Newton

“ Does any one really imagine that Newton or Einstein has ever attempted to explain gravitation? To say that gravitation is a property of matter or a property of space-time in the neighbourhood of matter is just as much of an explanation as to say that sweetness is a property of sugar; for in the last analysis, what is matter—what is space-time? If we say that matter is an aggregate of molecules, atoms, electrons, protons, what of it? What are electrons? ”

“ Newton’s Law of Motion is a law of maya: “To every action there is always an equal and contrary reaction; the mutual actions of any two bodies are always equal and oppositely directed.” Action and reaction are thus exactly equal. “To have a single force is impossible. There must be, and always is, a pair of forces equal and opposite.” ”

“ 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. ”

“ At this point we may state that neither Newton, nor any of Newton’s successors including Einstein, have been able to advance even a plausible theory as to the nature of this gravitational force. We know that this force pulls a stone to the ground; we know, thanks to Newton, the laws regulating the motions due to gravity; but what this force we call gravity really is we do not know. The mystery is as deep as the mystery of the origin of life. ”

“ Prior to Newton, mathematics, chiefly in the form of geometry, had been studied as a fine art without any view to its physical applications other than in very trivial cases. [1] But with Newton all the resources of mathematics were turned to advantage in the solution of physical problems. Thenceforth mathematics appeared as an instrument of discovery, the most powerful one known to man, multiplying the power of thought just as in the mechanical domain the lever multiplied our physical action. ”

“ The moral as well as the intellectual grandeur of the life of Newton would tempt us to enlarge, but we must merely say, ere we pass on, to the youthful inquirer—read about Newton, think about Newton, and the more [Pg 104] you know of him the more will your understanding honour him, your heart love him, and your desire strengthen to approach him in virtue, wisdom, and usefulness.
SIR WILLIAM HERSCHEL, Newton’s greatest successor in astronomical discovery, may claim an equality with him, as a true and noble disciple of perseverance. ”

“ As in the physical creation, so in the moral, there is but one rule for the individual and the mass. It was the lofty discovery of Newton, that the simple law which determines the fall of an apple prevails everywhere throughout the Universe,—ruling each particle in reference to every other particle, large or small,—reaching from earth to heaven, and controlling the infinite motions of the spheres. ”

“ Judging from what we know of physical laws, we may expect the which belongs to it to be distinguished by having simple mathematical properties. Physics, this time as a physics of fields, is again pursuing the object of reducing the totality of natural phenomena to a single physical law: it was believed that this goal was almost within reach once before when Newton’s Principia, founded on the physics of mechanical point-masses, was celebrating its triumphs. But the treasures of knowledge are not like ripe fruits that may be plucked from a tree. ”

“ And behind the weight laid upon the imagination by mass and matter is the perhaps more oppressive weight of custom and convention. “Every body”—so commences Newton’s famous law—“continues in its state of rest or motion in a straight line.” ”

“ In speaking of Newton we are tempted to paraphrase a line from the Scriptures: Before Newton the Solar System was without form, and void; then Newton came and there was light. To have discovered a law not only applicable to matter on this earth, but to the planets and sun and stars beyond, is a triumph which places Newton among the super-men.
What Newton’s law of gravitation must have meant to the people of his day can be pictured only if we conceive what the effect upon us would be if someone—say Marconi—were actually to succeed in getting into touch with beings on another planet. ”

“ And an entire command of the conceptions and processes of mathematics is not only consistent with, but is the necessary condition and principal instrument of every important step in the discovery of physical principles. Newton was eminent above the philosophers of his time, in no one talent so much as in the power of mathematical deduction. When he had caught sight of the law of universal gravitation, he traced it to its consequences with a rapidity, a dexterity, a beauty of mathematical reasoning which no other person could approach ”

“ In his Preface, Newton says, “Rational Mechanics must be the science of the Motions which result from any Forces, and of the Forces which are required for any Motions, accurately propounded and demonstrated. For many things induce me to suspect, that all natural phenomena may depend upon some Forces by which the particles of bodies are either drawn towards each other, and cohere, or repel and recede from each other: and these Forces being hitherto unknown, philosophers have pursued their researches in vain. ”

“ Newton himself, however, endeavoured to account for gravitation by differences of pressure in an aether (see Art. Attraction, Vol. iii. p. 64) ; but he did not publish his theory, "because he was not able from experiment and observation to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature."
On the other hand, those who imagined aethers in order to explain phenomena could not specify the nature of the motion of these media, and could not prove that the media, as imagined by them, would produce the effects they were meant to explain. ”

“ Now, any one who turns to Newton's "Principia" will find that to the enunciation of the Second Law of Motion nothing whatever is appended but an amplified restatement there is not even an illustration, much less a proof. And from this law, this axiom, this immediate intuition or "datum of consciousness," Newton proceeds forthwith to draw those corollaries respecting the composition of forces which underlie all dynamics. What, then, must be thought of Newton, who explicitly assumes that which the reviewer thinks it absurd to assume implicitly? ”

