Mach’s principle

History of modified inertia

Modified theories of inertia attempt to explain inertial forces as a result of an interaction of gravitational origin through Mach’s principle. Additionally, gravitation can arise naturally, as well as the equivalence principle and the gravitational constant. We review Mach, Reissner, Schrödinger, Sciama, Treder, Barbour, Lynden-Bell and Katz,… and many more authors with different approaches, to define the status of modified inertia theories.

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Mach’s principle: introduction to MOND and modified inertia

Mach’s principle deeply influenced Einstein’s General Relativity, and following attempts to extend gravity theories. It’s implications and ideas are explained in relation to relative acceleration, inertial forces, Newton’s bucket of water experiment, and the gravitational constant, as an introduction to theories of modified inertia such as MOND.

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Modified gravity and inertia: Mach’s principle, MOND, origin of inertia, origin of the gravitational constant

The lack of a phenomenological explanation of Modified Newtonian Dynamics and its falling short in galaxy clusters suggest that MOND is an approximation of a more fundamental theory of modified gravity or inertia. There are strong indications that point towards a Machian origin of MOND, providing an explanation for the apparent dark matter effects in galaxies. The origin of inertia and a derivation of the gravitational constant are also related to these problems in gravitation.

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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.

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