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To understand the demonstration, it is necessary to read the whole theory.
Let's consider an object on Earth (Fig. 1). The volume of this object causes a curvature of spacetime which exerts a gravitational force on it of g = 9.81 m.s-2 on the surface of Earth.
Let's now consider the same object accelerated out of any gravitational field. We can represent this object in two different views (fig. 2a and 2b).
In both cases, acceleration a is identical to g, i.e. a = 9.81 m.s-2.
Without any reference, a local observer cannot know if the curvature of spacetime is due to a pressure on the object (fig. 2a) or to its acceleration (fig. 2b). In fact, figures 2a and 2b are identical and depend on where the observer stands, as described in Special Relativity.
- By definition, g = 9.81 m.s-2 (fig. 1) is identical to a = 9.81 m.s-2 (fig. 2a and 2b),
- These examples uses the same object. Therefore, the curvature of spacetime produced by the closed volume of this object is identical,
- From these two points, the "mass effect" produced by these curvatures will be identical
We deduce that the "gravitational mass effect" (fig. 1) is identical to the "inertial mass effect" (fig. 2a or 2b):
Gravitational mass effect
Inertial mass effect