Quantum Mechanics Within the Cartesian Relativity Framework: Resolving Double-Slit Anomalies through Algorithmic Rendering, Probabilistic Pruning, and the Energetic Lattice Tax
Abstract This paper resolves the wave-particle duality and the measurement problem of the double-slit experiment by applying the Cartesian Relativity Framework [1, 2]. We posit that quantum superposition exists strictly as an unrendered probability distribution within the "Backend" of spacetime—a domain devoid of geometric volume and physical time. The physical detection of a particle is a forced "Render Event" onto a discrete, integer-based coordinate topology. By defining the wave function as a continuous Gaussian probability curve mapping to a quantized physical lattice—governed by a fundamental "Resolution Limit" that removes the reliance on mathematical infinity—we provide a deterministic mechanism for Quantum Dithering, Probabilistic Pruning, and the energetic "Lattice Tax" required to maintain non-rendered states. We address potential critiques regarding non-local domains and the energy costs of entanglement, demonstrating how this framework provides superior macro-to-micro coherence over standard interpretations. Finally, we propose falsifiable observational metrics: the laboratory Jitter Shadow, Render Exclusion Zones, and the measurable energetic overhead of logical address synchronization. Footnotes / References: [1] Kerr, A. J. (2026). Cartesian Relativity and the Zeno Non-singularity: A Unified Theory of Quantum Rendered Spacetime and Elastic Coordinate Topology. Zenodo. https://doi.org/10.5281/zenodo.20046745 [2] Kerr, A. J. (2026). Cartesian Spacetime and Macroscopic Gravity: Topological Gradients, Data Collisions, and Planetary Hydrostatic Equilibrium. Zenodo. https://doi.org/10.5281/zenodo.20078172
Abstract This paper resolves the wave-particle duality and the measurement problem of the double-slit experiment by applying the Cartesian Relativity Framework [1, 2]. We posit that quantum superposition exists strictly as an unrendered probability distribution within the "Backend" of spacetime—a domain devoid of geometric volume and physical time. The physical detection of a particle is a forced "Render Event" onto a discrete, integer-based coordinate topology. By defining the wave function as a continuous Gaussian probability curve mapping to a quantized physical lattice—governed by a fundamental "Resolution Limit" that removes the reliance on mathematical infinity—we provide a deterministic mechanism for Quantum Dithering, Probabilistic Pruning, and the energetic "Lattice Tax" required to maintain non-rendered states. We address potential critiques regarding non-local domains and the energy costs of entanglement, demonstrating how this framework provides superior macro-to-micro coherence over standard interpretations. Finally, we propose falsifiable observational metrics: the laboratory Jitter Shadow, Render Exclusion Zones, and the measurable energetic overhead of logical address synchronization. Footnotes / References: [1] Kerr, A. J. (2026). Cartesian Relativity and the Zeno Non-singularity: A Unified Theory of Quantum Rendered Spacetime and Elastic Coordinate Topology. Zenodo. https://doi.org/10.5281/zenodo.20046745 [2] Kerr, A. J. (2026). Cartesian Spacetime and Macroscopic Gravity: Topological Gradients, Data Collisions, and Planetary Hydrostatic Equilibrium. Zenodo. https://doi.org/10.5281/zenodo.20078172
Building upon the foundational principles of the Cartesian Relativity Framework (CRF) established in Parts I–III [1, 2, 3] and the Unified Field Equation of Coordinate Duality defined in Paper IV [4], this paper formalizes the mechanical architecture of the electron. By replacing the mathematical abstraction of the point-particle with the Rendered Address Cluster, we define the electron as a state of Threshold Confinement operating at the absolute limit of the lattice's rendering thresholds. This formalization provides a strictly deterministic, geometric derivation for Spin-½, defining it as a 720-degree algorithmic routing cycle required to maintain structural integrity (E/c2) against the Lower Rendering Threshold (h). The paper further resolves the observer-dependent paradoxes of legacy quantum mechanics through State Volatility, where the electron’s proximity to the rendering floor allows it to oscillate between the Rendered Address Index (RAI)and the Probabilistic Address Index (PAI). Furthermore, we demonstrate that atomic orbital transitions and the Lamb Shift [8] are governed by rigorous Newtonian kinetic conservation [7] and topological congestion. Finally, by defining the positron through Inverse Topological Routing, the framework mathematically resolves matter-antimatter annihilation as an Overwhelming RAI Collision. This preserves absolute energetic and kinetic continuity within the algorithmic cycle (dt), rendering temporal retro-causality [9] unnecessary by demonstrating that annihilation is a geometric cancellation of confinement loops that returns localized energy to a probabilistic state. Footnotes / References Kerr, A. J. (2026). Cartesian Relativity and the Zeno Non-singularity. Zenodo. https://doi.org/10.5281/zenodo.20046745 Kerr, A. J. (2026). Cartesian Spacetime and Macroscopic Gravity. Zenodo. https://doi.org/10.5281/zenodo.20078172 Kerr, A. J. (2026). Quantum Mechanics Within the Cartesian Relativity Framework. Zenodo. https://doi.org/10.5281/zenodo.20080687 Kerr, A. J. (2026). Decoding Hilbert Space: The Cartesian Relativity Framework Unified Field Equation for Spacetime Rendering. Zenodo. Einstein, A. (1905). Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Annalen der Physik, 323(13), 639-641. Planck, M. (1900). Über das Gesetz der Energieverteilung im Normalspectrum. Annalen der Physik. Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica. Jussu Societatis Regiae. Lamb, W. E., & Retherford, R. C. (1947). Fine Structure of the Hydrogen Atom by a Microwave Method.Physical Review, 72(3), 241-243. Feynman, R. P. (1949). The Theory of Positrons. Physical Review, 76(6), 749-759.
