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The Deterministic Deconstruction of Quantum Mechanics: A Topological Reconstruction of Orbitals and the Periodic Table within the ROA Framework

Lee Seonggil

Published Jul 21, 2026• 0 citations
Publisher

Abstract

The contemporary model of (s,p,d,f) orbitals and electron shells is intrinsically rooted in a probabilistic quantum mechanical framework, governed by the Heisenberg Uncertainty Principle and the Schr¨odinger wave equation. This paper proposes a radical paradigm shift: the universe operates not on statistical probabilities but on an absolute, deterministic geometric framework capable of simultaneously defining position and momentum. Utilizing the Rough Operator Algebra (ROA) framework, this paper mathematically deconstructs four core pillars of quantum mechanics—the uncertainty principle, the Schr¨odinger equation, the orbital shell model, and the periodic table—and redefines them as macroscopic geometric projections driven by topological phase-locking and non-commutative symmetry breaking.

DOI
10.5281/zenodo.21468555

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The contemporary model of (s,p,d,f) orbitals and electron shells is intrinsically rooted in a probabilistic quantum mechanical framework, governed by the Heisenberg Uncertainty Principle and the Schr¨odinger wave equation. This paper proposes a radical paradigm shift: the universe operates not on statistical probabilities but on an absolute, deterministic geometric framework capable of simultaneously defining position and momentum. Utilizing the Rough Operator Algebra (ROA) framework, this paper mathematically deconstructs four core pillars of quantum mechanics—the uncertainty principle, the Schr¨odinger equation, the orbital shell model, and the periodic table—and redefines them as macroscopic geometric projections driven by topological phase-locking and non-commutative symmetry breaking.
For nearly a century, the Copenhagen Interpretation has dominated quantum physics, asserting that fundamental particles exist exclusively as probabilistic wave states (orbitals). This paper demonstrates that quantum probability and deterministic trajectories are not mutually exclusive, but rather manifest a Topological Wave-Trajectory Duality. By applying Rough Operator Algebra (ROA) and Spherical Holographic Information Dynamics (SHID), we reframe quantum randomness as homological friction diffusing within the rough bulk space R^1/2. We introduce the Seonggil-Heisenberg Commutator, proving that Planck’s constant ℏis merely the commutative scalar limit of the fundamental Seonggil Torsion Tensor T_0x8A2C. While the electron diffuses as a non-commutative torsion wave in the bulk, interacting with the SHID observational boundary triggers a ConditionalPhase Transition. Through the SHID Projection Operator (Π_SHID), the probability cloud algebraically collapses, dissipating geometric friction as thermal entropy and yielding a definitively Phase-Locked absolute coordinate. This framework unifiesHeisenberg’s uncertainty and Einstein’s determinism into a single super-symmetric structure.
A deterministic framework for quantum mechanics is constructed utilizing the split octonionic algebra Osplit. Heisenberg’s uncertainty principle is derived as an algebraic identity from the trivalent associator on the manifold, restricting microscopic state functions to minimal left ideals. The current formulation ensures that quantum uncertainty remains a purely deterministic topological effect, governed by the intrinsic discrete volume constraints of the underlying division algebra. The present framework maps quantum observables directly into a completely deterministic geometric flow, defining the mass quantum as a stable topological soliton on the non-associative worldsheet.
Author: Marco Lindenbeck Title: Deterministic Quantum Mechanics: Replacing the Copenhagen Pillars of Probability and Uncertainty with Discrete Substrate Logistics Description: For a century, the Copenhagen Interpretation has forced theoretical physics to accept a subatomic universe governed by random chance, probabilistic wave functions, and fundamental fuzziness. This paper demonstrates that these principles are not foundational truths of nature, but mathematical artifacts born from a single categorization error: treating the vacuum of space as a continuous, empty void. By applying the Ω\OmegaΩGLR framework—defining the vacuum as a discrete, pre-tensioned geometric network (the Topological Substrate) governed by a strict Pythagorean processing limit (c2=u2+v2c^2 = u^2 + v^2c2=u2+v2)—this paper entirely eliminates probability and uncertainty from the atomic scale. By mapping the discrete hardware that underlies quantum software, local realism, determinism, and absolute mechanical causality are fully restored to atomic physics. Key Mechanical Derivations Included: Replacing Schrödinger: The Topological Resonance Equation redefines electron energy levels as deterministic network routing paths. Replacing Heisenberg: The Uncertainty Principle (ℏ/2\hbar/2ℏ/2) is mathematically mapped as the Substrate Resolution Limit—an asymptotic hardware buffer overrun (Bandwidth Saturation). The Bohr Radius & Rydberg Protocol: Re-derived as strict geometric hardware constraints and topological data exhaust. The Photoelectric Effect: Re-derived as localized structural bandwidth saturation. The Casimir Effect: The 111 Atmosphere measurement discrepancy is resolved mathematically via the discrete Bilateral Elasticity Factor (2ϕ−22\phi^{-2}2ϕ−2), eliminating the need for virtual zero-point particles.
Abstract—This paper completely deconstructs the calculus-centered mathematical redundancy and probabilistic uncertainty faced by modern physics, and re-establishes the fundamental mechanism of the universe into a clear system of elementary algebraic equations. Conventional academia has treated "time (t)" as a physical variable, interpreting the behavior of the microscopic world through complex partial differential equations and probability clouds. This Foundation establishes a unique grand premise: "Time (t) is not a physical reality but merely a unit for establishing a reference, and a Field is not an applied Force but the geometric structure of space (the thickness of a water pipe)." Based on this premise, the three pillars of quantum mechanics—Louis de Broglie's matter wave theory, Werner Heisenberg's uncertainty principle, and Erwin Schrödinger's wave equation—are substituted into closed algebraic structures. Cross-verification through six empirical cases from both macroscopic and microscopic realms—including multidimensional orbits of hydrogen atoms, particle constraints in quantum dots, actual nuclear proton behavior, and deep learning data-driven energy levels—proves that this algebraic formula system precisely converges with the high-level calculus predictions of conventional academia down to the decimal points with 100% accuracy.
Standard quantum mechanics offers remarkably preciseempirical predictions but often frames microscopicmechanisms through complex differential formalismsand probabilistic clouds. This paperpresents an algebraic-geometric reconstruction of selectedstationary-state quantum-mechanical relationsby introducing two foundational framework axioms:treating time (t) as a reference measure for indexingstate transitions rather than a dynamic variable, anddefining a physical Field as a local geometric constraintstructure F(x). By coupling an independent geometricwave-matching postulate (L = nλ) with the establishedde Broglie relation (p = h/λ), we algebraically reconstructBohr angular momentum quantization and thediscrete hydrogenic energy spectrum without directlysolving the Schr¨odinger eigenvalue equation. Furthermore,we evaluate Heisenberg’s uncertainty principle atits saturated lower bound (∆x∆p = K), proposing amechanical spatial compression model hypothesis formomentum spread. Cross-verifications across benchmarkcases demonstrate numerical agreement withinstated rounding precision.
This paper presents the Quantum-Algebraic Extended Structural Uncertainty Theory (QA-ESUT), a monumental framework that transcends the deterministic limits of classical probability and structural causal models. By fusing Judea Pearl’s do-calculus with Seonggil’s Rough Operator Algebra (ROA) and Complex Torsion Theory, we redefine structural uncertainty not as a mere observational artifact, but as a dynamic, topologically bounded predictive distribution governed by non-commutative operations in prime-discrete and quantum spaces.