Formulation of Particle Mass and Creation Mechanics via the Resilient Thermodynamic Elastic Boundary Theory (RTEBT)

This paper introduces the unified framework of the Resilient Thermodynamic Elastic Boundary Theory (RTEBT), proposing a membrane-centric model of physical reality that addresses fundamental limitations in traditional point-particle and fixed-background quantum field models. Under the RTEBT framework, space is modeled as a 3D elastic boundary embedded within a higher-dimensional ambient space (The Bulk). Elementary particles are formulated not as fundamental solid objects, but as localized, resonant topological wave-knots trapped in specific vibrational modes (Φ) on the elastic matrix. Key theoretical highlights of this work include:1. Elastic Quantum Fields: Space-time is treated as a dynamic, elastic surface overlaid by overlapping quantum energy fields where localized energy build-up induces strain deformations.2. Quantized Energy Tiers & Pair Creation: Particle creation and annihilation (such as electron-positron collisions) are modeled mechanically through quantized energy tier thresholds (Wₙ) and boundary strain limits, explaining radiation loss (photons) and field collapse into cheaper energy tiers.3. Emergent Mass Mechanics: Mass (meff) is demonstrated to be a non-intrinsic property arising from structural drag—the resistance produced as trapped vibrational energy pushes against the surface tension (σ) and extrinsic curvature strain (K) of the spacetime matrix.4. Unified Lagrangian Action (LRTEBT): We present the complete unified Lagrangian incorporating bulk curvature (R), thermodynamic entropy expansion (η(Δ S)), boundary surface tension, extrinsic curvature bending moduli (α, β), and an informational conservation flux (τ ∇_μ I^μ). A formal mathematical proof deriving effective mass (meff) via integration of the stress-energy tensor (T₀₀) over localized elastic boundary deformations is included.