Reference: Einstein’s 1920 Book
This paper presents Part 1, Chapter 14 from the book RELATIVITY: THE SPECIAL AND GENERAL THEORY by A. EINSTEIN. The contents are from the original publication of this book by Henry Holt and Company, New York (1920).
The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding. Feedback on these comments is appreciated.
The heading below is linked to the original materials.
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The Heuristic Value of the Theory of Relativity
Our train of thought in the foregoing pages can be epitomised in the following manner. Experience has led to the conviction that, on the one hand, the principle of relativity holds true, and that on the other hand the velocity of transmission of light in vacuo has to be considered equal to a constant c. By uniting these two postulates we obtained the law of transformation for the rectangular co-ordinates x, y, z and the time t of the events which constitute the processes of nature. In this connection we did not obtain the Galilei transformation, but, differing from classical mechanics, the Lorentz transformation.
The Principle of Relativity works in conjunction with the velocity of light simply because light is serving as a “point of zero inertia” for all inertial systems in the material domain, which is characterized by the rigidity of the rectangular co-ordinates x, y, z and t. The point of zero inertia makes it possible to account for subtle change in inertia in the material domain, and their effect on velocity. This effect was not accounted for by the Galileian transformation.
The law of transmission of light, the acceptance of which is justified by our actual knowledge, played an important part in this process of thought. Once in possession of the Lorentz transformation, however, we can combine this with the principle of relativity, and sum up the theory thus:
Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space- time variables x, y, z, t of the original co-ordinate system K, we introduce new space-time variables x’, y’, z’, t’ of a co-ordinate system K’. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or, in brief: General laws of nature are co-variant with respect to Lorentz transformations.
The x, y, z, t co-ordinates are a function of inertia. The Lorentz transformations provide this function for the material domain only in an approximate but fairly accurate manner. In other words, general laws of nature are co-variant with respect to Lorentz transformations in the material dimension only.
The law of transmission of light is incomplete until a relationship is found between light’s velocity and its inertia (quantization).
This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced.
Inertia may be defined by finding the relationship of the x, y, z, t co-ordinates with mass.
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FINAL COMMENTS
Lorentz transformation is more accurate than the Galileian transformation because it takes into account the changes in velocity due to subtle changes in inertia in the material domain. These changes are accounted for because taking the large velocity of light as constant is equivalent to treating light as a point of zero inertia. This allows subtle changes in inertia to be converted into equivalent changes in velocity.
The Principle of Relativity is simply accounting the variation in inertia through the rectangular co-ordinates x, y, z and t. This relationship needs to be understood better and related with mass.
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