This working note examines the double-slit experiment as a grid-resolution phenomenon within Grid-Rendering Cosmology (GRC). GRC treats quantum uncertainty as arising from a fundamental node scale lgl_g lg in a discrete geometric substrate, modulated by an entropy-clarity function C(S)=exp(−S/Smax)C(S) = \exp(-S/S_{\max}) C(S)=exp(−S/Smax). The note develops a UV-cutoff formulation in which the GRC amplitude is defined as the Fourier integral truncated at kmax=π/lgk_{\max} = \pi/l_g kmax=π/lg. The deviation from standard quantum mechanics is exactly defined as the omitted Fourier tail, and asymptotically evaluated for Gaussian slit profiles. The result shows exponential suppression: ∣ΔA∣≲(lg/πσ2)exp(−π2σ2/2lg2)|\Delta A| \lesssim (l_g/\pi\sigma^2)\exp(-\pi^2\sigma^2/2l_g^2) ∣ΔA∣≲(lg/πσ2)exp(−π2σ2/2lg2) for σ≫lg\sigma \gg l_g σ≫lg. A previously proposed polynomial ansatz O((lg/d)2)\mathcal{O}((l_g/d)^2) O((lg/d)2) is hereby withdrawn. The geometric distinction from standard QM is principled but not experimentally accessible for sub-Planckian lgl_g lg. The primary empirically accessible distinction is relocated to entropy-sensitive decoherence (P3) and higher-order measurement statistics (P4). The operational definition of local entropy SS S is identified as the critical open gap (G2) blocking empirical closure of P3. This note is an ontological and minimal-model extension of GRC to the sub-L0 quantum regime; it is not an empirical closure paper.
This working note examines the double-slit experiment as a grid-resolution phenomenon within Grid-Rendering Cosmology (GRC). GRC treats quantum uncertainty as arising from a fundamental node scale lgl_g lg in a discrete geometric substrate, modulated by an entropy-clarity function C(S)=exp(−S/Smax)C(S) = \exp(-S/S_{\max}) C(S)=exp(−S/Smax). The note develops a UV-cutoff formulation in which the GRC amplitude is defined as the Fourier integral truncated at kmax=π/lgk_{\max} = \pi/l_g kmax=π/lg. The deviation from standard quantum mechanics is exactly defined as the omitted Fourier tail, and asymptotically evaluated for Gaussian slit profiles. The result shows exponential suppression: ∣ΔA∣≲(lg/πσ2)exp(−π2σ2/2lg2)|\Delta A| \lesssim (l_g/\pi\sigma^2)\exp(-\pi^2\sigma^2/2l_g^2) ∣ΔA∣≲(lg/πσ2)exp(−π2σ2/2lg2) for σ≫lg\sigma \gg l_g σ≫lg. A previously proposed polynomial ansatz O((lg/d)2)\mathcal{O}((l_g/d)^2) O((lg/d)2) is hereby withdrawn. The geometric distinction from standard QM is principled but not experimentally accessible for sub-Planckian lgl_g lg. The primary empirically accessible distinction is relocated to entropy-sensitive decoherence (P3) and higher-order measurement statistics (P4). The operational definition of local entropy SS S is identified as the critical open gap (G2) blocking empirical closure of P3. This note is an ontological and minimal-model extension of GRC to the sub-L0 quantum regime; it is not an empirical closure paper.
