The Special Relativity Theory

Einstein's Theories of Relativity and Gravitation by Albert Einstein, is part of the HackerNoon Books Series. You can jump to any chapter in this book here. The Special Relativity Theory

The Special Relativity Theory

In our account of the Einstein theory we have not followed its historical order of development for two reasons. Firstly, the earlier Special Relativity Theory properly belongs to a school of thought diametrically opposed to that furnishing the “General Theory of Relativity” and, secondly, the latter cannot be obtained from the former by the process of generalization as commonly understood. Einstein, when proposing the earlier theory, adopted the position of the empiricist so that to him the phrase, a point in space, had no meaning without a material framework of reference in which to measure space distances. When he came to investigate what is meant by time and when he asked the question “what is meant by the statement that two remote events are simultaneous?” it became evident that some mode of communication between the two places is necessary; the mode adopted was that by means of light-signals. The fundamental hypothesis was then made that the velocity of such signals is independent of the velocity of their source (some hypothesis is necessary if we wish to compare the time associated with events, when one material reference-system is used, and the corresponding time when another in motion relative to the first is adopted). It develops [285]that time and space measurements are inextricably interwoven; there is no such thing as the length of a body or the duration of an event but rather these are relative to the reference-system.2 Minkowski introduced the idea of the space of events—of four dimensions—but this space was supposed Euclidean like the three-dimensional space of his predecessors. To Einstein belongs the credit of taking from this representation a purely formal mathematical character and of insisting that the “real” space—whose distances have a physical significance—is the four-dimensional space. But we cannot insist too strongly on the fact that in the gravitational space of the general theory there is no postulate of the constancy of velocity of a light-signal and accordingly no method of assigning a time to events corresponding to that adopted in the special theory. In this latter theory attention was confined to material systems moving with uniform velocity with respect to each other and it developed that the velocity of light was the ultimate velocity faster than which no system could move—a result surprising and a priori rather repugnant. It is merely a consequence of our mode of comparing times of events; if some other method—thought transference, let us say—were possible the velocity of this would be the “limiting velocity.”

In conclusion we should remark that the postulated equivalence of “gravitational” and “centrifugal” forces demands that anything possessed of inertia will be acted upon by a gravitational field and [286]this leads to a possible identification of matter and energy. Further our guiding idea (a) will prompt us to say, following the example of Faraday in his electrical researches, that the geodesics of a gravitational space have a physical existence as distinct from a mere mathematical one. The four-dimensional space we may call the ether, and so restore this bearer of physical forces to the position it lost when, as a three-dimensional idea in the Special Relativity Theory, it had to bear an identical relation to a multitude of relatively moving material systems. The reason for our seemingly paradoxical title for an essay on Relativity will be clear when it is remembered that in the new theory we consider those space-time properties which are absolute or devoid of reference to any particular material reference-frame. Nevertheless, although the general characteristics of the theory are thus described, without reference to experiment, when the theory is to be tested it is necessary to state what the four coordinates discussed actually are—how they are determined by measurement. It is our opinion that much remains to be done to place this portion of the subject on a satisfactory basis. For example, in the derivation of the nature of the gravitational space, surrounding a single attracting body, most of the accounts use Cartesian coordinates as if the space were Euclidean and step from these to polar coordinates by the formulæ familiar in Euclidean geometry. But these details are, perhaps, like matters of elegance, if we shall be allowed to give Einstein’s quotation from Boltzmann, to be left to the “tailor and the cobbler.”[287]

1Not all gravitational fields may be transformed away by a proper choice of coordinates. If this were so, the space, whose nature is independent of any choice of coordinates, would always be Euclidean.—Author. ↑

2Thus when it it said that a body contracts or that a clock runs slow when it is put in motion no actual physical change is implied. The judgment of different observers—one at rest with respect to the body and one not—are different.—Author. ↑

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