Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.

XIV. ** 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. |
1 |

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: |
2 |

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. |
3 |

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. | 4 |