The Dialectical Unity of Global and Local Information: The Fundamental Origin of the Affinity between Information as Primary Existence and Quantum Mechanics
This paper presents a rigorous demonstration that the fundamental origin of the natural affinity between information ontology and quantum mechanics lies in the eternal asymmetry between global information (the full information algebra 𝔄) and local information (the observable algebra 𝒩). Starting from the core axioms of the Pan-Information Unified Field Theory (PIUFT)—idempotency of information confirmation and trace-preserving information conservation—the paper strictly proves that the kernel space ker(E) necessarily exists and that any observer is necessarily a local information structure, permanently unable to access the full information algebra. The conditional expectation E: 𝔄 → 𝒩 acts as the projection bridge, transforming the global structure of completeness, determinacy, commutativity, real numbers, and classicality into the local structure of incompleteness, indeterminacy, non-commutativity, complex numbers, and quantumness. All core features of quantum mechanics—the emergence of Hilbert space via the GNS construction, operator non-commutativity, complex probability amplitudes, the uniqueness of the Born rule, and quantum entanglement—are rigorously derived as inevitable algebraic consequences of local information incompleteness. The universal incompleteness of physical laws—singularity breakdown in general relativity, the quantum measurement problem, the redundancy of free parameters in the Standard Model, and the second law of thermodynamics—is unified under a single algebraic root: the asymmetric allocation of information quotas between the global and the local. The trace conservation law τ(𝔄) = τ(𝒩) + τ(ker(E)) guarantees that global and local information are not two independent worlds but two perspectives on the same hyperfinite type III₁ von Neumann factor, constituting a strict dialectical unity. The paper further derives a series of testable observational predictions, including the precise proportions of dark energy, dark matter, and ordinary matter, all algebraically determined by the Jones index χ = 4 of the A₁₁ subfactor with zero free parameters. This work establishes the first complete philosophical and mathematical framework that unifies quantum foundations, cosmological dark components, the incompleteness of physical laws, and the cognitive boundaries of observers under a single principle of information asymmetry.
This paper presents a rigorous demonstration that the fundamental origin of the natural affinity between information ontology and quantum mechanics lies in the eternal asymmetry between global information (the full information algebra 𝔄) and local information (the observable algebra 𝒩). Starting from the core axioms of the Pan-Information Unified Field Theory (PIUFT)—idempotency of information confirmation and trace-preserving information conservation—the paper strictly proves that the kernel space ker(E) necessarily exists and that any observer is necessarily a local information structure, permanently unable to access the full information algebra. The conditional expectation E: 𝔄 → 𝒩 acts as the projection bridge, transforming the global structure of completeness, determinacy, commutativity, real numbers, and classicality into the local structure of incompleteness, indeterminacy, non-commutativity, complex numbers, and quantumness. All core features of quantum mechanics—the emergence of Hilbert space via the GNS construction, operator non-commutativity, complex probability amplitudes, the uniqueness of the Born rule, and quantum entanglement—are rigorously derived as inevitable algebraic consequences of local information incompleteness. The universal incompleteness of physical laws—singularity breakdown in general relativity, the quantum measurement problem, the redundancy of free parameters in the Standard Model, and the second law of thermodynamics—is unified under a single algebraic root: the asymmetric allocation of information quotas between the global and the local. The trace conservation law τ(𝔄) = τ(𝒩) + τ(ker(E)) guarantees that global and local information are not two independent worlds but two perspectives on the same hyperfinite type III₁ von Neumann factor, constituting a strict dialectical unity. The paper further derives a series of testable observational predictions, including the precise proportions of dark energy, dark matter, and ordinary matter, all algebraically determined by the Jones index χ = 4 of the A₁₁ subfactor with zero free parameters. This work establishes the first complete philosophical and mathematical framework that unifies quantum foundations, cosmological dark components, the incompleteness of physical laws, and the cognitive boundaries of observers under a single principle of information asymmetry.
