The evolution of scientific thought from Newton to Einstein

by A. D'Abro

Before we proceed farther, a number of objections must be discussed. It might be claimed that whereas the earth could be conceived of as rotating among the stars, it would be quite impossible to consider the stars as rotating round the earth, since in this case centrifugal force would cause the stars to fly apart to infinity. A criticism of this sort arises from a confusion between the Newtonian attitude and the new one. With Newton’s ideas the argument would hold, for the stars would indeed be describing gigantic circles in absolute space. But in the present instance the space of the stars themselves has usurped the position of absolute space, since it is in this star-conditioned space that circular motion generates centrifugal forces. And in their own space the stars are obviously at rest whether or not we regard them as rotating, together with their space, around the earth. Hence, centrifugal force does not arise on the stars, though it will be felt on the earth’s surface. An equivalent way of explaining the same point would be to say: The stars as rotating round the earth are not subjected to centrifugal force, for they are rotating with respect to nothing; the mass of the earth being insignificant in comparison with the totality of the star-masses.

There exists also another type of objection which is based on causality and on our consciousness of effort. For example, we may claim that when, through an act of our will, we spin round on our heel, we know perfectly well that it is our body that is rotating among the stars, and not the stars that are rotating around us. In support of our claim, we should point out that no feeble efforts of ours could ever have started the stars and nebulæ rotating backwards. Curiously enough, where objections of this sort are made, the critic is often fully prepared to accept the relativity of velocity. But, as Einstein points out, arguments of a very similar sort might also be advanced against this simpler type of relative motion. For instance, would not the engineer claim that it must be his train that is moving, and not the earth that is gliding backwards? Could he not also support his contention by pointing out that when he stops feeding the furnace, all motion eventually ceases?

Possibly a more lucid illustration of the relativity of velocity would be afforded by considering the case of a bird in flight. The bird may be conscious of its efforts and realise that when it ceases to beat its wings, its motion through the atmosphere is arrested. It would therefore be entitled to assert that its velocity was maintained through its own efforts, hence was of its own making.

But it is obvious that this velocity created by the bird would be, not absolute velocity through space, but velocity through or relative to the atmosphere. Knowing nothing of the pre-existing velocity of the atmosphere through space, the bird could know nothing of its own absolute motion; and this is all that the principle of the relativity of velocity asserts. And so, were the velocity of the atmosphere through space equal and opposite to the relative velocity of the bird through the atmosphere, the bird’s efforts would result in maintaining its body at absolute rest. Hence, the awareness of effort is no criterion of the existence of absolute motion; relative motion alone is involved.

Exactly the same arguments can be extended to the relativity of rotation, except that in this case we are confronted with the peculiar difficulty arising from the existence of centrifugal force. Mach’s stand obviates this difficulty by introducing a definite physical assumption. Our purpose is, of course, not to justify Mach’s mechanics (for this can be done only through precise experiment, not by a general line of talk), but merely to show that it does not lead to absurdities when the argument based on causality is applied.

Let us consider, then, what is implied in the statement: “We know that it is we who are rotating on our heel among the stars; not the stars that are rotating around us.” When this distinction is made, the critic is assuming tacitly that there exists a super-space acting as an absolute frame of reference with respect to which rotation acquires a meaning; for in the absence of an assumption of this sort, the distinction he wishes to defend would, of course, be meaningless.

The statement, then, reduces to the following: “We know that the material universe is non-rotating in the super-space; hence, when we start rotating on our heel with respect to the stars, we know that it is we who are rotating in the super-space, the stars remaining at rest.” This was essentially Newton’s stand when he identified the super-space with absolute space. But Newton at least had given physical significance to this stand by ascribing centrifugal force to a rotation in this absolute space. When, however, we follow Mach and reject Newton’s physical assumption, the absolute space is deprived of all possibility of manifesting itself physically. And so the critic’s assertion loses all physical significance, since henceforth the only space in which rotation can manifest itself physically is the star-space.

The metaphysician might argue, however, that Mach’s interpretation of centrifugal force does not obviate the existence of a super-space, but merely denies us the ability to establish its existence by physical means. Let us grant this contention and see where it leads us. When we assert that it is we who are rotating on our heel, we are assuming implicitly that prior to our rotation the universe and our body were non-rotating in the super-space. Were we to cast any doubt on the correctness of this initial assumption, no conclusions could be drawn. For suppose that initially the universe, together with our body, was rotating clockwise in the super-space; then, as a result of an anti-clockwise rotation on our heel, it would now be we who were non-rotating in the super-space, while the universe of stars persisted in its state of rotation. Hence, the stars would be rotating around us. So we see that according to our initial assumptions as to the state of rotation of our universe in the super-space, we could derive any conclusions we pleased. The problem reduces, then, to determining the precise rotationary motion of our universe in the super-space. Now, inasmuch as this rotation is precluded from manifesting itself in any physical way, since centrifugal force has already been accounted for, the problem can of course never be solved by the physicist. As for the metaphysician, unless he can furnish us with some supra-physical means of determining the true situation, he also will be incapable of supplying us with the required information. It follows that if Mach’s premises are accepted, the entire super-space conception becomes meaningless, for any assumption whatever can be made in regard to it with impunity.

In short, Mach’s views do not conflict with causality; for we may always say that our efforts have been exerted on our body and not on the stars. But we must recognise that our efforts have set our body in rotation with respect to the star-space, and not with respect to a space which transcends the existence of the material universe.

Now, although a number of thinkers were in sympathy with Mach’s attitude, owing to their belief that all motion in a perfectly empty universe must be meaningless, yet the physical difficulties confronting his idea were so great that classical science had never taken it seriously. Euler had discarded the possibility of any such stellar action, and even quite recently Planck had criticised Mach for his stand. It was not that in theory a possible stellar action should be excluded on general principles; for physics had made us acquainted with foreign actions of a similar nature, the best-known of which would be illustrated by the gravitational action of the sun on the planets. Then again, when we wish to cut through an apparently empty space with a knife, we may experience considerable difficulty if the space happens to be permeated by a powerful magnetic field. We cannot, therefore, exclude the possibility that the stars might in some way generate a field endowing space with a structure which we had mistakenly taken to represent the absolute intrinsic structure of space. Science, however, cannot content herself with vague qualitative analogies; and before a mechanics such as Mach’s could be entertained, it would be necessary for it to succeed in accounting for the existence of centrifugal and Coriolis forces on a body in rotation with respect to the stars. This accounting would have to be made, not merely in some vague qualitative way, but quantitatively also, to a high order of precision. Such, indeed, are the requirements that all hypotheses in physics must satisfy. Now, all that Mach had done had been to postulate a possible stellar influence; he had not even attempted to justify his ideas rigorously. Indeed, even had he investigated the problem more deeply, he would have failed; for in his day space-time was unknown.