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 _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.
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.
XV.
GENERAL RESULTS OF THE THEORY
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