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Hydrogen 1s Orbital from Stochastic Collapse Testing the Quantum Measurement Problem via the Fine-Structure Constant

Massimiliano Blandino

Published Aug 6, 2026• 0 citations
Publisher

Abstract

We test a recently proposed algebraic resolution of the quantum measurement problem by deriving the fine-structure constant from the same dissipative collapse dynamics, and by verifying that the resulting stochastic collapse reproduces the Schrödinger distribution for the hydrogen 1s orbital. Working within the Jordan-Clifford immersive framework on the 14-dimensional operational subspace $\mathcal{H} = \mathbb{C}^{14}$ associated with the Fano incidence geometry, we show that the stochastic collapse equation $$dc_i = -\frac{1}{2}\gamma c_i(1 - 2p_i + \sum_j p_j^2)dt + \sqrt{\gamma}c_i(dW_i - \sum_j p_j dW_j)$$ contains the decoherence rate $\gamma = \sqrt{\lambda_{\text{graphon}}}$, where $\lambda_{\text{graphon}} = \Lambda_1/\Lambda_0 \approx 1.99765$ is the spectral gap of the graphon kernel emerging from the Fano 2-22 moduli space. The immersion of the measurement apparatus in the continuum flow identifies $\gamma$ with the spatial coupling coefficients of the MPS transfer operator. In the asymptotic limit $k \to \infty$, $\lambda_{\text{graphon}} \to 2$, hence $\gamma \to \sqrt{2}$. Substituting into the MPS duality $\alpha^{-1} = \ln\lambda_{\max} - \pi$ yields: $$\alpha^{-1} = \ln\lambda_{\max}(\sqrt{2}) - \pi = 137.0359991678.$$ This value is consistent with Rubidium atom interferometry (2020), the revised $g-2$ determination (2024-2025), and CODATA 2022 within $1\sigma$. As a further test of the collapse dynamics, we simulate the positional collapse of the hydrogen 1s orbital on a radial grid with $10{,}000$ stochastic trajectories. The ensemble mean $\langle r \rangle_{\mathrm{model}} = 1.49868\,a_0$ reproduces the Schrödinger expectation value $\langle r \rangle_{\mathrm{Sch}} = 1.50012\,a_0$ to within $1.44\times 10^{-3}\,a_0$. A Kolmogorov-Smirnov test ($p = 0.131$) and a bootstrap 95\% confidence interval confirm that the ensemble distribution is statistically indistinguishable from the quantum mechanical prediction. The construction contains no free parameters and is falsifiable via the bound $q \le 45$ on continued fraction quotients. The derivation and the hydrogen benchmark together provide an experimental test of the proposed resolution of the measurement problem. 🌐 Live SPARQL Semantic Queries & Knowledge Graph Architecture This research deposit is integrated with the Blandino Research Knowledge Graph (BR-KG). Direct SPARQL query interfaces and machine-readable RDF endpoints are available below for automated data extraction and semantic interoperability: Live SPARQL Query: Full Micro-Node Graph Exploration (Q1–Q72) — Dynamic table query extracting all 72 indexed nodes, properties (P1–P12), and verification suite relationships. Interactive 2D Knowledge Graph Visualizer — Real-time 2D network rendering of cluster dependencies and topological factorizations. Live SPARQL Query: Linked Open Data & External DOI Cross-Mappings — Cross-reference mappings between internal nodes (Q3–Q36), Zenodo DOIs, FAIRsharing Record 8936, and Wikidata URIs. Public REST API Endpoint (RDF/JSON-LD) — Standardized endpoint for programmatic query execution.

DOI
10.5281/zenodo.21814908

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A Possible Algebraic Resolution of the Quantum Measurement Problem via Dissipative Refinement Flow on Fano Incidence Geometry

