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Construction of the Unified Constraint Field Theory Based on the Meta-Axiom of Persistence and Interdisciplinary Verification Plan

Peijiang Ma

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Taking Persistence as the first axiom, construct a Unified Constraint Field Theory framework to reconstruct the underlying logic of physics and solve the core conflict between quantum mechanics and relativity. Meanwhile, extend this framework to all disciplines such as chemistry, biology, economics and sociology, unify interpretation of core problems of each discipline at the ontological level, and form a globally applicable meta-scientific system.

DOI
10.17605/osf.io/p8m6g

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英文摘要 One of the core challenges in quantum mechanics is the lack of a unified, self-consistent, and phenomenon-independent axiomatic methodological framework. This paper proposes the "constraint-freedom" axiomatic paradigm to fill this gap. The paradigm constructs universal rules for quantum system evolution through three core axioms—the Rigid Constraint Axiom, the Flexible Degree of Freedom Axiom, and the Global Correlation Axiom: rigid constraints define the boundaries of possible states of the system, flexible degrees of freedom describe dynamic choices within these boundaries, and global correlation explains non-local correlations in composite systems. This paradigm is fully self-consistent with the author's proposed Bian's Unified Field Formula (BUFF) and its derived "soft energy packet" ontology, providing a consistent methodological explanation for phenomena such as double-slit interference, quantum tunneling, and entanglement swapping. Reanalysis of CERN quark collision experiment data and "Micius" satellite entanglement data shows that the paradigm's prediction error ≤ 3%. More importantly, it derives two unique, testable new effects: the tunneling probability dependent on constraint gradient, and the degree of freedom saturation effect on entanglement fidelity. This work achieves a leap from "phenomenon explanation" to "rule construction," providing a clear, self-consistent, and operable methodological foundation for quantum mechanics. 中文摘要 量子力学的核心挑战之一在于缺乏统一、自洽且独立于现象的公理化方法论框架。本文提出“约束-自由”公理化范式以填补这一空白,该范式通过三大核心公理——刚性约束公理、柔性自由度公理、全局关联公理,构建量子系统演化的普适规则:刚性约束界定系统可能状态的边界,柔性自由度描述边界内的动态选择,全局关联解释复合系统的非局域关联。该范式与作者提出的卞氏统一场公式(Bian's Unified Field Formula, BUFF)及其导出的“软能量包”本体论完全自洽,为双缝干涉、量子隧穿、纠缠交换等现象提供了一致的方法论解释。重新分析欧洲核子研究组织(CERN)夸克碰撞实验与“墨子号”卫星纠缠实验数据,结果显示范式预测误差≤3%。更重要的是,其推导出两个独特的可检验新效应:约束梯度依赖的隧穿概率、自由度饱和对纠缠保真度的影响。本文实现了从“现象解释”到“规则构建”的跨越,为量子力学提供了清晰、自洽且可操作的方法论基础。

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On the basis of quantum-mechanical realism and the philosophical view that “determinism and indeterminism are mutually dual and symbiotically coexisting,” philosophical and physical perspectives are integrated to propose the “constraint–uncertainty” hypothesis in this paper. Combined with a temporal ontology of “a determined history and an open future,” a unified interpretative framework for quantum phenomena is established. First, in conjunction with experimental results on fullerene quantum interference and spin decoherence in diamond NV centers, the core hypothesis is proposed: when a system is subject to a single dominant constraint, its behavior exhibits deterministic characteristics and uncertainty is suppressed; when subject to multiple competing constraints, its behavior becomes indeterministic and determinism is weakened. It is further clarified that the “constraint” in this work refers to a physically real underlying dynamical mechanism. Second, based on this hypothesis and temporal ontology, a self-consistent interpretation is provided for quantum phenomena such as wave-function superposition and quantum entanglement. It is argued that the “constraint–uncertainty” hypothesis offers an ontological basis for the Heisenberg uncertainty principle, thereby correcting the imprecise characterization in mainstream quantum theory that reduces uncertainty to an intrinsic property of particles. This paper further explores the tension between quantum mechanics and general relativity, suggesting that they correspond to different physical regimes governed by distinct constraint structures. A complete constraint-based model should naturally incorporate gravity, potentially offering a new perspective for the unification of the two theories. This paper further elaborates on the issues concerning temporal ontology. The author holds that variability serves as the meta-setting of physics, and the irreversibility of time is essentially a combination of variability and uncertainty, which also gives rise to the openness of the future. The uniqueness of the subject’s existential position determines the definiteness of history.