This paper presents the Pan-Information Unified Field Theory (PIUFT), a first-principles algebraic framework that reconstructs quantum mechanics from two core axioms: the confirmation operation and information truncation. Using Tomita-Takesaki modular flow, GNS construction, and fusion category theory, we derive all key postulates of quantum mechanics—including the Hilbert space structure, Born rule, unitary evolution, quantum entanglement, and the Schrödinger equation—without any additional assumptions. The theory reveals that quantum "weirdness" arises from the inherent information truncation of finite observers, rather than being fundamental to nature itself. We also discuss the potential implications for quantum gravity and experimental predictions beyond the standard model.
This paper provides a rigorous derivation of all core postulates of quantum mechanics from a single axiom: the existence of binary distinction. No prior assumptions—Hilbert space, wave function, probability amplitude, or unitary evolution—are introduced as external inputs. The derivation proceeds in six chapters: Chapter 1 establishes the axiom of binary distinction and proves that the imaginary unit i is the algebraic necessity of iterative distinction operations: Δ applied twice equals a reversal (-1), therefore one distinction corresponds to multiplication by i. Chapter 2 demonstrates that complex probability amplitudes are the unique algebraic carriers of the binary split between confirmed information (real part) and concealed information (imaginary part). Chapter 3 proves the Born rule as the unique solution to information deviation minimization under truncation constraints—the squared modulus is the sole functional form compatible with positivity, normalization, and classical-degenerate compatibility. Chapter 4 derives unitary evolution as the traversal of all indistinguishable paths during the suspension interval between confirmation operations. Schr\"{o}dinger's equation emerges as the differential limit of this traversal under modular flow. Chapter 5 establishes that measurement collapse is not a mysterious nonunitary process but the re-execution of the confirmation operation, projecting the suspended superposition onto a single confirmed eigenstate. The collapse probability is identical to the Born rule derived in Chapter 3. Chapter 6 demonstrates that quantum entanglement is the split-window projection of a shared confirmation projector—two entangled particles share the same confirmation projection in the full-dimensional information field, and spatial separation is merely the appearance of local windows in the observable domain. Bell inequality violation follows directly from the non-homomorphic property of the truncation projection. The entire formalism emerges without fitting parameters, without interpretation debates, and without external physical assumptions. Quantum mechanics is thus revealed not as the fundamental language of the universe, but as the inevitable cognitive structure of any finite observer executing information confirmation and truncation on the full-dimensional information field. All conclusions are strictly demarcated by a "boundary of honesty," distinguishing logically necessary deductions from directional inferences requiring further mathematical hardening.
We present a complete derivation of all core postulates of quantum mechanics from the single primordial axiom of Idempotent Emergent Ontology (IEO): existence is confirmation, and confirmation is idempotent (E^2 = E). No prior assumptions—Hilbert space, wave function, probability amplitude, Schrödinger equation, or measurement postulate—are introduced as external inputs. The derivation proceeds through a systematic 19-theorem architecture: Peaks 1-3 establish the mathematical foundation: the GNS construction uniquely generates the Hilbert space from the confirmation algebra; the imaginary unit i emerges as the algebraic necessity of the confirmation closed loop; the Born rule is derived as the unique solution to trace-quota minimization under idempotent projection. Peaks 4-6 derive the dynamics: the Schrödinger equation emerges from the modular automorphism group restricted to the observable domain; measurement collapse is the re-execution of the idempotent projection; quantum entanglement is