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We propose a possible algebraic resolution of the quantum measurement problem by deriving wavefunction collapse as a consequence of dissipative dynamics, rather than postulating it as an additional axiom. Working within the Jordan-Clifford immersive framework previously developed on the 14-dimensional operational subspace $\mathcal{H} = \mathbb{C}^7_+ \oplus \mathbb{C}^7_- \cong \mathbb{C}^{14}$ associated with the Fano incidence geometry, we extend the GENERIC-type refinement flow $$\frac{\partial W}{\partial k} = -\{W, S\} - \mathcal{M} \frac{\delta S_{\mathrm{ent}}}{\delta W}$$ to include a measurement coupling term. The apparatus is modeled by projection operators $P_i$ onto the spectral components of the Dirac operator $\mathcal{D}$, whose spectrum is finite and discrete: $$\sigma(\mathcal{D}) = \{+3, -3, +\sqrt{2}^{\times 6}, -\sqrt{2}^{\times 6}\}.$$ We prove a pure collapse theorem: under a single regularity assumption --- positivity and boundedness of graphon kernels --- the refinement flow drives initial states into measurement basins whose normalized volumes equal the Born probabilities. The key conceptual advance is the recognition that the measurement apparatus is not external to the dynamics but is immersed in the continuum spacetime emergent from the graphon refinement flow. The immersion is formalized by a continuous projection operator $\mathcal{P}_{\mathrm{meas}}$ from the graphon phase space to the span of the spectral projectors $P_i$, establishing that the apparatus is a structure defined within the same operatorial image of the flow, not an external observer imposed by hand. Consequently, the decoherence rate observed by the apparatus is the square root of the graphon spectral gap: $$\lambda_{\mathrm{dec}} = \sqrt{\lambda_{\mathrm{graphon}}} = \sqrt{\Lambda_1/\Lambda_0} \to \sqrt{2},$$ in the asymptotic regime $\lambda_{\mathrm{graphon}} \to 2$. This replaces the previously assumed spatial rate $\sqrt{2}$ with an algebraically derived rate $\lambda_{\mathrm{dec}}$, eliminating the need for cross-terms or ad hoc coupling angles. The irreversible nature of the collapse follows from the entropy production inequality $dS_{\mathrm{ent}}/dk \geq 0$, which establishes an intrinsic arrow of time encoded in the positivity of the dissipative metric. The stochastic dynamics is governed by an Ito quantum state diffusion equation with centered noise $(P_i - \langle P_i \rangle_\psi) dW_i$, which ensures the martingale property $\mathbb{E}[P_i(k)] = P_i(0)$ and guarantees that the Born rule emerges as a consequence of the martingale convergence theorem, not as an independent postulate. All algebraic parameters are rigidly constrained by the Fano incidence structure and the graphon Lov\'asz limit. The construction contains no freely adjustable parameters beyond the regularity assumption R1. The numerical verification, based on 3000 Monte Carlo trajectories, confirms that the asymptotic frequencies converge to the Born probabilities with $L_2$ error decaying as $1/\sqrt{N}$, in full agreement with the central limit theorem. This work provides a purely algebraic and geometric derivation of the Born rule and wavefunction collapse, offering a possible resolution to one of the deepest open problems in the foundations of quantum mechanics. 🌐 Live SPARQL Semantic Queries & Knowledge Graph Architecture This research deposit is integrated with the Blandino Research Knowledge Graph (BR-KG). Direct SPARQL query interfaces and machine-readable RDF endpoints are available below for automated data extraction and semantic interoperability: Live SPARQL Query: Full Micro-Node Graph Exploration (Q1–Q72) — Dynamic table query extracting all 72 indexed nodes, properties (P1–P12), and verification suite relationships. Interactive 2D Knowledge Graph Visualizer — Real-time 2D network rendering of cluster dependencies and topological factorizations. Live SPARQL Query: Linked Open Data & External DOI Cross-Mappings — Cross-reference mappings between internal nodes (Q3–Q36), Zenodo DOIs, FAIRsharing Record 8936, and Wikidata URIs. Public REST API Endpoint (RDF/JSON-LD) — Standardized endpoint for programmatic query execution.

