Modified Newtonian Dynamics (MOND) can be interpreted as a realization of Mach’s principle, by which inertia decreases when masses are removed from the neighbourhood of a body. By considering the mass distribution inside the observable radius of the universe (our past light cone), MOND can be reformulated without fundamental constants except for the speed of light. This is achieved through Sciama’s interpretation of the gravitational constant as a derived parameter from the matter field potential of the universe, and by identifiying MOND’s acceleration scale with the scalar inverse-squared distance sum of masses or with the average receding acceleration of such mass distribution at large in the universe. Modified theories of inertia can explain inertia phenomenologically as arising from an interaction with the rest of the universe, in which the equivalence principle and gravity follow naturally by considering relative quantities as required by Mach’s principle. A theory of modified inertia à la Mach which explains dark matter in galaxy rotation curves should approximate to this Machian MOND formulation or to a similar and equivalent one.
MOND as a transformation between non-inertial reference frames via Sciama’s interpretation of Mach’s Principle
Milgrom’s Modified Newtonian Dynamics (MOND) correction to Newtonian gravity is shown to be equivalent to a more fundamental transformation between a non-inertial local reference frame and the fixed background of the observable universe, complying with Mach’s principle. This Machian MOND approximation is a necessary feature of a nonlinear phenomenological theory of modified inertia or modified gravity which incorporates Mach’s principle in agreement with galaxy rotation curves.
A Complete Classical Framework for Unifying Gravity and Inertia
Inertia is explained in non-relativistic classical mechanics by a unified theory of gravity and inertia based on the free-inertia mechanics of H. Jürgen Treder. It implements Mach’s principle and inertia having a gravitational origin without anisotropic inertial mass. Inertia arises from a velocity-dependent part of the gravitational potential. The weak equivalence principle, the gravitational constant, inertial mass and inertial forces are derived naturally. By Dennis Braun.