There is substantial evidence that Modified Newtonian Dynamics (MOND) is related to Mach’s principle, as stated in several occasion by Mordehai Milgrom, original author of MOND. The coincidences of MOND’s acceleration scale constant with cosmology, and the fact that MOND can be thought as a modification to Newton’s second law of inertia, motivates a search for the origin of MOND in Mach’s principle, which implies that local dynamics are affected by the mass distribution at large and its motion, and implies that inertia has a gravitational origin.
Moreover, most of the literature built following Mach’s principle implies that the gravitational constant is not fundamental, but a derived parameter following its coincidence in both units and orders of magnitude of G=c^2 / (Mu/Ru) with Mu and Ru the mass and size of the observable universe.
Machian theories of inertia, such as those of Reissner, Schrödinger, Sciama, Treder… etc, also offer a natural explanation for the equivalence principle, instead of being postulated axiomatically as in General Relativity.
Machian MOND: a variable acceleration scale constant in galaxy clusters
MOND predicts galaxy rotation curves but falls short in galaxy clusters. A variable acceleration scale constant in MOND is proposed within a Machian interpretation, which predicts a boost of accelerations in galaxy clusters without the need for new constants or free parameters, in constrast to EMOND. We test the proposed formulation in a toy model and generalize the it by introducing a directionless field as a scalar sum of inverse-squared distance mass contributions. In colaboration with Juan D. Santander.
MOND as a transformation between non-inertial reference frames via Sciama’s interpretation of Mach’s Principle
The motivations to search for Milgrom’s Modified Newtonian Dynamics (MOND) in Mach’s principle are explored from a complete explanation of Mach’s principle related to MOND phenomenology. The Machian MOND approximation is a necessary feature of a theory of modified inertia or modified gravity which incorporates Mach’s principle in agreement with galaxy rotation curves.
On the Unification of Gravity and Inertia in Classical Mechanics
The origin of inertia is explained in non-relativistic classical Lagrangian 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.