We shall now consider these basic problems in greater detail, and endeavour to understand why it was that Newton was compelled to accept absolute motion. Inasmuch as the absoluteness or the relativity of motion cannot be settled by a priori reasoning, we are compelled to appeal to experiment. Suppose, then, we perform mechanical experiments in the interior of some gigantic rigid box. The facts disclosed by experiment will be as follows: So long as, with respect to this box, the stars appear to occupy fixed positions, the course of our experiments will remain unchanged regardless of whether we operate in this part or in that part of the box. In other words, our mechanical experiments offer us no means of deciding as to our location in space. We may infer therefrom that experiment suggests the relativity of position, which means that position can be defined only with respect to other bodies, or at least to observable points of reference. This relativity of position entails as a direct consequence the homogeneity of space. In precisely the same way we should find that the orientation of our box, together with that of the mechanical apparatus it contained, would also fail to manifest itself by any variation in the course of our experiment; whence we infer the relativity of orientation, or the isotropy of space.
But what about motion through space? The mere fact that position in space was relative might suggest at first blush that motion, being a mere change in position, should also be relative. But, here again, the problem we are dealing with is one of physics, not one of pure mathematics or of metaphysics. Now, if we perform our mechanical experiment first in a box which is non-rotating with respect to the stars, then in one which is in relative rotation, a considerable change can be detected in the course of the experiment. Yet the relativity of motion would imply that this change in the nature of the box’s relative motion should entail no perceptible difference; hence we are compelled to conclude that in contradistinction to position and orientation, motion cannot be relative. Motion through space is not a mere matter of point of view; we can detect it even in the absence of any perceptible landmarks in space.
A more thorough investigation of this problem led Newton to differentiate between two grand categories of motion: one of which appeared relative, in that it was impossible to detect it in the absence of landmarks in space; the other of which appeared absolute, since it was accompanied by physical disturbances and dynamical manifestations which could be detected and measured without our having to take landmarks in space into consideration. 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. It is this duality in the manifestations of motion that renders classical mechanics so unsatisfactory.
Two courses were open to Newton:
1. Either he might have assumed that space was absolute; that all motion was absolute, but that accelerated and rotationary motions alone could be detected by mechanical experiments;
2. Or else he might have assumed that space possessed a dual nature; absolute for rotationary motions, but relative for uniform translationary, or Galilean, motion.
Newton preferred the first alternative; and the Newtonian principle of relativity, which stressed the impossibility of detecting absolute velocity through mechanical experiments, acted as a damper, not on the absolute nature of space and motion, but on our ability to detect absolute velocity mechanically.
There were a number of reasons that most assuredly prompted him to this choice. In the first place, a duality in the nature of space and of motion was not easy to conceive of. Furthermore, a circumstance which influenced Newton’s successors was the fact that, after all, the Newtonian principle of relativity concerned solely mechanical phenomena. It was still possible that electromagnetic experiments would reveal the absolute velocity in which Newton believed but which had ever eluded science.
Nevertheless, many of Newton’s successors preferred to adopt the second alternative. They assumed that experiment had revealed a duality in the nature or structure of space and had proved its relativity for uniform translationary motion. They were not perturbed over the fact that electromagnetic and optical experiments might finally succeed in detecting absolute velocity; for they argued that were such experiments successful, all they would reveal would be velocity through the ether, not absolute velocity through empty space. According to this attitude the Newtonian principle of relativity emphasised no longer the inability of mechanical experiments to detect absolute velocity through empty space, but stressed the fact that absolute velocity was entirely meaningless.
Now the important point is the following: Whichever of the two previous attitudes we accept, that of Newton or that of many of his successors, space must still remain absolute in either case. For, in either case, space would be absolute for acceleration and rotation, regardless of what it might turn out to be for velocity. In much the same way, if an object is faintly coloured it is coloured; the faintness of the colouring cannot alter this fact. Hence, when we consider space, the entire question centres round the following problem: Is rotational motion truly absolute? If not, hence if centrifugal force cannot be attributed to rotation in space, whence does this force arise?