•Aug 2, 2026•0 citations

MAGNETIC ORBITALS - The FIRST VISUAL REVELATION of QUANTUM GEOMETRIES in the MACROSCOPIC WORLD

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First publication: 15 July 2025 This research introduces an experimental methodology capable of revealing geometrical structures corresponding to spherical harmonics within macroscopic magnetic fields , making visible field configurations that have never before been experimentally observed in the real world. Atomic orbitals represent some of the most recognizable geometrical structures emerging from quantum mechanics. They arise as solutions of the Schrödinger equation for the hydrogen atom and are mathematically described by spherical harmonics . In modern physics these structures are traditionally interpreted as probability distributions associated with the quantum state of the electron, rather than as spatial geometries directly observable at the macroscopic scale. In this work, a three-dimensional experimental visualization of structures isomorphic to atomic orbitals is presented for the first time. These structures are obtained through the detection and spatial mapping of magnetic field configurations using Hall-effect sensors. The experimental method employs a bipolar Hall sensor operating in dynamic scanning mode while maintaining a constant angular orientation relative to the magnetic source. This measurement configuration introduces a different observational framework compared to conventional representations of magnetic fields derived directly from Maxwell’s equations. When the magnetic field is explored by explicitly considering dipole-dipole interactions and by maintaining a fixed sensor orientation during spatial scanning , the measurements correspond to local projections of the magnetic field along a constant angular direction. The spatial reconstruction of these projections reveals three-dimensional field structures that exhibit a remarkable correspondence with the spherical harmonic geometries associated with the atomic orbitals of the hydrogen atom . These configurations do not normally appear in standard visualizations of magnetic fields, such as field lines or equipotential surfaces, because their emergence requires a measurement approach capable of highlighting the angular components of dipolar interactions. From this observation derives the title of the research. The structures observed in this work coincide with forms historically associated exclusively with the quantum solutions of the Schrödinger equation for the hydrogen atom. However, in this context they emerge as measurable geometric configurations of a macroscopic magnetic field , suggesting the existence of a structural relationship between these two physical descriptions. The research has also been deliberately structured to provide interpretations consistent with both classical mechanics and quantum mechanics , offering the reader multiple theoretical perspectives. By using the classical geometry of magnetic fields as an interpretative framework, several concepts typically associated with quantum mechanics acquire an unexpectedly intuitive and geometrically rational representation. This approach allows the exploration of possible structural connections between the probabilistic formalism of quantum mechanics and geometric patterns emerging from observable macroscopic physical fields , offering an alternative interpretative perspective on the relationship between classical physics and quantum phenomena. The work also includes a fully replicable experimental methodology for generating and visualizing these structures by scanning one or more permanent magnets using Hall sensors, effectively providing a procedure comparable to a form of three-dimensional magnetic tomography ("Magnetic CT Scan") . Official DOI: https://doi.org/10.5281/zenodo.15936280 A Professionally Printed Edition is also available on Amazon: MAGNETIC ORBITALS

•Mar 16, 2026•0 citations

MAGNETIC ORBITALS - The FIRST VISUAL REVELATION of QUANTUM GEOMETRIES in the MACROSCOPIC WORLD

Marsio Salcuni

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•Mar 6, 2026•0 citations

Resolving the Quantum Measurement Problem: Deriving the Born Rule and Wavefunction Collapse from First Principles

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Abstract:The quantum measurement problemthe fundamental conict between the deterministic, unitary evolution described by the Schrödinger equation and the stochastic, irreversible outcomes observed in experimentshas remained unresolved since the inception of quantum mechanics nearly a century ago. Here we demonstrate that the Chrono-Singularity Unication (CSU) framework provides a complete, rst-principles resolution of all ve components of the measurement problem with zero adjustable parameters. From a minimal informational substrate ΨI characterized by three internally-calibrated constants (α = ln 2, β = ln 2, w = −1), we derive: (i) the Born rule P = |ψ| 2 as a mathematical necessity via the GNS construction and spectral theorem; (ii) the emergence of the preferred (position) basis through Dobrushin concentration bounds on redundant environmental records; (iii) single denite outcomes from the sampled-history ontology without dynamical collapse; (iv) full compatibility with special relativity through topological linking that preserves no-signaling while permitting Bell-inequality violation; and (v) unique, falsi- able experimental predictions including a mass-dependent gravitational decoherence oor testable in near-future molecular interferometry experiments. Significance:This framework provides the exact geometric scaling required to resolve the Hubble tension and derives the Diósi-Penrose gravitational decoherence floor (τ=ℏ/ΔEG) strictly as a low-energy macroscopic limit. This paper serves as the theoretical foundation for a fully deterministic, parameter-free unification of quantum mechanics and general relativity.

