Equivalence of Gravitation and Inertia

Abstract After a review of the Newtonian theory of gravitation in terms of its potential function, this chapter starts the study of general relativity (GR) with the introduction of the equivalence principle (EP). The weak EP (equality of gravitational and inertial masses) was extended by Einstein to the strong EP (equivalence between inertia and gravitation for all interactions). This implies the existence of “local inertial frames” at every spacetime point. In a sufficiently small region, a “local inertial observer” will not sense any gravitational effect. The equivalence of acceleration and gravity means that GR (with physics laws valid in all coordinate systems, including accelerating frames) must necessarily be a theory of gravitation. The strong EP is used to deduce results for gravitational redshift and time dilation, as well as gravitational bending of a light ray. The operation of GPS is shown to depend crucially on relativistic time dilation effects.