conservation of energy

Conservation of energy is one of the deepest statements classical physics makes about the world. In an isolated system — one that exchanges no energy with its surroundings — the total of all forms of energy, however classified (kinetic, gravitational, elastic, chemical, thermal, electromagnetic), stays constant as the system evolves. Change the form and you can sometimes do something useful; change the total, and you will never succeed.

The law was not obvious. It emerged over a century of work: from Leibniz's 1686 vis viva, through Émilie du Châtelet's 1740 experiments, Joseph Black's latent heat (1760s), Mayer and Joule's mechanical equivalent of heat in the 1840s, to Helmholtz's 1847 synthesis Über die Erhaltung der Kraft, which united the various energies of classical physics into a single conserved currency. It is now recognised as a consequence, via Noether's theorem, of the fact that the laws of physics are invariant under translations in time.

In macroscopic terms it means every joule that seems to "disappear" can be accounted for elsewhere — in thermal motion, in sound, in chemical bonds, in radiation. A hockey puck's lost kinetic energy is thermal jiggling of the ice; a falling skydiver's energy becomes turbulent air; an exploding stick of dynamite's chemical energy becomes heat, sound, and expanding gas kinetic energy. The books always balance.