Newtonian gravitation

“ The gravitational theory, which emerges out of the general theory of relativity, is, in contradistinction to the Newtonian theory, built up, not upon an elementary law of the gravitational forces, but upon an elementary law of the motion of a body in the gravitational field. ”

“ This leads to a considerable simplification, because identity replaces causation. On the Newtonian theory no explanation of gravitation would be considered complete unless it described the mechanism by which a piece of matter gets a grip on the surrounding medium and makes it the carrier of the gravitational influence radiating from the matter. ”

“ Newton himself, as we have seen, had no theory of gravitation, or at least was extremely careful not to publish it if he ever had one. Later disciples, however, have been less cautious, and the Newtonian view has been erected into something of a theory. This assumes that all matter attracts all matter, and this quite independently of its state of excitation. The intensity of the attraction has been formulated in the well-known law that gravity is proportional to the mass and inversely proportional to the square of the distance. ”

“ The most serious objection against the Newtonian law as an exact law was that it had become ambiguous. The law refers to the product of the masses of the two bodies; but the mass depends on the velocity—a fact unknown in Newton's day. Are we to take the variable mass, or the mass reduced to rest? ”

“ We can only say that astronomers have as yet but stepped upon the threshold of the universe, and fixed the telescope's great eye upon that which is within.
Let us then begin by reminding the reader what is meant by the Newtonian law of gravitation. It appears all things possess the remarkable property of attracting or pulling each other. Newton declared that all substances, solid, liquid, or even gaseous—from the massive cliff of rock down to the invisible air—all matter can no more help pulling than it can help existing. ”

“ In short, the principles of conservation endured only when we enlarged our understanding of mass, momentum and energy; and Newtonian mechanics had to be amended as a result of Einstein’s discoveries in the special theory of relativity.
Let us now study the problems of conservation in the general theory when we make use not merely of a Galilean frame of reference, but of any frame whatever, hence when our space is permeated with a field of inertial forces or, again, with a field of gravitation. We shall discover once more that conservation is required by the general theory ”

“ According to Newton’s law of motion, we have
(Force) = (inertial mass) × (acceleration) ,
where the "inertial mass" is a characteristic constant of the accelerated body. If now gravitation is the cause of the acceleration, we then have
(Force) = (gravitational mass) × (intensity of the gravitational field) ,
where the "gravitational mass" is likewise a characteristic constant for the body. ”

“ The thoughtful philosopher Doctor Young, about a century later, commenting on Newton's suggestion of an aetherial medium — rarer toward and within dense bodies, — with great ingenuity remarks: "The effects of gravitation might be produced by a medium thus constituted, if its particles were repelled by all material substances with a force decreasing like other repulsive forces, simply as the distances increase. Its density would then be everywhere such as to produce the appearance of an attraction varying like that of gravitation. ”

“ The planets likewise act upon each other; and as their relative distances are perpetually varying, certain perturbations are caused in the system, which, though minute in each particular case, become considerable by accumulation, and yet are ultimately corrected and repaired by the same cause that produces them. Newton left to posterity the task of thoroughly investigating these inequalities, of showing them to be a result of the law of gravitation, and establishing the permanence of the system, notwithstanding the accumulating influence of its internal disturbances. ”

“ Our inability to differentiate between a field of inertial forces generated by acceleration and one of gravitation generated by matter is due solely to a miraculous coincidence, that of the equality of the two masses. Again, when, in the elevator falling in the earth’s gravitational field, we experience no feeling of weight, it is not that the gravitational field has vanished; it is solely that the field of gravity has been counteracted by an equal and opposite field of inertia generated by the elevator’s accelerated motion. ”

“ This brought about the strange view that inertial and gravitational phenomena, which are probably not less intimately connected with one another than electric and magnetic phenomena, have nothing to do with one another. The phenomenon of inertia is placed at the base of classical mechanics as the fundamental property of matter, whereas gravitation is only, as it were, introduced by Newton's law as one of the many possible forces of nature. The remarkable fact of the equality of the inertial and gravitational mass of bodies only appears as an accidental coincidence. ”

