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 E0 in the form of radiation without suffering an alteration in velocity in the process, has, as a consequence, its energy increased by an amount
[ [11]
E0 is the energy taken up, as judged from a co-ordinate system moving with the body.
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 E0, then its inertial mass increases by an amount