the split-window projection of a shared confirmation projector. Peaks 7-19 extend the framework to the complete quantum formalism: decoherence, path integrals, quantum tunneling, identical particle statistics, quantum logic, the Dirac equation, quantum field theory, geometric phases, S-matrix algebra, and the zero-redundancy closure theorem. All 19 standard postulates of quantum mechanics are downgraded from axioms to derived theorems. The framework contains zero free parameters—the effective Planck constant \hbar_{\text{eff}} = 1/\chi is rigidly determined by the Jones index \chi = 4. Quantum mechanics is thus revealed not as the fundamental language of the universe, but as the inevitable algebraic structure of any finite observer executing confirmation operations on the full-dimensional modal space. A detailed "Boundary of Honesty" distinguishes rigorously proven theorems from directional inferences requiring further mathematical hardening.本文从自幂涌现本体论(IEO)的唯一原初公理——存在即确认,确认即幂等(E^2 = E)——出发,完整导出了量子力学的全部核心公设。全推导不预设希尔伯特空间、波函数、概率幅、薛定谔方程或测量公设。论证通过系统的19峰定理架构展开: 第一至三峰建立数学基础:GNS构造从确认代数中唯一生成希尔伯特空间;虚数单位i作为确认闭合环的代数必然而涌现;玻恩规则作为幂等投影下迹配额极小化的唯一解被导出。 第四至六峰导出动力学:薛定谔方程从模自同构群在显在域上的限制中涌现;测量坍缩是幂等投影的再度执行;量子纠缠是共享确认投影的分窗口表观分裂。 第七至十九峰将框架扩展至完整量子形式体系:退相干、路径积分、量子隧穿、全同粒子统计、量子逻辑、狄拉克方程、量子场论、几何相位、S矩阵代数、零冗余性闭合定理。 量子力学的全部19条标准公设全部从公理降格为导出定理。框架零自由参数——有效普朗克常数 \hbar_{\text{eff}} = 1/\chi 由Jones指标 \chi = 4 刚性锁定。量子力学因此被揭示为不是宇宙的基本语言,而是任何有限观测者对全维模态空间执行确认操作时必然涌现的代数结构。 详细的“诚实边界”标注严格区分了已完成严格证明的定理与待进一步数学硬化的方向性推断。
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.
This paper proposes a fundamental framework based on information geometry that unifies quantum mechanics, thermodynamics, and spacetime geometry into a single foundational theory. Starting from three elementary axioms regarding information as the primary physical ontology, we derive the universal information metric, construct the information action functional, and show that all known physical laws emerge as extremal conditions of this functional. The theory recovers standard quantum mechanics, classical thermodynamics, and general relativity in appropriate limits, while predicting new relations between quantum entanglement, gravitational curvature, and entropy. We conclude that all physical phenomena—matter, energy, spacetime, and interactions—are equivalent to geometric structures on the space of quantum information states.
Addressing the fundamental metaphysical question of the origin of Being, this paper takes de Broglie’s classical wave mechanics (1924) as its scientific foundation and constructs a self‑consistent interpretive framework of information ontology. It establishes three core axioms: information as the primordial ground, relations prior to entities, and global conservation of information. On this basis, the paper further derives the origin of spatiotemporal dimensions from the laws of information interaction: each basic flip configuration of information corresponds to the generation of a spatial dimension; after three‑dimensional topological closure is completed, the inevitably produced “pending redundant information” that cannot be synchronously and self‑consistently integrated gives rise to the dimension of time within its queuing sequence. Spacetime is therefore not an a priori container but the first compensatory stratum of structure through which information moves toward self‑consistent expression. Subsequently, by means of de Broglie’s phase field, the paper deduces the entire evolutionary chain from pure information distinctions and primordial phase oscillation to the emergence of material hierarchies and quantum‑observation interactions. It argues that quantum measurement and wave‑function collapse are essentially topological remappings and information‑coupling consolidations of heterogeneous phase fields; gravitation and cosmic expansion can be reduced to macroscopic effects of phase gradients. Throughout the text, physical references are strictly limited to de Broglie’s classical wave mechanics, without introducing non‑standard physical models. This study supplements fundamental physical philosophy with a relational‑ontology approach and provides a unified information‑theoretic metaphysical interpretation for foundational problems such as wave–particle duality, the origin of spacetime, and the nature of gravity.