Conservation of energy
It is stated as follows:
- The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system.
Meanwhile, in 1843 Joule independently discovered the law by an experiment, now called the "Joule apparatus", in which a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the gravitational potential energy lost by the weight in descending was equal to the thermal energy (heat) gained by the water by friction with the paddle.
Unfortunately for Mayer, his work was overlooked in favour of Joule's, and Mayer attempted to commit suicide. Later, Mayer's reputation was restored by a sympathetic account in John Tyndall's Heat: A Mode of Motion (1863).
The classical form of the energy conservation law (and in fact the notion of energy in the first place) is directly related (through the corresponding equation of motion) to the force- concept describing the interaction of particles. The latter can be shown to be necessarily instantaneous (i.e. Newtonian) as otherwise one would not be able to define a force objectively, i.e. independent of the state of motion of the observer. One can therefore say that the law of energy conservation does, by definition, only strictly hold for this case of a static interaction of particles, but is not more than an arbitrary ad hoc concept if applied to other situations, in particular those involving light: two light waves can be made to extinguish each other completely if superposed with the correct phase, which proves that a form of energy conservation does not apply here.