Newtonian physics

“ 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. ”

“ 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. ”

“ Why did Newton, followed by the whole of classical science, believe that gravitation, the fall of bodies, did not belong to the mechanics of which he formulated the laws? Why, in a word, did he regard gravitation as a force or—to use a vaguer but more general term—an action which prevents heavy bodies from changing their positions freely in space? [Pg 103]
Because of the principle of inertia. This principle, the foundation of the whole Newtonian mechanics, may be expressed thus: a body which is not acted upon by any force maintains its velocity and direction unchanged. ”

“ 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. ”

“ As a matter of fact, it is little short of a miracle, in view of the insignificance of our mathematical ability, that theoretical physics should have been possible at all. Had our solar system contained two suns such as are present in the double-star systems, or had one of the planets been comparable in size to the sun, it is safe to say that Newton, in spite of his genius, would never have discovered his law of gravitation ”

“ 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? ”

“ Newton himself does not appear to have been averse to explaining gravity by impulse. So little is it true that if one theory be true the other must be false. The attempt to explain gravity by the impulse of streams of particles flowing through the universe in all directions, which I have mentioned in the Philosophy, is so far from being inconsistent with the Newtonian theory, that it is founded entirely upon it. And even with regard to the doctrine, that the heavenly bodies move by an inherent virtue ”

“ For if Newton had been obliged to verify the theory of gravitation, not by deducing from it Kepler's laws, but by deducing all the observed planetary positions which had served Kepler to establish those laws, the Newtonian theory would probably never have emerged from the state of an hypothesis. ”

“ Chemistry here comes to the aid of mechanics, and we may say boldly that that matter, which is identical with ours, is subject, like it, to the laws of gravitation. Certainly, when Newton decomposed a beam of white light, and laid the first basis of the theory of the spectrum, he had not the slightest suspicion that his law of gravitation would, at a later period, find in it wings to carry it into regions where all measurement ceases and all calculation is powerless. ”

“ In making such a revision it is desirable to retain as many as possible of the simpler principles of Newtonian mechanics. Some of the consequences have already been presented [2] of a system of mechanics which retains the conservation laws of mass, energy, and momentum, and defines force as the rate of increase of momentum; but to agree with the theory of relativity introduces an idea foreign to Newtonian mechanics by considering that both the mass and velocity of a body are variable. ”

“ That every particle of matter in the universe attracts every other particle with a force that varies directly with the mass of the particles and inversely as the squares of their mutual distance. Newton did not vault at once to the full expression of this law, though he had formulated it fully before he gave the results of his investigations to the world. ”

“ If signals cannot go any faster than the speed of light, then it turns out that the method of describing the forces instantaneously is very poor. So in Einstein’s generalization of gravitation Newton’s method of describing physics is hopelessly inadequate and enormously complicated, whereas the field method is neat and simple, and so is the minimum principle. ”

“ Merely because in mathematics—in the case of , for example—the laws of Euclidean geometry were accepted from the start, whereas in physics preliminary information of this sort is denied us. And it is the same with all the magnitudes and constants of physics. It is impossible to predetermine by logical means the value of the invariant velocity, or of the gas constant, or of the size of the earth or of an electron. In every case, we must have recourse to physical measurements of one sort or another, for the constants of physics present no character of rational necessity. ”

“ Pre-eminent among these laws, because of its simplicity, its universality, and its undeviating truth, stands that enunciated by Newton (commonly called the law of gravitation) , that matter attracts matter with a force inversely as the square of the distance. Newton showed, that by this law, the general condition of things on the surface of the earth is governed; and the globe itself, with all upon it, kept together as a whole. He demonstrated that the motions of the planets round the sun, and of the satellites about the planets, were subject to it. ”

“ In the mechanics reformed according to the world-postulate, the disharmonies which have disturbed the relations between Newtonian mechanics and modern electrodynamics automatically disappear. I shall now consider the position of the Newtonian law of attraction to this postulate. I will assume that two point-masses m and m1 describe their world-lines; a moving force-vector is exercised by m upon m1, and the expression is just the same as in the case of the electron, only we have to write +mm1 instead -ee1. ”

