Einstein 1920: Heuristic Value of Relativity

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, zand the time tof 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 has to do with consistency among all laws of Physics. The inconsistency between Galilei and Lorentz transformation simply points to a missing relationship between motion and inertia. The velocity of transmission of light depends on the inertia of light. The velocity of a body in space depends on the inertia of that body. There is a definite relationship between motion and inertia throughout the spectrum of substance (radiation and matter).

The rigidity of the rectangular co-ordinates x, y, z and the time t of the events, which constitute the processes of nature, also depends on the inertia they represent. These coordinates are relatively rigid in the material domain, but not so rigid in the radiation domain. This shall play an important role in the determination of the relationship between motion and inertia.

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:

The law of transmission of light is incomplete until a relationship is found between light’s velocity and its inertia (quantization).

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, tof 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 general laws of nature shall be co-variant with respect to Lorentz transformations only in the limiting condition when the velocity of light is infinite and its inertia zero. Since that is not case we cannot raise Lorentz transformations to the status accorded by Einstein.

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.

Lorentz transformation is valid only for material domain where the inertia of matter is many orders of magnitude larger than the inertia (quantization) of light.

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