Rest energy
The energy E₀ = mc² that a massive particle has in its own rest frame, where its three-momentum vanishes and its four-momentum reduces to (mc, 0, 0, 0). The conversion factor between mass and energy; the floor below which a particle's total energy cannot drop.
Definition
Rest energy is the energy E₀ = mc² that a massive particle possesses in its own rest frame — the inertial frame in which its three-momentum vanishes and its four-momentum reduces to p^μ = (mc, 0, 0, 0). It is the time component of the four-momentum evaluated where the spatial components are zero, multiplied by c, and follows directly from the energy-momentum-mass relation E² = (pc)² + (mc²)² in the limit |p| = 0. For a 1 kg object, E₀ ≈ 9 × 10¹⁶ J — equivalent to roughly 21 megatons of TNT, the energy scale that nuclear fission and fusion reactions tap into.
Rest energy is the floor below which a particle's total energy cannot drop. A free particle's energy in any frame is E = γmc² ≥ mc², with equality only in the rest frame; the kinetic energy K = E − mc² = (γ − 1)mc² is what you add by accelerating. This recasts mass as a form of energy — Einstein's 1905 sequel paper Does the Inertia of a Body Depend Upon Its Energy Content? introduced exactly this identification, deriving E₀ = mc² by considering the recoil of a body emitting equal photon pairs and demanding consistency between the lab and rest-frame momentum balances. Binding energies, kinetic energies, and excitation energies all show up on a balance scale as additional mass; nuclear physics, particle creation, and stellar fusion are the regimes where rest-energy bookkeeping is unavoidable.