This paper has shown that within the Relativistic Space-Time Domain D₁ inertial and gravitational mass cannot be considered to be the same. However, the equality of inertial and gravitational mass has been stated in the literature to be fundamentally important to the theory of gravitation as represented by the General Theory. An examination of a proposed proof is therefore necessary. The proof presented in [3] is therefore reviewed below.

To perform this critique it is first necessary to establish an adequate definition of both parameters. This is best done by repeating the definitions found in [3].

"Inertial mass is the measure of the ability of a body to resist acceleration. For a given force the acceleration is inversely proportional to the inertial mass."

"Gravitational mass is the measure of the ability of a body to produce a gravitational field and to suffer the action of such a field. In a given field the force experienced by a body is proportional to the gravitational mass."

With regard to the latter definition, no opinion is made at this point on the first part of this definition, i.e. that concerning the ability of a body to produce a gravitational field. This critique is only concerned with the latter part of the definition.

The proposed proof of the equality of these two definitions is then developed in [3] as follows, (the nomenclature used here is as per the Reference).

Via the assertion that a gravitational field can be defined by a Newtonian Potential, the force experienced by a gravitating mass is then stated to be

(A1)

where U is the Newtonian Potential, (gM/r), and m_gr the gravitational mass of the gravitating body.

Using Newton's laws of motion it is also stated that

(A2)

where is the acceleration and m_in the inertial mass.

The forces in (A1) and (A2) are then assumed to be equal so that it is then stated that

(A3)

and from this, Galileo's law is used to equate m_in and m_gr.

The use of (A2) involves an assumption that has not been stated. That assumption is that Newton's laws of motion are applicable to gravitationally induced motion in exactly the same manner as they are in artificially produced motion. This assumption concerns the manner in which each force is applied. Because the gravitational effect is a field effect the force involved in the motion is, as has been stated before, generated within the body and effects each and every atom simultaneously and equally. The only stress on the molecular and atomic bonds of the material is due to the very small differences in position of each atom within the field. This is considered to be the only way that the force generated can be proportional to the energy, (or gravitational), mass of the body.

On the other hand, in artificially produced motion the force is applied over an area of surface contact. It is transmitted to the rest of the fabric of the body through its molecular and atomic bonds. The law that governs this latter type of motion was developed using mechanical experimentation in which the test force was applied in just this way. Both constant and variable forces may have been used but the inertial mass of the test body would have remained a function of its rest mass and acquired velocity. Although the experiments were conducted with great accuracy they would not have been able to distinguish between the various mass values that are applicable in such experiments, i.e. rest, energy and inertial mass. Consequently, the law as originally constructed would only have referred to the mass of the body without any defining parameter. However, since its discovery, (A2) has been theoretically confirmed as correct for artificially induced motion, i.e. as in [2]. The same however, cannot be said for purely gravitationally induced motion. Once again, despite the accuracy and precision with which the mechanical experiments to study gravity were performed, they would not have been able to distinguish between the mass values involved and, would have resulted in the same conclusion regarding the laws of gravitational motion, as for artificial. However, a theoretical or otherwise proof of the applicability of (A2) to gravitational motion, has not since been produced. It is therefore considered questionable whether the use of (A2) is valid in the derivation of a proof of the equality of inertial and gravitational mass, especially where the variability of the parameters concerned is on a relativistic level.

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