Zhang Xiangqian's Unified Field Theory: From State Vectors to Quantum Control and Correction, Then to the Unified Geometric Theory of Antigravitational Waves
Under the core paradigm of "physics is geometry" in Zhang Xiangqian's Unified Field Theory (UFT), this paper systematically completes the full geometric reconstruction from non-relativistic quantum mechanics, open quantum systems, quantum information theory to quantum control and error correction.All derivations logically originate from three core postulates—spacetime light-speed cylindrical spiral motion, the light-speed constraint equation, and the geometrization postulate—thoroughly reducing the entire mathematical structure of quantum mechanics to the geometric properties of spacetime vibration modes. Key achievements include: 1) Interpreting state vectors, superposition principle, coherence, density matrix, and decoherence as inevitable manifestations of spatiotemporal vibration modes, amplitude-coherent superposition, geometric phase locking, vibrational ensemble statistics, and geometric phase dispersion, respectively. Deriving the decoherence rate , where represents the geometric phase coupling strength; 2) Established geometric interpretations for trace, purity, norm coherence, and relative entropy coherence, directly relating them to the total number of vibrational units, coherence strength, and non-diagonal long-range phase correlations, while providing the geometric origin of typical two-level system Hamiltonians; 3) Rigorously derives the Liouville–von Neumann equation, Lindblad principal equation, and Bloch equation from UFT geometric dynamics, expressing relaxation rates and decoherence times as functions of the fluctuation spectral density of environmental geometric parameters; 4) Unifies the interpretation of light-matter interactions, superconducting macroscopic coherence, and spin dynamics as outcomes of spacetime flexural fields, phase-locked collective modes, and geometric coupling, deriving UFT geometric formulations for the Jaynes–Cummings model, London equation, Josephson relations, and NMR Bloch equations; 5) Reveals the geometric essence of spin echo and CPMG sequences—temporal inversion of geometric phase and frequency-domain windowing—providing the frequency-domain convolution relationship between decoherence factors and environmental spectra; 6) Interpreted the logical subspace of stabilizer codes as a geometric constrained subspace of vibrational modes, revealing the error correction process as a three-step operation of geometric projection, geometric classification, and geometric relocking, and provided the geometric meaning of the fault tolerance threshold . 7) Finally, the theory is extended to the active regulation and long-range propagation mechanisms of anti-gravitational fields. Based on the geometric chirality principle of UFT, five theoretical pathways for achieving long-range propagation of anti-gravitational waves are systematically evaluated, providing a clear theoretical blueprint for gravitational engineering, space propulsion, and gravitational wave communication. All derivations undergo rigorous dimensional consistency verification, forming a logical closed loop with prior UFT achievements (mass-frequency equivalence, geometric expression of the fine-structure constant, system, electromagnetic-gravitational unified theory, etc.), while smoothly converging to existing quantum theories under corresponding limits.This work signifies that the UFT paradigm of "physics as geometry" has extended from classical physics, electromagnetism, and relativistic quantum mechanics to the core domains of quantum information and quantum engineering. It provides a robust first-principles geometric foundation for understanding the essence of quantum mechanics and actively safeguarding quantum technologies. This record is formatted and submitted by Lynn Lou Beran on behalf of the author. The author is solely responsible for the content.
Under the core paradigm of "physics is geometry" in Zhang Xiangqian's Unified Field Theory (UFT), this paper systematically completes the full geometric reconstruction from non-relativistic quantum mechanics, open quantum systems, quantum information theory to quantum control and error correction.All derivations logically originate from three core postulates—spacetime light-speed cylindrical spiral motion, the light-speed constraint equation, and the geometrization postulate—thoroughly reducing the entire mathematical structure of quantum mechanics to the geometric properties of spacetime vibration modes. Key achievements include: 1) Interpreting state vectors, superposition principle, coherence, density matrix, and decoherence as inevitable manifestations of spatiotemporal vibration modes, amplitude-coherent superposition, geometric phase locking, vibrational ensemble statistics, and geometric phase dispersion, respectively. Deriving the decoherence rate , where represents the geometric phase coupling strength; 2) Established geometric interpretations for trace, purity, norm coherence, and relative entropy coherence, directly relating them to the total number of vibrational units, coherence strength, and non-diagonal long-range phase correlations, while providing the geometric origin of typical two-level system Hamiltonians; 3) Rigorously derives the Liouville–von Neumann equation, Lindblad principal equation, and Bloch equation from UFT geometric dynamics, expressing relaxation rates and decoherence times as functions of the fluctuation spectral density of environmental geometric parameters; 4) Unifies the interpretation of light-matter interactions, superconducting macroscopic coherence, and spin dynamics as outcomes of spacetime flexural fields, phase-locked collective modes, and geometric coupling, deriving UFT geometric formulations for the Jaynes–Cummings model, London equation, Josephson relations, and NMR Bloch equations; 5) Reveals the geometric essence of spin echo and CPMG sequences—temporal inversion of geometric phase and frequency-domain windowing—providing the frequency-domain convolution relationship between decoherence factors and environmental spectra; 6) Interpreted the logical subspace of stabilizer codes as a geometric constrained subspace of vibrational modes, revealing the error correction process as a three-step operation of geometric projection, geometric classification, and geometric relocking, and provided the geometric meaning of the fault tolerance threshold . 