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The Stability of Matter as the Fundamental Axiom: Analytic Signal Framework for Unifying Quantum Mechanics and Cosmology

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This paper advances the Unified Quantum Mechanics (UQM) framework by elevating the empirical stability of matter to the status of a cosmological first principle. While previous work established the operator formalism, this work posits that the foundational conflicts of 20th-century physics—Real vs. Complex, Deterministic vs. Probabilistic, and Continuous vs. Discrete—are resolved specifically by this stability axiom. The central innovation is the advancement of the Analyticity Mandate, which constrains all physical wavefunctions to be causal, positive-energy analytic signals ($E>0$). This mandate is mathematically implemented by identifying the imaginary unit $i$ with the physical, non-local temporal Hilbert transform operator ($i \equiv \mathcal{H}_t$), transforming the Schrödinger and Dirac equations into deterministic, real-valued field equations—the Unified Real Wave Equation. We uncover a fundamental symmetry at the heart of unification: the analytic signal constraint required to ontologically complete quantum theory simultaneously derives the geometric structure of General Relativity, demonstrating that both paradigms originate from the single axiom of matter stability. We establish that this analytic complexification constitutes a mathematically rigorous and physically necessary procedure, transforming the underlying real spacetime-energy field into a unified dynamical framework that naturally subsumes both quantum phenomena and gravitational evolution. This framework culminates in a unified Theory of Everything described by the fundamental action: $S_{\text{UQM}} = \int d^4x \sqrt{-g} \left(\frac{c^4}{16\pi G} (R - 2\Lambda) + \mathcal{L}_{\text{SM}}\right)$, where the Lagrangian density describes both geometry and matter as manifestations of a single real field $\psi_R$ under the Analyticity Mandate. The complete theory is expressed through the coupled system: $G_{\mu\nu} = \kappa T_{\mu\nu}[\psi_R] \quad \text{and} \quad \psi = \psi_R - i\mathcal{H}_t[\psi_R] \quad \text{with} \quad E > 0.$ We present the following quantitative results and mechanisms: (1) We derive the Cosmic Cycle Period $T_{cycle} \approx 7.14 \times 10^{11}$ years for the cubic model (Spherical model: $\approx 7.00 \times 10^{11}$ years) and the maximum expansion factor $Z_{max} \approx 2.20 \times 10^{10}$ (Spherical: $\approx 1.36 \times 10^{10}$), by solving the cosmic equation of state governed by the electron's vacuum stability horizon $l_{crit} \approx 5.35$ cm (Spherical diameter: $D_{crit} \approx 6.64$ cm). (2) We identify the Fermionic Rigidity mandated by the Pauli Exclusion Principle as the specific geometrodynamic trigger for the non-singular Big Bounce, avoiding the entropy paradoxes of Conformal Cyclic Cosmology. (3) We restore Global Noether Conservation by reinterpreting cosmological redshift as mechanical work performed against the elastic tension of the vacuum plenum ($\rho_{\Lambda}$). (4) We formalize the \emph{Singh Stability Conjecture}, proposing a hierarchy of verification protocols including a Rapid-Dispersion interferometric experiment designed to test the specific cosmological parameter limits of the vacuum. The resulting ontology is a monistic Spacetime-Energy substance, where the Einstein Field Equation $G_{\mu\nu} = \kappa T_{\mu\nu}$ represents the phase equilibrium between the geometry of the vacuum and the density of matter. UQM thus completes Einstein's unification program by providing a deterministic, realist, and geometrically coherent foundation for all physical phenomena. We formally propose a community-wide verification program, defining definitive falsification tests through laboratory experiments, cosmological observations, and Gedankenexperiments. Within this program, we distinguish between parametric constraints and ontological validity, asserting that the ultimate falsification of the framework requires the empirical demonstration of stable negative-energy states.

•Nov 25, 2025•0 citations
Taking Persistence as the first axiom, construct a Unified Constraint Field Theory framework to reconstruct the underlying logic of physics and solve the core conflict between quantum mechanics and relativity. Meanwhile, extend this framework to all disciplines such as chemistry, biology, economics and sociology, unify interpretation of core problems of each discipline at the ontological level, and form a globally applicable meta-scientific system.
