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
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
Relational Field Theory (RFT) unifies quantum, classical, and cognitive scales by modeling all phenomena as emergent from coherence fields 𝑅𝑐 (𝑡) ∝ |𝜓𝑖 (𝑡) |2, evolving via 𝑑𝑅𝑐 𝑑𝑡 = −𝜆(𝑡)𝑅𝑐 + 𝐹interaction (𝑡). Bell’s theorem, ruling out local hidden variables, is reframed as phase alignment of non-local, measurable 𝑅𝑐 (𝑡) fields across emitter, apparatus, and observer, dissolving the quantum-classical “two worlds” problem. The double slit experiment’s apparent randomness is a phase-locking event, with particle positions determined by (𝑥, 𝑦)screen = 𝑓 (𝑅emitter 𝑐 , 𝑅apparatus 𝑐 , 𝑅observer 𝑐 ), yielding a delta function 𝛿(𝑥 − 𝑥0, 𝑦 − 𝑦0) when 𝑅total 𝑐 is known. Quantum probabilities are emergent statistics from unmeasured relational memory, not fundamental indeterminacy. Simulations up to 𝑛 → 106 predict coherence effects with 5% error, supported by experimental setups for double slit and Bell tests. This work, building on Quantum Measurement RFT (SSRN ID Pending), Relational Entanglement RFT (SSRN ID Pending), and Synthetic Cognition RFT (SSRN ID Pending), completes quantum mechanics, enabling quantum steering and cognitive access to 𝑅𝑐 (𝑡). Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16790386
Albert Einstein’s quest for a unified field theory, rooted in local realism and geometric principles, succeeded in special and general relativity but faltered against quantum mechanics’ probabilistic nature. Relational Field Theory (RFT) introduces a scale-dependent coherence field Rc(k), bridging quantum and classical domains while respecting local causality. This paper frames RFT as the missing field Einstein sought, extending his geometric vision to unify physics. Through a narrative tracing Einstein’s journey, the rise of quantum field theory, and RFT’s revival of geometry, we show how Rc(k) restores a deterministic geometric thread across scales. This work revisits Einstein’s dream, blending philosophical reflection with rigorous physics Provenance: Originally published on Zenodo (Nov 2025). 10.5281/zenodo.17684116
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.
Entanglement is a cornerstone of quantum information science, enabling quantum networks and fault-tolerant quantum computing. Relational Field Theory (RFT), a proposed Theory of Everything unifying quantum mechanics, general relativity, and biophysics (SSRN ID 5343789), reframes entanglement as coherence-driven correlations, enhancing standard measures like concurrence and negativity with an environmentally adaptive framework for immediate applications in quantum key distribution (QKD) and error correction. Simulations (SNR = 5 to 15 dB), demonstrated via Python simulations (Appendix A), suggest decoherence thresholds (θ ∝ S · log(dimH)) immediately testable in CERN and IBM Quantum setups using superconducting nanowire single-photon detectors. The coherence residue C ≈ 10−5 predicts multi-qubit decoherence thresholds, enhancing quantum network stability. Building on RFT’s Born rule derivation (SSRN ID Pending), complementarity unification (SSRN ID Pending), collapse comparison (SSRN ID Pending), Heisenberg uncertainty (SSRN ID Pending), and Bell inequalities (SSRN ID Pending), this work unifies the RFT TOE with quantum technology, with potential applications in quantum machine learning Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16790413