7) Finally, the theory is extended to the active regulation and long-range propagation mechanisms of anti-gravitational fields. Based on the geometric chirality principle of UFT, five theoretical pathways for achieving long-range propagation of anti-gravitational waves are systematically evaluated, providing a clear theoretical blueprint for gravitational engineering, space propulsion, and gravitational wave communication. All derivations undergo rigorous dimensional consistency verification, forming a logical closed loop with prior UFT achievements (mass-frequency equivalence, geometric expression of the fine-structure constant, system, electromagnetic-gravitational unified theory, etc.), while smoothly converging to existing quantum theories under corresponding limits.This work signifies that the UFT paradigm of "physics as geometry" has extended from classical physics, electromagnetism, and relativistic quantum mechanics to the core domains of quantum information and quantum engineering. It provides a robust first-principles geometric foundation for understanding the essence of quantum mechanics and actively safeguarding quantum technologies. This record is formatted and submitted by Lynn Lou Beran on behalf of the author. The author is solely responsible for the content.
Abstract This paper is the third part of the third volume of the Back-Particle Theory. Building upon the dynamic intrinsic displacements, unified wave equation, and emergence of electromagnetic potentials established in Parts I and II of Volume 3, it systematically completes the geometric interpretation of quantum behavior, the emergent derivation of relativistic structure, and the geometric construction of the Dirac equation. Starting from the enormous degrees of freedom (∼ 10¹⁰⁴) of the back-particle array and its deterministic chaos, we demonstrate that quantum probability is not a fundamental postulate but an inevitable result of finite-information coarse-grained descriptions of the array’s chaotic dynamics, with the Born rule P = |ψ|² interpreted as a statistical expression of the excitation weights of specific vibration modes of the array. Through canonical quantization of the array displacement field, we rigorously derive the uncertainty principle Δx Δp ≥ ℏ_eff/2 and the zero-point fluctuation formula, and derive the decoherence rate Γ_dec ∼ (Θ_env/ℏ_eff)(Δr/d₀)² from the system-environment coupling model. Furthermore, starting from the homogeneous wave equation of the free array and requiring its form invariance under inertial frame transformations, we rigorously derive the Lorentz transformation, proving that the space-time structure of special relativity is a natural emergence of the array’s wave geometry. Based on the second-order classical dynamical equation of intrinsic displacements, we rigorously derive the Dirac equation through operator factorization by introducing the Clifford algebra γ^μ, where the spinor field Ψ is constructed from the intrinsic displacements (d_A, d_f) via symmetry mapping, the mass term ω₀/c originates from the array’s restoration frequency, the spin operator satisfies the SU(2) algebra, and spin 1/2 emerges naturally from the quantization of intrinsic angular momentum. All derivations strictly follow the principles of causal unidirectionality, field superposition, dimensional purity, and parameter emergence, with all parameters emerging in a closed manner from the basic set {A, F, f, f_ext, ρ₀, c} and the lattice geometric factors, achieving a complete logical closed loop from classical array dynamics to quantum mechanics. Keywords: Back-Particle; Emergence of Quantum Probability; Born Rule; Uncertainty Principle; Decoherence; Lorentz Transformation; Dirac Equation; Spinor Field; Spin 1/2; Clifford Algebra; Geometric Quantum Mechanics
This Volume III develops a complete geometric formulation of quantum mechanics, demonstrating that quantum phenomena emerge from the very structure of spacetime. We demonstrate that Einstein's field equations—when interpreted in the spectral domain and taking phase coherence into account—already contain the entire structure of quantization. Quantum mechanics appears not as an axiom, but as a geometric consequence. Based on the experimental and mathematical results consolidated in Volumes~0, I, and II, the present work shows that quantization need not be postulated: it arises inevitably from three fundamental geometric elements—proper frequency, parallel transport, and phase coherence. The action appears as the phase accumulated along the worldline, and its discretization into coherence windows, derived without external hypotheses, naturally leads to the condition Sn=nh and to all associated quantum phenomenology. We derive the Schrödinger equation as the limit of short windows, obtain the commutator [x,p]=iℏ from the incompatibility between spatiotemporal synchronizations, and reinterpret interference, propagators, and decoherence as spectral properties of parallel transport. The Hilbert space arises as the spectral space of the metric, observables correspond to generators of isometric deformations, while the collapse is understood as the geometric selection of coherent subspaces. The formalism extends to relativistic particles, spin, quantum statistics, the Dirac equation, harmonic oscillators, and field quantization, where spectral modes of the metric assume the role of particles: photons as harmonic 1-forms, weak modes as connections of 2-forms, gluons as 3-forms, and the Higgs as the fundamental scalar curvature mode. The reinterpretation of the Standard Model thus becomes a direct consequence of spectral geometry. The Volume culminates in the Central Theorem —Geometry = Quantization— showing that the entire quantum structure is a manifestation of the spectral granularity of spacetime. We conclude with experimental predictions and falsification criteria, as well as the conceptual framework necessary for Volume~IV, dedicated to the complete quantization of the metric within the same paradigm.
