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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
 
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