We develop a physical framework in which the elementary excitations of quantum theoryarise as localized singularities of spacetime endowed with a rapidly cycling internaloscillation. The singularity forces a closed-loop internal motion defined on a two-sheetedcover of spatial rotation, making the internal time intrinsically double-valued. Thisgeometric structure enforces the spinorial $4\pi$ rotation law and supplies the four fundamentaloscillatory modes—two spatial circular windings and two temporal windings—from which theWeyl and Dirac equations emerge as the minimal linear evolution laws. The spinor is thusnot an algebraic postulate but the natural representational encoding of the internalgeometry of a singular spacetime excitation. The internal oscillation travels along a curved worldline, forming a helicalspacetime trajectory whose drift, chirality, energy sign, and mass all arise from thegeometric coupling between internal rotation and external motion. Promoting the internalstate to a spatial spinor field provides a mesoscale representation of the excitation’sinternally coherent “clock–gyroscope’’ state across space, enabling superposition andinterference without requiring the excitation itself to be spatially extended. Measurement is interpreted as a localized collision between the singularity and anapparatus. The outcome corresponds to geometric mode selection between the internaloscillation and the detector’s own dynamical modes, while detection probabilities arisefrom the spatial spinor field evaluated over the mesoscale region of interaction. Interferencerequires temporal coherence of the detector rather than multi-path propagation of a spatialwave, and the familiar quantum statistics emerge from the distribution of localizedworldline collisions across repeated trials. This singularity-based framework reproduces the empirical content of quantum mechanicswhile replacing its postulates with concrete dynamical and geometric principles. It unifiesspin, chirality, particle–antiparticle structure, interference, and measurement within asingle spacetime mechanism, and it provides experimentally testable deviations from standardquantum theory in regimes where detector coherence or worldline geometry is altered.
We develop a physical framework in which the elementary excitations of quantum theoryarise as localized singularities of spacetime endowed with a rapidly cycling internaloscillation. The singularity forces a closed-loop internal motion defined on a two-sheetedcover of spatial rotation, making the internal time intrinsically double-valued. Thisgeometric structure enforces the spinorial 4π rotation law and supplies the four fundamentaloscillatory modes—two spatial circular windings and two temporal windings—from which theWeyl and Dirac equations emerge as the minimal linear evolution laws. The spinor is thusnot an algebraic postulate but the natural representational encoding of the internalgeometry of a singular spacetime excitation. The internal oscillation travels along a curved worldline, forming a helicalspacetime trajectory whose drift, chirality, energy sign, and mass all arise from thegeometric coupling between internal rotation and external motion. Promoting the internalstate to a spatial spinor field provides a mesoscale representation of the excitation’sinternally coherent “clock–gyroscope’’ state across space, enabling superposition andinterference without requiring the excitation itself to be spatially extended. Measurement is interpreted as a localized collision between the singularity and anapparatus. The outcome corresponds to geometric mode selection between the internaloscillation and the detector’s own dynamical modes, while detection probabilities arisefrom the spatial spinor field evaluated over the mesoscale region of interaction. Interferencerequires temporal coherence of the detector rather than multi-path propagation of a spatialwave, and the familiar quantum statistics emerge from the distribution of localizedworldline collisions across repeated trials. This singularity-based framework reproduces the empirical content of quantum mechanicswhile replacing its postulates with concrete dynamical and geometric principles. It unifiesspin, chirality, particle–antiparticle structure, interference, and measurement within asingle spacetime mechanism, and it provides experimentally testable deviations from standardquantum theory in regimes where detector coherence or worldline geometry is altered.
We present a structured summary of an oscillatory-spacetime framework in which the standard formalism of quantum mechanics arises from a single physical assumption. In this approach, elementary particles are modeled as localized spacetime singularities carrying an intrinsic oscillatory degree of freedom. The persistence and transport of this oscillation account for wavefunction structure, superposition, energy--momentum relations, spin, relativistic dynamics, antiparticles,and electromagnetic interactions without the introduction of independent postulates. This paper does not rederive the framework, but organizes its development by reviewing the key experimental observations that motivated quantum mechanics, summarizing the core assumptions of the standard theory, and showing how these structures emerge within the oscillatory-spacetime picture. The result is a compact guide for readers familiar with quantum mechanics that clarifies how its diverse elements can be unified within a single physical model.
