In this work, we extend the 9-dimensional Ultra-Spacetime-Time-Evolution (9D-USTE) framework to explain the origin of quantum double-slit interference from pure geometric field dynamics. Based on the 3+6 dimensional spacetime structure (3D macroscopic spacetime plus a compact 6D internal manifold), a scalar field σ (radion field) governing the volume of the 6D compact internal manifold is shown to exhibit wave-like propagation across the entire spatial region, while the corresponding particle is localized in 3D macroscopic space. We demonstrate that the observed interference pattern is directly identified with the squared gradient of the σ field, whose fluctuations pass through both slits and superimpose. The particle trajectory is guided by the geometric field distribution, yielding a fully deterministic geometric interpretation of quantum duality without wavefunction collapse, nonlocality, or probabilistic postulates. Quantitative estimates of the σ field mass m_σ are provided, and the correspondence between the σ-field wavelength and the de Broglie wavelength is established by fitting existing electron and C₆₀ double-slit experimental data. We further discuss how the compact 6D internal manifold provides a geometric mechanism to address Bell inequality-related nonlocality concerns, distinguishing the 9D-USTE framework from existing Bohmian mechanics and Kaluza-Klein theories. This work advances 9D-USTE as a consistent geometric alternative for unifying classical gravity and quantum phenomena.
In this work, we extend the 9-dimensional Ultra-Spacetime-Time-Evolution (9D-USTE) framework to explain the origin of quantum double-slit interference from pure geometric field dynamics. Based on the 3+6 dimensional spacetime structure (3D macroscopic spacetime plus a compact 6D internal manifold), a scalar field σ (radion field) governing the volume of the 6D compact internal manifold is shown to exhibit wave-like propagation across the entire spatial region, while the corresponding particle is localized in 3D macroscopic space. We demonstrate that the observed interference pattern is directly identified with the squared gradient of the σ field, whose fluctuations pass through both slits and superimpose. The particle trajectory is guided by the geometric field distribution, yielding a fully deterministic geometric interpretation of quantum duality without wavefunction collapse, nonlocality, or probabilistic postulates. Quantitative estimates of the σ field mass m_σ are provided, and the correspondence between the σ-field wavelength and the de Broglie wavelength is established by fitting existing electron and C₆₀ double-slit experimental data. We further discuss how the compact 6D internal manifold provides a geometric mechanism to address Bell inequality-related nonlocality concerns, distinguishing the 9D-USTE framework from existing Bohmian mechanics and Kaluza-Klein theories. This work advances 9D-USTE as a consistent geometric alternative for unifying classical gravity and quantum phenomena.
This work provides a deterministic geometric interpretation of the double-slit experiment, moving beyond probabilistic quantum mechanical models. By utilizing a five-dimensional Kaluza-Klein metric framework with a dynamic scalar warping field \Phi(r), we demonstrate that interference patterns are manifestations of particle interaction with higher Kaluza-Klein harmonics (n > 0) in the fifth dimension. Furthermore, the collapse of the wavefunction upon measurement is derived as a dynamical consequence of the warping field localizing in the zero-mode state (n=0). This framework suggests that quantum phenomena can be understood as macroscopic manifestations of higher-dimensional spacetime geometry.
The double-slit experiment has long been interpreted as evidence of wave-particle duality and quantum superposition. Here we propose a deterministic alternative rooted in Trembling Spacetime Relativity Theory (TSRT), where particles always follow localized proper-time geodesics within a causally structured but metrically fluctuating spacetime. Apparent interference fringes arise not from wavefunction superposition, but from the deterministic redirection of particle geodesics due to curvature perturbations shaped by the slit geometry. The observed distribution of arrival positions is governed by two geometric mechanisms: (i) the slit separation, which sets the angular deflection range of redirected geodesics, and (ii) a minimal action threshold that enforces a resolution limit based on causal distinguishability. Planck’s constant emerges naturally from this causal constraint as the smallest resolvable geodesic action difference, without any quantum postulates. TSRT provides analytical predictions for fringe spacing and intensity distribution across a wide range of particles—photons, electrons, and neutrons—by applying geometric deflection laws to causally permitted geodesics. These predictions align closely with established experimental results. In addition, the TSRT framework enables simulation of arbitrary configurations by modeling ensembles of geodesics subject to metric trembling, providing a fully geometric alternative to quantum superposition.
