It is easy to see that Newton’s description is more creative by far than Kepler’s, and still more so than Ptolemy’s. Thus, Kepler’s laws merely enable us to foretell the future positions of the planets, and nothing more. If we abided by these laws, we should probably assume that elliptical orbits were the only ones that could exist. Newton’s law, on the other hand, enables us to predict that other types of orbits (parabolas and hyperbolas) are equally capable of existence, and in this way the motions of certain comets are brought into the general synthesis. All we have to do is to note the instantaneous position and velocity of a body with respect to the sun, and we can foresee immediately the precise orbit it will follow. Hence, our powers of prevision, as deduced from Newton’s law, are much greater than they were in Kepler’s day.
Again, consider the phenomenon of the precession of the equinoxes. Prior to Newton’s discoveries this phenomenon was always a mystery, unconnected with all other phenomena. Now its cause is clear. It is due to the uneven pull exerted by the sun and moon on our planet, brought about by its radially unsymmetrical shape (illustrated by the protuberance of its equator). The result will be a periodic to-and-fro oscillation of the earth’s axis with respect to the sun. Owing to the earth’s, rotation this swinging motion will generate a gyroscopic couple which will cause our planet to wobble like a top. The net result is that even had the phenomenon of precession been unknown to astronomers, mathematicians would have anticipated it as an inevitable consequence of the earth’s unsymmetrical shape and of the law of gravitation. And it is the same in innumerable instances. Newton’s description has thus widened the scope of the general synthesis of nature. It has shown the intimate connection which exists between such apparently independent phenomena as the motions of cyclones, the phenomenon of the tides, the feeling of weight, planetary motions, the precession of the equinoxes, the annual variations of the angles of aberration, etc. It has allowed us to anticipate the existence of one phenomenon from that of another. All these discoveries were rendered possible by our choice of the inertial frame for the reference of motion; so we realise that a description in terms of the inertial frame is creative, whereas one in terms of the non-rotating earth leads us nowhere.
Of course, now that we have learned so much, thanks to the introduction of the inertial frame, there is nothing to prevent us from interpreting all our results and all our relationships backwards, as it were, in terms of a non-rotating earth. But by transplanting, in this way, all the results obtained from the first description into the new description, no really new description would have been obtained; all we should have accomplished would have been to obtain a parody on the first one. In the same way, a record run backwards on the pianola does not constitute a new tune, but merely a parody on the original one. Obviously, this is not the method we must follow when we seek to construct a new synthesis. We must not merely transpose the results of the old synthesis in terms of the new one; we must operate directly.
But then, in the problem we are here discussing, had the description in terms of the inertial frame been unknown, the motion of the sun with respect to the fixed earth would in itself have been so complex as to defy mathematical investigation. As judged from the earth, the sun would appear to circle round it every 24 hours (neglecting niceties); and as at different seasons of the year its distance from the earth would vary, its course would be a spiral expanding, and then contracting, every six months.
Under the circumstances, the law of areas would not be satisfied; that is to say, if we considered the line joining sun to earth, it would not sweep over equal areas in equal times. Now, a general theorem of mechanics proves that whenever a body is moving under the attraction of a central body, the law of areas is always verified; whence we must conclude that the sun could never be considered as rotating round the earth under the sole action of the earth’s attraction. Supplementary forces would have had to be brought into play, but their introduction would have been so arbitrary, and the mathematical difficulties so great that even Newton might have been nonplussed; and we should have remained as ignorant of the harmony of the heavens as were the Greeks.
In the examples discussed, we have limited ourselves to problems of extreme simplicity; but even in these simple problems we have seen that different descriptions, though equivalent in theory, were far from equivalent in practice. When we come to consider problems of greater complexity, such as those with which modern science deals, the uniqueness of one particular type of description stands out with increased definiteness, and it is this particular simple continuous description where everything is harmonious and connected that is deemed to constitute the real description. Only when we follow this unique description do we find it possible to forestall nature by forecasting her actions in advance, and as a result claim that we have discovered reality.
The conclusions to be drawn from the preceding discussions are then as follows: From a purely kinematical point of view, it is simpler to take an inertial frame as frame of reference when the planetary motions are considered; this is the essence of Copernicus’ discovery. Also, when dynamical phenomena are considered, it is simpler to select an inertial frame with respect to which rotation will be measured. In short, the inertial frame imposes itself as conducive to the simplest interpretation of all phenomena whether mechanical or astronomical, so that we may say that there exists a privileged frame of reference in space. Here we are merely stating facts which are in no wise subject to controversy.
We might, of course, content ourselves with this discovery and neglect to consider the “why” and “wherefore.” But if we wish to pass beyond, if we wish to seek a palpable cause for the existence of a privileged frame in space, we are driven to one of two conclusions. Either we must say that the existence of a privileged frame arises from the nature of space itself, in which case we are driven to a space which possesses dynamical properties per se; and this is absolute space in which an inertial frame is privileged because it is non-rotating. Or else we must assume that space itself has nothing to do with the matter, and that the existence of the privileged frame arises from extraneous conditions, from the presence of the stars, the will of the Supreme Being, the shape of the earth, the number of existing planets, or anything else we may care to imagine.
There is not the slightest doubt that so long as we restrict our attention to the limited number of facts known to Newton, the simplest solution is the first, and its adoption constitutes the essential characteristic of the Newtonian position. There is, however, no necessity to conceive of this absolute space in the light of a metaphysical reality. All we need say is: Everything occurs as though there existed an absolute background of space, hence as though absolute space existed. This was the attitude of classical science until the advent of Einstein’s theory. We hope to make these vital points clearer in the course of this chapter.
Prior to Newton, the problem of space and motion appears to have been any one’s guess. To mention only two of Newton’s contemporaries, Descartes guessed that motion was relative, while More guessed that motion and space were absolute. These guesses were unsupported by any kind of scientific evidence, one way or another. It is true that More, for instance, seems to have realised the necessity of considering scientific examples in support of his claims, but his illustrations were too poorly interpreted to be of any scientific interest. Thus, in a letter to Descartes, he notes that a man walking at a rapid pace experiences fatigue, whereas his friend lying in repose experiences none; whence More concludes that motion and space must be absolute. But had he considered a man standing motionless for hours while his friend was being borne away, sitting at ease in a carriage, one may wonder what conclusion he would then have reached.