to the height of 1,000 feet above the earth's surface and we have 2,000,000 foot-pounds of potential energy, or preferably a body that in returning to its original position will gather 2,000,000 foot-pounds of energy. Is this energy inherent in the body? Newton's letter to Bentley shows us that he was opposed to such a view. One thing is sure, there is no perceptible change in the mass and chemical composition of the body at the height of a thousand feet.
In the "Principia" Newton makes no attempt to explain gravitation, but in one of his optical queries he writes thus: "If the pressure in the medium is less in the neighborhood of dense bodies than at a greater distance from them, dense bodies will be drawn toward each other, obeying the law of gravitation if diminution of pressure is inversely as the distance."
Hooke, a contemporary of Newton and a man of great ingenuity, attempted a wave theory of gravitation from his observation that bodies floating on water agitated by waves were drawn toward the center of disturbance. The action of a body immersed in water was not considered. Since his time various attempts have been made to explain gravitation as due to a wave-motion. At the last meeting of the American Association for the Advancement of Science, Mr. Brush, of Cleveland, Ohio, presented a paper[2] in which he accounts for gravitation by ether-waves. His theory was doubtless suggested by radiation pressure. His theory demands an ether possessed of intrinsic energy. As before stated, the views of many modern physicists permit this. He assumes that this energy is due to waves; but the frequency is so much less than that of heat or light that molecules will not respond; and hence bodies do not become warm. He thinks that the energy of the ether is a generalized type whose degradation has been brought about by repeated absorptions and remissions. To substantiate this view he cites the case of the earth and the sun, in which rays of one length are absorbed by the earth and longer ones are emitted. He accepts the view of J. J. Thomson that all energy is kinetic energy of the ether. Before attempting to explain the mechanism of gravitational attraction he paves the way by referring to a well-known phenomenon in light. If we take an opaque body in a room with luminous walls it will experience pressure on all sides because we now know that light-waves have both energy and momentum. If we now introduce a second body each will be in the shadow of the other or will screen the other; and hence the radiation pressure is less on the side of each body which faces the other; and hence there will be a tendency for the bodies to be pushed together.
Now substitute for the light-waves waves of great length and less frequency, and owing to their low frequency they will affect the interior molecules as well as the surface ones, and hence we will have a volume or mass effect and not a surface effect as in light. This is in accord with Newton's law, for the force is proportional to the mass. We may picture. . . molecules of matter buffeted about in every direction by ether-waves in which they are entangled, like a suspended precipitate in turbulent water." Now introduce a second body and the pressure in the direction of the line joining these two is less than in any other direction, as each is in the 'shadow' of the other; hence they are pushed together. Notice that according to his theory gravity is not a tension, but a pressure. Mr. Brush's theory, like all other theories regarding gravitation, is beset with difficulties. If gravitation is due to a type of radiation transmitted at finite speed it ought to be subject to aberration as is light. To avoid this Brush takes longitudinal waves and assumes the elasticity of ether is such that their velocity is much greater than that of light waves which are transverse. Longitudinal waves in the ether have not yet been detected. However, this is no final argument against their existence as new and striking discoveries are being made every year. These longitudinal waves force us to conclude that the ether is at least slightly compressible. If compressible we are inclined, from our knowledge of matter to think of the ether as discrete or molecular. If discrete the particles are elastic and we have to postulate a second ether to explain the elasticity of the molecules of the first. This destroys the simplicity of the ether.
J. J. Thomson in his Silliman Lectures (page 160) enunciates a view somewhat similar to that given by Brush. In place of longitudinal waves he used short ether-pulses something like the Röntgen and gamma rays are supposed to be. This view presents the aberrational difficulty, as do other views which attempt to explain gravitation by a type of radiation. On this view any change in gravitation would be propagated with the velocity of light; and certain phenomena in astronomy require the gravitational effect to be propagated much faster than light.
Near the beginning of the paper we showed that the gravitative attraction between small charged bodies is very small compared with the electrical effects. Now if we assume that the linear equations of the ether are only approximate we may account for this relatively small gravitational effect from terms involving differentials of second or higher orders. Larmor[3] opposes this view because the introduction of higher order term not only disturbs the simplicity of the ether scheme, but also leads to optical dispersion in free space. If such dispersion exists it must be very minute, as bodies emerging from eclipses show no appreciable change in color. However, when we compare the gravitational force with the electrical force we see the former is so very small that the higher order term introduced to account for gravitation might give us a dispersion too minute for observation. But, as usual, we meet insurmountable difficulties. On this view the velocity of transmission would be of the same order as that of light; and while we do not know whether the speed is finite at all, we do know that if it is finite it greatly exceeds that of light.
Hence at present gravitation seems to be precluded from the electromagnetic scheme, owing to speed of propagation. Since in the last ten years we have tried to unify, it is unfortunate that it rebels against admission into our scheme. Many have pronounced it a mode of activity in the ether not specified but entirely different from the electromagnetic mode.
Replace Brush's long waves or Thomson's short electromagnetic pulse by rapidly moving corpuscles and we have Le Sage's theory. According to Le Sage space is filled with minute particles, ultramundane corpuscles, moving rapidly in all directions; hence a single body experiences an impetus on all sides; but if we take two bodies each screens the other and they are pushed together. Notice the force is one of pressure and not of tension. At first sight the impulse due to the impact would seem to be proportional to the effective area whereas according to Newton's law it ought to be proportional to the mass; but when we compare the diameter of a molecule with the distance between molecules, we see that only a small portion of the particles are arrested and that the number arrested is proportional to the number of molecules in the body (the mass).
