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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

image024

[11] E0 is the energy taken up, as judged from a co-ordinate

system moving with the body.