This work presents the Mass–Geometry Phase (MQP) framework, a dynamical collapse model in which the quantum-to-classical transition is described as a phase transition mediated by spacetime geometry. The framework introduces an order parameter that quantifies the degree of coupling between quantum states and classical geometry, without postulating new fundamental forces or stochastic modifications of quantum mechanics. Classical localization emerges dynamically when a curvature- or decoherence-related stimulus exceeds a critical threshold, leading to spontaneous symmetry breaking between non-geometric and geometric phases of matter. The model provides a unified description across Newtonian and relativistic regimes and predicts experimentally testable deviations in mesoscopic quantum systems. This article constitutes the core formulation of the MQP framework, intended as a reference work unifying previous exploratory notes and satellite papers.
This work presents the Mass–Geometry Phase (MQP) framework, a dynamical collapse model in which the quantum-to-classical transition is described as a phase transition mediated by spacetime geometry. The framework introduces an order parameter that quantifies the degree of coupling between quantum states and classical geometry, without postulating new fundamental forces or stochastic modifications of quantum mechanics. Classical localization emerges dynamically when a curvature- or decoherence-related stimulus exceeds a critical threshold, leading to spontaneous symmetry breaking between non-geometric and geometric phases of matter. The model provides a unified description across Newtonian and relativistic regimes and predicts experimentally testable deviations in mesoscopic quantum systems. This article constitutes the core formulation of the MQP framework, intended as a reference work unifying previous exploratory notes and satellite papers.
We introduce the Mass–Geometry Phase (MQP) framework, a collapse model grounded on a gravitationally induced order parameter χ(x, t) whose dynamical evolution governs the emergence of classical geometry from quantum nonlocality. The model is based on a reaction–diffusion equa- tion with viscosity, incorporating a curvature–dependent stimulus S and yielding stable localized solutions (“collapse bubbles”) that mark the transition from geometric non-occupation to classical localization. Numerical simulations reveal stable fixed points, mass thresholds, and retro-reactive gravitational feedback consistent with a predictive and falsifiable scheme. We provide analytical mappings connecting the effective Landau potential to macroscopic collapse rates, derive scaling laws for collapse times and bubble sizes, and identify experimental regimes where MQP departs from GRW/DP/CSL theories. The resulting framework constitutes a unified geometric interpretation of quantum-classical transition, with implications for interferometry, optomechanics, and early-universe conditions.
This document serves as the anchor reference of the Modified Quantum Parameter (MQP) framework. The MQP describes the quantum–classical transition as a process of geometric relaxation with finite response time, characterized by an emergent order parameter χ. The framework introduces a non-instantaneous geometric response without postulating new fundamental interactions, interpreting wavefunction collapse as a spontaneous symmetry-breaking process induced by geometric stimuli. This article consolidates and unifies a series of previously released technical notes and exploratory studies by the author, providing the central definitions, equations, and physical interpretation of the MQP. All related works should be understood as applications or extensions of the formalism presented here.
AbstractThis work presents a unified geometric framework for quantum reality through four interconnected papers. It proposes that the coherent, non-separable correlations described by Hilbert space originate from an unobservable Energy Space, a fundamental substrate beyond spacetime that preserves perfect coherence and all conservation laws, thereby providing a geometric interpretation of quantum entanglement. Within this framework, the relation E = hf is interpreted as an encoding relation rather than a statement of physical energy actualization. During measurement, structural branching may occur, but Energy Space ensures that only one geometrically valid branch undergoes physical localization. Spacetime emerges from Energy Space as a passive geometric medium with intrinsic dynamic capabilities, giving rise to quantum objects and their interactions.Quantum objects are interpreted as dynamic geometric patterns of spacetime possessing an encoded geometric identity. Their physical properties, including mass, charge, spin, momentum, energy, wavelength, and phase, are fundamentally encoded in Energy Space and become physically actualized according to the interaction context and the degree of coherence or decoherence. The stability, transformation, and propagation of quantum objects are determined by their geometric compatibility with spacetime and with other quantum geometries.Electromagnetic, weak, and strong interactions are interpreted as direct interactions between compatible quantum-object geometries, whereas gravity is regarded as an indirect geometric interaction mediated through spacetime geometry. Geometric interactions may produce superposition, transformation into new quantum-object geometries, or the formation of larger composite geometric structures, providing a unified geometric interpretation of interactions, confinement, and composite systems.Within this geometric framework, a recursive geometric scaling parameter satisfying the invariant relation is proposed. Based on this hierarchy, phenomenological recursive scaling relations are developed for the lepton and quark families, suggesting a possible underlying geometric structure governing fermion masses, generational hierarchy, and relative stability.Finally, the Peak-Coupling Theory proposes that quantum localization and decoherence occur through discrete peak-coupling events between interacting quantum geometries at oscillatory extrema within a quantum wave packet. The wave envelope and phase continuously modulate the distribution of possible coupling events, while observable interaction probabilities may emerge from the squared magnitude of local coupling amplitudes, providing a possible geometric route toward the emergence of Born-rule probabilitiesTogether, these four papers present a unified conceptual framework in which Energy Space, spacetime, quantum objects, physical interactions, particle hierarchies, quantum measurement, and localization are interpreted as interconnected manifestations of an underlying geometric reality.These ideas are developed across four papers: Paper 1: Energy Space and Geometric Nature of Quantum Objects and Spacetime Paper 2: Quantum Geometry Paper 3: Lepton and Quark Generational Phenomenological Patterns; and Paper 4: Peak-Coupling Theory of Quantum Interaction
Este documento apresenta a formulação matemática central do Modelo Quântico de Parâmetro (MQP). O colapso gravitacional quântico é descrito pela evolução do parâmetro de ordem χ(r,t) segundo uma equação de reação-difusão acoplada a um estímulo gravitacional S, modelado pelo gradiente do potencial newtoniano ou pelo invariante de Kretschmann. Introduzimos a função taxa r(S), o termo dissipativo γ, o ruído ξ e a estrutura da transição de fase quântico-clássica. Este texto consolida o núcleo teórico rigoroso do MQP. This document presents the mathematical formulation of the Mass–Geometry Phase (MQP) model. Gravitational quantum collapse is described through the evolution of an order parameter χ(r,t), governed by a reaction-diffusion equation coupled to a gravitational stimulus S, represented by the gradient of the Newtonian potential or the Kretschmann scalar. We introduce the rate function r(S), the dissipative term γ, the noise ξ, and the structure of the quantum-to-classical phase transition. This work consolidates the rigorous theoretical core of the MQP framework.