The objections to Le Sage's theory are almost too numerous to mention. First and foremost, the enormous speed at which these corpuscles must travel not to resist planetary motion involves an enormous supply of energy from a source outside our universe. On this theory the source of gravitation is ultramundane. Again if these corpuscles are elastic there would be no screening action on the part of a body as the corpuscles would carry away their energy in reflexion. If the corpuscles are inelastic, bodies ought to increase in size. As the corpuscles transfer their momentum to bodies they lose kinetic energy, and according to Maxwell the loss sufficient to account for gravitation if converted into heat would keep the body white hot. Sir J. J. Thomson has shown that it is not necessary to suppose the energy is transformed into heat. In place of heat rays he suggests that the particles might give rise to a very penetrating radiation just as the cathode particles are supposed to give rise to the short ether-pulse known as Röntgen rays.
The fact that a physicist of Kelvin's rank has tried to patch up a theory that is so superficial shows how hard put to we are when we attempt to explain gravitational attraction.
About thirty years ago Zöllner explained gravitation on the assumption that the molecules carry positive and negative charges and the attraction between two unlike charges exceeds the repulsion between like charges. Lorentz, assuming a neutral body to be an assemblage of positive and negative electrons, has used the same hypothesis.
At Cambridge University during the fall term of 1908, Sir J. J. Thomson gave a course of lectures on "Ether and Matter" and in that course he devoted about three lectures to gravitation. Take two charged plates and in place of drawing the resultant Faraday lines of force (a Faraday line is a line beginning on a unit positive charge and terminating on a unit negative charge) consider the components (see Fig. 1).
Outside the plates we have opposite effects in the same direction, hence they annul. Between the plates we have opposite effects in opposite directions and the effects are equivalent and hence cumulative. The tension will depend upon the number of lines and the closeness together. Each positive line will increase the tension of a positive line and a negative line will diminish the tension of a positive line. If a positive line increases the tension of a positive line just as much as a negative line decreases it, and if a negative increases the tension of a negative just as much as a positive decreases it, then the resultant tension between the plates will be zero, since there are just as many positive as negative lines. But if the effect (increase) of a positive on a positive is not the same as a negative on a positive there will be a resultant tension between the plates.
Now take an unelectrified body which we consider an assemblage of positive and negative charges. Lines of force will start on the positive charges and terminate on the negative ones, and just as there was a tension between the plates if the effect of a positive on a positive was not the same as a negative on a negative, so there will be a tension around this unelectrified body, if the above is true. Hence by making the assumption that the lines of force from a positive charge are not the same as those from a negative charge, the increase in tension of a positive on a positive is not the same as the decrease of a negative on a positive and we shall have a resulting tension. This might give rise ta forces in the body of which the most important is gravitation. Here are Professor Thomson's own words taken from my class notes: "Matter I regard as made up of positive and negative charges. . . . Each unit charge is the termination of a line of force. I do not regard the positive and negative lines side by side as the same."
If you are looking for a Herculean task put the theory to test. Before starting let me remind you that the effect of the earth's field on an electron is something like 30 million times that of gravity and that it is not easy to screen a magnetic force. We see then that this theory is beset with difficulties before which the experimenter at present is helpless. Again, it complicates the simplicity of the electronic theory of electricity. Again, electrical attraction depends upon the medium. On this theory should not gravitational attraction also depend upon the medium? A summary of Professor Thomson's lectures on gravitation was published in Cambridge Philosophical Society Proceedings during the spring of 1909.
Various other theories have been promulgated but they must be passed by. Those interested in the subject will want to read Osborne Reynold's theory. Kelvin's hydrodynamical theory, which involves both the creation and destruction of matter, is rather unique.
Some despairing of ever finding a physical explanation have taken hold of Riemann's idea of space as a manifold. As this is wholly extra-physical and not in my realm I shall do no more than mention it.
Thus the phenomenon of gravitation remains a mystery; for so far every hypothesis made seems to have insurmountable difficulties. I am not sure that any of them shed light enough to even convince us that we are on the right track. It seems to have little or nothing in common with various other things of which we have some knowledge. A few years ago when radio-active substances were discovered, we found phenomena which at first did not seem to agree with well-known chemical and physical laws; but as experimentation progressed confirmation became more general and to-day many, if not all, the discrepancies have disappeared. Not so with gravitation. It still remains one of the least understood properties of matter. Probably if we could learn something of the mechanism of gravitation, that attraction between particles which only manifests itself at very small distances (cohesion) might be better understood.
Nearly two hundred and fifty years ago one of the greatest intellects connected with science turned his attention to gravitation. In that two hundred and fifty years physical science has made rapid advances. A boy who has completed a year's work in elementary physics could entertain Newton in electricity were it possible for the great philosopher to return to earth. After learning of the great progress in electricity, I can imagine him in his eager desire for knowledge turning to the boy and expecting some light on gravitation. Alas, not only the high school boy, but not even the most learned can give any definite information on gravitation. The problem is about where Newton left it.