Scaling and the Virial Theorem in Mechanics and Action-at-a-Distance Electrodynamics

As a consequence of scale invariance, a conservation law is derived in nonrelativistic mechanics with a homogeneous potential. The virial theorem is an immediate consequence of this conservation law. A slightly different scale transformation is then presented, which yields the same conservation law but which can also be applied to the relativistic Coulomb problem. Finally, both the conservation law and the virial theorem are derived for relativistic two-body theory in the Wheeler-Feynman formalism, where they provide a generalization of the expression for the energy of a two-body system with circular orbits.