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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.
GENERAL RESULTS OF THE THEORY
Part III: Considerations on the Universe as a Whole 18
It is clear from our previous considerations that the (special) theory of relativity has grown out of
electrodynamics and optics. In these fields it has not appreciably altered the predictions of theory, but it has
considerably simplified the theoretical structure, i.e. the derivation of laws, and -- what is incomparably more
important -- it has considerably reduced the number of independent hypothese forming the basis of theory.
The special theory of relativity has rendered the Maxwell-Lorentz theory so plausible, that the latter would
have been generally accepted by physicists even if experiment had decided less unequivocally in its favour.
Classical mechanics required to be modified before it could come into line with the demands of the special
theory of relativity. For the main part, however, this modification affects only the laws for rapid motions, in
which the velocities of matter v are not very small as compared with the velocity of light. We have experience
of such rapid motions only in the case of electrons and ions; for other motions the variations from the laws of
classical mechanics are too small to make themselves evident in practice. We shall not consider the motion of
stars until we come to speak of the general theory of relativity. In accordance with the theory of relativity the
kinetic energy of a material point of mass m is no longer given by the well-known expression
eq. 15: file eq15.gif
but by the expression
eq. 16: file eq16.gif
This expression approaches infinity as the velocity v approaches the velocity of light c. The velocity must
therefore always remain less than c, however great may be the energies used to produce the acceleration. If we
develop the expression for the kinetic energy in the form of a series, we obtain
eq. 17: file eq17.gif
When eq. 18 is small compared with unity, the third of these terms is always small in comparison with the
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