This work presents a constraint-based meta-framework for understanding persistent foundational dualities across physics, biology, and consciousness studies. Rather than proposing new physical mechanisms or historical cosmologies, it formalizes a post-reductionist perspective in which no globally sufficient singular description of reality is admissible. The framework replaces substance with persistence as the primary ontological primitive and treats irreducible dualities (e.g., wave–particle, observer–observed, gene–environment) as structural necessities rather than epistemic gaps. Scientific progress is reframed as translation between complementary descriptions instead of unification by collapse. Consciousness is formally introduced as a coherence-seeking interface process that operates across irreducible dualities, explaining its persistent tension with fragmentation and meaning without invoking metaphysical claims, panpsychism, or interventionist implications. From the axioms follow explicit structural limits, including the impossibility of a final theory, a total observer, permanent non-dual consciousness, or total control of complex systems. The framework is compatible with existing physical and biological theories and is intended as a stabilizing methodological guide for post-reductionist science. Ethical containment is built in by design: no inference from this work licenses the manipulation, collapse, or redesign of foundational dualities.
As the third paper in the *Monistic Ontology* series, this work strictly adheres to the ontological axiom system established in the first paper of the series, *Monistic Ontology* (hereinafter referred to as the "General Outline"), without introducing any new ad hoc assumptions. Taking the intrinsic fundamental frequency of the global unified field fj = 2.2687318315 × 1023 Hz, endogenously calibrated in the second paper of the series, as the sole quantitative anchor, this paper presents a unified, self-consistent realist ontological interpretation of the core phenomena of quantum mechanics based on the "local resonant standing wave" particle ontology model, aiming to resolve the long-standing interpretation dilemma of quantum mechanics. This paper clarifies that the apparent "counter-intuitive" characteristics of quantum phenomena are the natural manifestation ofthe inherent properties of the fundamental frequency vibration of the global unified field at the microscale. There is no "quantum superposition state" independent of the unified field ontology, nor is it necessary to introduce the non-local "action at a distance" hypothesis. With no additional axioms, no ad hoc assumptions, and no free fitting parameters, this paper endogenously derives the quantitative formula for the coherence length of quantum entanglement, and the calculated results are in good agreement with the experimental data of the thousand-kilometer scale satellite-ground entanglement from China’s Micius Satellite. This work attempts to realize the underlying ontological unification of quantum mechanics and relativity, provides a quantum theoretical basis for the subsequent unified interpretation of the four fundamental interactions, and completes the logical connection from the quantitative anchor to the quantum ontology of the series research.
By expanding the research paradigm and reconciling the two binary oppositions of "relative and absolute" and "quantum and classical" in physics, a new theoretical framework that is compatible with relativity and quantum mechanics is proposed. Firstly, excavate and establish three universal axioms: Axiom 1 (consensus guarantees equal rights), Axiom 2 (objective existence independent of measurement), and Axiom 3 (universality of causality and dialectical logic), based on which to criticize the logical contradictions of existing theories. In the field of relativity, this article points out that there is a logical paradox in the explanation of "clock slowing down depends on relative motion" in special relativity (A clock is both faster and slower than B clock), and proposes a relative absolute spacetime view that "absolute motion leads to clock slowing down". By extending the Lorentz transformation, absolute motion and relative motion are unified, solving problems such as the twin paradox. At the same time, based on the prediction of the Dirac equation for negative mass matter, the "negative mass spacetime curvature paradox" is proposed, challenging Einstein's physical explanation of spacetime curvature and arguing that it is only a mathematical tool (the mathematical expression of gravity) rather than a physical reality. In the field of quantum mechanics, this article criticizes the Copenhagen interpretation for violating Axiom 2 (denying the independent eigenstates of microscopic particles). By modifying the Schrödinger equation twice (For the first time, electromagnetic potential energy was replaced with gravitational potential energy, and the Schrödinger-Tu equation was established to describe macroscopic objects such as the Earth's revolution; The second step is to convert potential energy into electromagnetic/gravitational force and derive the wave mechanics equation of classical mechanics laws, such as Newton's second law with force operator), proves that quantum and classical