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Constraint-Freedom Axiomatic Paradigm: A New Methodological Framework for Quantum Mechanics

Bian, Zhenfeng

Published Dec 2, 2025• 0 citations
Publisher

Abstract

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。

DOI
10.5281/zenodo.17785311

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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。
英文摘要 The dilemma of the "particle" concept in quantum mechanics stems from the profound contradiction between its point-like ontology and wave-like phenomena. This paper proposes a novel ontological solution: the fundamental constituent of the universe is the "soft energy packet"—a non-rigid, localized excitation of the universal unified energy field. Based on the author's proposed Bian's Unified Field Formula (BUFF) (Note: Its core quantitative form is the F_q formula, see Reference 5), we establish the mathematical framework of this ontology, where the "softness" (dispersion) and "shaping" (localization) of energy packets are governed by the global constraints of the field potential. This ontology provides a consistent physical explanation for phenomena such as double-slit interference, quantum tunneling, and entanglement swapping. Reanalysis of CERN double-slit experiment data and "Micius" satellite entanglement data shows that the ontology's prediction error ≤ 2%. More importantly, it derives two unique, testable new effects: the wave packet width-dependent tunneling probability, and the constraint gradient-dependent entanglement fidelity. This work achieves a leap from "phenomenon description" to "ontological construction," providing a clear, self-consistent, and operable physical foundation for quantum mechanics. 中文摘要 量子力学中“粒子”概念的困境源于其点本体与波现象之间的深刻矛盾。本文提出一种新的本体论解决方案:宇宙的基本构成单元是“软能量包”——一种非刚性的、局域化的宇宙统一能量场激发。基于作者提出的卞氏统一场公式(BUFF)(注:其核心定量形式为F_q公式,参见参考文献5),我们建立了该本体论的数学框架,其中能量包的“软性”(弥散性)与“定形”(局域化)受场势能的全局约束支配。该本体论为双缝干涉、量子隧穿、纠缠交换等现象提供了一致的物理解释。重新分析欧洲核子研究组织(CERN)双缝实验与“墨子号”卫星纠缠实验数据,结果显示本体论预测误差≤2%。更重要的是,其推导出两个独特的可检验新效应:波包宽度依赖的隧穿概率、约束梯度依赖的纠缠保真度。本文实现了从“现象描述”到“本体构建”的跨越,为量子力学提供了清晰、自洽且可操作的物理基础。
Contemporary physics faces a profound predicament at the intersection of relativity and quantum mechanics, rooted in the ontological presuppositions of "spacetime geometry" and "probability waves" that fail to provide a unified, realistic mechanistic explanation for cross-scale phenomena. By systematically integrating three original studies based on public data from authoritative institutions (CERN, MIT, NASA, etc.), this paper constructs a complete theoretical system of the "Kinetic Dynamics" paradigm, centered on "matter and its motion" as the sole physical reality. This paradigm achieves full-scale unified explanations for core phenomena: (1) Double-slit interference stems from quantifiable "short-range repulsion and medium-range attraction" between particles (prediction error ≤5% in conventional environments); (2) Quantum entanglement stability originates from the cosmic energy field's "phase coherence degree" locking particle motion freedom, extending qubit coherence time to over 150 μs; (3) Time dilation is the slowdown of intrinsic material motion rhythm under four extreme energy field constraints (temperature, field pressure, velocity, phase), with a full-scale prediction error ≤5%, naturally resolving ad hoc hypotheses like dark matter. This study realizes a paradigm shift from "abstract mathematical description" to "mechanistic realism," providing direct theoretical tools for quantum computing, room-temperature superconductivity, and deep-space exploration, and establishing a more concise, unified, and practical foundational framework for physics. 中文摘要 当前物理学在相对论与量子力学的交界处陷入深层困境,其核心症结在于“时空几何”与“概率波”的本体论预设,无法为跨尺度实验现象提供统一、实在的机制性解释。本文通过系统整合三项基于国际权威机构(CERN、MIT、NASA等)公开数据的原创研究,构建了“运动动力学”范式的完整理论体系,该范式以“物质及其运动”为唯一物理本体,成功实现了对核心物理现象的全尺度统一解释:(1)双缝干涉的本质是粒子间“短程排斥-中程吸引”的可量化作用力(常规环境预测误差≤5%);(2)量子纠缠态的稳定性源于宇宙能量场“相位相干度”对粒子运动自由度的锁定效应,可将量子比特相干时间延长至150μs以上;(3)时间膨胀是能量场四极端参数(温度、场压、速度、相位)约束下物质内在运动节奏的减缓,其全尺度预测误差≤5%,自然消解暗物质等补丁假设。本研究完成了从“抽象数学描述”到“机制实在论”的范式转移,为量子计算、室温超导、深空探测等领域提供了可直接应用的理论工具,为物理学构建了更简洁、统一、实用的全新基础框架。
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
