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→What the Equation Means: More preliminaries.
::Total energy (kinetic + potential) is always conserved.
::Total energy (kinetic + potential) is always conserved.
Kinetic energy is the obvious kind, the energy of motion. It's the energy of a thrown baseball.
Radiation (for example, light) also counts as kinetic energy—the motion of photons. Light carries force and momentum. The force carried by light is not as obvious as the force of a thrown baseball, but it is there. The force of sunlight has been proposed for long-term space travel. It is also the force that causes the [[Pioneer anomaly]] and the force that makes a comet's tail stream away from the Sun.
Potential energy is the other kind—"hidden" energy. It's what is needed to make the principle of conservation of energy work. That is, when kinetic energy seems to come into existence, it's because potential energy was converted into kinetic energy. The wound-up spring of a clock has potential energy, that runs down over time, being converted into the ticking sound. A battery has potential energy that runs down when it provides electricity to make things move. Various chemical substances have characteristic amounts of potential energy, that may be converted to or from kinetic energy when chemical reactions occur. For example, Sodium and Chlorine have more potential energy than Sodium Chloride. Explosives have more potential energy that their constituent atoms. Radioactive atoms have more potential energy than their "daughter" atoms.
Hundreds of years of research by chemists (and, before that, the alchemists) worked out the potential energies that are characteristic of various substances, and that the potential and kinetic energies are accurately converted from one to the other, leading to the principle of conservation of total energy.
An interesting fact is that, normally, one considers only ''changes'' in potential energy; one doesn't need an absolute scale. A rock at the top of a hill has more potential energy than after it rolls to the bottom of the hill, but the energy at the bottom isn't necessarily zero. We could dig a hole and let it roll down farther, with its energy going negative. Only changes matter. Now it turns out that, once one accepts the implications of E=mc², one ''could'' assign an absolute potential energy to something—its mass times c², and changes in potential emergy would work out correctly because of the mass changes. But that isn't necessary, and, in any case, it would require accepting E=mc² and would therefore be getting ahead of the story.
==History of Experimental Verification==
==History of Experimental Verification==