Nevertheless we must now draw attention to the fact that a theory of this phenomenon was given by H. A. Lorentz long before the statement of the theory of relativity.  This theory was of a purely electrodynamical nature, and was obtained by the use of particular hypotheses as to the electromagnetic structure of matter.  This circumstance, however, does not in the least diminish the conclusiveness of the experiment as a crucial test in favour of the theory of relativity, for the electrodynamics of Maxwell-Lorentz, on which the original theory was based, in no way opposes the theory of relativity.  Rather has the latter been developed trom electrodynamics as an astoundingly simple combination and generalisation of the hypotheses, formerly independent of each other, on which electrodynamics was built.

  Notes

*) Fizeau found eq. 10 , where eq. 11

is the index of refraction of the liquid.  On the other hand, owing to the smallness of eq. 12 as compared with I,

we can replace (B) in the first place by eq. 13 , or to the same order of approximation by

eq. 14 , which agrees with Fizeau’s result.

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.