On the Mechanical Origin of Inertia and Gravity: A Heuristic Model Based on Extended Vibrating Shell Structures

The physical origin of the equivalence between inertial and gravitational mass remains one of the fundamental open questions in classical physics. This paper proposes a heuristic mechanical model wherein elementary particles are conceptualized not as dimensionless points, but as spatially extended structures composed of concentric, vibrating spherical shells arisingfrom a nonlinear scalar field. Within this framework, inertia is derived as the active structural resistance of these shells to deformation during acceleration. Conversely, gravitation emerges as a passive topological tendency of overlapping shell systems to restore asymptotic concentricity to minimize energy. We demonstrate that Newton’s inverse-square law (1/r²) arises naturally as a geometric consequence of the radial dilution of shell density. Furthermore, the model addresses historical optical paradoxes by postulating a selective drag mechanism: the spherical geometry implies that while radial interactions are significant, tangential drag is negligible. This constraint offers a consistent interpretation of both the null result of the Michelson-Morley experiment and the observation of Stellar Aberration, without invoking an absolute static ether. Although the model is a classical approximation, it provides a coherent derivation of the Equivalence Principle, suggesting that inertia andgravity are dual manifestations of a single underlying structural dynamic. Keywords: Inertia, Gravity, Shell Model, Classical Field Theory, Equivalence Principle.