Definition
Mass–energy equivalence is the principle that mass and energy are two manifestations of a single conserved physical quantity, related by E = mc².
Einstein derived the relation in a four-page 1905 paper, "Does the inertia of a body depend upon its energy content?" — published months after his founding paper on special relativity. It is famously the only equation Hawking included in A Brief History of Time.
Why it matters
How it works
The 1905 derivation considered a body at rest emitting two equal pulses of light in opposite directions. By Lorentz-transforming the energies into a frame where the body is moving, Einstein showed the body must have lost an amount of mass equal to the emitted energy divided by c². The conclusion: emitting energy reduces inertia.
The relation is exact for rest energy. A body of rest mass m has a rest energy E₀ = mc² even when it is not moving. When it moves, its total relativistic energy is E = γmc² where γ = 1/√(1 − v²/c²). In the low-speed limit this reduces to the familiar E ≈ mc² + ½mv² — Newtonian kinetic energy as a tiny correction to the dominant rest-energy term.
The most direct experimental signature is in nuclear physics. Weigh the constituents of a deuterium nucleus (proton + neutron) separately, then weigh the bound deuteron: the deuteron is lighter by a mass defect of ~2.2 MeV/c², the binding energy. The same accounting balances every fusion reaction in stars, every fission reaction in reactors, every particle creation in colliders, and every annihilation event in detectors. It is one of the most stringently tested relations in physics.