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Operationalisation of Stabilisation, State Mappings and Non-Unitary Dynamics

H.N. van Roon

Published Apr 1, 2026• 0 citations
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Abstract

Paper 12 in the series “The Articulation of Postulate P1”. This paper operationalises stabilisation within the P1 framework by introducing measurable criteria for the coherence density c, constructing the parametric state mapping c↦ρ(c), and deriving the c-dependent dissipative generator Λdiss(c). It shows how Level‑1 representational dynamics give rise to Level‑2 physical descriptions and identifies experimental signatures accessible to decoherence and vacuum‑sensitive probes.

DOI
10.5281/zenodo.19361311

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Paper 12 in the series “The Articulation of Postulate P1”. This paper operationalises stabilisation within the P1 framework by introducing measurable criteria for the coherence density c, constructing the parametric state mapping c↦ρ(c), and deriving the c-dependent dissipative generator Λdiss(c). It shows how Level‑1 representational dynamics give rise to Level‑2 physical descriptions and identifies experimental signatures accessible to decoherence and vacuum‑sensitive probes.
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.
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.
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.
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.
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.