•Mar 8, 2026•0 citations
We test a recently proposed algebraic resolution of the quantum measurement problem by deriving the fine-structure constant from the same dissipative collapse dynamics, and by verifying that the resulting stochastic collapse reproduces the Schrödinger distribution for the hydrogen 1s orbital. Working within the Jordan-Clifford immersive framework on the 14-dimensional operational subspace H=C14\mathcal{H} = \mathbb{C}^{14}H=C14 associated with the Fano incidence geometry, we show that the stochastic collapse equation dci=−12γci(1−2pi+∑jpj2)dt+γci(dWi−∑jpjdWj)dc_i = -\frac{1}{2}\gamma c_i(1 - 2p_i + \sum_j p_j^2)dt + \sqrt{\gamma}c_i(dW_i - \sum_j p_j dW_j)dci​=−21​γci​(1−2pi​+∑j​pj2​)dt+γ​ci​(dWi​−∑j​pj​dWj​) contains the decoherence rate γ=λgraphon\gamma = \sqrt{\lambda_{\text{graphon}}}γ=λgraphon​​, where λgraphon=Λ1/Λ0≈1.99765\lambda_{\text{graphon}} = \Lambda_1/\Lambda_0 \approx 1.99765λgraphon​=Λ1​/Λ0​≈1.99765 is the spectral gap of the graphon kernel emerging from the Fano 2-22 moduli space. The immersion of the measurement apparatus in the continuum flow identifies γ\gammaγ with the spatial coupling coefficients of the MPS transfer operator. In the asymptotic limit k→∞k \to \inftyk→∞, λgraphon→2\lambda_{\text{graphon}} \to 2λgraphon​→2, hence γ→2\gamma \to \sqrt{2}γ→2​. Substituting into the MPS duality α−1=ln⁡λmax⁡−π\alpha^{-1} = \ln\lambda_{\max} - \piα−1=lnλmax​−π yields: α−1=ln⁡λmax⁡(2)−π=137.0359991678.\alpha^{-1} = \ln\lambda_{\max}(\sqrt{2}) - \pi = 137.0359991678.α−1=lnλmax​(2​)−π=137.0359991678. This value is consistent with Rubidium atom interferometry (2020), the revised g−2g-2g−2 determination (2024-2025), and CODATA 2022 within 1σ1\sigma1σ. As a further test of the collapse dynamics, we simulate the positional collapse of the hydrogen 1s orbital on a radial grid with 10,00010{,}00010,000 stochastic trajectories. The ensemble mean ⟨r⟩model=1.49868 a0\langle r \rangle_{\mathrm{model}} = 1.49868\,a_0⟨r⟩model​=1.49868a0​ reproduces the Schrödinger expectation value ⟨r⟩Sch=1.50012 a0\langle r \rangle_{\mathrm{Sch}} = 1.50012\,a_0⟨r⟩Sch​=1.50012a0​ to within 1.44×10−3 a01.44\times 10^{-3}\,a_01.44×10−3a0​. A Kolmogorov-Smirnov test (p=0.131p = 0.131p=0.131) and a bootstrap 95% confidence interval confirm that the ensemble distribution is statistically indistinguishable from the quantum mechanical prediction. The construction contains no free parameters and is falsifiable via the bound q≤45q \le 45q≤45 on continued fraction quotients. The derivation and the hydrogen benchmark together provide an experimental test of the proposed resolution of the measurement problem. 🌐 Live SPARQL Semantic Queries & Knowledge Graph Architecture This research deposit is integrated with the Blandino Research Knowledge Graph (BR-KG). Direct SPARQL query interfaces and machine-readable RDF endpoints are available below for automated data extraction and semantic interoperability: Live SPARQL Query: Full Micro-Node Graph Exploration (Q1–Q72) — Dynamic table query extracting all 72 indexed nodes, properties (P1–P12), and verification suite relationships. Interactive 2D Knowledge Graph Visualizer — Real-time 2D network rendering of cluster dependencies and topological factorizations. Live SPARQL Query: Linked Open Data & External DOI Cross-Mappings — Cross-reference mappings between internal nodes (Q3–Q36), Zenodo DOIs, FAIRsharing Record 8936, and Wikidata URIs. Public REST API Endpoint (RDF/JSON-LD) — Standardized endpoint for programmatic query execution.
We propose a possible algebraic resolution of the quantum measurement problem by deriving wavefunction collapse as a consequence of dissipative dynamics, rather than postulating it as an additional axiom. Working within the Jordan-Clifford immersive framework previously developed on the 14-dimensional operational subspace H=C+7⊕C−7≅C14\mathcal{H} = \mathbb{C}^7_+ \oplus \mathbb{C}^7_- \cong \mathbb{C}^{14}H=C+7​⊕C−7​≅C14 associated with the Fano incidence geometry, we extend the GENERIC-type refinement flow ∂W∂k=−{W,S}−MδSentδW\frac{\partial W}{\partial k} = -\{W, S\} - \mathcal{M} \frac{\delta S_{\mathrm{ent}}}{\delta W}∂k∂W​=−{W,S}−MδWδSent​​ to include a measurement coupling term. The apparatus is modeled by projection operators PiP_iPi​ onto the spectral components of the Dirac operator D\mathcal{D}D, whose spectrum is finite and discrete: σ(D)={+3,−3,+2×6,−2×6}.\sigma(\mathcal{D}) = \{+3, -3, +\sqrt{2}^{\times 6}, -\sqrt{2}^{\times 6}\}.