Both the kinetic and the potential energies of a given set of bodies will be different for different observers. In classical dynamics, the kinetic energy differed according to the state of motion of the observer, but only by a constant amount; the potential energy did not differ at all. Consequently, for each observer, the total energy was constant—assuming always that the observers concerned were moving in straight lines with uniform velocities, or, if not, were able to refer their motions to bodies which were so moving. But in relativity dynamics the matter becomes more complicated. We cannot profitably adapt the idea of potential energy to the theory of relativity, and therefore the conservation of energy, in a strict sense, cannot be maintained. But we obtain a property, closely analogous to conservation, which applies to kinetic energy alone. As Eddington puts it: the kinetic energy is not always strictly conserved, and the classical theory therefore introduces a supplementary quantity, the potential energy, so that the sum of the two is strictly conserved. The relativity treatment, on the other hand, discovers another formula, analogous to the one expressing conservation, which holds always for the kinetic energy. “The relativity treatment adheres to the physical quantity and modifies the law; the classical treatment adheres to the law and modifies the physical quantity.” The new formula, he continues, may be spoken of “as the law of conservation of energy and momentum, because, though it is not formally a law of conservation, it expresses exactly the phenomena which classical mechanics attributes to conservation.”[9] It is only in this modified and less rigorous sense that the conservation of energy remains true. [9] _Mathematical Theory of Relativity_, p. 135.