# Einstein

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.

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