MOND as a transformation between non-inertial reference frames via Sciama's interpretation of Mach's Principle

Abstract

Moderhai Milgrom's Modified Newtonian Dynamics (MOND) correction to Newtonian gravity or inertia is shown to be equivalent to a more fundamental formulation considering a non-inertial local reference frame and the fixed background of the observable universe, in the spirit of Mach's principle. Both Newton's gravitational constant $G\sim c^2/(M_u/R_u)$ and Milgrom's MOND acceleration scale constant $a_0\sim GM_u/R_u^2$ are replaced by two varying, measurable, and cosmological quantities determined by the causally connected mass and size of the universe. They arise from an inverse and an inverse squared distance scalar fields of matter density, respectively. This Machian interpretation of MOND is invariant under global rescalings of mass, length, and time across all regimes and is free from fundamental constants and free parameters, except for the speed of light. Machian MOND satisfies the fundamental consequences of Mach's principle not featured in Newton's and Einstein's theories: the decrease of inertia of a body when masses are removed from its neighborhood, and in the absence of a cosmic background, rotational motion is undefined up to the speed of light. Consequently, Machian MOND provides the necessary limiting behavior to which any phenomenological non-linear theory of modified inertia or gravity that incorporates Mach's principle, in agreement with galaxy rotation curves, should reduce as an effective approximation.