σ(D)={+3,−3,+2​×6,−2​×6}. We prove a pure collapse theorem: under a single regularity assumption --- positivity and boundedness of graphon kernels --- the refinement flow drives initial states into measurement basins whose normalized volumes equal the Born probabilities. The key conceptual advance is the recognition that the measurement apparatus is not external to the dynamics but is immersed in the continuum spacetime emergent from the graphon refinement flow. The immersion is formalized by a continuous projection operator Pmeas\mathcal{P}_{\mathrm{meas}}Pmeas​ from the graphon phase space to the span of the spectral projectors PiP_iPi​, establishing that the apparatus is a structure defined within the same operatorial image of the flow, not an external observer imposed by hand. Consequently, the decoherence rate observed by the apparatus is the square root of the graphon spectral gap: λdec=λgraphon=Λ1/Λ0→2,\lambda_{\mathrm{dec}} = \sqrt{\lambda_{\mathrm{graphon}}} = \sqrt{\Lambda_1/\Lambda_0} \to \sqrt{2},λdec​=λgraphon​​=Λ1​/Λ0​​→2​, in the asymptotic regime λgraphon→2\lambda_{\mathrm{graphon}} \to 2λgraphon​→2. This replaces the previously assumed spatial rate 2\sqrt{2}2​ with an algebraically derived rate λdec\lambda_{\mathrm{dec}}λdec​, eliminating the need for cross-terms or ad hoc coupling angles. The irreversible nature of the collapse follows from the entropy production inequality dSent/dk≥0dS_{\mathrm{ent}}/dk \geq 0dSent​/dk≥0, which establishes an intrinsic arrow of time encoded in the positivity of the dissipative metric. The stochastic dynamics is governed by an Ito quantum state diffusion equation with centered noise (Pi−⟨Pi⟩ψ)dWi(P_i - \langle P_i \rangle_\psi) dW_i(Pi​−⟨Pi​⟩ψ​)dWi​, which ensures the martingale property E[Pi(k)]=Pi(0)\mathbb{E}[P_i(k)] = P_i(0)E[Pi​(k)]=Pi​(0) and guarantees that the Born rule emerges as a consequence of the martingale convergence theorem, not as an independent postulate. All algebraic parameters are rigidly constrained by the Fano incidence structure and the graphon Lov\'asz limit. The construction contains no freely adjustable parameters beyond the regularity assumption R1. The numerical verification, based on 3000 Monte Carlo trajectories, confirms that the asymptotic frequencies converge to the Born probabilities with L2L_2L2​ error decaying as 1/N1/\sqrt{N}1/N​, in full agreement with the central limit theorem. This work provides a purely algebraic and geometric derivation of the Born rule and wavefunction collapse, offering a possible resolution to one of the deepest open problems in the foundations of quantum mechanics. 🌐 Live SPARQL Semantic Queries & Knowledge Graph Architecture This research deposit is integrated with the Blandino Research Knowledge Graph (BR-KG). Direct SPARQL query interfaces and machine-readable RDF endpoints are available below for automated data extraction and semantic interoperability: Live SPARQL Query: Full Micro-Node Graph Exploration (Q1–Q72) — Dynamic table query extracting all 72 indexed nodes, properties (P1–P12), and verification suite relationships. Interactive 2D Knowledge Graph Visualizer — Real-time 2D network rendering of cluster dependencies and topological factorizations. Live SPARQL Query: Linked Open Data & External DOI Cross-Mappings — Cross-reference mappings between internal nodes (Q3–Q36), Zenodo DOIs, FAIRsharing Record 8936, and Wikidata URIs. Public REST API Endpoint (RDF/JSON-LD) — Standardized endpoint for programmatic query execution.
First publication: 15 July 2025 This research introduces an experimental methodology capable of revealing geometrical structures corresponding to spherical harmonics within macroscopic magnetic fields , making visible field configurations that have never before been experimentally observed in the real world. Atomic orbitals represent some of the most recognizable geometrical structures emerging from quantum mechanics. They arise as solutions of the Schrödinger equation for the hydrogen atom and are mathematically described by spherical harmonics . In modern physics these structures are traditionally interpreted as probability distributions associated with the quantum state of the electron, rather than as spatial geometries directly observable at the macroscopic scale. In this work, a three-dimensional experimental visualization of structures isomorphic to atomic orbitals is presented for the first time. These structures are obtained through the detection and spatial mapping of magnetic field configurations using Hall-effect sensors. The experimental method employs a bipolar Hall sensor operating in dynamic scanning mode while maintaining a constant angular orientation relative to the magnetic source. This measurement configuration introduces a different observational framework compared to conventional representations of magnetic fields derived directly from Maxwell’s equations. When the magnetic field is explored by explicitly considering dipole-dipole interactions and by maintaining a fixed sensor orientation during spatial scanning , the measurements