When
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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 _mc_2 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.
The most important result of a general character to which the special
theory of relativity has led is concerned with the conception of mass.
Before the advent of relativity, physics recognised two conservation
laws of fundamental importance, namely, the law of the conservation of
energy and the law of the conservation of mass these two fundamental
laws appeared to be quite independent of each other. By means of the
theory of relativity they have been united into one law. We shall now
briefly consider how this unification came about, and what meaning is
to be attached to it.
The principle of relativity requires that the law of the conservation
of energy should hold not only with reference to a co-ordinate system
_K_, but also with respect to every co-ordinate system _K _ which is in
a state of uniform motion of translation relative to _K_, or, briefly,
relative to every Galileian system of co-ordinates. In contrast to
classical mechanics; the Lorentz transformation is the deciding factor
in the transition from one such system to another.
By means of comparatively simple considerations we are led to draw the
following conclusion from these premises, in conjunction with the
fundamental equations of the electrodynamics of Maxwell: A body moving
with the velocity _v_, which absorbs[11] an amount of energy _E_0 in
the form of radiation without suffering an alteration in velocity in
the process, has, as a consequence, its energy increased by an amount
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