This paper presents a minimal arc-geometric reconstruction of single-electron double-slit interference within the conceptual framework of Arc Theory. The central aim is not to reject the empirical success of standard quantum mechanics, but to show that a nonstandard geometric ontology can be expressed in a traditional mathematical-physical form, with explicit definitions, axioms, propositions, derivations, and stated limitations. Starting from the proposed arc-geometric constraint R = DA, where R denotes the curvature radius of the external zero-weight ring and DA denotes the intrinsic arc-radius of the electronic arc-helix, the paper derives the de Broglie relation lambdaA = h/p through phase closure and action quantization. The double-slit condition d sin(theta) = m lambdaA is then reconstructed as a consequence of arc-branch phase closure under boundary-induced splitting. The paper further formulates the double-slit process in terms of four structural operators: the arc-branching operator SAlpha, the inter-branch coherence kernel SigmaAlphaBeta, the arc-difference field DeltaAlphaBeta, and the measurement-localization operator LambdaD. In this formulation, the Born density is interpreted not as a primitive probabilistic substance, but as the observable projection density of an underlying high-dimensional arc trajectory onto a lower-dimensional detection interface. In compact form, the proposed interpretation may be written as: rhoArc(x) = |A(x)|^2 where A(x) denotes the projected arc amplitude and rhoArc(x) denotes the observable arc-projection density. A central part of the work is the quantitative formulation of topological friction. The proposed self-decoherence rate GammaSelf is expressed as a functional of curvature mismatch, torsion mismatch, and deviation from the R = DA constraint: GammaSelf = Integral over GammaA of [ gammaKappa * (DeltaKappaA)^2 + gammaTau * (DeltaTauA)^2 + gammaR * ((R - DA)/R)^2 ] dmuA This gives a precise geometric meaning to internal self-decoherence and separates it from ordinary external environmental decoherence. The paper also demystifies observational collapse by representing measurement as environment-induced arc localization. In the proposed formalism, the disappearance of interference is described by the suppression of off-diagonal coherence terms: rhoAlphaBeta -> muAlphaBeta * rhoAlphaBeta with muAlphaBeta -> 0 corresponding to complete which-path distinguishability or environmental trace formation. The scope of the paper is deliberately limited. It does not claim to derive the numerical values of Planck's reduced constant, electron mass, electric charge, magnetic moment, or the electron g-factor. Rather, it provides a mathematically disciplined reconstruction of the kinematics of single-electron double-slit interference and proposes a possible geometric foundation beneath the standard probabilistic formalism. The paper is intended as a preprint-level contribution to the foundations of quantum theory, mathematical physics, and alternative geometric models of microscopic phenomena.
This paper provides a full comparison between standard QM/QFT and GR-CS, showing how interference, decoherence, measurement, and path integrals are reinterpreted in a geometry containing no spatial curvature. Decoherence is treated as the gradual emergence of an anchoring current \mathcal{J}_N, while measurement becomes a localized anchoring event that ties a quantum excitation to the time field. The document includes advanced modules covering functional integrals on a static N(x) background, QFT operators in GR-CS, null-structure vs. quantum phase, and the non-geometric role of the vacuum. All empirical predictions of standard quantum theory are preserved; the ontology is transformed.
Within orthodox quantum mechanics, the only empirical content of any physical claim is a change in the outcome statistics of a declared measurement. In the modern formulation of measurement theory this declaration is an instrument (a family of completely positive maps) or equivalently a POVM together with an implementation. In curved spacetimes, localized measurement theory supplies the appropriate notion of a “local interface”: a finite laboratory worldtube with finite switching, whose induced observables lie in the causal hull and whose instruments compose causally. This paper proves a closure result: for any declared localized measurement, all geometric dependence (metric, connection, curvature, horizons) can affect outcome statistics only through exactly two operational apertures: • Phase / support aperture: the implemented localized instrument or channel on the accessible algebra, including any differential proper‑time or propagation‑dependent phase and any geometry‑dependent support of the induced observable. • Entropy aperture: the accessibility restriction itself (restriction of the global state to the accessible algebra), equivalently a trace over inaccessible degrees of freedom, with the corresponding mixedness/entropy as the interface invariant. There is no third independent slot in the quantum‑mechanical probability rule into which “quantum gravity” can be inserted. Common‑mode phases are operationally null. Sub‑resolution “micro‑selection” is inadmissible without a refined POVM/instrument. And “mediator” talk without a mediator POVM is non‑identifiable, because Stinespring dilations are never unique. The closure is robust: within finite‑response classes, small perturbations of couplings or geometry produce proportionally small changes in outcome statistics. The result does not deny the possibility of new physics beyond orthodox QM. It eliminates a specific move that has repeatedly appeared in quantum‑gravity discourse: treating curvature as an additional, independently specifiable ingredient of orthodox quantum‑mechanical prediction at a local interface.
