Mass-energy equivalence
Einstein's 1905 result E = mc² — that mass and energy are the same physical quantity expressed in different units, with c² as the conversion factor. Binding energies and kinetic energies register on a balance as mass; the foundation of nuclear physics, fusion, fission, and particle production.
Definition
Mass-energy equivalence is the principle E = mc² — that mass m and energy E are the same physical quantity expressed in different units, with c² as the conversion factor. Einstein derived it in his 1905 sequel paper Does the Inertia of a Body Depend Upon Its Energy Content?, the third of the Annus Mirabilis relativity papers, by considering a body that emits equal photons in opposite directions and applying conservation of momentum and energy in two inertial frames. The body loses energy ΔE to radiation, but its mass also drops by ΔE/c² — the mass deficit is the energy carried away. The argument generalises: any system that gains or loses energy gains or loses mass by the same factor 1/c².
The consequences are vast. The ~7 MeV/nucleon binding energy of iron-56 is exactly the mass deficit between iron and the sum of its constituent nucleons; tapping it via fusion (lighter nuclei combining) or fission (heavier nuclei splitting) releases energy converted from rest mass at megaton scales. Particle accelerators routinely create new massive particles by slamming high-energy beams together — the rest mass of the new particles comes from the kinetic energy of the colliders, balanced by four-momentum conservation. Stars run on hydrogen-to-helium fusion, converting roughly 0.7% of their fuel mass into radiation. The Compton effect, pair production, and threshold-energy calculations are all bookkeeping exercises in mass-energy equivalence: the four-momentum invariant p² = m²c² is the central scalar that organises every collision calculation in modern physics.