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Relativity: The Special and General Theory

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 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 coordinate system K, we introduce new space-time variables x1, y1, z1, t1
of a co-ordinate system K1. 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.
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.
 
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