The Vibrational Fabric of Spacetime: A Model for the Emergence of Mass, Inertia, and Quantum Non-Locality

This article presents a unified theoretical framework where the geometry of spacetime, the inertia of matter, and quantum non-locality emerge from a single fundamental substrate: a vibrational network. We model space as a dynamic network of vibrating nodes, its elastic properties calibrated by the fundamental constants \( \hbar \) and \( \mathit{c} \). Mass is not a primitive property but is identified with the energy stored in the deformation of this network. The non-linearity of this medium at high energy allows for the self-trapping of waves into stable structures identified as particles. A reflection-based IN/OUT wave mechanism confers upon these particles an inherently non-local character, providing a mechanical explanation for the violation of Bell's inequalities and the holographic principle. A key result is the formal derivation of the Planck scale \( \ell_P \) and the quantum of action \( \hbar \) from the network's properties. Crucially, we demonstrate how General Relativity emerges from the dynamics of this network as a refractive effect, where energy density variations determine the effective "refractive index" of space, naturally leading to geodesic deviation and curvature. In this model, inertial mass \( m_i \) and gravitational mass \( m_g \) are distinct emergent properties of a shared underlying deformation, linked by the gravitational constant \( G \), which quantifies the network's susceptibility to deformation.