Dynamical Consequences and Quantum Manifestation: Coherence-Dependent Behaviour and the Modified Path Integral under Postulate P1 (Part 2/3)

H.N. van Roon

Published Feb 9, 2026• 0 citations

Abstract

This work is Part 2 of a three‑paper series developing the physical consequences of Postulate P1. Building on the formal framework established in Part 1, this paper develops the dynamical interpretation of quantum behaviour as a direct consequence of representational coherence and structural openness. The analysis introduces the remainder term x and the minimal coherence threshold Cmin⁡, which together determine the transition between classical stability and quantum manifestation.Quantum phenomena—interference, tunneling, superposition, entanglement, and cloud‑chamber tracks—are reinterpreted as expressions of representational multiplicity within an open domain rather than as properties of ontological particles or waves. The paper introduces a modified path‑integral framework in which integration domains are intrinsically incomplete and amplitudes become coherence‑weighted. The classical extremal condition δS=0 is replaced by the structurally mandated condition δS=x, unifying classical and quantum regimes as coherence‑dependent manifestations of the same representational structure.The work further develops the emergence of interaction, symmetry, and conservation laws as coherence‑stability regimes rather than fundamental ontological constraints. Several observational implications are identified, including potential departures from standard quantum mechanics in near‑dissolution, ultra‑low‑coherence, and boundary‑instability regimes. This paper provides the dynamical core of the P1 framework and prepares the way for Part 3, where established physical laws will be derived as limiting cases of maximal coherence.

DOI: 10.5281/zenodo.18566784

Related papers

The Formalism of Domain-Bound Dissolution: Path Integrals and the Emergence of the Cosmological Constant Λ from the P1 Postulate

H.N. van Roon

This work is the first part of a three‑paper series that develops the physical and mathematical consequences of Postulate P1, extending the conceptual architecture established in the six‑paper sequence The Articulation of Postulate P1. Whereas the earlier sequence clarified the ontological and representational foundations of fundamental undefinedness, the present paper initiates the formal continuation of that framework. The central contribution of this paper is a reinterpretation of the variational principle under P1. Because no representational domain can achieve closure, the classical condition δS = 0 cannot hold globally. The Euler–Lagrange equation is therefore reformulated as a boundary formalism in which the extremum condition is replaced by a structural remainder term χ. This term expresses the inherent incompleteness of representation and marks the transition between classical behavior (χ → 0) and quantum behavior (χ ≠ 0). The path‑integral formalism is retained but reinterpreted: its integration domain cannot be ontological under P1, and χ becomes the structural signature of domain‑bound openness. The paper introduces two key structural quantities: the minimal representable coherence Cmin⁡, which defines the threshold of manifestation, and the meta‑structural remainder χ, which expresses the impossibility of representational closure. Their distinction clarifies the emergence of residual constants such as Λ without invoking vacuum energy or physical substrates. The cosmological constant appears as a representational residue of dissolution rather than a dynamical field. This paper establishes the formal and conceptual foundations for the trilogy. Paper 2 will develop the dynamical consequences for quantum systems, and Paper 3 will synthesize the full physical picture, showing how established theories arise as limiting cases of maximal representational coherence.

Feb 5, 20260 citations

Regime Dynamics of Coherence and the Level-1 Foundations of Quantum Phenomena

H.N. van Roon

This paper develops the regime‑based structure of the coherence parameter c(t) as the organising principle of Level‑1 representational physics. Building on the stabilisation criteria and state‑mapping formalism introduced in Paper 12, it identifies three coherence regimes—high‑c, intermediate‑c, and low‑c—and shows how major quantum and relativistic phenomena arise as direct consequences of transitions between these regimes. Decoherence is reformulated as a fundamental representational drift driven by the monotonic decrease of c(t), rather than as an environment‑induced process. Tunneling is reinterpreted as bandwidth exit: a Level‑1 mode becomes evanescent in low‑coherence regions and reappears when stabilisation becomes possible again. Entanglement and Bell violations are described as manifestations of shared Level‑1 modes, whose breakdown under decreasing coherence naturally yields classical correlations. Horizon‑like behaviour emerges as a coherence boundary rather than a geometric surface. The resulting framework unifies decoherence, tunneling, entanglement, Bell inequalities, and horizon phenomena under a single representational principle. Paper 13 thus provides the dynamical bridge between the operational constructions of Paper 12 and the empirical analyses developed in Paper 14.

