Photon–Lattice Δf Mechanism (USP Field Theory) Deterministic Resonant Quantum Mechanics and the Geometry of Photon–Lattice Interaction

This paper introduces Resonant Quantum Mechanics (RQM1) — the first deterministic framework replacing probabilistic quantum models with Δf resonance geometry. Every photon–matter interaction is redefined as a geometric Δf exchange between field tension and lattice oscillation capacity (C_osc). Reflection, absorption, and emission arise from resonance thresholds, not probability. RQM1 unifies previous USP Field Theory milestones: msf:44696 (Double-Slit) — Photon as secondary emission of excess Δf tension msf:45706 (Reversal Genesis) — Collapse-to-release transition via Δf₍crit₎ msf:45708 (Resonant π Geometry) — Curvature-linked emission geometry msf:45711 (Resonant Misinterpretation) — Mathematical harmony as phase balance The included Figure 1 visualizes the photon–lattice mechanism: the incoming Δf photon field interacts with the lattice, storing or releasing energy based on Δf thresholds. This work forms the foundation of the Resonant Quantum Mechanics (RQM) series in USP Field Theory. Note: In earlier USP documents, this concept was introduced under the term “Resonance Quantized Model.” It has now evolved into “Resonant Quantum Mechanics (RQM)” to align with advanced publications and better reflect its broader deterministic framework within USP Field Theory. 🔹 Harmonization Note (DOI Integration) This publication is harmonized with the experimental foundation established in USP Field Theory – Temperature & Resonance: Testable Experiments (2025), DOI: 10.5281/zenodo.16788099. That work defines the laboratory verification path for Δf relaxation, η-controlled transparency, and resonant thermal emission, providing the testable framework for all Δf-based temperature, energy, and transparency laws across the USP Field Theory series (msf: 45706 – 45714).