Emergent Gravity from Discrete Quantum-Mass Cells: A Tension Field Approach - Lattice Tension Theory

This work proposes a discrete model of spacetime in which the fundamental structure of the universe consists of elementary spatial units referred to as quantum cells, characterized by dimensions on the Planck-length scale. In this framework, spatial dimensionality emerges from the arrangement of these cells, while time arises as a dynamical parameter associated with the presence and interaction of matter.

Matter is interpreted as stable topological configurations formed by finite collections of quantum cells. Gravitational phenomena are described as the macroscopic manifestation of stress propagation within the quantum-cell network. This idea is formalized through Lattice Tension Theory (LTT), where the gravitational field is represented by a tension field T(r,t)T(\mathbf{r}, t)T(r,t) evolving within the discrete medium.

The dynamics of this field are described by a nonlinear wave equation incorporating both propagation and density-dependent coupling within the lattice. In this formulation, gravitational interaction emerges from collective tension gradients rather than from fundamental mass sources.

Preliminary analytical and numerical considerations indicate that the model can reproduce several qualitative gravitational phenomena, including Newtonian behavior at small scales, approximately flat galactic rotation curves without the introduction of dark matter, gravitational lensing effects, and propagating tension disturbances analogous to gravitational waves. Black-hole–like states arise when lattice tension exceeds a critical threshold.

Although the framework remains exploratory, it provides a conceptually simple and potentially testable approach to emergent gravity in a discretized spacetime structure. Several open problems and possible observational consequences are outlined for further investigation.