“ This modern theory of the relativity of all uniform motion is essentially a return to the original Newtonian view, temporarily disturbed by the introduction of aether problems; for in Newton's dynamics uniform motion of the whole system has not—and no one would expect it to—have any effect. But there are considerable difficulties in the limitation to uniform motion. Newton himself seems to have appreciated the difficulty ”

“ Newton is not well understood even in our days. Some dictionaries say that Newton discovered the law of gravity. This law was introduced by Newton to save his theory. The inertia principle states that any material body, which is left free, is moving in a straight line, with constant velocity to infinity. But in the external reality such a phenomenon is not met. The planets are moving on closed trajectories in space. The only solution to save the theory was to invent a new force, which was called "gravity". ”

“ Moreover, his assertion that the notion of a body acting where it is not, is one that no competent thinker could entertain, is antagonistic to the whole current conception of attractive and repulsive forces, and therefore of "the attractive force of gravitation." What, then, was that labour of unsurpassed magnitude and excellence and immortal influence which Newton did perform? In the first place, Newton defined the laws, rules, or observed order of the phenomena of motion, which come under our daily observation, with greater precision than had been before attained ”

“ 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. ”

“ To all matter we attribute two properties, gravitation and inertia. Without these two matter cannot exist. The greatest of the natural laws states that the power of gravitational attraction is proportional to the mass of the body. This law of Newton, almost neglected in the thoughts of physicists, undoubtedly has vast import of the very deepest meaning. Shall it mean that all matter is finally constructed of uniform and similar primordial atoms or can we find some other explanation? ”

“ But it is obvious that we have no right to assume that Newton’s law or those of mechanics are above all suspicion. The laws of physical science present no a priori inevitableness; and our sole reason for accepting them is because they appear to be borne out to a high degree of approximation when we compare their rational consequences with the results of observation. Approximation is thus all we can aspire to in physical science; and even classical scientists recognised the possibility that more precise observation might prove Newton’s law and those of mechanics to stand in need of correction. ”

“ And since similar, equal, and equally swift bodies, moving through mediums of the same density, whose particles do not fly from each other mutually, will strike against an equal quantity of matter in equal times, whether the particles of which the medium consists be more and smaller, or fewer and greater, and therefore impress on that matter an equal quantity of motion, and in return (by the 3d Law of Motion) suffer an equal re-action from the same, that is, are equally resisted ”

“ This supposition allows it to be believed that all the stars are of similar phenomena, that there is a gravity or attraction on their surface, and that this gravity or attraction acts upon all other celestial bodies. With this frame of thought in his mind, Newton at last came to believe that all bodies attract each other by the force of gravity, that their movements are determined by the force which they exert mutually upon one another, and that the system of the universe is regulated by a single force,—gravity, or attraction. ”

“ 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. ”

“ For such hard Particles being heaped up together, can scarce [Pg 390] touch one another in more than a few Points, and therefore must be separable by much less Force than is requisite to break a solid Particle, whose Parts touch in all the Space between them, without any Pores or Interstices to weaken their Cohesion. And how such very hard Particles which are only laid together and touch only in a few Points, can stick together, and that so firmly as they do, without the assistance of something which causes them to be attracted or press'd towards one another, is very difficult to conceive. ”

“ 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. ”

“ According to Sir Isaac Newton's principles of gravity, the particle of matter that happened to be the largest would attract the smaller in its neighbourhood, which would increase the power of attraction in proportion to the increase of matter, until all in the universe would be collected into one vast body in the centre of space, and there remain motionless and at rest forever. ”

“ Having established this universal law, Newton was able not only to determine the weight which the same body would have at the surface of the sun and the planets, but even to calculate the quantity of matter in the sun and in all the planets that had satellites, and also to determine their density or specific gravity. ”