If our interest is purely philosophical, we may wish to be informed briefly of the nature of Einstein’s conclusions so as to examine their bearing on the prevalent philosophical ideas of our time. Unfortunately for this simplified method of approach, it is scarcely feasible. The conclusions themselves involve highly technical notions and, if explained in a loose, unscientific way, are likely to convey a totally wrong impression. But even assuming that this first difficulty could be overcome, we should find that Einstein’s conclusions were of so revolutionary a nature, entailing the abandonment of our ideas on space, time and matter, that their acceptance might constitute too great a strain on our credulity. Either we would reject the theory altogether as a gigantic hoax, or else we should have to accept it on authority, and in this case conceive it in a very vague and obscure way.
From a perusal of the numerous books that have been written on the subject by a number of contemporary philosophers, the writer is firmly convinced that the only way to approach the theory, even if our interest be purely philosophical, is to study the scientific problem from the beginning. And by the beginning we refer not to Einstein’s initial paper published in 1905; we must go back much farther, to the days of Maxwell and even of Newton. Here we may mention that however revolutionary the theory of relativity may appear in its philosophical implications, it is a direct product of the scientific method, conducted in the same spirit as that which inspired Newton and Maxwell; no new metaphysics is involved. Indeed Einstein’s theory constitutes but a refinement of classical science; it could never have arisen in the absence of that vast accumulation of mathematical and physical knowledge which had been gathered more especially since the days of Galileo. Under the circumstances it is quite impossible to gain a correct impression of the disclosures of relativity unless we first acquaint ourselves with the discoveries of classical science prior to Einstein’s time. It will therefore be the aim of this book, before discussing Einstein’s theory proper, to set forth as simply as possible this necessary preliminary information.
Modern science, exclusive of geometry, is a comparatively recent creation and can be said to have originated with Galileo and Newton. Galileo was the first scientist to recognise clearly that the only way to further our understanding of the physical world was to resort to experiment. However obvious Galileo’s contention may appear in the light of our present knowledge, it remains a fact that the Greeks, in spite of their proficiency in geometry, never seem to have realised, the importance of experiment (Democritus and Archimedes excepted).
To a certain extent this may be attributed to the crudeness of their instruments of measurement. Still, an excuse of this sort can scarcely be put forward when the elementary nature of Galileo’s experiments and observations is recalled. Watching a lamp oscillate in the cathedral of Milan, dropping bodies from the leaning tower of Pisa, rolling balls down inclined planes, noticing the magnifying effect of water in a spherical glass vase, such was the nature of Galileo’s experiments and observations. As can be seen, they might just as well have been performed by the Greeks. At any rate, it was thanks to such experiments that Galileo discovered the fundamental law of dynamics, according to which the acceleration imparted to a body is proportional to the force acting upon it.
The next advance was due to Newton, the greatest scientist of all time if account be taken of his joint contributions to mathematics and physics. As a physicist, he was of course an ardent adherent of the empirical method, but his greatest title to fame lies in another direction. Prior to Newton, mathematics, chiefly in the form of geometry, had been studied as a fine art without any view to its physical applications other than in very trivial cases.[1] But with Newton all the resources of mathematics were turned to advantage in the solution of physical problems. Thenceforth mathematics appeared as an instrument of discovery, the most powerful one known to man, multiplying the power of thought just as in the mechanical domain the lever multiplied our physical action. It is this application of mathematics to the solution of physical problems, this combination of two separate fields of investigation, which constitutes the essential characteristic of the Newtonian method. Thus problems of physics were metamorphosed into problems of mathematics.
But in Newton’s day the mathematical instrument was still in a very backward state of development. In this field again Newton showed the mark of genius, by inventing the integral calculus. As a result of this remarkable discovery, problems which would have baffled Archimedes were solved with ease. We know that in Newton’s hands this new departure in scientific method led to the discovery of the law of gravitation. But here again the real significance of Newton’s achievement lay not so much in the exact quantitative formulation of the law of attraction, as in his having established the presence of law and order at least in one important realm of nature, namely, in the motions of heavenly bodies. Nature thus exhibited rationality and was not mere blind chaos and uncertainty. To be sure, Newton’s investigations had been concerned with but a small group of natural phenomena (planetary motions and falling bodies), but it appeared unlikely that this mathematical law and order should turn out to be restricted to certain special phenomena; and the feeling was general that all the physical processes of nature would prove to be unfolding themselves according to rigorous mathematical laws.
It would be impossible to exaggerate the importance of Newton’s discoveries and the influence they exerted on the thinkers of the eighteenth century. The proud boast of Archimedes was heard again—“Give me a lever and a resting place, and I will lift the earth.”—But the boast of Newton’s successors was far greater—“Give us a knowledge of the laws of nature, and both future and past will reveal their secrets.”
To-day these hopes appear somewhat childish, but this is because we have learnt more of nature than was ever dreamt of by Newton’s contemporaries. Nevertheless, although we recognise that we can never be demigods, the mathematical instrument in conjunction with the experimental method, still constitutes our most fruitful means of progress.
Now Newton, in his application of mathematics to the problems of physics, had been concerned only with the very simplest of physical problems—planetary motions, mechanics, propagation of sound, etc. But when it came to applying the mathematical method to the more intricate physical problems, a considerable advance was necessary in our scientific knowledge, both mathematical and empirical. Thanks to the gradual accumulation of physical data, and thanks to the efforts of Newton’s great successors in the field of pure mathematics (Euler, Lagrange, Laplace), conditions were ripe in the first half of the nineteenth century for a systematic mathematical attack on many of nature’s secrets.
The mathematical theories constructed were known under the general name of theories of mathematical physics. In so far as they represented a mere application of mathematics to natural phenomena, they had their prototype in Newton’s celestial mechanics. The only difference was that they dealt with a wide variety of physical phenomena (electric, hydrostatic, etc.), no longer with those of a purely mechanical nature. The most celebrated of these theories (such as those of Maxwell, Boltzmann, Lorentz and Planck) were concerned with very special classes of phenomena. But with Einstein’s theory of relativity, itself a development of mathematical physics, the scope of our investigations is so widened that we are appreciably nearer than ever before to the ideal of a single mathematical theory embracing all physical knowledge. This fact in itself shows us the tremendous philosophical interest of the theory of relativity.