Unified Field Theory Based on Four-Dimensional Spacetime Density Tensor: Global Unification of Bohmian Pilot Wave, Gauge Fields and Five Fundamental Interactions
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 $\mathrm{SU}(2)$ weak and $\mathrm{SU}(3)$ 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 $\mathrm{U}(1)$ electromagnetic, $\mathrm{SU}(2)$ weak and $\mathrm{SU}(3)$ 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 $\mathrm{U}(1)/\mathrm{SU}(2)/\mathrm{SU}(3)$ 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.
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.
We develop a complete geometric framework in which each quantum particle possesses its own private spacetime—a world-block—constructed from Fermi–Walker coordinates. The intrinsic spatial metric on each proper-time slice is a dynamical field governed by an action with a universal stiffness constant A0. A single world-block exhibits kinematic non-locality: the metric perturbation at a point depends on the entire wavefunction through an integral relation, while maintaining dynamic locality via causal wave equations. This duality captures the essential non-locality of quantum mechanics without violating relativistic causality. When two particles interact, their world-blocks are stitched along a common boundary, forming a single compound world-block in ordinary four-dimensional spacetime. The stitching imposes local matching conditions that yield a non-separable strain field, providing a geometric account of quantum entanglement. Measurements correspond to fixing boundary conditions on one part of the compound block; the correlated outcome on the distant part is automatically determined by the shared global geometry, not by any superluminal signal. Thus, the apparent non-locality of EPR correlations is explained as a manifestation of geometric connectivity within a single 4D manifold, consistent with Bell’s theorem because the geometry itself is non-local. In the continuum limit of many overlapping blocks, coarse-graining restores an effective local description, and Newton’s law of universal gravitation emerges exactly, with Newton’s constant given by G = 3c4/(8πA0). The model offers a unified, deterministic, and fully relativistic foundation for quantum mechanics and gravity, without invoking extra dimensions or stochastic elements. Experimental signatures in ultrafast interferometry and possible connections to dark energy are discussed. The framework aligns with recent developments in emergent gravity and provides a concrete geometric realization of spacetime from quantum entanglement.
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 presents a unified gauge-theoretic framework that resolves fundamental incompatibilities between General Relativity and the Standard Model by rejecting the axiom of linear time. The KnoWellian Universe Theory (KUT) proposes that time possesses an irreducible ternary structure composed of three perpetually interacting realms: the Past (Control), the Instant (Consciousness), and the Future (Chaos). Through a U(1)⁶ gauge symmetry, KUT generates six fundamental gauge fields that mediate not only spatial gravity but also two cosmological forces identified as Dark Energy (outward Control flow) and Dark Matter (inward Chaos collapse). Central to the framework is the KnoWellian Resonant Attractor Manifold (KRAM)—a dynamic, higher-dimensional memory substrate underlying spacetime itself. This work presents a radically modified Bohmian pilot-wave mechanism wherein the Chaos field (pilot wave) physically "etches" the complete history of quantum events into KRAM's geometric structure, creating persistent "attractor valleys." This mechanism provides concrete physical explanations for fine-tuning, morphic resonance, and the emergence of linear particle tracks from spherically symmetric wavefunctions (the Mott Problem). The framework redefines mass as the "activation energy of existence" required for irreversible rendering of potentiality into actuality, providing a formal solution to the Yang-Mills Mass Gap problem. It demonstrates that mathematical questions about completed infinities, such as the Riemann Hypothesis, are "un-renderable" within a procedural universe. KUT makes multiple specific, falsifiable predictions including: (1) Cairo pentagonal tiling geometry in CMB anisotropies, (2) coherent "ghost" patterns in cosmic voids from prior cycles, (3) geometric derivation of the fine-structure constant α ≈ 1/137, (4) Cairo lattice topology in high-coherence brain states, (5) spectral break in stochastic gravitational wave background, and (6) absence of primordial B-mode polarization. By integrating physics, ontology, and consciousness into a single coherent Lagrangian, this work offers a complete, paradox-free, and empirically testable description of reality as participatory process rather than passive object. Changes in Version 2 (January 10, 2026) Nomenclature Standardization Field notation consistency: Standardized triadic field notation for clarity and physical interpretation Changed φ_C → φ_M (M for Mass/Matter, emphasizing rendered actuality in the Control field) Changed φ_X → φ_W (W for Wave, emphasizing unrendered potentiality in the Chaos field) Retained φ_I (Instant/Consciousness field, the synthesizing mediator) Symbolic consistency: Standardized bounded infinity notation from c⁺ to c+ throughout document Technical Corrections Updated DOI to reflect current Zenodo record: 10.5281/zenodo.18210128 Corrected publication date to January 10, 2026 Updated "Last Modified" metadata to January 10, 2026 Rationale for Field Notation Changes The new nomenclature (φ_M, φ_I, φ_W) provides clearer physical interpretation: φ_M (Mass): Represents the rendered, particle-like, actualized state of reality (Control field from the Past) φ_W (Wave): Represents the unrendered, wave-like, potential state of reality (Chaos field from the Future) φ_I (Instant): Represents the consciousness-mediated synthesis occurring at the eternal "now" This triadic correspondence (Mass-Instant-Wave) aligns more intuitively with wave-particle duality, making the framework more accessible while maintaining mathematical rigor. The M-I-W notation reinforces that particles (M) and waves (W) are not separate entities but different ontological states of the same underlying field structure, mediated through conscious interaction (I). Document Integrity All equations, theorems, proofs, physical interpretations, and predictions remain mathematically and conceptually identical to Version 1. These changes affect only notation and metadata, not substantive content or theoretical claims. Keywords: KnoWellian Universe Theory, ternary time, gauge theory, KRAM, pilot wave, quantum mechanics, consciousness, dark matter, dark energy, mass gap, Mott problem, procedural ontology, morphic resonance, fine-structure constant, CMB anisotropies Subject Categories: Theoretical Physics, Quantum Mechanics, Cosmology, Philosophy of Physics, Consciousness Studies
