A Theory of Inertia Based on Mach’s Principle

Abstract

A non-relativistic theory of inertia based on Mach’s principle is presented as has been envisaged, but not achieved, by Ernst Mach in 1872. The central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element d m to the inertia of a particle m 0 experiencing an acceleration from rest is proportional to cos 2 α , where α is the angle between the line connecting m 0 and d m and the direction of the acceleration. Apsidal precession for planets circling around a central star is not a consequence of this theory, thereby avoiding the prediction of an apsidal precession with the wrong sign as is done by Mach-like theories with isotropic inert mass.