Background: The unification of General Relativity and Quantum Mechanics represents a fundamental challenge in theoretical physics due to their mutually exclusive conceptual foundations: continuous deterministic geometry versus probabilistic wave functions. While the de Broglie-Bohm pilot-wave theory offers a deterministic, trajectory-based alternative to the standard probabilistic framework, it introduces a non-local, ad-hoc "Quantum Potential" (Q) to account for phenomena such as interference and non-locality. The lack of a geometric origin for Q in standard spacetime remains a significant conceptual barrier to a fully unified theory. Purpose: This paper aims to resolve this interpretational crisis by proposing that the Quantum Potential is not a fundamental or mysterious external force, but rather a derived geometric artifact. We postulate that the physical universe is fundamentally a 4-dimensional Complex Manifold (ℂ4), extending the standard Riemannian spacetime manifold to include imaginary coordinates. Methods: To establish this geometric basis, we treat the quantum wave function not as an abstract probabilistic amplitude, but as a physical, holomorphic map describing a particle's deterministic trajectory through this complex spacetime. Utilizing the Cauchy-Riemann conditions, we demonstrate that the Bohmian amplitude (R) is strictly coupled to the particle's location in the imaginary dimension. We then analyze the dynamics of particles following geodesics within ℂ4. By projecting the complex geodesic equation of motion onto the observable real slice (ℝ4), we separate the real and imaginary components of the complex 4-velocity to observe the energy balance. Conclusions: Our derivation reveals that the Quantum Potential (Q) emerges naturally and is mathematically identical to the kinetic energy component associated with a particle's hidden motion in these imaginary dimensions. This formulation successfully recovers the predictions of the Schrödinger equation while removing the ad-hoc nature of Bohmian mechanics. Furthermore, it interprets quantum non-locality—such as the interference observed in the double-slit experiment—as purely local, deterministic geodesic motion around topological singularities in a curved complex manifold. Ultimately, this framework provides a unified geometric description wherein gravity is the curvature of real coordinates, electromagnetism is the torsion of imaginary coordinates, and quantum mechanics is inertial motion through this complex geometry.
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.
The double-slit interference experiment remains one of the most puzzling phenomena in quantum mechanics. Standard quantum mechanics explains it through wave-particle duality, superposition, and wavefunction collapse—all mathematical postulates without physical mechanisms. Within the Huaxia Spacetime Total Conservation Theory (H-SET), the electron is not a point particle but a helical dislocation loop in the space medium with spatial extension determined by the space quantum coherence scale. Interference arises because the elastic field of a single electron loop simultaneously covers both slits, and the two emergent elastic waves interfere on the screen. The effective de Broglie wavelength is derived as the geometric extension of the dislocation loop in the momentum direction, yielding identical numerical values to standard quantum mechanics but with a physical origin. Observation-induced disappearance of interference is explained as the destruction of elastic boundary conditions at the slits by the macroscopic elastic field of the detector, not by mysterious wavefunction collapse. Three testable predictions are provided: precise fringe spacing for fullerene (C₆₀) interference, the quantitative relationship between path distinguishability and fringe visibility, and the mass limit for macromolecular interference.
This article presents a conceptual interpretation of the double-slit experiment using Feynman's path integral formulation. Rather than treating a quantum particle as a point-like object following a single trajectory, the particle's propagation is viewed as a distributed structure in 4D spacetime. In the path-integral picture, this structure is represented by a coherent sum over possible paths between emission and detection. From this perspective, the observed interference pattern emerges from the phase relationships between these possible spacetime paths. The article distinguishes between propagation and interaction. Propagation is described as an extended 4D process, while measurement appears as a localized spacetime event within a 3D spatial slice, producing the point-like detections observed in the double-slit experiment. The aim is not to propose a new physical theory or to explain the mechanism of collapse, but to provide an intuitive geometric interpretation of the standard quantum formalism and its relationship between quantum propagation, interference, and localized measurement outcomes. This is a conceptual essay and interpretive synthesis, not a proposal of a new physical theory.