correspond to local projections of the magnetic field along a constant angular direction. The spatial reconstruction of these projections reveals three-dimensional field structures that exhibit a remarkable correspondence with the spherical harmonic geometries associated with the atomic orbitals of the hydrogen atom . These configurations do not normally appear in standard visualizations of magnetic fields, such as field lines or equipotential surfaces, because their emergence requires a measurement approach capable of highlighting the angular components of dipolar interactions. From this observation derives the title of the research. The structures observed in this work coincide with forms historically associated exclusively with the quantum solutions of the Schrödinger equation for the hydrogen atom. However, in this context they emerge as measurable geometric configurations of a macroscopic magnetic field , suggesting the existence of a structural relationship between these two physical descriptions. The research has also been deliberately structured to provide interpretations consistent with both classical mechanics and quantum mechanics , offering the reader multiple theoretical perspectives. By using the classical geometry of magnetic fields as an interpretative framework, several concepts typically associated with quantum mechanics acquire an unexpectedly intuitive and geometrically rational representation. This approach allows the exploration of possible structural connections between the probabilistic formalism of quantum mechanics and geometric patterns emerging from observable macroscopic physical fields , offering an alternative interpretative perspective on the relationship between classical physics and quantum phenomena. The work also includes a fully replicable experimental methodology for generating and visualizing these structures by scanning one or more permanent magnets using Hall sensors, effectively providing a procedure comparable to a form of three-dimensional magnetic tomography ("Magnetic CT Scan") . Official DOI: https://doi.org/10.5281/zenodo.15936280 A Professionally Printed Edition is also available on Amazon: MAGNETIC ORBITALS
First publication: 15 July 2025 This research introduces an experimental methodology capable of revealing geometrical structures corresponding to spherical harmonics within macroscopic magnetic fields , making visible field configurations that have never before been experimentally observed in the real world. Atomic orbitals represent some of the most recognizable geometrical structures emerging from quantum mechanics. They arise as solutions of the Schrödinger equation for the hydrogen atom and are mathematically described by spherical harmonics . In modern physics these structures are traditionally interpreted as probability distributions associated with the quantum state of the electron, rather than as spatial geometries directly observable at the macroscopic scale. In this work, a three-dimensional experimental visualization of structures isomorphic to atomic orbitals is presented for the first time. These structures are obtained through the detection and spatial mapping of magnetic field configurations using Hall-effect sensors. The experimental method employs a bipolar Hall sensor operating in dynamic scanning mode while maintaining a constant angular orientation relative to the magnetic source. This measurement configuration introduces a different observational framework compared to conventional representations of magnetic fields derived directly from Maxwell’s equations. When the magnetic field is explored by explicitly considering dipole-dipole interactions and by maintaining a fixed sensor orientation during spatial scanning , the measurements correspond to local projections of the magnetic field along a constant angular direction. The spatial reconstruction of these projections reveals three-dimensional field structures that exhibit a remarkable correspondence with the spherical harmonic geometries associated with the atomic orbitals of the hydrogen atom . These configurations do not normally appear in standard visualizations of magnetic fields, such as field lines or equipotential surfaces, because their emergence requires a measurement approach capable of highlighting the angular components of dipolar interactions. From this observation derives the title of the research. The structures observed in this work coincide with forms historically associated exclusively with the quantum solutions of the Schrödinger equation for the hydrogen atom. However, in this context they emerge as measurable geometric configurations of a macroscopic magnetic field , suggesting the existence of a structural relationship between these two physical descriptions. The