A unifying physically meaningful relativistic action

Abstract

Abstract The motion of an object under the influence of force fields and/or media is described by means of a world-line with least action in its influenced spacetime. For any spacetime point x and a four-vector u, measured in the frame of an inertial observer, a unifying and physically meaningful action function L(x, u) generating the action is defined. To ensure independence of the observer and of the parametrization on the world-line, L(x, u) must be Lorentz invariant and positive homogeneous of order 1 in u. The simplest such L(x, u) depends on two four-potentials. In most cases, these potentials can be defined directly from the sources of the fields without the need for field equations. The unified dynamics equation resulting from this action, properly describes the motion in any electromagnetic field, in any static gravitational field, in a combined electromagnetic and gravitational field, as well as the propagation of light and charges in isotropic media.