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Logic Field Theory: Deriving Quantum Field Theory from the Three Fundamental Laws of Logic

Year: 2025
Type: article
Abstract: We present Logic Field Theory (LFT), a framework deriving quantum field theory from the Three Fundamental Laws of Logic without assuming physical postulates. Starting from Identity, Non-Contradiction, and Excluded Middle, we show that quantum mechanics emerges as the unique mathematical structure consistent with logical coherence. KEY RESULTS:- Necessity of complex amplitudes over real or quaternionic alternatives- Unique emergence of the U(1)×SU(2)×SU(3) gauge structure - Derivation of exactly three fermion generations- The Born rule as a theorem rather than postulate- Resolution of the measurement problem through logical strain dynamics CRITICAL PREDICTION: LFT predicts decoherence scaling as τ_D ∝ ξ² (positive exponent) versus standard quantum mechanics' τ_D ∝ ξ⁻¹ (negative exponent), enabling decisive experimental validation. This opposite-sign prediction provides an unambiguous test distinguishing LFT from standard QM. METHODOLOGY: All core derivations (D01-D06) are formally verified in Lean 4. The mathematical chain proceeds from graph-theoretic admissibility through complex necessity, gauge emergence, Born rule derivation, and strain dynamics to concrete experimental predictions. EXPERIMENTAL PROTOCOLS: Section 7 details measurement procedures across six orders of magnitude in coherence length (10⁻¹⁰ to 10⁻⁵ m), with expected precision Δ(slope) < 0.1 achievable with 10⁴ measurements. REPOSITORY: Complete theory documentation, mathematical derivations, and Lean proofs available at https://github.com/jdlongmire/LFT_GEN_19_LEAN STATUS: Independent research, no institutional funding. Paper presents testable predictions for near-term experimental validation. LICENSE: Theory documentation CC BY-NC-SA 4.0; Lean code MIT License.
DOI: 10.5281/zenodo.16884442
Language: English
Open Access status: green
OpenAlex ID: W6969083958
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