This paper serves as the standing public summary of the Relational Field corpus, introducing the universal coherence law and its continuity form. It bridges empirical phenomena and mathematical proofs presented in RFT-2 and RGT-2.
In standard quantum mechanics, the factor is introduced to produce unitary, oscillatory time evolution. In Relational Field Theory (RFT), acquires a physical meaning: it is the generator of reversible relational coherence. Starting from the universal coherence law , we isolate the phase-preserving regime and show with . The wavefunction and Schrödinger dynamics follow directly, without additional postulates. This reframes as coherence preservation (orthogonal to amplitude flow), unifying classical decay and quantum phase rotation under a single relational principle.
This paper forms part of the Relational Field Theory Technical Note Series (0.1–0.3), mapping the continuum from ontological boundary to measurable coherence density. This work extends Notes 0.1–0.2, completing the ontological-to-measurable mapping of Relational Field Theory (RFT). It introduces a relational coherence density metric, ρc = Rc(local) Rc(univ) , bridging micro-coherence (quantum behavior) and macro-coherence (gravitational/cosmological structure). Singularities at ρc → 0 (undefined variation, see Note 0.1) and ρc → ∞ (divergent stability, see Note 0.2) frame this metric, unifying emergent phenomena—quantum decoherence to cosmic acceleration—within a testable ontology for physical transitions Provenance: Originally published on Zenodo (Oct 2025). 10.5281/zenodo.17400900
Relational Field Theory (RFT) models quantum computing as emergent coherence dynamics, reframing qubits, entanglement, and decoherence as phenomena of residue fields 𝑅𝑐 (𝑥, 𝑡). Unlike conventional hardware-dependent approaches, RFT offers a complementary perspective, suggesting coherence stabilization via minimal 𝜆(𝑥, 𝑡), potentially easing environmental constraints. Qubit states and entanglement arise from 𝑅𝑐 (𝑥, 𝑡) configurations, while decoherence is expressed as residue field decay via 𝜆(𝑥, 𝑡). This framework complements existing quantum architectures and proposes testable alternatives to current hardware limits. We predict measurable residue anomalies in Bose-Einstein condensates (BECs) (Δ𝑅𝑐 = (1.0 ± 0.2) × 1029 J/m3) and potential signatures in hybrid quantum-classical systems, offering a roadmap for testing RFT’s relevance to quantum information processing. We invite experimental scrutiny to explore whether coherence dynamics can unify quantum computing, thermodynamics, and cosmology under a single framework Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16790423
This document presents the formal mathematical axiomization of Relational Field Theory (RFT), establishing a single ontological primitive— the bounded scalar coherence field —and deriving the self-referential domain constraint .The Axiom Sheet (A1–A9) formalizes the Kernel identity, coherence evolution equation, domain threshold conditions, Genesis principle, and measurement-as-locking interpretation. A second section provides representative derived theorems showing how known physical laws emerge as limiting behaviors of and , including: Schrödinger equation as phase-locked Kernel dynamics Newtonian mechanics as low-curvature Rc trajectories General relativity as effective curvature geometry of Rc Maxwell/gauge structure as coherence-preserving invariants Thermodynamics as entropy of coherence loss Absence of physical singularities from Rc-threshold constraints This document serves as the foundational formal layer for the full RFT corpus, establishing the axiomatic base from which all subsequent proofs and derivations follow.