“ Newton’s conception of the earth’s gravitation as extending as far as the moon gave further importance to the distinction between mass and weight; for if a body were removed from the earth to the moon, then its mass would be unchanged, but the acceleration due to the earth’s attraction would be 60 × 60 times less, and its weight diminished in the same proportion. ”

“ To say, therefore, that a rotation of the firmament round a test-body would affect the field of force surrounding the body is equivalent to stating that a rotation of the stars would be capable of affecting the distribution of the metrical field round the body and of dragging the geodesics along. There is no reason to be surprised at some such effect taking place, seeing that the phenomenon of gravitation connotes that matter, whether at rest or in motion, must affect the curvature of space-time, hence the lay of the metrical field. ”

“ I have next to assert that this fact is irrelevant; and that Newton, while probably seeing it to be a necessary implication of geometrical laws that central forces vary inversely as the squares of the distances, did not see it to be a necessary implication of any laws, geometrical or dynamical, that there exists a force by which the celestial bodies affect one another; and therefore doubtless saw that there was no a priori warrant for the doctrine of gravitation. ”

“ In this connection every student should be warned against the popular notion that Newton discovered the explanation of gravitation. Nothing could be further from the truth. Indeed, Newton himself expressly disclaims any such thing; and insists that, while he has succeeded in describing some of the phenomena of gravitation, he will not even venture a guess as to the cause of gravitation. It need hardly be added that today we apparently are as far from any satisfactory explanation of gravitation as in the days of Newton. ”

“ Newton himself regarded this “action at a distance” as impossible, and believed that there was some hitherto undiscovered mechanism by which the sun’s influence was transmitted to the planets. However, no such mechanism was discovered, and gravitation remained a puzzle. The fact is that the whole conception of “force” is a mistake. The sun does not exert any force on the planets; in Einstein’s law of gravitation, the planet only pays attention to what it finds in its own neighborhood. ”

“ The classical conception of gravitation is based on Newton’s account of what happened; but it is time to hear what the apple had to say. The apple with the usual egotism of an observer deemed itself to be at rest; looking down it saw the various terrestrial objects including Newton rushing upwards with accelerated velocity to meet it. Does it invent a mysterious agency or tug to account for their conduct? No; it points out that the cause of their acceleration is quite evident. Newton is being hammered by the molecules of the ground underneath him. ”

“ And the advantage thus derived, as we have seen, is not confined to the astronomer, who has often been able, by making fundamental physical and chemical discoveries, to repay his debt to the physicist and chemist for the apparatus and methods which he owes to them.
NEWTON AND EINSTEIN Take, for another example, the greatest law of physics—Newton's law of gravitation. Huge balls of lead, as used by Cavendish, produce by their gravitational effect a minute rotation of a delicately suspended bar, carrying smaller balls at its extremities. But no such feeble means sufficed for Newton's purpose. ”

“ Turning, then, to our tentative scheme of gravitation in terms of a curved space, we see that there is nothing in it to suggest the peculiar accelerated motions of planets and projectiles, so that we are unable to account for all the effects that Newton ascribed to gravitation. Worse still, with a theory of space-curvature the motions of bodies along their trajectories would be uniform, since geodesics are described with constant velocity. ”

“ All spaces are not equally Full. For if all spaces were equally full, then the specific gravity of the fluid which fills the region of the air, on account of the extreme density of the matter, would fall nothing short of the specific gravity of quick-silver, or gold, or any other the most dense body; and therefore, neither gold, nor any other body, could descend in air. For bodies do not descend in fluids, unless they are specifically heavier than the fluids. And if the quantity of matter in a given space, can, by any rarefaction, be diminished, what should hinder a diminution to infinity? ”

“ All results harmonizing, Newton was justified in reaching the conclusion that gravitation is a universal property of matter. It remained, as we shall see, for nineteenth-century scientists to prove that the same force actually operates upon the stars, though it should be added that this demonstration merely fortified a belief that had already found full acceptance. ”