Abstract :
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.
