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

This paper proposes Lattice Tension Theory (LTT), a robust alternative to General Relativity that models spacetime as a discrete, elastic lattice of quantum-mass cells at the Planck scale. Moving away from the geometric curvature paradigm, LTT describes gravity as the macroscopic manifestation of a scalar tension field (T) within this physical lattice. Key Innovations and Theoretical Advantages: Discrete Architecture: Replaces the smooth manifold with a cubic quantum cell framework, providing a natural bridge between discrete micro-structures and macroscopic gravitational dynamics. Resolution of Singularities: Effectively eliminates the infinite densities found in black holes through a "lattice rupture" mechanism. By defining a physical threshold (T₂ₑ₈ₓ), the theory prevents mathematical singularities and replaces them with a finite, high-energy state. Dark Matter Alternative: LTT accounts for flat galactic rotation curves and the Baryonic Tully-Fisher Relation (BTFR) as a direct consequence of the vacuum solution of the master equation. This provides a self-contained explanation for galactic dynamics without requiring unobserved dark matter particles. Empirical Validation: The framework has been cross-verified against 14 independent observational and laboratory benchmarks, including the Cassini spacecraft radio link experiment, gravitational wave observations (GW170817), and pulsar timing (Hulse-Taylor). Distinctive Prediction: Unlike General Relativity, LTT predicts a photon orbit radius of exactly r = 2GM/c². This provides a clear, discriminating test for the theory through upcoming high-resolution imaging by the Next Generation Event Horizon Telescope (ngEHT). This research offers a unified mathematical apparatus that addresses long-standing cosmological anomalies while maintaining strict consistency with established relativistic observations.