For exactly one century, the standard interpretation of quantum mechanics has conflated predictive statistical mathematics with physical ontology. By mistaking a mathematical map of probabilities for the physical territory of reality, twentieth-century physics enshrined Wave-Particle Duality and Wave-Function Collapse as fundamental tenets of nature, abandoning physical determinism for phenomenological mysticism. This repository contains the formal manuscript and executable visual proofs demonstrating that the paradox of Young's Double Slit experiment is entirely resolvable via macroscopic fluid thermodynamics. Utilizing the Informational Constraint Framework (ICF) and Macroscopic Relaxation Theory, we demonstrate that the electron is not a shape-shifting probability cloud, but a highly compressed, localized macroscopic geometry (the Core) propagating a continuous thermodynamic strain-gradient (the Wake) through a spatial substrate of strictly finite data-processing capacity. The Axiom of Propagation: The Wake shapes the terrain; the Core rides the terrain. By decoupling the Core from the Wake, this paper systematically derives single-slit kinematics, double-slit interference, the fundamental zero-mass nature of the photon, and the true physical reality of the "Observer Effect" strictly through the deterministic actions of continuous fluid topology. The cathedral of quantum probability is conceptually obsolete; it is herein mathematically replaced by the macroscopic thermodynamics of the spatial vacuum. Repository Contents: The_Double_Slit_Falsification.pdf: The complete theoretical manuscript, including the cross-domain unified index. icf_double_slit_animator.py: The executable Python script containing the macroscopic fluid topology animation proof. Double_Slit_Interference.gif & Single_Slit_Substrate_Strain.gif: High-resolution animated proofs of the Core/Wake topology. Double_Slit_Storyboard.png: High-resolution diagram of the topological phases.
Building upon the unified 4D geometry of the Causal Smoothing Framework, this paper resolves three foundational paradoxes of quantum mechanics: wave-particle duality in the double-slit experiment, the measurement problem (wave function collapse), and the origin of particle-antiparticle asymmetry. By defining particles as time-like topological knots (ds² < 0) and quantum fields as the deterministic causal smoothing of vacuum momentum fluxes along the null boundary (ds² = 0), this framework discards probabilistic observer-driven collapse. The double-slit experiment is analyzed under two distinct boundary conditions (continuous emission and single-particle emission), demonstrating that quantum statistics are simply the macroscopic interference of vacuum geometry guiding discrete knots through a chaotic ER=EPR substrate. Furthermore, the framework provides a strict geometric proof for why fermions require distinct antiparticles while gauge bosons act as their own antiparticles, rooted entirely in the chiral phase of the localized metric shear.
Legacy quantum mechanics relies on abstract probability distributions to explain Wave-Particle Duality, abandoning physical determinism in favor of Statistical Uncertainty. This manuscript resolves that anomaly by defining the Quantum Vacuum as a highly pressurized, structured fluid medium. Under the Electron Flow Model (EFM), elementary particles are not dimensionless mathematical points, but localized fluid solitons propagating through the Universal Vacuum Flux. Our analysis demonstrates that the observed interference patterns in the Double-Slit Experiment are generated by the Macroscopic Physical Bow Waves of the soliton. These Bow Waves sever and recombine after passing through the slits to create a standing wave interference pattern of Pressurized Ridges and Thermodynamic Troughs. The localized particle itself travels strictly through a single path, naturally surfing these pressure ridges to land on the detector screen. This framework moves beyond interpretation by establishing clear, Falsifiable Predictions that structurally distinguish the EFM from standard Quantum Mechanics: Viscous Damping: Predicts an additional mechanical channel of decoherence driven by dynamic fluctuations in the ambient pressure of the vacuum flux, scalable by the fluid bulk viscosity. Absolute Vacuum Pressure Shift: Suggests a measurable fringe compression in orbital cold-atom interferometry relative to sea level, driven by the absolute density of the vacuum flux. The v-Causal Temporal Limit of Delayed Choice: Establishes a concrete 0.51-picosecond switching threshold for tabletop delayed-choice experiments (48 m), scaling linearly to 12.6 nanoseconds at satellite-class baselines (1,200 km). The EFM predicts a physical persistence of the interference pattern—and a breakdown of quantum correlations—if measurement switching occurs faster than the finite acoustic transit time of the fluid tether. The Unified Fluid Cosmos Framework: This paper serves as Manuscript 21 Version 1 in the comprehensive series, Marabūt's Theory