The Heisenberg Uncertainty Principle is conventionally interpreted as a fundamental limit of nature's precision or as a consequence of measurement disturbance. In this paper, we propose a structural reinterpretation within the Static-Dynamic Recursive Information Space (SDRIS) framework. We demonstrate that quantum uncertainty is mathematically isomorphic to the Time-Bandwidth Product in signal processing. By modeling the vacuum as a discrete information grid, we identify the uncertainty relation not as an intrinsic indeterminism of the object, but as a Representation Limit arising from the projection of infinite information onto a finite-bandwidth substrate. Key Results: Geometric Derivation: We derive the uncertainty inequality σxσk≥1/2 strictly from the properties of the Fourier Transform on a lattice, identifying the Planck constant ℏ as the scaling parameter converting grid bandwidth into physical momentum (p=ℏk). Numerical Verification: Included Python simulations (FFT) confirm that Gaussian wavepackets minimize the uncertainty product to exactly 0.5. This proves that "fuzziness" is effectively the compression artifact of a finite-resolution universe. Ontological Shift: The paper recovers the standard quantum mechanical limit while providing a rigorous geometric foundation based on discrete signal theory, removing the need for an axiomatic "indeterminacy principle." Includes: Full mathematical derivation (Fourier Duality). Python Simulation Notebook (102_18116715_SDRIS_Born_Rule_Simulation_Code_v1_0.ipynb) verifying the lower bound.
This paper develops a fully empirical, physics-grounded reinterpretation of the double-slit experiment using the same flux-ledger framework established in Modules A–D of the Zero Infinity Research Program. By expressing quantum interference in terms of probability current density, boundary flux, and environmental decoherence, the work shows that the double-slit phenomenon requires no mysteries, hidden forces, or nonlocal metaphysics. Instead, the interference pattern emerges naturally from: Conservation of probability current, Phase-coherent flux across an open boundary, and Loss of coherence encoded as a measurable entropy-flux term Ψ∞. The analysis re-derives the standard results—interference fringes, collapse under measurement, and decoherence scaling—from first principles while embedding them within the broader conservation trilogy: Φ∞ (boundary energy flux) Ψ∞ (entropy/memory flux) Π∞ (momentum flux) This connects quantum optics to the same flux-driven framework used to model black hole mergers, spacecraft recoil, comet polarization curves, and organic spectral coherence in earlier modules. The paper also integrates cross-disciplinary results from decoherence theory, Bohmian mechanics, optical coherence tomography, and open quantum systems, showing how each maps cleanly onto a boundary-flux formalism. The result is a physically rigorous, mathematically transparent, and conceptually unifying explanation of the double-slit experiment—one that preserves standard quantum mechanics while clarifying how and where interference information is stored, exported, and erased. This work extends the Zero Infinity Program into quantum foundations, offering a synthesis of classical wave mechanics, quantum probability current, thermodynamic export, and information flow across system boundaries.
Full Vers.3 / The Morphic Resolution of the Young’s Slits Paradox: Wave-Particle Duality as a Morphic Guidance Phenomenon DOI : 10.5281/zenodo.17928212 Nelson Karabudak - Independent Researcher nelson.karabudak@gmail.com Abstract The double-slit experiment remains central to the foundations of quantum mechanics: a single particle produces an interference pattern as if it traversed both slits simultaneously, yet the insertion of a path-marking measurement suppresses this interference. This paper presents a structural resolution based on the Karabdak Unified Theory (KUT). In this framework, the Geometric Fabric is treated as an active field of informational potentiality. The particle is defined as a localized "Coherence Knot" guided by a delocalized Morphic Potential. We demonstrate mathematically that the act of measurement injects an information density into the fabric, which alters its metric rigidity. This creates an effective refractive index that can arrest the propagation of the guiding wave, producing an abrupt, deterministic reduction in interference visibility. Key Contributions Microscopic Derivation: The effective propagation velocity is derived from a minimal Lagrangian formulation including a detector bath and Feynman-Vernon influence functional. Thermodynamic Consistency: The model resolves the energy balance via a fluctuation-dissipation relation, linking the friction coefficient to the background temperature of the fabric. Falsifiable Signature: The theory predicts a specific sigmoidal visibility curve with a distinct "plateau-drop" signature, contrasting with the continuous exponential decay of standard decoherence models. Unified High-Energy Limit (Mirror Effect): The derived impedance formula implies a universality where relativistic acceleration—like information density—drives the fabric’s rigidity to infinity, validating the "Mirror Effect" and topological traversal mechanisms predicted at cosmological scales. Technical Notes on Datasets (Annex F) The numerical tables provided in the full text follow these conventions: Normalization: Information density I is normalised to the critical density (I_crit = 1.0). Visibility Calculation: V(I) is computed from the derived logistic model. Confidence Intervals: 95% CIs are estimated from bootstrap methods on N = 10^4 impacts. Keywords Quantum Mechanics, Young's Slits, Wave-Particle Duality, Karabdak Unified Theory, Morphic Potential, Geometric Fabric, Measurement Problem, Mirror Effect, Lagrangian Mechanics.