Previous works of this series have realized the classical unification of gravitation and electromagnetic fields based on the spacetime density tensor, and the intrinsically generated high-order couplings consistently explain various observational anomalies of compact celestial objects. As a realistic quantum framework, existing schemes for unifying Bohmian theory and gravity generally adopt a dual structure that separates spacetime from the pilot wave. The nonlocality of quantum entanglement in multi-particle systems leads to fundamental conflicts with the local causality of relativity. Meanwhile, torsion-free Riemannian geometry cannot accommodate spin-1/2 fermion spinors, nor can it intrinsically generate the short-range SU(2) weak and SU(3) strong gauge interactions, making it difficult to fully embed the Standard Model of quantum field theory. On the basis of maintaining the monistic ontological postulate of the spacetime density tensor, this paper carries out theoretical expansion in two stages. First, the Bohmian pilot wave, quantum potential and multi-particle entanglement are defined as global coherent perturbations of the spacetime density tensor. This work strictly distinguishes the field structures, dynamic equations and propagation mechanisms of separable quantum states and entangled quantum states, and reconstructs the covariant quantum guiding equation. It resolves the paradox between quantum nonlocality and relativistic causality from an ontological perspective, achieving the unification of classical field theory and Bohmian quantum mechanics. Second, Einstein–Cartan (EC) geometry is introduced with the additional degree of freedom of spacetime torsion. Two types of quantum correlations, namely orbital entanglement and spin entanglement, are differentiated. Fermion spinor fields, as well as U(1) electromagnetic, SU(2) weak and SU(3) strong gauge interactions, are all mapped to local chiral twists and color topological torsional perturbation modes of spacetime. Four core innovations are presented in this paper: 1. Quantum effects are attributed to global coherent fluctuations of spacetime density. The essential geometric differences between ordinary separable quantum states and entangled states are clarified. Entanglement originates from the global coherent deformation of spacetime rather than superluminal action, thoroughly eliminating the dual separation between quantum fields and spacetime. 2. With the aid of EC torsion geometry, fermion spinors are no longer background-independent fields but geometric projections of local spin torsion of spacetime, realizing the geometric ontology of intrinsic spin. 3. The complete set of U(1)/SU(2)/SU(3) gauge symmetries arise intrinsically from multi-scale topological perturbations of the spacetime density tensor, removing the artificial introduction of gauge groups as implemented in the Standard Model. 4. A complete covariant unified field system covering gravitation, electromagnetism, Bohmian quantum effects, weak interactions and strong interactions is constructed, alongside a quantitative calculation system for orbital entanglement and spin entanglement. Under corresponding limiting conditions, the system rigorously reduces to General Relativity, Maxwell's equations, covariant Bohmian dynamics, electroweak Lagrangian and standard QCD Lagrangian. Key physical phenomena including parity violation of the weak interaction, color confinement, asymptotic freedom and quantum nonlocality are consistently explained via geometric structures. This study ultimately establishes a self-consistent unified field theory with a single ontology, which is compatible with classical field theory, realistic Bohmian quantum mechanics and the Standard Model of quantum field theory.
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
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 work presents an extended, mathematically complete formulation of the Information Geometry Unification Principle (IGUP), a foundational framework in which quantum mechanics, statistical thermodynamics, general relativity, and spacetime geometry emerge from a single information-theoretic ontology. We begin with rigorous axioms defining information as the primary physical substance, then systematically construct the Bures–Fisher–Rao metric on the manifold of quantum density matrices. We derive the universal information action functional and perform full variational derivations to obtain the unified field equations. We show explicitly how standard physical theories including the Schrödinger equation, Heisenberg picture, Liouville mechanics, classical thermodynamics, and Einstein field equations are recovered in appropriate limiting regimes. We further derive geometric expressions for entanglement, entropy, temperature, energy, and force. The theory resolves longstanding conceptual tensions between unitary quantum evolution and gravitational irreversibility, provides a natural resolution to the black hole information paradox, and yields eight concrete, experimentally testable predictions. This extended version includes full tensor calculus, covariant derivatives, curvature expansions, and limit theorems, amounting to a self-contained theory of everything based on Geometry=Information.