Apr 4, 20260 citations

Coherence Dynamics and Observable Deviations (Paper 14 in The Articulation of Postulate P1)

H.N. van Roon

Paper 14 develops the quantitative coherence dynamics that follow from the representational framework introduced in Papers 11–13 of The Articulation of Postulate P1. Building on the dissipative generator formulated in Paper 12 and the coherence‑regime structure of Paper 13, this work derives explicit dynamical equations for the bandwidth function c(t). These equations yield closed‑form expressions for coherence drift, decoherence timescales, tunneling corrections, and finite‑time coherence boundaries. The results provide the first operational bridge between Level‑1 representational dynamics and experimentally accessible Level‑2 behaviour. The framework predicts measurable deviations from standard quantum mechanics in regimes where c(t) varies appreciably, including drift‑induced decoherence, coherence‑dependent tunneling suppression, and horizon‑like loss of representability. Paper 14 therefore completes the transition from conceptual reinterpretation to quantitative prediction, preparing the ground for the experimental proposal developed in Paper 15.

Apr 4, 20260 citations

Experimental Signatures of Coherence Dynamics

H.N. van Roon

This paper develops the first experimental test of the representational framework introduced in Papers 1–14. Building on the coherence dynamics derived in Paper 14 and the regime structure established in Paper 13, it identifies a measurable deviation from standard quantum mechanics arising from the coherence‑dependent dissipation rate γ(c)=γ0e−βc. The paper shows that this exponential form is not an arbitrary ansatz but the minimal monotone function compatible with the structural and phenomenological constraints of the framework. Using a superconducting flux‑qubit architecture, the work derives the predicted tunneling suppression, specifies the observable signatures, and identifies the parameter regimes in which the deviation becomes experimentally accessible. The analysis demonstrates robustness under alternative dissipation laws and under controlled environmental noise. With this paper, the representational programme completes its transition from conceptual reinterpretation to empirical testability, providing a concrete experimental pathway for probing the coherence dynamics at the core of Postulate P1.

Apr 4, 20260 citations

Quantum Mechanics: A Relational Redefinition

Denis Bailey

This paper develops a relational framework that reinterprets quantum mechanics as the behavior of a continuous generative field governed by the propagation and resolution of orientation under constraint. In this account, superposition reflects unresolved constraint geometry, collapse arises when constraint stabilizes and forces coherence to resolve, tunneling emerges from the propagation of constrained orientation through regions of elevated constraint density, and entanglement results from shared constraint boundaries that enforce joint coherence resolution across separation. Probability is reframed as coherence‑weighting across unresolved resolution paths, and the classical limit appears when constraint geometry becomes sufficiently stable to produce deterministic updates. The wavefunction is interpreted as a mathematical encoding of coherence across constraint geometry rather than a physical object or epistemic state. This unified mechanism dissolves the conceptual divides between classical, quantum, electromagnetic, and energetic behavior, situating all physical phenomena within a single operator framework grounded in the continuous structure of the relational field. The result is a coherent, mechanism‑level redefinition of quantum mechanics that integrates its core phenomena without invoking discontinuities, intrinsic randomness, or dual ontologies.

Mar 14, 20260 citations

03 - Emergence of Quantum Mechanics and Born Measure from a Coherence-Driven TwoField Discrete Framework

Enrico Ferrero

This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article develops the emergence of Hilbert-space structure and Schrödinger-type effective dynamics from the coherent two-field sector established in Paper 02. The work demonstrates that the global coherence constraints imposed on the discrete informational substrate naturally generate an effective complex representation endowed with linear superposition properties and unitary-preserving evolution. The analysis shows that the two-component coherent sector admits a mathematically stable reformulation equivalent to a Hilbert-space structure, and that the effective evolution of the coherent amplitudes leads to a Schrödinger-type dynamical equation without introducing quantum mechanics as an initial assumption. The article further derives the probabilistic interpretation associated with the effective amplitudes and clarifies how quantum-like statistical behavior emerges from the internal coherence conditions of the underlying discrete system. No quantum postulates are assumed at the foundational level. The purpose of the article is to demonstrate that the formal structures associated with quantum mechanics can emerge as effective consequences of coherence-preserving informational dynamics. The article does not assume quantum mechanics as a foundational theory and does not postulate the Hilbert-space formalism a priori. Instead, the work demonstrates that, within the internal hypotheses and coherence constraints of the proposed discrete informational framework, structures mathematically equivalent to Hilbert-space representations and Schrödinger-type evolution can arise as effective emergent descriptions. The purpose of the derivation is therefore not to reproduce standard quantum mechanics by assumption, but to show that quantum-like formal structures may consistently emerge from deeper coherence-preserving informational dynamics.

May 13, 20260 citations