theories are compatible within the same mathematical framework. In the experiment, it was demonstrated through the "anti-interference electron diffraction experiment" that a strong magnetic field only changes the shape of diffraction fringes without causing them to disappear, denying the inevitability of quantum decoherence. The establishment of "generalized wave dynamics" and "relative absolute spacetime view" breaks the binary opposition of traditional theories and provides a new paradigm for the unity of relativity and quantum mechanics. The core value of these jobs lies in: In terms of theoretical innovation, reconstruct the space-time and quantum interpretation system, while retaining the original mathematical form system; In terms of experimental verification, design feasible schemes such as hollow glass disk Jones experiment and geometric optical velocimetry experiment; In terms of philosophical significance, replacing "mathematical symmetry" with "content unity" and returning to the objectivity of physical mechanisms. The research conclusion indicates that by expanding paradigms and axiomatic constraints, the contradiction between relativity and quantum mechanics can be transformed into a complementary relationship, laying the foundation for the great unity of physics theory
英文摘要 One of the core challenges in quantum mechanics is the lack of a unified, self-consistent, and phenomenon-independent axiomatic methodological framework. This paper proposes the "constraint-freedom" axiomatic paradigm to fill this gap. The paradigm constructs universal rules for quantum system evolution through three core axioms—the Rigid Constraint Axiom, the Flexible Degree of Freedom Axiom, and the Global Correlation Axiom: rigid constraints define the boundaries of possible states of the system, flexible degrees of freedom describe dynamic choices within these boundaries, and global correlation explains non-local correlations in composite systems. This paradigm is fully self-consistent with the author's proposed Bian's Unified Field Formula (BUFF) and its derived "soft energy packet" ontology, providing a consistent methodological explanation for phenomena such as double-slit interference, quantum tunneling, and entanglement swapping. Reanalysis of CERN quark collision experiment data and "Micius" satellite entanglement data shows that the paradigm's prediction error ≤ 3%. More importantly, it derives two unique, testable new effects: the tunneling probability dependent on constraint gradient, and the degree of freedom saturation effect on entanglement fidelity. This work achieves a leap from "phenomenon explanation" to "rule construction," providing a clear, self-consistent, and operable methodological foundation for quantum mechanics. 中文摘要 量子力学的核心挑战之一在于缺乏统一、自洽且独立于现象的公理化方法论框架。本文提出“约束-自由”公理化范式以填补这一空白,该范式通过三大核心公理——刚性约束公理、柔性自由度公理、全局关联公理,构建量子系统演化的普适规则:刚性约束界定系统可能状态的边界,柔性自由度描述边界内的动态选择,全局关联解释复合系统的非局域关联。该范式与作者提出的卞氏统一场公式(Bian's Unified Field Formula, BUFF)及其导出的“软能量包”本体论完全自洽,为双缝干涉、量子隧穿、纠缠交换等现象提供了一致的方法论解释。重新分析欧洲核子研究组织(CERN)夸克碰撞实验与“墨子号”卫星纠缠实验数据,结果显示范式预测误差≤3%。更重要的是,其推导出两个独特的可检验新效应:约束梯度依赖的隧穿概率、自由度饱和对纠缠保真度的影响。本文实现了从“现象解释”到“规则构建”的跨越,为量子力学提供了清晰、自洽且可操作的方法论基础。
On the basis of quantum-mechanical realism and the philosophical view that “determinism and indeterminism are mutually dual and symbiotically coexisting,” philosophical and physical perspectives are integrated to propose the “constraint–uncertainty” hypothesis in this paper. Combined with a temporal ontology of “a determined history and an open future,” a unified interpretative framework for quantum phenomena is established. First, in conjunction with experimental results on fullerene quantum interference and spin decoherence in diamond NV centers, the core hypothesis is proposed: when a system is subject to a single dominant constraint, its behavior exhibits deterministic characteristics and uncertainty is suppressed; when subject to multiple competing constraints, its behavior becomes indeterministic and determinism is weakened. It is further clarified that the “constraint” in this work refers to a physically real underlying dynamical mechanism. Second, based on this hypothesis and temporal ontology, a self-consistent interpretation is provided for quantum phenomena such as wave-function superposition and quantum entanglement. It is argued that the “constraint–uncertainty” hypothesis offers an ontological basis for the Heisenberg uncertainty principle, thereby correcting the imprecise characterization in mainstream quantum theory that reduces uncertainty to an intrinsic property of particles. This paper further explores the tension between quantum mechanics and general relativity, suggesting that they correspond to different physical regimes governed by distinct constraint structures. A complete constraint-based model should naturally incorporate gravity, potentially offering a new perspective for the unification of the two theories. This paper further elaborates on the issues concerning temporal ontology. The author holds that variability serves as the meta-setting of physics, and the irreversibility of time is essentially a combination of variability and uncertainty, which also gives rise to the openness of the future. The uniqueness of the subject’s existential position determines the definiteness of history.
