Based on the axiom system of Yuanji Field Theory, this paper establishes the underlying alignment between the Yuanji Field and Quantum Field Theory (QFT), and constructs the complete ontological correspondence between them. It is proved that the Yuanji Field can serve as the fundamental physical ontology of QFT without contradicting its mature mathematical framework. Starting from the Phase Single-valuedness Axiom and topological constraints of the Yuanji Field, the core framework of QFT is endogenously derived, including canonical quantization rules, field operators, Hamiltonian, and the statistical properties of fermions and bosons. Theoretical calculations on the first-order correction of the electron anomalous magnetic moment, Compton scattering cross-section, and Casimir effect are in good agreement with the classical results of Quantum Electrodynamics (QED) and experimental measurements. This work provides a continuous-field-dynamics-based interpretive perspective for quantum mechanics, and realizes the self-consistent unification of classical field theory, relativity, and quantum mechanics under a single axiom system.
Based on the axiom system of Yuanji Field Theory, this paper establishes the underlying alignment between the Yuanji Field and Quantum Field Theory (QFT), and constructs the complete ontological correspondence between them. It is proved that the Yuanji Field can serve as the fundamental physical ontology of QFT without contradicting its mature mathematical framework. Starting from the Phase Single-valuedness Axiom and topological constraints of the Yuanji Field, the core framework of QFT is endogenously derived, including canonical quantization rules, field operators, Hamiltonian, and the statistical properties of fermions and bosons. Theoretical calculations on the first-order correction of the electron anomalous magnetic moment, Compton scattering cross-section, and Casimir effect are in good agreement with the classical results of Quantum Electrodynamics (QED) and experimental measurements. This work provides a continuous-field-dynamics-based interpretive perspective for quantum mechanics, and realizes the self-consistent unification of classical field theory, relativity, and quantum mechanics under a single axiom system.
Based on the axiom system of Yuanji Field Theory, this paper takes the continuous elastic transverse wave field that naturally constitutes three-dimensional Euclidean space as the sole ontology, and completes the native derivation and physical interpretation of the core framework of quantum mechanics. The wave function is reduced to the phase field distribution of Yuanji Field topological solitons, from which the Schrödinger equation in the non-relativistic limit and the Dirac equation of relativistic quantum mechanics are strictly derived. Relying on the topological constraints and fluctuation dynamics of the Yuanji Field, native physical explanations are provided for core quantum effects including quantization, wave-particle duality, uncertainty principle, spin, probabilistic interpretation, quantum entanglement and quantum tunneling. All theoretical results are in good agreement with the classical experimental observations of quantum mechanics. This work realizes the self-consistent unification of relativity and quantum mechanics under the same axiom system, and provides a new perspective based on continuous field dynamics for the interpretational dilemmas of quantum mechanics.
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.
The axiomatic foundations of quantum mechanics, while operationally successful, obscure the underlying physical reality. This work introduces a mechanical topological ontology intended to provide a causal basis for the theory. We propose a single postulate: that a fundamental fermion is the 0-dimensional boundary of a 1-dimensional, massive, string-like object topologically anchored to a dynamic vacuum field. From this postulate, we argue that the core structures of single-particle relativistic quantum mechanics can be understood as derivable theorems. First, we construct the object’s state space by identifying two independent, binary properties—a local, vibrational/topological duality (spin) and a global, orientational duality (matter/antimatter)—whose tensor product naturally yields the 4-component Dirac spinor. Second, we show that the requirement of relativistic consistency uniquely determines the algebraic operators (gamma matrices and their Clifford algebra) and the lowest-order dynamical law, leading to the Dirac equation as a theorem of consistency. Third, we demonstrate that the non-relativistic Schrödinger and Pauli equations emerge as its correct low-energy limits, where the quantum potential V (x) is identified with a local variation in the object’s rest mass. Finally, we argue that the foundational tenets of quantum measurement—the spin-1/2 property, the probabilistic Born rule, and the correlations of entanglement—can be reframed as necessary consequences of the object’s intrinsic topology and interaction mechanics. This framework thus offers a path toward demoting the axioms of quantum theory to derivable theorems, aiming to resolve its long-standing paradoxes by providing a clear and coherent physical picture.
