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UDCT v4.0: A Dynamic Geometric Framewor9k for the Double-Slit Paradox and Measurement Problem

Won Shik Paik

Published Jun 20, 2026• 0 citations
Publisher

Abstract

This paper extends the Unified Dimensional Cohesion Theory (UDCT v4.0) to the quantum domain by replacing the probabilistic foundations of quantum mechanics with a deterministic, geometric framework. We argue that the long-standing difficulties of quantum mechanics, including the measurement problem and the double-slit paradox, arise not from the intrinsic nature of particles, but from the structural assumption that spacetime provides a static, inert background. By extending the dynamic compactification mechanism into the microscopic regime, we introduce a non-local temporal memory kernel and dynamic geometric back-reaction at the quantum scale. Within this framework, quantum behavior emerges as the deterministic response of localized energy densities interacting with a living, responsive higher-dimensional geometry. This model offers a new geometric paradigm that aims to establish a physically transparent description of quantum foundations.

DOI
10.5281/zenodo.20779758

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This paper extends the Unified Dimensional Cohesion Theory (UDCT v4.0) to the quantum domain by replacing the probabilistic foundations of quantum mechanics with a deterministic, geometric framework. We argue that the long-standing difficulties of quantum mechanics, including the measurement problem and the double-slit paradox, arise not from the intrinsic nature of particles, but from the structural assumption that spacetime provides a static, inert background. By extending the dynamic compactification mechanism into the microscopic regime, we introduce a non-local temporal memory kernel and dynamic geometric back-reaction at the quantum scale. Within this framework, quantum behavior emerges as the deterministic response of localized energy densities interacting with a living, responsive higher-dimensional geometry. This model offers a new geometric paradigm that aims to establish a physically transparent description of quantum foundations.
Unified Dimensional Cohesion Theory (UDCT v4.2) proposes that quantum phenomena such as double-slit interference can arise from the deterministic interaction between localized energy and a dynamically responsive microscopic spacetime endowed with memory. In this work, we present extensive two-dimensional numerical simulations to investigate this hypothesis. We implemented causal memory kernels acting on the Minkowski metric and systematically explored particle dynamics in a double-slit geometry. Through comprehensive parameter studies, we identified three distinct dynamical regimes: a weak-coupling regime recovering classical trajectories, an over-coupling regime characterized by chaotic scattering, and an intermediate regime of controlled spreading induced by geometric memory. Among the memory kernels examined, a damped oscillatory kernel produced the strongest suppression of trajectory spreading, achieving a minimum standard deviation of approximately 8.4. These results demonstrate that microscopic metric memory can exert significant deterministic influence on particle trajectories. However, clear bimodal interference patterns have not yet been observed, and stronger spreading control was often accompanied by reduced detection efficiency. Our findings establish a quantitative foundation for exploring geometric mechanisms underlying quantum phenomena while highlighting key challenges that remain for reproducing full interference patterns through spacetime hysteresis alone.
We present a detailed numerical investigation of the internal encoding of path information in the double-slit experiment within the Unified Dimensional Cohesion Theory (UDCT) v4.4 framework. We replace the previous static geometric memory kernel with a Dynamic Self-Regulating Bidirectional Back-Reaction (DSBB) paradigm. In this framework, the spacetime geometry itself dynamically responds to curvature errors induced by the projected wavefunction through a self-regulating feedback field B(r,t), whose damping is controlled by Gamma(B) = (1/tau_0)(1 + beta |B|^2). This eliminates any ad-hoc memory history while enabling real-time bidirectional coupling between the probability density and the effective geometric potential V_DSBB. Using the split-step Fourier method on a 256×256 grid, we demonstrate in two-dimensional simulations with a physically realistic double-slit barrier that the DSBB field develops clear spatial asymmetry between the two paths, internally encoding which-path information without external measurement. Furthermore, we introduce a Detector Freezing Mechanism that overwhelms the self-regulating loop at mid-evolution, driving the system toward classical bimodal distributions. Our results show near-perfect unitarity (norm conservation to \~10^{-15}) and provide concrete evidence that dynamic self-regulation in spacetime geometry can resolve the measurement problem and path distinguishability in a physically transparent manner. The DSBB framework offers significant conceptual and numerical advantages over the static memory approach of v4.3.
We present a detailed numerical investigation of the internal encoding of path information in the double-slit experiment within the Unified Dimensional Cohesion Theory (UDCT 4.3) framework. Using the Auxiliary Variable Method, we evolve a geometric memory field concurrently with the wavefunction in a strictly unitary manner. In one-dimensional simulations, we systematically vary the memory coupling strength γ across the range [0, 100] with fixed relaxation time τ = 0.12 and perform quantitative analysis of interference visibility and peak broadening. Visibility is computed using peak detection with prominence thresholding on the final probability density. In two-dimensional simulations with a physically realistic double-slit barrier, we demonstrate that the geometric memory field develops a clear spatial asymmetry between the two slits. This asymmetry is quantified and shown to encode which-path information internally without any external measurement. We compare our wavefunction-based approach with previous trajectory-based formulations (v4.2) and discuss the advantages and limitations of each. Our results provide concrete evidence that geometric memory can serve as a physically grounded internal mechanism for path distinguishability in quantum systems.
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.
Abstract: The Density Functional Continuum Theory (DFC) redefines quantum mechanics not as a fundamental theory, but as an effective statistical description of a continuous classical medium. Within this framework, the long-standing measurement problem — the emergence of definite outcomes, the Born probability rule, and irreversibility — is resolved through a causal, strictly deterministic mechanism. The theory shows how the microscopic structure of this medium and its intrinsic nonlinear dynamics, without any additional postulates, lead to the collapse of superpositions and the registration of a unique outcome. Moreover, the apparent nonlocal correlations of EPR are explained without recourse to “spooky action at a distance,” solely on the basis of geometric phase constraints. DFC thus provides both a complete solution to the measurement problem and a unified, testable foundation for quantum physics.
We present a theoretical framework in which quantum wave–particle duality and measurement-induced localization emerge from the dynamics of an extended excitation propagating in a continuous medium. By modeling quantum entities as effectively higher-dimensional or spatially extended oscillatory structures whose observable behavior corresponds to their constrained intersection with three-dimensional space, we reinterpret quantum probability, wavefunction collapse, and the double-slit experiment without modifying the formalism of quantum mechanics. Measurement is described as a dynamical pressure or damping interaction that reduces the observable coherence length of the excitation. Numerical simulations of a double-slit geometry demonstrate continuous transition between wave-like interference and particle-like localization under increasing measurement strength. The model is consistent with standard uncertainty relations and decoherence theory, while providing an intuitive geometric and hydrodynamic interpretation of quantum phenomena.