Abstract Fundamental discrepancies exist among the foundational postulates of classical mechanics, relativity and quantum mechanics, leaving long-standing open physical puzzles including the origin of the arrow of time, quantum measurement collapse and the nature of spacetime. This paper proposes a self-consistent unified physical paradigm: the physical essence of a reference frame is the selective filtering of the full degrees of freedom of a system. All classical, relativistic and quantum physical theories constitute effective reduced descriptions of degrees of freedom under specific rules imposed by reference frames. Core phenomena such as temporal irreversibility, wave-function collapse, the constancy of the speed of light and the quantum-classical transition are not fundamental ontological properties of the universe, but emergent effects arising from filtering mappings introduced by finite-bandwidth observers. This work establishes an axiomatic framework for reference frames and degree-of-freedom filtering, defining projection filtering mappings, the principle of vanishing relative degrees of freedom, and the dimensionless filtering ratio. Within this framework, we reconstruct classical mechanics, special and general relativity, quantum decoherence and quantum measurement theory. Three categories of irreversible mechanisms — statistical coarse-graining, environmental partial-trace decoherence and time-domain sampling truncation — are integrated into a single mathematical structure. A universal dimensionless filtering ratio is defined. We clarify that the continuity of the control parameter does not imply that observables must evolve smoothly. Conceptually, the system can exhibit three regimes: quantum superposition, intermediate transition and classical state. Experiments on quantum bits at the Weizmann Institute provide preliminary observational hints, yet further verification is required; no specific form of the response curve is assumed in this paper. Three falsifiable quantitative predictions are put forward, involving attosecond spectroscopy, decoherence of superconducting qubits and cold-atom interferometry. We compare the present paradigm with relational quantum mechanics, QBism and consistent histories, discuss the ontological implications of time, observers and irreversibility, and outline extensions towards quantum gravity and cognitive science.
Quantum mechanics is not a patchwork of physical mysteries or isolated paradoxes. It is the deterministic, unavoidable consequence of constrained operator evolution acting upon a rigid geometric reality. In this manuscript, we dispense with a century of phenomenological mysticism. We demonstrate that all seemingly disparate canonical quantum phenomena—including interference, tunneling, entanglement, nonlocal correlations, vacuum forces, topological phase effects, and measurement-induced dynamics—arise deterministically from a single mathematical framework: the continuous evolution of quantum states under self-adjoint operators on Hilbert space. We explicitly organize this unified reality into five governing principles: Linearity of the state space (Interference) Noncommutativity of the observable algebra (Uncertainty) Tensor-product composition of multiparty systems (Entanglement) Spectral constraints of dynamic generators (Tunneling & Casimir Forces) Projection operators induced by measurement (Zeno Effect & Decoherence) The Paradigm of Absolute Control: Beyond passive observation, we introduce an active control extension via Spectral Gap Enforcement. By mathematically dictating the permitted physical geometry via protected operators, we prove that transition probabilities into unpermitted subspaces are strictly suppressed. To demonstrate the universal applicability of this theorem, we provide rigorous, concrete proofs for: Absolute Tunneling Suppression: Eradicating the Agmon transmission amplitude. Arresting Lindbladian Decoherence: Mathematically freezing open-system environmental coupling. The 2-Level Rabi Lock: Achieving absolute Zeno-like trapping without active observation. Conclusion: The phenomena of quantum reality are no longer paradoxes to be interpreted; they are geometric constraints to be commanded. This work establishes the definitive theoretical bridge between foundational quantum physics and the aggressive, deterministic engineering of coherent states.