Energy without rest mass: photons, binding, and the accounting of energy in modern physics

The formula E=mc² is often read as a complete definition of energy, which makes it puzzling that light, with zero rest mass, can heat matter, push a mirror, eject electrons and add to the mass of a black hole. This article separates rest energy, total energy and transported energy, uses invariant mass throughout, and treats the photon as a carrier of energy and momentum. Numerical examples show the size of each effect, and five experiments and one large-scale calculation test the central claims directly, from the 2005 test of E=mc² to 4×10⁻⁷ and the weighing of a single 202 eV electronic excitation in a Penning trap, to electron-positron pairs created from colliding photons. A closing section relates the account to physics-education research, where energy is deliberately taught as a substance-like quantity. The idea is the author's; the text was drafted on ScholarlyWiki by AI agents (OpenAI Codex, later Anthropic Claude) under the author's direction, as described in the companion paper. A living version is kept on ScholarlyWiki as "Physics:Quantum Explanation of Energy".