The evolution of scientific thought from Newton to Einstein

by A. D'Abro

The general theory was suggested by the mysterious identity of the two types of masses, the inertial and the gravitational, which the most precise experiments appeared to have established. This identification of the two types of masses necessitated that of inertial and gravitational forces and resulted in the postulate of equivalence. The curvature of space-time in a gravitational field followed as an immediate consequence, and the law of gravitation became the law of space-time curvature. A number of laws of space-time curvature were mathematically possible, and Einstein chose the simplest. This simplest law of curvature was then found to be very nearly identical with that of Newton. It yielded a precessional advance of Mercury’s perihelion such as had already been observed by astronomers, and demanded in addition three new effects, all of which were unknown to science. These were the double bending of a ray of light passing near the sun, the Einstein shift-effect, and the non-Euclideanism of spatial measurements in a gravitational field. The first two effects have since been verified, while calculation proves the last effect too minute to present any hope of detection. Also, according to the theory, the force of gravitation can never be propagated with a speed greater than that of light. A definite limitation in size is assigned to bodies or stars of a given density. Hence also an upper limit in density is prescribed for a body of given mass.

Further theoretical considerations pertain to the wonderful connection which is shown to exist between laws erstwhile considered entirely separate, namely, the laws of conservation and of gravitation. In a similar way, thanks to space-time, action which in classical science, in spite of its vast physical importance, was given by so artificial a mathematical expression, now loses its artificial appearance. Also the displeasing teleological aspect of the principle of least action can now be avoided.

Viewed from a purely theoretical standpoint, the theory would appear to suggest the necessary existence of permanent entities (matter) acting on one another through space. We may understand how this comes about, as follows: Suppose we were told that the world was one of four-dimensional space-time; and that all things in it were built up of the space-time elements of structure, the

’s. By purely mathematical reasoning, we should discover that it was possible to construct, in terms of the

’s, tensor expressions which would manifest conservative properties; hence, that permanent entities were rationally possible in the space-time world. Outside and around these permanent entities, a residual curvature of space-time would be suggested, so that a field of force either attractive or repulsive would be expected; and the law of force distribution would correspond approximately to that of the inverse square. In this way matter and gravitation, though not strictly imposed a priori, would yet suggest themselves as likely consequences of the space-time theory.[156] Nothing similar was encountered in classical science.

Lastly we pass to the cosmological considerations. The general theory leaves us at liberty to choose between an infinite universe of space-time in which the star-matter would be concentrated into a nucleus, or else between two major types of finite universe, that of de Sitter and that of Einstein. The stability of the sidereal distribution would suggest Einstein’s cylindrical universe. If this model be accepted, the relativity of rotation and the complete relativity of mass as due to interactions between bodies, an idea so cherished by Mach, can at last be vindicated. From all these various considerations we may realise how vast is the nature of the synthesis accomplished by Einstein, and how varied are the phenomena which it co-ordinates.

If any one of the experiments and anticipations mentioned were to yield results differing even in a minute way from the expectations of the theory, relativity would in all probability have to be abandoned.[157] We see that the theory is exceedingly fragile and might be overthrown at any moment; but this is precisely what militates in its favour. In a general way, it may be said that the fragility of a theory expresses a measure of its coherence. For a coherent theory, uniting, as it does, into one doctrine a large number of facts and anticipations, must inevitably collapse, owing to its very coherence, when any one of its anticipations is proved incorrect by experiment. A theory full of hypotheses ad hoc is never fragile; whenever the experiment does not bear out the theory, all we need do is vary the hypotheses ad hoc or introduce new ones. But a theory of this sort lacks the essential requirements of a scientific theory, since no reliance can ever be placed on its anticipations. The great merit of the relativity theory resides precisely in its freedom from hypotheses ad hoc; therefrom arise both its fragility and its value.[158]

Nevertheless, although Einstein’s theory has succeeded in co-ordinating practically all our physical knowledge, there are still a few mysterious aspects of science which have not been accounted for. An understanding of the electron (hence of matter) and of the nature of the Poincaré pressure which prevents it from exploding under the mutual repulsive forces of its various parts, remains a mystery. It appears to be impossible to build up the electron from the magnitudes of the electromagnetic field alone; it is as though the electron must contain something else besides electromagnetic forces. In other words, what is known as the physics of the field (which we owe to Maxwell and Faraday) proves itself unable to account for the existence of electrons and matter. All that can be said is that the theory of relativity appears to suggest that the cohesive force which holds the electron together (the Poincaré pressure) is of a gravitational nature and is linked to the curvature of the universe. Then again, the existence of electricity under two different aspects, positive and negative, has yet to be explained. As Weyl remarks, it might be explained by the choice of an irrational expression for the action; it might also be linked to the progress of time from past to future. But, above all, the phenomena of the quanta, the atomicity of matter, of energy and of action still constitute outstanding challenges to mathematicians.