structural:summarization, structural:scholar_edition
Extension for systems in motion

Unlike a system's energy in an inertial frame, the relativistic energy (E r e l {\displaystyle E_{\rm {rel}}}) of a system depends on both the rest mass (m 0 {\displaystyle m_{0}}) and the total momentum of the system. The extension of Einstein's equation to these systems is given by:

or

E r e l = (m 0 c 2) 2 + (p c) 2 {\displaystyle {\begin{aligned}E_{\rm {rel}}={\sqrt {(m_{0}c^{2})^{2}+(pc)^{2}}}\,\!\end{aligned}}}

where the (p c) 2 {\displaystyle (pc)^{2}} term represents the square of the Euclidean norm (total vector length) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered. This equation is called the energy–momentum relation and reduces to E r e l = m c 2 {\displaystyle E_{\rm {rel}}=mc^{2}} when the momentum term is zero. For photons where m 0 = 0 {\displaystyle m_{0}=0}, the equation reduces to E r e l = p c {\displaystyle E_{\rm {rel}}=pc}.