Free Fall as a Response to a Spatial Gradient in the Speed of Light

<div xmlns="http://www.tei-c.org/ns/1.0"> In this paper, we demonstrate that the free-fall acceleration induced by a mass originates from a spatial gradient in the speed of light, resulting from the contracted space surrounding the mass. This gradient is sensed by the elementary particles composing free-falling bodies, compelling them to accelerate toward the mass. We have previously shown that gravity arises from contracted -not curved -space around a mass [1], and that gravitation slows light and contracts measuring rods, thereby ensuring the invariance of the speed of light for all local observers [2]. Building upon our framework on the essence of inertia-where mass is understood as a practical term describing the resistance of a body to acceleration [3] -we conclude that a mass generates a spatial gradient in the speed of light. This gradient, interacting with the internal structure of elementary particles, drives the phenomenon of free fall. What has traditionally been interpreted as an attractive gravitational force between masses is redefined here as the dynamical response of particles to spatial variations in light speed. From this principle, we derive Newton's law of gravitation and rigorously establish the equivalence of gravitational and inertial mass. </div>