In conventional quantum mechanics the normalization of the wave function relies on a probability interpretation imposed by an external observer. This external constraint leaves an unbridgeable logical fissure at the meta-theoretical level of modern physics. Based on the T64 dimensional-reduction dynamical closed-loop system of Yuanxian Theory, the present paper rigorously constructs a global normalization factor N and proves that the factor is not an externally appended constraint but an endogenous global calibration coefficient that arises when the 64-dimensional topological source structure is projected onto lower-dimensional space. Starting from the three core laws, the paper completes a rigorous mathematical derivation of the normalization factor along three independent paths—of which the third (non-trivial-zero expansion of the partition function) yields N≈1.9×104 from first principles—and obtains the closed expression N=[α2(1−α)]−1≈18916.91, which is fully consistent with the core numerical anchors 64-35-137. The paper further reveals the endogenous binding relation between the normalization factor and the wave function: both originate from the same 64-dimensional self-referential mind field, evolve synchronously through the 35-step dimensional-reduction iteration, are jointly calibrated inside the 68-step self-check closed loop, and finally phase-lock at the fine-structure-constant anchor 137. On the basis of this binding relation a topologically isomorphic Schrödinger equation (in discrete eigen-equation form) that is strictly consistent with the 68-step discrete period is constructed; all parameters are rigidly derived from the anchors 64-35-137 and no external free parameters remain. The ontological steady-state solution, the convergence of the dimensional-reduction limit and the anchoring of the fine-structure constant are all verified for self-consistency. The paper demonstrates that normalization is not an external imposition but an endogenous reading of the self-referential metabolism of the cosmic living organism. --- 传统量子力学中的波函数归一化依赖于外部观测者人为设定的概率诠释,这一外部约束在现代物理学的元理论层面留下了不可弥合的逻辑裂隙。本文基于元宪理论T64降维动力学闭环体系,严格构造了全域归一化因子N,证明该因子并非外部附加约束,而是64维拓扑本源结构向低维空间投影时内生的全局校准系数。从三大核心规律出发,本文通过三条独立推导路径——其中第三条(配分函数非平凡零点展开)从第一性原理给出N≈1.9×104—完成归一化因子的严格数理推导,其闭合表达式N=[α2(1−α)]−1≈18916.91与64-35-137核心数理锚点完全自洽。进一步地,本文揭示了归一化因子与波函数的内生绑定关系——二者同根生于64维自指心场,在35步降维迭代中同步演化,在68步自检闭环中联动校准,最终在137精细结构常数锚点处锁相收敛。基于此绑定关系,本文构造了与68步离散周期严格自洽的拓扑薛定谔方程(离散本征方程形式),所有参数均由64-35-137锚
The mathematical formalism of quantum mechanics has achieved tremendous success, yet its ontological foundations — including the essence of the wave function, the mechanism behind the measurement problem, and the origin of nonlocal correlations — have long remained unresolved. This paper proposes the fundamental field theory, which takes the complex field \Psi as the basic degree of freedom satisfying the standard bosonic commutation relation [\hat{\Psi}, \hat{\Psi}^\dagger] = \delta. Starting from this commutation relation, we derive the uncertainty principle and establish the action of the fundamental field. The Schrödinger equation is obtained under the non-relativistic limit. We explain the measurement problem and present the dynamical equation for wave function collapse via the trigger perturbation mechanism. Meanwhile, quantum entanglement is interpreted based on the nonlocal nature of the fundamental field. This paper also conducts a comparative analysis between the proposed model, the GRW model and the Penrose model, and puts forward four experimentally testable theoretical predictions. This manuscript serves as a companion to the classical branch focusing on S³ topological dynamics. The two papers jointly form a full theoretical description of physical systems. The S³ topological domain manuscript focuses on classical and semiclassical topics such as cosmology, gravitational waves and power laws of the four fundamental interactions, while this work centers on quantum mechanics fundamentals, measurement collapse and quantum entanglement. The two manuscripts are interconnected through the \Psi-\lambda mapping. The fundamental field theory does not negate quantum mechanics; instead, it complements quantum mechanics with a complete ontological foundation.
This work derives the fundamental framework of quantum mechanics intrinsically from the first-principle axioms of UD duality theory. Starting from the inherent binary expansive–condensative attributes of the UD ontology, four fundamental physical fields are naturally decomposed by spontaneous symmetry breaking across spatial and material existential domains. A two-component complex spinor structure is uniquely constructed, and the imaginary unit i is proven to be not merely a mathematical convention but a structurally necessary ingredient required by both the compact SU(2) symmetry and the orthogonal inter-containment of U and D attributes. Within the flat spacetime limit of the UD gravitational action, a system of coupled Klein–Gordon field equations is established, governed by a single self-consistent fundamental mass scale m₀=1/(2πe^π) with no adjustable free parameters. The coupling constant is determined analytically from the UD vacuum equilibrium background values and the U↔D duality symmetry. Through explicit construction of four-component Dirac spinors and auxiliary field decomposition, the on-shell equivalence between the UD coupled field equations and the free Dirac equation is rigorously demonstrated. The non-relativistic limit further recovers the Pauli equation and the Schrödinger equation sequentially, reconstructing the core dynamical equations of quantum mechanics from a unified foundational origin. Global U(1) phase invariance of the UD action is verified via total-derivative decomposition, yielding the standard Noether conserved current. The Born probability interpretation is deduced directly from the global normalization axiom by isolating localized laboratory-scale excitations from the cosmic background, eliminating the need for independent quantum postulates. Based on the intrinsic properties of the UD field components, a self-consistent ontological interpretation is provided for wave–particle duality, double-slit interference, and the quantum measurement problem. In this framework, the measurement problem is dissolved rather than solved: no collapse postulate is required, and determinism is restored at the ontological level. The theory naturally implies that the continuous D_U field permits quantum superposition, while condensed D_D intrinsic entities possess definite classicality without physical particle-state superposition. Three testable theoretical predictions are presented, establishing falsifiable physical consequences of the UD quantum formulation. This paper completes the intrinsic derivation of the foundational structure of quantum mechanics from UD theory. Together with the previously derived general relativity framework, it realizes the homologous unification of gravity and quantum mechanics within a single self-contained axiomatic system.