Abstract This work presents a unified geometric framework for quantum reality through four interconnected papers. It proposes that the coherent, non-separable correlations described by Hilbert space originate from an unobservable Energy Space, a fundamental substrate beyond spacetime that preserves perfect coherence and all conservation laws, thereby providing a geometric interpretation of quantum entanglement. Within this framework, the relation E = hf is interpreted as an encoding relation rather than a statement of physical energy actualization. During measurement, structural branching may occur, but Energy Space ensures that only one geometrically valid branch undergoes physical localization. Spacetime emerges from Energy Space as a passive geometric medium with intrinsic dynamic capabilities, giving rise to quantum objects and their interactions. Quantum objects are interpreted as dynamic geometric patterns of spacetime possessing an encoded geometric identity. Their physical properties, including mass, charge, spin, momentum, energy, wavelength, and phase, are fundamentally encoded in Energy Space and become physically actualized according to the interaction context and the degree of coherence or decoherence. The stability, transformation, and propagation of quantum objects are determined by their geometric compatibility with spacetime and with other quantum geometries. Electromagnetic, weak, and strong interactions are interpreted as direct interactions between compatible quantum-object geometries, whereas gravity is regarded as an indirect geometric interaction mediated through spacetime geometry. Geometric interactions may produce superposition, transformation into new quantum-object geometries, or the formation of larger composite geometric structures, providing a unified geometric interpretation of interactions, confinement, and composite systems. Within this geometric framework, a recursive geometric scaling parameter satisfying the invariant relation is proposed. Based on this hierarchy, phenomenological recursive scaling relations are developed for the lepton and quark families, suggesting a possible underlying geometric structure governing fermion masses, generational hierarchy, and relative stability. Finally, the Peak-Coupling Theory proposes that quantum localization and decoherence occur through discrete peak-coupling events between interacting quantum geometries at oscillatory extrema within a quantum wave packet. The wave envelope and phase continuously modulate the distribution of possible coupling events, while observable interaction probabilities may emerge from the squared magnitude of local coupling amplitudes, providing a possible geometric route toward the emergence of Born-rule probabilities Together, these four papers present a unified conceptual framework in which Energy Space, spacetime, quantum objects, physical interactions, particle hierarchies, quantum measurement, and localization are interpreted as interconnected manifestations of an underlying geometric reality. These ideas are developed across four papers: Paper 1: Energy Space and Geometric Nature of Quantum Objects and SpacetimePaper 2: Quantum GeometryPaper 3: Lepton and Quark Generational Phenomenological Patterns; and Paper 4: Peak-Coupling Theory of Quantum Interaction
This preprint introduces a deterministic collapse-based framework in which time, mass, and spacetime geometry emerge from the statistics of modal-collapse events. The key dynamical quantity is the coherence factor Ξ, defined by the average inter-collapse interval. Ξ governs the conversion between coordinate and physical time (dτ = Ξ dt), determines inertial mass (m = E/Ξ²), and generates the effective metric (g_tt = –Ξ⁻², g_rr ∝ Ξ^p with p ≈ 1.9). Smooth Schrödinger evolution and general relativistic geometry are recovered as limiting cases of the same dynamical system: rare collapse cycles produce classical behaviour, fluctuating collapse produces quantum behaviour, and runaway collapse (Ξ → 0) gives rise to gravitational collapse and the breakdown of smooth geometry. The runaway regime mathematically enforces a lowest-frequency electromagnetic emission channel, predicting that radiation in collapse-driven transients must begin in the radio band and only later extend to higher frequencies. The accompanying supplementary TXT document provides the complete proof set of all five falsifiable predictions, with no tunable parameters: (1) universal radio-first ordering of electromagnetic discharge in runaway events, (2) universal curvature exponent p ≈ 1.9, (3) classical stability when ⟨ΔN_eff⟩ < 0, (4) time dilation fully determined from collapse-interval statistics, and (5) radio-only discharge at the onset of runaway collapse. This work proposes that collapse dynamics — rather than measurement or spacetime postulates — constitute the fundamental mechanism from which quantum behaviour, classical stability, and gravitational collapse all emerge.