The evolution of scientific thought from Newton to Einstein

by A. D'Abro

for the infinite universe, or with the additional

term for the finite universe). We have mentioned on various occasions that more complicated laws were also possible provided we were willing to consider those involving the derivatives of the potentials to an order higher than the second.

Nevertheless, in spite of these various possibilities, the principle of covariance does allow us to narrow down our choice of permissible laws; it therefore retains considerable heuristic value. And it was thanks to this principle that Einstein, as we remember, was able to formulate the simplest possible law of gravitation even before awaiting the verdict of experiment and precise observation.

We may also note that the general principle of relativity does not signify that all observers are on the same footing. The irrelevance of the observer holds only in so far as the mathematical expression of the laws of nature is concerned; and it would not be true to suppose that a rotating observer could ever beguile himself into believing that he was at rest in a Galilean frame, or that a man tossed about in a ship’s cabin would assume that the sea was perfectly calm.

In short, we see that the general principle of relativity possesses essentially a mathematical and formal significance; the absoluteness of rotation remains, as before, an empirical fact which we cannot conjure away. It is only when we accept the hypothesis of the cylindrical universe, permitted but not obligated by the general principle, that the relativity of all motion in the Machian sense may be possible.

In this book we have attempted to enumerate the most salient features of Einstein’s work. There are, of course, a number of aspects which it has been impossible to mention, owing to the highly technical arguments that they would involve. Nevertheless, from what little has been said, certain general conclusions appear to be legitimate.

The theory of relativity has taught us that, strangely enough, there is nothing in the world of physics to justify our natural belief in the separateness of space and time. It is this discovery, entailing that of the four-dimensional world of space-time, that constitutes the most important contribution of the theory to our knowledge of the universe. What gives added significance to the four-dimensional world is the fact that those entities with which physicists deal are found to be vectors and tensors in its substance, and not in that of some other world. This, in itself, gives physical reality to space-time, and removes from it all trace of fictitiousness.

In addition to the existence of space-time and its invariant intervals, the really novel views which the theory forces upon us consist in the relativity of such primary concepts as length, duration, simultaneity, mass, force, etc., to which temperature should also be added. We also obtain new views on causal connections, and a better understanding of the principle of action and of the principles of conservation. Matter becomes fused with energy and disappears as a substance, and conservation is not rigorous. Furthermore, matter possibly creates space-time, and all motion may be relative. As for mass, it may be of an entirely relational nature, just like weight.

If we confine ourselves to the better-established philosophical aspects of the theory, we may say that it proves that nature is ruled by mathematical laws, at least to a first approximation; but this fact was already known to scientists many years ago, following Newton’s discoveries in celestial mechanics. So far as the unity of nature is concerned (a belief which was indissolubly connected with the very existence of science), the theory merely confirms the scientific attitude by revealing a degree of unity of sublime simplicity and beauty. When it comes to deciding whether nature must be viewed in an idealistic or a realistic sense, relativity affords little new information; and, as before, those who wish to adopt a realistic attitude towards the objective world of science are at liberty to do so, though, as we have mentioned, there are a number of reasons which render this philosophy most unsatisfactory. At any rate, the sole difference between relativity and classical science, in their bearing on realism and idealism, consists in the fact that the objective world of science is now one of space-time, no longer one of separate space and time.