# Relativity: The Special and General Theory

General Results of the Theory

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 hypotheses 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

but by the expression

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

When is small compared with unity, the third of these terms is always small in

comparison with the second,

which last is alone considered in classical mechanics. The first term mc2 does not contain

the velocity, and requires no consideration if we are only dealing with the question as to