The extension of Bohmian mechanics to the relativistic domain, and to quantum field theory presents specific theoretical difficulties. The non-local nature of the pilot-wave guidance equations inherently requires a temporal ordering of spacelike separated events. Historically, this requirement has been satisfied by introducing an arbitrary preferred foliation of spacetime, which leads to covariance concerns. Furthermore, the standard Bohmian particle model struggles to accommodate particle creation and annihilation events, which are characteristic of quantum field theory (QFT). This paper constructs a theoretical framework that is rigorously Lorentz-invariant, and compatible with QFT. The proposed synthesis couples the Tomonaga-Schwinger equation for the relativistic wave functional with a hypersurface Bohm-Dirac model (HBDM). To ensure Lorentz invariance without adding absolute spatiotemporal structure, the necessary foliation is covariantly determined by the universal wave function. To address particle non-conservation, the deterministic trajectories are supplemented by a Bell-type stochastic Markov jump process defined on Fock space, utilizing minimal jump rates derived directly from the interaction Hamiltonian. A hybrid model is adopted, assigning localized particle beables to fermions, and continuous field beables to bosons. The exact equivariance of the probability distributions across the covariantly defined leaves of the foliation is proven, demonstrating that the model reproduces the empirical predictions of standard regularized QFT. In an appendix, we discuss the modeling of neutrinos. Finally, this framework is interpreted with the multi-fold theory. In this context, the covariantly determined foliation emerges physically from a discrete, non-commutative spacetime concretized by 2D random walks of massless Higgs bosons. The multi-fold mechanism and the E/G conjecture (entanglement is gravity) provide a local, physical model for the non-local Bohmian guidance equations, while space-time matter induction and scattering explain the origin of the proposed hybrid field-particle beables as patterns and condensates of these random walks. Sizes or scales also align with multi-fold modeling of QFT with 2D random walks, and spacetime non-commutativity to support Quantum Physics and Fermions. These add to many examples where the multi-fold preons as massless Higgs bosons can microscopically interpretate Quantum Physics behaviors.
We propose an exploratory framework for a Bohmian model of quantum matter propagating on a classical curved spacetime background. The gravitational sector is governed by classical Einstein field equations throughout; no quantisation of spacetime is attempted. The wave function emerges as the scalar contraction Ψ=ψνψν∈C of a complex-valued tensorial field ψμ, encoding quantum dynamics in a geometric object. The wave tensor interacts with spacetime via the stress–energy tensor Tμν, mediated by a real scalar field a of dimension volume, so that aTμνψμψν yields the correct potential energy. We derive a covariant Adapted Schrödinger Equation as the unique minimal covariant lift of the standard equation, justify it from four guiding principles, and verify three internal consistency checks. Under seven explicit approximations the framework reproduces the Schrödinger equation with Coulomb potential for the hydrogen atom. We also derive a dynamical equation for ψμ that entails the Adapted Schrödinger Equation by contraction. Two open problems are then resolved. First, a complete Lagrangian formulation is provided: a real-valued action for Ψ yields the Adapted Schrödinger Equation via the Euler–Lagrange equations; a separate action for ψμ, extended by a non-polynomial term, yields the full dynamical equation variationally. Second, two experimental predictions are derived. Expanding to first post-Newtonian order, the perturbation Hamiltonian has coefficients (3, 1) on the kinetic and potential operators; via the virial theorem these produce a coordinate-time blueshift, which after photon propagation yields the universal Einstein gravitational redshift δν/ν=Φ/c2, confirming consistency with the equivalence principle. The same kinetic coefficient independently predicts that free quantum wave packets spread more slowly by the fractional amount 3|Φ|/c2, a correction absent in standard non-relativistic quantum mechanics.
We propose a unified physical framework in which four-dimensional spacetime vacuum is the unique physical reality, and all quanta are its localized topological excitations. Matter particles correspond to stable knot-like configurations, while radiation quanta correspond to weak propagating ripples of the same substrate. From this single ontological commitment, we derive: (1) wave–particle duality is resolved—particle behavior belongs to the localized excitation, wave behavior to the disturbance field it generates in spacetime; (2) double-slit interference arises from coherent superposition between a quantum's newly sourced disturbance and its own historical disturbance field, not from ontological self-superposition; (3) the wave function is a statistical tool encoding ensemble distributions of trajectories modulated by disturbance feedback, and collapse is epistemic convergence rather than a physical process; (4) quantum entanglement corresponds to Planck-scale topological connectivity (microscopic Einstein–Rosen bridges), preserving relativistic causality; (5) gravity is the macroscopic accumulation of universal but individually weak quantum–vacuum couplings, explaining both its microscopic weakness and macroscopic dominance without requiring a graviton; (6) the four fundamental interactions are differentiated coupling modes of quanta to one spacetime vacuum field; and (7) apparent dark matter and dark energy are reinterpreted as collective topological curvature and large-scale vacuum self-relaxation, respectively. We formulate falsifiable predictions at both laboratory and cosmological scales, including disturbance–corpuscle separation interferometry, tunable decoherence threshold measurements, and galaxy rotation–topology correlations. The framework compresses the conventional axiomatic structure of quantum mechanics and cosmology into one master axiom and eliminates at least twenty-eight independent interpretive assumptions.