This paper advances the Unified Quantum Mechanics (UQM) framework by elevating the empirical stability of matter to the status of a cosmological first principle. While previous work established the operator formalism, this work posits that the foundational conflicts of 20th-century physics—Real vs. Complex, Deterministic vs. Probabilistic, and Continuous vs. Discrete—are resolved specifically by this stability axiom. The central innovation is the advancement of the Analyticity Mandate, which constrains all physical wavefunctions to be causal, positive-energy analytic signals (E>0E>0E>0). This mandate is mathematically implemented by identifying the imaginary unit iii with the physical, non-local temporal Hilbert transform operator (i≡Hti \equiv \mathcal{H}_ti≡Ht​), transforming the Schrödinger and Dirac equations into deterministic, real-valued field equations—the Unified Real Wave Equation. We uncover a fundamental symmetry at the heart of unification: the analytic signal constraint required to ontologically complete quantum theory simultaneously derives the geometric structure of General Relativity, demonstrating that both paradigms originate from the single axiom of matter stability. We establish that this analytic complexification constitutes a mathematically rigorous and physically necessary procedure, transforming the underlying real spacetime-energy field into a unified dynamical framework that naturally subsumes both quantum phenomena and gravitational evolution. This framework culminates in a unified Theory of Everything described by the fundamental action: SUQM=∫d4x−g(c416πG(R−2Λ)+LSM)S_{\text{UQM}} = \int d^4x \sqrt{-g} \left(\frac{c^4}{16\pi G} (R - 2\Lambda) + \mathcal{L}_{\text{SM}}\right)SUQM​=∫d4x−g​(16πGc4​(R−2Λ)+LSM​), where the Lagrangian density describes both geometry and matter as manifestations of a single real field ψR\psi_RψR​ under the Analyticity Mandate. The complete theory is expressed through the coupled system: Gμν=κTμν[ψR]andψ=ψR−iHt[ψR]withE>0.G_{\mu\nu} = \kappa T_{\mu\nu}[\psi_R] \quad \text{and} \quad \psi = \psi_R - i\mathcal{H}_t[\psi_R] \quad \text{with} \quad E > 0.Gμν​=κTμν​[ψR​]andψ=ψR​−iHt​[ψR​]withE>0. We present the following quantitative results and mechanisms: (1) We derive the Cosmic Cycle Period Tcycle≈7.14×1011T_{cycle} \approx 7.14 \times 10^{11}Tcycle​≈7.14×1011 years for the cubic model (Spherical model: ≈7.00×1011\approx 7.00 \times 10^{11}≈7.00×1011 years) and the maximum expansion factor Zmax≈2.20×1010Z_{max} \approx 2.20 \times 10^{10}Zmax​≈2.20×1010 (Spherical: ≈1.36×1010\approx 1.36 \times 10^{10}≈1.36×1010), by solving the cosmic equation of state governed by the electron's vacuum stability horizon lcrit≈5.35l_{crit} \approx 5.35lcrit​≈5.35 cm (Spherical diameter: Dcrit≈6.64D_{crit} \approx 6.64Dcrit​≈6.64 cm). (2) We identify the Fermionic Rigidity mandated by the Pauli Exclusion Principle as the specific geometrodynamic trigger for the non-singular Big Bounce, avoiding the entropy paradoxes of Conformal Cyclic Cosmology. (3) We restore Global Noether Conservation by reinterpreting cosmological redshift as mechanical work performed against the elastic tension of the vacuum plenum (ρΛ\rho_{\Lambda}ρΛ​). (4) We formalize the \emph{Singh Stability Conjecture}, proposing a hierarchy of verification protocols including a Rapid-Dispersion interferometric experiment designed to test the specific cosmological parameter limits of the vacuum. The resulting ontology is a monistic Spacetime-Energy substance, where the Einstein Field Equation Gμν=κTμνG_{\mu\nu} = \kappa T_{\mu\nu}Gμν​=κTμν​ represents the phase equilibrium between the geometry of the vacuum and the density of matter. UQM thus completes Einstein's unification program by providing a deterministic, realist, and geometrically coherent foundation for all physical phenomena. We formally propose a community-wide verification program, defining definitive falsification tests through laboratory experiments, cosmological observations, and Gedankenexperiments. Within this program, we distinguish between parametric constraints and ontological validity, asserting that the ultimate falsification of the framework requires the empirical demonstration of stable negative-energy states.