Seminário do Grupo de Física Teórica

Author: Sofiane Faci

Title: The origin of inertia

Abstract: This work gives the formal derivation of Mach’s principle. Mach had stated that there should be a physical law that relates the motion of the distant stars to the local inertial frame. Or as Einstein put it in a 1923 letter to Mach ”inertia originates in a kind of interaction between bodies”. We show that this ’kind of interaction’ is nothing but the gravitational interaction with the whole Universe. This is done by summing up the gravitational interaction of a given mass m with all masses in the visible Universe. The individual contributions are given by McVittie metric, which gives the solution of a mass particule in an FLRW background. In particular we compute the potential energy and its gradient. As a result we find that the potential energy is equal to the mass energy. Tat is, Einstein’s equation is not intrinsic. The gradient of the potential energy yields inertial forces, such as centrifugal forces. Since forces don’t depend on the reference frame this formula holds in the rest frame of the mass m. Consequently the sum of local focres always compensates the global gravitational force to allow m to be locally at rest. This way Newton’s empirical second law finds its origin. When the mass has a constant vector speed, the gravitational interaction with the Universe yields no force and the problem reduces to Galileo’s.