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.
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.
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.
In this paper, we study the effect of a which-path memory ancilla on the three-slit interference pattern within the framework of the bright--dark state description [Phys. Rev. Lett. 134, 133603 (2025)]. Whereas two slits give one bright mode, a photonic mode that couples to the detector atoms, and one dark mode, which does not couple to the detector atoms, three slits lead to one detector-coupled bright mode and a two-dimensional dark-mode subspace in the three-dimensional path space. We first discuss the classical three-slit interference pattern in terms of probability leakage into the dark subspace. We then study the von Neumann entropy
SD of the dark subspace and the coherence measures of the reduced photonic state obtained by tracing out the memory: dark-sector coherence
CD and bright--dark coherence
CBD. These quantities bring out the internal quantum structure of the two-dimensional dark subspace. We show that, whereas
CD is not by itself a basis-independent physical observable,
CBD is basis-invariant. We establish that, for two paths,
CBD is fixed entirely by the populations and the single pairwise coherence, whereas for multiple paths,
M≥3, it acquires a genuinely multipath contribution generated by asymmetry among the pairwise which-path overlaps. Finally, we distinguish the part of the path-coherence loss that is recoverable through a suitable measurement of the memory from the irreducible coherence deficit imposed by an uncontrolled environment.
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.
UDCT v4.7: Parametric Robustness of the Emergent Born Rule in the DSBB Stability Landscape This paper presents a comprehensive One-Factor-at-a-Time (OFAT) robustness verification of the dynamically emergent Born Rule within the Double-Slit Born-Backreaction (DSBB) framework of the Unified Dynamic Cohesion Theory (UDCT v4.7). Building on the geometric derivation established in UDCT v4.5, we subject the DSBB system to twelve independent parametric perturbations across four key parameters: wavepacket width σ (±10%), detector freezing time t_freeze (±0.1), coupling strength λ (±20%), and effective temperature k_eff (±20%). Results show that the L2 relative error between the full 2D microscopic simulation and the theoretical zeroth-order solution remains tightly bounded within ±0.44% of the baseline value (2.41%), while preserving 100% bimodal structural integrity in all cases. These findings provide strong quantitative evidence that the emergent Born-like probability distribution functions as a robust geometric attractor inherent to the DSBB Stability Landscape. A major goal of this work is full reproducibility. The accompanying reproducibility package implements a dual-mode execution system (Mode A: Paper Reproduction Mode; Mode B: Full Scratch Mode) together with a self-healing environment designed to be accessible even to undergraduate students. This work establishes a high-precision, reproducible benchmark for future investigations into the geometric origin of quantum probability.