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Einstein

Relativity: The Special and General Theory
Albert Einstein: Relativity
Part I: The Special Theory of Relativity
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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