of Gravity. It presents the Electron Flow Model (EFM), a generative, fluid-dynamic framework designed to fundamentally replace Albert Einstein's General Relativity and standard Quantum Mechanics. The EFM shatters classical circularity with a single, undeniable foundational premise: Gravity is Pressure, not curvature, and not an intrinsic mass property. Published Manuscripts in this Series: Manuscript 01: The Push-Pull Mechanics of Vacuum Flux (The Foundational Framework) — https://doi.org/10.5281/zenodo.18874694 Manuscript 02: Resolving the Weyl Potential Anomaly — https://doi.org/10.5281/zenodo.19784494 Manuscript 03: Mechanistic Resolution of Jet Deflection in Cygnus X-1 — https://doi.org/10.5281/zenodo.19790983 Manuscript 04: Quantum Mechanics of Stellar Chain Reactions and EVGS Formation — https://doi.org/10.5281/zenodo.19801398 Manuscript 05: The Heliospheric Grand Data Matrix — https://doi.org/10.5281/zenodo.20128776 Manuscript 06: Fluid-Dynamic Reinterpretation of Gravity, Black Holes, and Gravitational Waves — https://doi.org/10.5281/zenodo.20129518 Manuscript 07: Fluid-Dynamic Reinterpretation of the Kinematic Sunyaev-Zeldovich Effect — https://doi.org/10.5281/zenodo.20130259 Manuscript 08: Transcending the Singularity — Electron Void Gravitational Spheres — https://doi.org/10.5281/zenodo.20130801 Manuscript 09: The Final Parsec Problem Solved — https://doi.org/10.5281/zenodo.20134048 Manuscript 10: The Illusion of the Singularity — https://doi.org/10.5281/zenodo.20135533 Manuscript 11: The Illusion of Dark Energy — https://doi.org/10.5281/zenodo.20149141 Manuscript 12: The Illusion of Dark Matter — https://doi.org/10.5281/zenodo.20171372 Manuscript 13: The Illusion of Spacetime — https://doi.org/10.5281/zenodo.20172281 Manuscript 14: The Illusion of Spooky Action — https://doi.org/10.5281/zenodo.20173191 Manuscript 15: The Superluminal Mechanics of the Quantum Vacuum — https://doi.org/10.5281/zenodo.20173755 Manuscript 16: Empirical Validation of the Electron Flow Model — https://doi.org/10.5281/zenodo.20271062 Manuscript 17: Confronting the Cosmic Microwave Background — https://doi.org/10.5281/zenodo.20483713 Manuscript 18: Resolving the CMB Power Spectrum — https://doi.org/10.5281/zenodo.20493520 Manuscript 19: The Foundation of Stellar Dynamics — https://doi.org/10.5281/zenodo.20500168 Manuscript 20: Resolving the Black Hole Information Paradox — https://doi.org/10.5281/zenodo.20535631 Manuscript 21: Hydrodynamic Shockwaves and Wave-Particle Duality — https://doi.org/10.5281/zenodo.20620456 Manuscript 22: Resolving the Quantum Measurement Problem — https://doi.org/10.5281/zenodo.20628003 Manuscript 23: The Origin and Nature of the Vacuum Flux — https://doi.org/10.5281/zenodo.20754253 Manuscript 24: The Illusion of the Quantum Cat — https://doi.org/10.5281/zenodo.20768397 Manuscript 25: The Rock Giant Reclassification — https://doi.org/10.5281/zenodo.20899782 Manuscript 26: The Pioneer Anomaly and Electron Pressure Drag — https://doi.org/10.5281/zenodo.21346600 Data & Code Availability: To accompany this manuscript, we have open-sourced the complete Python mathematical engine and a fully interactive 3D web-based simulation of the EFM Volumetric Profiler. Researchers, developers, and students can visually explore the hydrodynamic vacuum flux across the celestial bodies at: Interactive 3D EFM Volumetric Profiler: https://marabutmarabut.github.io/Theory-of-Gravity Official GitHub Repository: https://github.com/MarabutMarabut/Theory-of-Gravity
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.
We propose a framework in which the quantum measurement problem dissolves when spacetime is treated as a discrete network of Planck-volume cells. The wave function represents genuinely uncommitted cell states; wave function collapse is the physical commitment of those cells by the causal propagation process; and quantum entanglement arises because correlated cells constitute a single unresolved rendering task with multiple spatial addresses. These three primary results follow logically from the framework's ontology and are clearly distinguished from more speculative directions throughout. We additionally derive that entropy is related to the Planck length via S_max proportional to c^3, predicting a maximum entropy turning point distinguishing this framework from standard cosmology's monotonically increasing entropy. Time travel is shown to be impossible by the same irreversibility mechanism, giving Hawking's chronology protection conjecture a physical derivation rather than remaining a conjecture. A candidate Born rule mechanism is proposed — probability arising from path integrals through the causal cell network — but is clearly labelled as unproven. The framework connects to Wheeler's one-electron hypothesis, Penrose Objective Reduction, and the decoherence programme. The Born rule derivation is identified as the central open problem. This is the second paper in a series on Pixel Theory. Companion Paper 1 (VSL cosmology) is published at https://doi.org/10.5281/zenodo.20491684