“ The connection of the persons of whom we have been speaking has a bearing on our subject, for it led, historically speaking, to the publication of Newton’s discoveries in physical astronomy. Rightly to propose a problem is no inconsiderable step to its solution; and it was undoubtedly a great advance towards the true theory of the universe to consider the motion of the planets round the sun as a mechanical question, to be solved by a reference to the laws of motion, and by the use of mathematics. So far the English philosophers appear to have gone, before the time of Newton. ”

“ If we view nature atomistically, it will be our desire to interpret phenomena in terms of attractions and repulsions between molecules, atoms or electrons. Following the success of Newton’s treatment of planetary motions, the scientists of the eighteenth and early nineteenth century endeavoured to pursue this method by reducing the entire world of physical science to attractions and repulsions between discrete particles. All sorts of laws were appealed to: inverse-cube laws and laws involving still higher powers. ”

“ But, according to relativity, Newton’s statement in turn is approximate. We must now say that the trajectory lies along an ellipse whose axis is slowly rotating. There is every reason to believe that even Einstein’s mechanics is but an approximation to truth; and Schrödinger’s wave mechanics is already supplanting it in the infinitely small. Indeed, there is every reason to suppose that however far we go, we shall always be dealing with approximations. Here, then, is an essential difference between physics and mathematics. ”

“ Both Newton and Einstein were led to their theory of gravitation by profound studies of the mathematics of motion, but as Newton’s conception of motion differed from Einstein’s, and as, moreover, important discoveries into the nature of matter and the relationship of motion to matter were made subsequent to Newton’s time, we need not wonder that the two theories show divergence; that, as we shall see, Newton’s is probably but an approximation of the truth. If we [17] confine our attention to our own solar system, the deviation from Newton’s law is, as a rule, so small as to be negligible. ”

“ Let us now return to Newton’s solution of the problem, since it constitutes the embodiment of classical mechanics. As we have seen, Newton, by positing his postulate of isolation, rendered inevitable a belief in some real absolute medium, space or the ether, from which rotation and acceleration would derive a real meaning. But here we must recall that mechanical experiments, though clearly differentiating a Galilean frame from a non-Galilean frame, were totally incapable of differentiating one Galilean frame from another. ”

“ Newton was able to present the problem in a very simple form by pointing out that in a sphere such as the earth or the moon, the entire mass might be considered as residing in the center of the sphere. For purposes of computation, the earth can be considered a particle, with its entire mass concentrated at the center of the particle. This viewpoint enabled Newton to extend his law of inverse squares to the remotest bodies in the universe. ”

“ When we consider the wonderful discoveries that have issued at Einstein’s hands from this identity of the two masses, we may find it strange that Newton or some other scientist should have failed to attach any theoretical importance to it. ”

“ The principle of Universal Gravitation, namely, that every particle of matter is attracted by, or gravitates to, every other particle of matter, with a force inversely proportional to the squares of their distances—is the discovery which characterizes The Principia. This principle the author deduced from the motion of the moon, and the three laws of Kepler—laws, which Newton, in turn, by his greater law, demonstrated to be true. ”

“ Physics can, however, effect nothing without thought; it has its categories and laws through thought alone, and without thought it does not effect any progress. Newton was mainly instrumental in introducing to physics the determinations respecting forces, which pertain to reflection; he raised science to the standpoint of reflection, and set the laws of forces in the place of the laws of phenomena. ”

“ What force holds that moon forever circling about the earth? An apple falls to the ground beside him and its thud awakens a train of thought in his mind. Can it be the same force in the two cases—is the moon but a larger apple forever falling toward the earth, urged by the force of gravity, and forever receding from the earth, urged by her own uniform motion? Fascinated by the thought, Newton sets to calculating. He has studied out the laws of uniform motion and of accelerated motion—now he combines the two and gets the law of circular motion. ”

“ Newton’s law of gravitation stated that the attractions exerted between bodies depended solely on their masses and mutual distances; the conditions of relative motion or rest of the bodies being considered irrelevant. But if Mach’s ideas are accepted, we must assume that in addition to the ordinary Newtonian attraction, a supplementary field of attraction, hitherto unsuspected, should arise if the bodies were in a state of relative acceleration, as in the case of the stars rotating round the earth, or the planets moving round the sun. ”

“ A train running smoothly along a straight track with constant speed is an illustration of the relative type of motion, while an abject rotating with respect to the stars, or a ship tossed at sea, affords us an illustration of the absolute type. In short, position, orientation and a certain type of motion manifested themselves as relative, whereas certain other types of motion manifested themselves as absolute. These were the facts of experiment, and they were summed up by the law of inertia, or again by the Galilean or Newtonian principle of relativity. ”

“ If we are concerned solely with the facts of planetary motion and mechanics known to Newton, then Newton’s laws of mechanics and his law of gravitation are by far the simpler. But if we supplement the facts known to him with those more recently discovered, Einstein’s synthesis has the advantage, for Newton’s co-ordination would necessitate a number of additional hypotheses ad hoc. In the same way, so far as our everyday experience is concerned, a non-rotating earth is the simpler solution, whereas, when the planetary motions are taken into consideration, the reverse holds true. ”

“ From the equality of action and reaction, to which no exception can be found, Newton concluded that the sun gravitated to the planets, and the planets to their satellites; and the earth itself to the stone which falls upon its surface ”