What does E = mc² actually say?

E = mc² says that mass and energy are two faces of the same thing: any object has an energy locked in its mass, and energy that stays with an object adds to its mass. Mass–energy equivalence is the relationship between mass and energy in a system's rest frame, and the two differ only by a multiplicative constant, the speed of light squared, and the units. Because the speed of light is large and squared, a small amount of mass corresponds to an enormous amount of energy.

Here is the surprise: Einstein didn't write E = mc² in his famous 1905 paper. That paper states that if a body gives off energy L by emitting light, its mass diminishes by L divided by c². He published the equation with a lowercase c in 1907. And he wasn't alone in linking energy and mass: earlier authors had done so too, though they thought the energy that contributes to mass came only from electromagnetic fields.

What does it mean in practice? All energy that travels with an object adds to its mass. Imagine a box of perfect mirrors with light bouncing inside: the individually massless photons add mass equal to their energy divided by c². Warm up the old platinum–iridium kilogram standard by 1 °C and its mass changes by 1.5 picograms. A water molecule weighs a little less than its separate atoms, and a stick of dynamite in theory weighs slightly more than the fragments after the explosion.

The most dramatic example is Trinity and Nagasaki. The bomb yielded 21 kilotons of TNT; about 1 kg of its roughly 6.15 kg of plutonium fissioned into lighter elements totalling almost exactly one gram less. The radiation and kinetic energy released in the explosion carried the missing gram of mass.