The evolution of scientific thought from Newton to Einstein

by A. D'Abro

As a matter of fact, there is no very essential difference between the solutions of Mach and Newton. Even if we follow Mach, unless we are to believe in action at a distance, we must assume that the stellar influences can reach us only as a result of a propagation from place to place through space. We may perfectly well assume that as a result of this influence space receives a definite structure, so that in fine the physical reality of rotation may still be ascribed to a rotation in space. There is a difference, however; for with Newton this structure of space is intrinsic to space itself and has nothing to do with the contingent presence of matter generally, whereas if we follow Mach this structure of space must be conceived of as extrinsic and caused by the matter of the universe. In the absence of matter, the structure of space would automatically disappear and the various frames become indistinguishable.

As we can see, Mach’s views lead to a partial vindication of the visual or kinematical principle of relativity. But the vindication is only partial, since in all cases the relativity of acceleration and rotation exists only as between the totality of the stars and a body, and not between any two bodies taken arbitrarily, as in the visual principle.

Against Mach’s solution there is the argument that the stars are too remote to produce any such palpable effects as the bursting of a rotating flywheel or the splashing of a revolving mass of water over the sides of the bucket. But, still more important, it appeared impossible for classical science to account for these dynamical actions attributed to the stars. Nevertheless, with the tremendous advance in our understanding of nature which the general theory of relativity has given us, Mach’s ideas become highly probable, though not completely vindicated at the present time. Astronomical observations conducted on the globular clusters may eventually solve the problem.

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. It appeared impossible to discover, therefore, which particular Galilean frame was to be considered at absolute rest in stagnant absolute space and which ones were to be regarded as moving through space with uniform translationary motions. In other words, when we confined ourselves to mechanical experiments, velocity through space was relative, the only velocity susceptible of mechanical detection being relative velocity, that is, velocity of one frame with respect to another. Acceleration and rotation, on the other hand, were absolute, and could be detected and measured mechanically without our having to appeal to a Galilean frame taken as term of comparison.

Were we to appeal to a Galilean frame in order to check up our computations, it would be a matter of complete indifference which particular Galilean frame we might select. As referred to any one of these Galilean frames, a body would manifest exactly the same acceleration and rate of rotation, whereas its velocity would, of course, vary with the Galilean frame to which it was referred. This is what is meant by the absolute character of acceleration in contradistinction to the relative character of velocity.

Of course, even an accelerated body could be made to appear at rest or to be moving with uniform motion if we selected a suitable frame. But the frame would have to be non-Galilean or accelerated in order to ensure this result, and we have seen that non-Galilean frames can never (at this stage, at least) be regarded as being at rest in space. It follows that the appearance of a body’s motion relatively to any of these non-Galilean frames could never be considered representative of the real motion of the body in space.

The Principle of Relativity of Classical Science merely summarises these discoveries by stating that it is impossible for an observer situated in a Galilean frame to ascertain by any mechanical experiment whether he is at rest in space or in a state of uniform translationary motion. A simple illustration will clarify the meaning of these statements.

Consider a train moving with constant speed along a straight course; obviously there is no trace of acceleration in the train’s motion, since no forces of inertia are felt in its interior. In common practice, we should speak of the train as having a definite speed of so many miles per second. But if we reflect we shall see that this constant speed is computed with respect to the earth’s surface, considered as defining a Galilean frame of reference. Were the earth suddenly to become invisible, we should have no physical means of determining the exact speed of the train through space. But suppose, now, that the train were slowing down, speeding up or rounding a curve. In this case, even if the earth were invisible, the train would still possess at each instant a definite acceleration and this acceleration would still be perceptible, and would be measured by the forces of inertia pulling and pushing the passengers about in the train. We see, then, that acceleration has an existence per se and that, in contrast to velocity, it is determinate even in the absence of a frame of reference. Now, it follows from the classical principle of relativity that, absolute velocity being meaningless (at least so far as mechanics is concerned), the only type of uniform translationary motion which can be detected by mechanical means reduces to relative uniform translationary motion of matter with respect to matter; that is, motion with respect to something observable. The magnitude of this relative motion depends essentially on the Galilean frame we may select.

Relative uniform translationary motion can, of course, be detected visually, but it can be detected also in a number of other ways. Thus the relative motion of a razor blade on a strop causes heat due to friction. The relative displacement of a knife between the two poles of an electromagnet produces induced currents which manifest themselves by rendering it difficult to cut through the lines of force of the field. The relative motion of an incandescent atom produces a shift in the spectral lines (Doppler effect), and it is thanks to this shift that astronomers are able to determine the radial velocities of the stars with respect to the earth. In other words, though absolute velocity can never be detected by mechanical experiments and is therefore meaningless in mechanics, yet relative velocity of matter with respect to matter can be detected in a number of ways; so that this relative type of velocity is the only one that has any physical significance, or at least any mechanical significance.

We have now to consider a number of difficulties that arise from Newton’s conception of absolute space. In the first place, although Newton had postulated absolute space and motion, the fact remained that of all the absolute motions, absolute acceleration and rotation were the only ones that had ever been detected, at least by mechanical means. It seemed strange, if absolute velocity were to have a meaning, as indeed it must if space were absolute, that it should be so obstinate in refusing to reveal itself. We could not hold that our inability to discover which one of the Galilean frames was truly at rest was due to the crudeness of our mechanical experiments; for the entire structure of Newtonian mechanics would have come crashing down had any such suggestion been proved correct.