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Coherence Fields and the Uncertainty Principle: A Stability Correspondence

Clinton Svancara

Published Jan 1, 2026• 0 citations
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Abstract

This paper investigates whether the coherence field Rc(t) of Relational Field Theory (RFT) admits a stability correspondence that is consistent with the form of the uncertainty principle. We start from the RFT evolution equation for Rc(t), identify uncertainty limits with fluctuations in coherence under measurement interactions, and show the correspondence in the high-stability limit. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the coherence dynamics reproduce the familiar uncertainty relation. No broader interpretive or foundational claims are made.

DOI
10.17605/osf.io/mp4tc

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This paper investigates whether the coherence field Rc(t) of Relational Field Theory (RFT) admits a stability correspondence that is consistent with the form of the uncertainty principle. We start from the RFT evolution equation for Rc(t), identify uncertainty limits with fluctuations in coherence under measurement interactions, and show the correspondence in the high-stability limit. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the coherence dynamics reproduce the familiar uncertainty relation. No broader interpretive or foundational claims are made.
This paper investigates whether the coherence field Rc(x, t) of Relational Field Theory (RFT) admits a linearized phase-coherent regime that is consistent with the form of the Schr¨odinger equation. We start from the RFT evolution equation for Rc, introduce the phase-coherent condition Rc = |Rc|eiϕ(x,t), perform a linearization around a stable coherence well, and derive the correspondence to the Schr¨odinger form. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the linearised dynamics reproduce the familiar equation. No broader interpretive or foundational claims are made.
This paper investigates whether the coherence field Rc(x, t) of Relational Field Theory (RFT) admits a phase-mode correspondence that is consistent with the gauge structure of the Maxwell equations. We start from the RFT evolution equation for Rc, note its global U(1) phase invariance, promote the symmetry to a local transformation, and derive the resulting vector field and field-strength tensor. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the phase mode reproduces the familiar Maxwell form. No broader interpretive or foundational claims are made.
This paper investigates whether the coherence field Rc(x, t) of Relational Field Theory (RFT) admits a correspondence whose trajectory summation is consistent with the path-integral formulation of quantum electrodynamics. We start from the RFT evolution equation for Rc, consider phase-coherent paths, and derive the effective action weighting. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the correspondence reproduces the familiar path-integral structure. No broader interpretive or foundational claims are made.
This paper reframes the Heisenberg uncertainty principle as a coherence-driven stability limit in Relational Field Theory (RFT), governed by the variational constraint \delta\int(1-R_c(t))dt=0. Uncertainty emerges as a trade-off imposed by coherence dynamics and measurement interaction, with thermodynamic dependence through entropy and temperature modulation. The work builds on RFT’s coherence-based derivation of the Born rule (OSF DOI: 10.17605/OSF.IO/UC6A3) and proposes falsifiable experimental signatures in modern quantum optics and ion-trap-class measurement platforms.
This paper shows that the core structure of Relational Field Theory (RFT) admits a consistent variational formulation under the same minimal constraints developed in the preceding derivation. Starting from a relational action constructed to satisfy closure and measurability requirements, the operational coherence functional ( R_c = \alpha \cdot \beta \cdot \gamma ) and the persistence law ( \frac{dR_c}{dt} = -\lambda R_c + F_{int} ) re-emerge as the minimal forms compatible with collapse invariance, relational closure, measurability, and stability. The work does not claim an independent first-principles derivation; rather, it demonstrates that the established RFT core is internally consistent with a least-action-like relational structure. This strengthens the foundational coherence of the framework and provides a bridge toward deeper mathematical and geometric extensions.
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