Relativistic energy and momentum combine naturally into the four-momentum $$p^\mu=\left(\frac{E}{c},\mathbf p\right).$$ Its Minkowski norm is invariant under Lorentz transformations: $$p^\mu p_\mu=\frac{E^2}{c^2}-p^2=m^2c^2.$$ This reproduces $$E^2=p^2c^2+m^2c^4.$$

Four-momentum is conserved in every isolated relativistic interaction: $$\sum p^\mu_{\rm initial}=\sum p^\mu_{\rm final}.$$ Because its squared norm is frame-independent, it provides a powerful way to analyze collisions without first choosing a convenient observer.

For a system of several particles, define total four-momentum $$P^\mu=\sum_i p_i^\mu.$$ The system's invariant mass $M$ satisfies $$M^2c^2=P^\mu P_\mu.$$ For two photons traveling in opposite directions with equal energy $E_\gamma$, total spatial momentum is zero while total energy is $2E_\gamma$, so $$Mc^2=2E_\gamma.$$ Although each photon individually has zero rest mass, the two-photon system can have nonzero invariant mass.

Particle experiments reconstruct invariant masses from measured final-state energies and momenta. A resonance appears as an excess of events near a particular invariant mass, allowing short-lived particles to be identified even when they decay before reaching a detector.