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 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.
The Born rule, stating that quantum probabilities are given by the squared modulus of the wavefunction (P = |ψ|2), is a cornerstone of quantum mechanics, yet its origin remains a foundational mystery. Unlike standard interpretations, Relational Field Theory (RFT) derives the Born rule dynamically, without assuming P = |ψ|2 as an axiom. Using the variational principle δ R (1−Rc(t)) dt = 0, we show that the coherence field Rc(t) ∝ |ψ|2 stabilizes quantum states during measurement, yielding squaredamplitude probabilities. Simulations for two- and three-level systems (SNR = 5 to 15 dB) and a numerical example validate this derivation, predicting testable signatures in quantum optics experiments (e.g., entangled photon pairs and trapped ions at CERN’s Quantum Technology Initiative, with time scales of t ≈ 10 s attainable in modern ion trap setups). Building on RFT’s unification of mass, gravity, and fundamental forces (SSRN ID 5343789), this work provides a natural, dynamic foundation for quantum probabilities, with applications to quantum computing error correction via stabilizer codes and collaborative opportunities at CERN. Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16789624
Bell inequalities demonstrate the nonlocality of quantum mechanics by showing that quantum correlations violate classical limits, ruling out local hidden variables. Relational Field Theory (RFT), a proposed Theory of Everything (TOE) unifying quantum mechanics, general relativity, and biophysics [2], reframes these inequalities as coherence-driven phenomena, where the coherence field Rc(t), governed by δ R (1 − Rc(t)) dt = 0, modulates non-local correlations through relational interactions. Unlike standard quantum mechanics, which attributes nonlocality to entangled wavefunctions, RFT derives it from Rc(t) dynamics with thermodynamic dependencies on entropy and temperature. Simulations (SNR = 5 to 15 dB) using superconducting nanowire single-photon detectors (SNSPDs) at CERN’s Quantum Technology Initiative suggest detectable signatures, such as coherence decay tied to entropy. Building on RFT’s derivation of the Born rule [7], unification of complementarity and sum-over-histories [8], comparison to objective collapse theories [9], and Heisenberg uncertainty [10], this work positions RFT as a transformative framework for quantum foundations, with applications to entanglement-based quantum computing. Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16789494
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.
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.
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
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