Nuclear and Atomic Physics

   

Quantum-Elastic Geometry: a Nonlinear Substrate Extension for Massive Regimes

Authors: Juan Moreno Borrallo

We present a minimal nonlinear extension of Quantum—Elastic Geometry (QEG), in which a single symmetric deformation tensor (G_{muu}) and its modal projections underpin the effective long-range sectors of gravity, electromagnetism, and thermo-entropic dynamics. The extension accounts for two additional empirical structures—finite-range interactions and hadronic-scale confinement—without introducing new fundamental fields beyond (G_{muu}). Finite range emerges when selected projected modes acquire geometric masses set by the local curvature of the substrate self-interaction potential, (m_X^2 equiv V_X''(0)), yielding Yukawa/Proca-type propagation. In the genuinely nonlinear regime, quartic (and higher) terms in (V(G)) can energetically favor filamentary minima; under suitable variational constraints, this leads to flux-tube configurations with approximately constant tension and an effective linear energy—separation scaling (confinement-like behavior).Crucially, the framework yields an endogenous classification of particle-like excitations: particles are finite-energy, localized eigenmodes or topologically stabilized defects of the elastic vacuum (G_{muu}), carrying quantized action. Under finite-action boundary conditions and a compact order-parameter sector, the Standard Model taxonomy is reorganized as sectors of the physical configuration space: fermions correspond to nontrivial spinorial or holonomy sectors, bosons to topologically trivial transport modes, leptons to elementary globally extendable defects, quarks to fractional defect configurations obstructed from isolated finite-action completion, and hadrons to closed composites in which obstruction classes cancel. The same construction yields a natural interpretation of generations as discrete radial excitation levels ((k = 0,1,2,ldots)) around a fixed defect topology—e.g., (k=0 to e), (k=1 to mu), (k=2 to tau)—thereby relating mass hierarchies to the spectral structure of a single underlying defect rather than to distinct fundamental species.

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[v1] 2026-01-22 21:29:20

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