On the origin of the inertia: The modified Newtonian dynamics theory

It is shown that the identity between inertial mass and gravitational mass is an assumption to establish the equivalence principle. In the context of Sciama’s inertia theory, the identity between the inertial mass and the gravitational mass is discussed and a certain condition which must be experimentally satisfied is given. The inertial force proposed by Sciama, in a simple case, is derived from Assis’ inertia theory based in the introduction of a Weber type force. The origin of the inertial force is totally justified taking into account that the Weber force is, in fact, an approximation of a simple retarded potential, see [Giné J. On the origin of the anomalous precession of Mercury’s perihelion. Chaos, Solitons & Fractals 2008;38(4): 1004-10. Giné J. On the origin of deflection of the light. Chaos, Solitons & Fractals 2008;35(1):1–6]. The way how the inertial forces are also derived from some solutions of the general relativistic equations is presented. We wonder whether the theory of inertia of Assis is included in the framework the General Relativity. In the context of the inertia developed in the present paper, we establish the relation between the constant acceleration a0, that appears in the classical modified Newtonian dynamics (MOND) theory, with the Hubble constant H0, i.e. a0≈cH0.