The evolution of scientific thought from Newton to Einstein

by A. D'Abro

We have now to consider in a very brief way certain of the philosophical problems which antedate Einstein’s discoveries, but with which his theory is intimately connected. Long before the advent of Einstein, problems pertaining to the relativity of motion through empty space had occupied the attention of students of nature. There were some who held that empty space, and with it all motion, must be relative; that states of absolute motion or absolute rest through empty space were meaningless concepts. According to these thinkers, in order to give significance to motion and rest, it was necessary to refer the successive positions of the body to some other arbitrarily selected body taken as a system of reference. We should thus obtain relative rest or motion of matter, with respect to matter. All these views were in full accord with our visual perceptions and they were expressed by what is known as the visual or kinematic principle of the relativity of motion. Other thinkers preferred to uphold the opposing philosophy. They assumed that space was absolute; that all motion must be absolute; that there was meaning to the statement that a body was in motion or at rest in space, regardless of the presence of other bodies to be used as terms of comparison. The controversy mighty have continued indefinitely, had it not been for the appearance of the scientist with his empirical methods of investigation.

Galileo and Newton were the first to recognise in a clear way that, provided certain very plausible assumptions were made, the dynamical evidence adduced from mechanical experiments proved the relativistic philosophy to be untenable. Classical science was therefore compelled to recognise the absoluteness of space and motion. It is true that many philosophers still defended the relativity of all motion. But their failure to take into consideration the real obstacles that seemed to bar the way to a relativistic conception of motion, coupled with the looseness of their scientific arguments, precluded their opinions from exercising any influence on scientific thought. Now it is to be noted that notwithstanding the absolute nature which Newton attributed to all states of motion and of rest in empty space, a certain type of absolute motion called Galilean[2] or again uniform translationary motion (defined by an absolute velocity but no absolute acceleration), was recognised by him as being incapable of detection, so far as experiments of a mechanical nature were concerned. This complete irrelevancy of absolute velocity or absolute Galilean motion to mechanical experiments was expressed in what is known as the Galilean or Newtonian or classical or dynamical principle of the relativity of Galilean motion through empty space. The existence of such a principle of relativity created a duality in the physical significance of motion, hence of space, but the philosophical importance of the principle, as referring to the problem of space, was lessened by the fact that this relativity applied solely to experiments of a mechanical nature. It was confidently assumed that electromagnetic and optical experiments would be successful in revealing the absolute Galilean motions which had eluded mechanical tests.

Such was the state of affairs when Einstein, in 1905, published his celebrated paper on the electrodynamics of moving bodies. In this he remarked that the numerous difficulties which surrounded the equations of electrodynamics, together with the negative experiments of Michelson and others, would be obviated if we extended the validity of the Newtonian principle of the relativity of Galilean motion (which applied solely to mechanical phenomena) so as to include all manner of phenomena: electrodynamic, optical, etc.

When extended in this way the Newtonian principle of relativity became Einstein’s special principle of relativity. Its significance lay in its assertion that absolute Galilean motion or absolute velocity must ever escape all experimental detection. Henceforth absolute velocity should be conceived of as physically meaningless, not only in the particular realm of mechanics, as in Newton’s day, but in the entire realm of physical phenomena. Einstein’s special principle, by adding increased emphasis to this relativity of velocity, making absolute velocity metaphysically meaningless, created a still more profound distinction between velocity and accelerated or rotational motion. This latter type of motion remained absolute and real as before. From this we see that the special principle was far from justifying the ultra-relativistic belief in the complete relativity of all motion, as embodied in the kinematical or visual principle of relativity.

It is most important to understand this point and to realise that Einstein’s special principle is merely an extension of the validity of the classical Newtonian principle to all classes of phenomena. Apart from this extension there is no essential difference between the two principles, since both deal exclusively with Galilean motion or velocity. Much of the criticism that has been directed against Einstein’s special theory, and in particular against its so-called paradoxes, can be traced to a confusion on the part of the critic between the very wide visual or kinematical principle of the relativity of all motion, including acceleration as well as velocity, and the much more restricted special principle which deals solely with velocity.

Owing to this initial error it has been assumed by some that the theory of relativity professes to have established the complete relativity of all motion. So far as the special theory is concerned, this assumption is obviously untenable; and a very marked distinction is maintained, as in classical science, between the significance of acceleration and of velocity. This distinction is by no means new, since it forms part and parcel of classical science; but in view of its importance to any one who wishes to obtain any insight into the philosophical implications of Einstein’s more difficult theory, we have deemed it advisable in the course of this book to devote a preliminary chapter to Newtonian mechanics. We may add that Einstein’s paper created an uproar, for it compelled us to reorganise in a radical way those fundamental forms of human representation which we call space and time.

After discussing the special theory we shall proceed to examine Einstein’s general theory, which he began to develop in 1912 and which he completed in 1916. The general theory deals more especially with gravitation, though it also sheds new light on the problem of the relativity of motion. It is our opinion that the reader will save himself much unnecessary trouble if he realises from the start that Einstein, even in the general theory, does not succeed in establishing the complete relativity of all motion. While it is true that acceleration loses much of its absoluteness, we are still far from being able to subscribe to the very wide visual or kinematical principle which the complete relativity of all motion would necessitate.

Following the general theory, Einstein entered into cosmological considerations on the form of the universe as a whole. This part of the theory is still highly speculative; and until such time as astronomical observations conducted on the globular clusters and the Milky Way have given their verdict, nothing definite can be said.

From the standpoint of the relativity of motion, this last part of Einstein’s theory is of fascinating interest; for should it be proved correct, the relativity of all motion might finally be justified and the bugaboo of absolute rotation dispelled forever. We should then be led to a modified form of the visual or kinematical principle of the complete relativity of motion; namely, to Mach’s mechanics. On the other hand, should astronomical observation deny the correctness of Einstein’s cosmological views, the theory would have failed to establish the complete relativity of all motion.

In addition to all this preliminary physical information with which it is necessary to be acquainted (Newtonian mechanics, electrodynamics) before proceeding to a study of Einstein’s theory, a considerable amount of purely mathematical knowledge must be mastered. Here we refer not to the actual technique of calculation, but to the general significance of the mathematical doctrines developed by the great mathematicians of the past.