Massless particles: $E_{\mathrm{rel}} = pc$

Let $c>0$, and let $E\ge 0$ and $p\ge 0$ be the energy and momentum magnitude of a particle satisfying the energy–momentum relation $E^2-(pc)^2=(m_0c^2)^2$ with rest mass $m_0=0$. Then

For photons, which have zero rest mass, the energy–momentum relation thus reduces to $E_{\mathrm{rel}}=pc$: their energy is due only to their momentum.

Formalization Note A massless particle travels at speed $c$, where the Lorentz factor is undefined, so it cannot be described by the velocity-based quantities $\gamma m c^2$, $\gamma m\mathbf v$ of the definition file (with $m=0$ those would both vanish). The statement is therefore phrased directly in terms of a pair $(E,p)$ satisfying the energy–momentum relation with $m_0=0$.