Theory of relativity

“ When the theory of relativity supplanted classical science, it was recognised that the classical equations of mechanics were only approximate, and it became necessary to reformulate the principle of action so as to render it compatible with the mechanics of relativity, hence also with space-time. ”

“ No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.
In the example of the transmission of light just dealt with, we have seen that the general theory of relativity enables us to derive theoretically the influence of a gravitational field on the course of natural processes, the laws of which are already known when a gravitational field is absent. ”

“ When we consider the new views that are forced upon us by the theory [Pg 420] of relativity, we find that certain refinements are necessary. The special theory of relativity has shown that there was no reason to dispute the status of those qualities thought to be primary by classical science so long as we restricted our investigations to the points of view of observers at rest with respect to the object; but that when observers in relative motion were considered, it became impossible to effect a synthesis of all the apparent shapes so as to obtain one sole impersonal or real spatial shape. ”

“ The theory of relativity has arisen from the study of what goes on in the regions where there are no electrons and protons. While the study of the atom has led us to discontinuities, relativity has produced a completely continuous theory of the intervening medium—far more continuous than any theory formerly imagined. ”

“ It is to be found rather in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space.1 In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude proportional to it. Under these conditions, the natural laws satisfying the demands of the (special) ”

“ Clearly physics cannot concern itself with all the possible complexities which may exist in nature, but have not hitherto betrayed themselves in any experiment.
The principle of relativity has implications of a most revolutionary kind. Let us consider what is perhaps an exaggerated case—or perhaps the actual case, for we cannot tell. Let the reader suppose that he is travelling through the aether at 161,000 miles a second vertically upwards; if he likes to make the positive assertion that this is his velocity, no one will be able to find any evidence to contradict him. ”

“ But relativity mechanics finds that there is no evidence that the circumstances of any observer can be such as to make his views preeminent. All are on an equality. Consider an observer in a projectile falling freely to the earth, and an observer in space out of range of any gravitational attraction. Neither nor feel any field of force in their neighbourhood. Yet in Newtonian mechanics an artificial distinction is drawn between their circumstances; is in no field of force at all, but is really in a field of force, only its effects are neutralised by his acceleration. ”

“ They explore the new field and bring back their spoils—a few simple generalisations—to apply them to the practical world of three-dimensions. Some guiding light will be given to the attempts to build a scheme of things entire. For the rest, physics will continue undisturbedly to explore the relative world, and to employ the terms applicable to relative knowledge, but with a fuller appreciation of its relativity. ”

“ So far also relativity theory has proved ineffectual in relation to this most profound physical problem of the present time. Should the form of the general equations some day, by the solution of the quantum problem, undergo a change however profound, even if there is a complete change in the parameters by means of which we represent the elementary process, the relativity principle will not be relinquished and the laws previously derived therefrom will at least retain their significance as limiting laws. ”

“ But to those who think that the relativity theory is a passing phase of scientific thought, which may be reversed in the light of future experimental discoveries, we would point out that, though like other theories it may be developed and corrected, there is a certain minimum statement possible which represents irreversible progress. Certain hypotheses enter into all physical descriptions and theories hitherto current, dating back in some cases for 2000 years, in other cases for 200 years. ”

“ The entire philosophy of the relativity theory is to separate entities which have no significance except as expressing relationships to the frame of the observer, from entities which can be conceived of as enduring regardless of the observer’s presence. We recognise these absolute entities as those which remain unaltered for all observers. Mathematically, they are expressed by invariants and tensors in space-time. ”