Page:Relativity (1931).djvu/75

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

${\frac {E_{0}}{\sqrt {1-{\tfrac {v^{2}}{c^{2}}}}}}$.

In consideration of the expression given above for the kinetic energy of the body, the required energy of the body comes out to be

${\frac {\left(m+{\tfrac {E_{0}}{c^{2}}}\right)c^{2}}{\sqrt {1-{\tfrac {v^{2}}{c^{2}}}}}}$.

Thus the body has the same energy as a body of mass $\left(m+{\tfrac {E_{0}}{c^{2}}}\right)$ 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 ${\tfrac {E_{0}}{c^{2}}}$; 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

1. $E_{0}$ is the energy taken up, as judged from a co-ordinate system moving with the body.