 |
 |
 |
 |
|
 |
 |
31
Relativity: The Special and General Theory
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 canservation 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 concervation of energy should hold not only
with reference to a co?ordinate system K, but also with respect to every co?ordinate system
K¹ 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 ¹
)
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
In consideration of the expression given above for the kinetic energy of the body, the required
energy of the body comes out to be
Thus the body has the same energy as a body of mass
moving with the velocity v. Hence we can say: If a body takes up an amount of energy E
0
,
then its
inertial mass increases by an amount
the inertial mass of a body is not a constant but varies according to the change in the energy of the
body. The inertial mass of a system of bodies can even be regarded as a measure of its energy.
The law of the conservation of the mass of a system becomes identical with the law of the
conservation of energy, and is only valid provided that the system neither takes up nor sends out
energy. Writing the expression for the energy in the form