The evolution of scientific thought from Newton to Einstein

by A. D'Abro

Had we sought to discern the non-Galilean nature of the earth frame by endeavouring to detect traces of inertial, centrifugal and Coriolis forces, the task would have been more difficult owing to the minuteness of these forces. Nevertheless, the forces have been detected, and they account for the protuberance of the equator, the clockwise and anti-clockwise motions of cyclones, the rotation of the plane of Foucault’s pendulum, the directions of trade winds and of ocean currents, etc.

Now, thus far we have not attempted to draw any general conclusions from the existence of these various frames. We have merely stated that they undeniably exist, since they have been revealed by experiment, and that it is simpler to refer the laws of physics, and particularly those of mechanics, to Galilean or inertial frames. When it comes to interpreting the deeper significance of all these facts, various alternatives present themselves, and in this chapter we will discuss Newton’s solution at some length.

The problem to determine is, “Why do different types of frames exist when our understanding of amorphous mathematical space would seem to preclude any such differences?” Here we may make one of two assumptions. Either we may assume that the differences in conditions which exist in the various frames (differences which are exemplified by varied distributions in the lay of the inertial forces, or again in their total absence) are intrinsic, or else we may assume that they are due to foreign influences. Newton adopted the first alternative, Mach and Neumann the second.

If we follow Newton we must assume that the peculiarities existing in our frames are not to be attributed to causes existing beyond them. We may therefore assume that the inertial forces would be exactly the same were the balance of the universe to be annihilated, so that to all intents and purposes we might consider our frames isolated from all external influences. We assume, then, that the various distributions of the inertial forces manifesting themselves in our various frames must be attributed to the conditions of rest and of motion of these frames, not with respect to the remainder of the universe, which would be as good as annihilated, but with respect to those limited portions of the ether or of space in which the frames are situated.

Newton thus objectivises space and, owing to the symmetrical conditions which endure in Galilean frames, assumes these latter to be at rest in space, whereas the non-Galilean ones are assumed to be accelerated or rotating. If, then, we remember that a strict correspondence exists between the centrifugal and Coriolis distribution of forces in a non-Galilean frame, and its rate of rotation as viewed from a Galilean one, we may assume that the space in which a Galilean frame is at rest is also that in which a non-Galilean frame is accelerated or rotating. There is, then, but one space, an absolute space with respect to which motion and rest have a physical significance. Galilean frames are those which are non-accelerated; non-Galilean ones are those which are accelerated or rotating in this absolute space. This was Newton’s solution, and provided we accept his postulate of isolation there appears to be no way of escaping it.

Under the circumstances Newton’s law of inertia, according to which a free body follows a straight course with constant speed in relation to a Galilean frame, acquires a more determinate significance. The law now implies that this motion is being described in absolute space—in a space, therefore, that possesses a definite structure and which is thereby able to guide the body along its straight course. Had space been entirely amorphous and relative, as we assumed originally, there would have been nothing to guide the body; and even had the latter possessed enough intelligence to guide itself, there would have been nothing in amorphous space for it to direct itself by.

A number of philosophers attacked the Newtonian hypothesis of absolute motion and absolute space. For instance, some of them remarked that this so-called absolute space might well be assimilated to a bubble of ether floating and rotating in a more embracing space, this other in yet another, ad infinitum; so that Newton’s absolute rotation would be meaningless. Needless to say, arguments of this sort are totally irrelevant to Newton’s stand and to science generally.

Classical science, by absolute space, meant one with respect to which motion, or at any rate accelerated motion and rotation, appeared to manifest themselves dynamically; and experiment proved conclusively that such a space existed. There was no use, and in fact no sense, in wondering whether this absolute space should be conceived of as rotating in some other space; for even if a hypothesis of this sort were ever to be vindicated, the fact remained that rotation appeared to be absolute in a certain space regardless of whether or not this space was the super-space par excellence. This was all that was meant by the absoluteness of rotation so far as science was concerned. In short, as scientists clearly recognised, there was only one way to refute Newton’s absolute space and motion, and that was to deny his postulate of isolation. Such, indeed, was the course adopted by Mach.

If we follow Mach and Neumann and assume that the various internal dynamical conditions which distinguish the various frames are due to influences of an extrinsic nature, we shall no longer be able to subscribe to Newton’s conclusions; for we shall no longer be able to assume that were the entire outside universe to be annihilated, the internal conditions in our frames would endure as before. Henceforth, when ascribing the appearance of centrifugal and Coriolis forces to the rotation of the body, we should have to imply that this rotation was relative to a something in the universe that was not the empty space in which the frame was situated. The natural conclusion was that this rotation was relative to that other form of existence, namely, to matter. Neumann suggested a mysterious body called the “Alpha Body,” to whose dynamical influence he ascribed the rise of inertial forces; but, as Poincaré remarked, “Of this mysterious Alpha Body all we can ever know is its name.” A hypothesis such as Neumann’s, which is incapable of verification, reduces to a mere metaphysical speculation of no scientific value whatsoever.

Mach adopted a much more plausible alternative. He assumed that the rotation of the frame which appeared to accompany centrifugal and Coriolis forces was a rotation with respect to the remainder of the physical universe, hence to the totality of the matter of the universe. As the vastest agglomeration of matter in the universe is given by the totality of the star masses, we are led to Mach’s conclusions, namely, that the forces of inertia arise from a relative rotation or acceleration of the frame with respect to the universe of stars. Were the stars, then, to be annihilated, centrifugal force and all forces of inertia would vanish, a rotating mass of water would not splash over the sides of a bucket, and so forth. It is, of course, scarcely necessary to mention that the actual visibility of the stars or our mere ability to imagine their existence has nothing to do with the problem; it is solely the causal influences produced by their masses and relative acceleration which are relevant.