rest energy

Rest energy is the astonishing idea, buried inside E = m c^2, that an object has energy simply by virtue of having mass — even when it is sitting perfectly still, not moving, not hot, not doing anything. Newtonian physics says a motionless object has zero kinetic energy and that is that. Relativity says no: hidden in its very mass is a vast reservoir of energy, waiting to be released if the mass can be converted.

Precisely: the rest energy of an object is E_0 = m c^2, where m is its mass and c is the speed of light. It is the total relativistic energy E = gamma m c^2 evaluated at rest, where the speed is zero and so gamma = 1. Because c is enormous (3 x 10^8 m/s) and c^2 is enormous squared, even a speck of mass corresponds to a staggering rest energy: the m c^2 of a single gram of anything is about 9 x 10^13 joules, comparable to the energy released by a large conventional explosion. Mass, in other words, is extraordinarily concentrated energy.

You never notice rest energy in daily life because ordinary processes tap only a whisper of it — chemical reactions convert a mass so tiny it is unmeasurable. Nuclear processes are different: fission and fusion turn a small but real fraction of mass into energy, which is why they release millions of times more than burning. The Sun shines by converting about 4 million tonnes of its mass into rest-energy-turned-light every second. Rest energy is the concrete meaning of mass-energy equivalence: mass is not separate from energy; it is one of energy's forms.