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Relativity: The Special and General Theory
Albert Einstein: Relativity
Part I: The Special Theory of Relativity
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 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
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 how the
energy of a point−mass; depends on the velocity. We shall speak of its essential significance later.