Abstract Time in physics is conventionally treated as an external real parameter that measures change without participating in it.This study introduces a framework in which time is represented as an intrinsic complex coordinate whose real component corresponds to observable (external) time and whose imaginary component represents the internal phase of physical existence. Within this complex-time structure, temporal evolution is described by a continuous phase rotation on a complex manifold. The amplitude–phase duality of this rotation may provide a unified perspective in which amplitude persistence corresponds to energy and probability conservation, while phase evolution appears to govern the reversible internal oscillation that gives rise to the perception of temporal continuity. The framework is formulated through a minimal variational principle that embeds the phase rotation within a consistent Lagrangian–Hamiltonian structure, linking internal oscillation with relativistic spacetime geometry. It can reproduce the dual relativistic limits of pure temporal rotation () and phase freezing (), and suggests that the coexistence of spatial motion and finite phase evolution may underlie the continuity perceived as the flow of time. Possible experimental implications—such as relativistic interferometry, quantum-clock comparisons, and condensed-matter analogs—are discussed as potential tests of the model. Although the theory remains conceptual and exploratory, it offers a mathematically coherent basis for viewing time as an internal oscillatory degree of freedom. The results suggest that temporal continuity may originate from internal phase coherence, and that macroscopic irreversibility could emergefrom its gradual loss—topics that warrant further investigation. Running Title: Complex-Time Structure and Unified Temporal Framework Keywords: Complex time; phase rotation; quantum–relativistic unification; intrinsic time coordinate; reversible temporal dynamics; phase coherence; variational principle; proper time; phase freezing; arrow of time; internal oscillation.
We present a geometric interpretation of intrinsic spin in which a point-like particle possesses an internal rotational degree of freedom associated with its proper-time evolution. Rather than identifying spin with the mechanical rotation of an extended body, the proposed framework introduces an internal phase variable parameterizing a compact manifold along the particle's worldline. The resulting internal clock evolves at twice the de Broglie mass-energy frequency, allowing the rest-frame wavefunction to be written as ψ(ϕ)=Ae−iϕ/2. This construction reproduces the characteristic two-state structure, spinorial 4π periodicity, and fundamental SU(2) representation of spin-21 particles. Because the internal phase acts as an evolution parameter rather than a canonical operator, the framework avoids the dimensionality and algebraic obstructions associated with quantizing a spatial angular coordinate. The construction extends consistently to the standard Dirac formalism, preserving the established structure of relativistic quantum mechanics and quantum field theory while providing a geometric interpretation of the origin of intrinsic spin.
This work presents a unified, interpretive account of quantum interference and delayed-choice experiments that applies equally to photons and massive particles. Rather than invoking spacetime trajectories, wave–particle duality, retrocausality, or collapse postulates, the paper locates quantum interference in the coherent evolution of internal, pre-geometric degrees of freedom defined over classical spacetime. Within this framework, “which-path” questions are not merely unanswered but fundamentally ill-posed: interference arises from global coherence of an internal field subject to experimental boundary conditions, while spacetime itself remains single-valued and classical at laboratory scales. The approach reproduces all standard quantum-mechanical predictions without modification and is explicitly interpretive rather than predictive. A central result is a unified explanation of why interference occurs across disparate physical systems—photons, electrons, atoms, and molecules—while decoherence manifests through system-dependent physical mechanisms. Photons and massive particles differ in how internal coherence is lost (e.g., electromagnetic absorption versus collisional and thermal interactions), but not in the underlying principle. Delayed-choice experiments are reinterpreted without paradox: changes to the apparatus modify boundary conditions for the internal field rather than retroactively altering particle histories. By removing spacetime paths from the fundamental ontology, the framework offers a consistent, path-free account of interference, decoherence, and localized detection that preserves the empirical success of quantum mechanics while clarifying its conceptual foundations.
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.
We derive the Dirac equation from three postulates concerning the internal complex structure of time: (P1) physical time comprises two orthogonal components, past-fixed (pf) and future-pending (fp); (P2) pf ⊥ fp; and (P3) |T|² = pf² + fp² = 1. These postulates entail that temporal evolution is a first-order phase rotation e^{iθ} (yielding the Schrödinger equation) and that spatial extension of the conservation law gives E² = m²c⁴ + c²p² (yielding the Minkowski metric). The first-order requirement and the causality constraint (both derived from the same postulates) jointly exclude the square-root Hamiltonian on grounds of non-locality, leaving matrix linearisation as the unique path. The resulting Clifford algebra {γ^μ, γ^ν} = 2g^{μν} encodes the Minkowski metric already derived from the postulates, completing a self-consistent chain from temporal ontology to the Dirac equation. The four-component spinor is interpreted as the direct product of the pf–fp doublet (2 components) and the two directions of phase rotation (particle/antiparticle), providing a physical origin for spin-1/2 and its 4π periodicity (Möbius structure). Charge conjugation C, parity P, and time reversal T are reformulated as phase-rotation reversal, spatial phase-gradient reversal, and phase-angle reversal, respectively; CPT invariance is proved as a direct consequence of |T|² = 1. Connections to prior quantum-circuit experiments — in which entanglement was found to be a necessary condition for the linear accumulation of measurement-induced irreversibility — are discussed in the context of the Dirac spinor’s inter-sector coupling. complex time; Dirac equation; Clifford algebra; spinor structure; CPT invariance; Minkowski metric; quantum–relativity unification; temporal ontology; measurement irreversibility