research has also been deliberately structured to provide interpretations consistent with both classical mechanics and quantum mechanics , offering the reader multiple theoretical perspectives. By using the classical geometry of magnetic fields as an interpretative framework, several concepts typically associated with quantum mechanics acquire an unexpectedly intuitive and geometrically rational representation. This approach allows the exploration of possible structural connections between the probabilistic formalism of quantum mechanics and geometric patterns emerging from observable macroscopic physical fields , offering an alternative interpretative perspective on the relationship between classical physics and quantum phenomena. The work also includes a fully replicable experimental methodology for generating and visualizing these structures by scanning one or more permanent magnets using Hall sensors, effectively providing a procedure comparable to a form of three-dimensional magnetic tomography ("Magnetic CT Scan") . Official DOI: https://doi.org/10.5281/zenodo.15936280 A Professionally Printed Edition is also available on Amazon: MAGNETIC ORBITALS
First publication: 15 July 2025 This research introduces an experimental methodology capable of revealing geometrical structures corresponding to spherical harmonics within macroscopic magnetic fields , making visible field configurations that have never before been experimentally observed in the real world. Atomic orbitals represent some of the most recognizable geometrical structures emerging from quantum mechanics. They arise as solutions of the Schrödinger equation for the hydrogen atom and are mathematically described by spherical harmonics . In modern physics these structures are traditionally interpreted as probability distributions associated with the quantum state of the electron, rather than as spatial geometries directly observable at the macroscopic scale. In this work, a three-dimensional experimental visualization of structures isomorphic to atomic orbitals is presented for the first time. These structures are obtained through the detection and spatial mapping of magnetic field configurations using Hall-effect sensors. The experimental method employs a bipolar Hall sensor operating in dynamic scanning mode while maintaining a constant angular orientation relative to the magnetic source. This measurement configuration introduces a different observational framework compared to conventional representations of magnetic fields derived directly from Maxwell’s equations. When the magnetic field is explored by explicitly considering dipole-dipole interactions and by maintaining a fixed sensor orientation during spatial scanning , the measurements correspond to local projections of the magnetic field along a constant angular direction. The spatial reconstruction of these projections reveals three-dimensional field structures that exhibit a remarkable correspondence with the spherical harmonic geometries associated with the atomic orbitals of the hydrogen atom . These configurations do not normally appear in standard visualizations of magnetic fields, such as field lines or equipotential surfaces, because their emergence requires a measurement approach capable of highlighting the angular components of dipolar interactions. From this observation derives the title of the research. The structures observed in this work coincide with forms historically associated exclusively with the quantum solutions of the Schrödinger equation for the hydrogen atom. However, in this context they emerge as measurable geometric configurations of a macroscopic magnetic field , suggesting the existence of a structural relationship between these two physical descriptions. The research has also been deliberately structured to provide interpretations consistent with both classical mechanics and quantum mechanics , offering the reader multiple theoretical perspectives. By using the classical geometry of magnetic fields as an interpretative framework, several concepts typically associated with quantum mechanics acquire an unexpectedly intuitive and geometrically rational representation. This approach allows the exploration of possible structural connections between the probabilistic formalism of quantum mechanics and geometric patterns emerging from observable macroscopic physical fields , offering an alternative interpretative perspective on the relationship between classical physics and quantum phenomena. The work also includes a fully replicable experimental methodology for generating and visualizing these structures by scanning one or more permanent magnets using Hall sensors, effectively providing a procedure comparable to a form of three-dimensional magnetic tomography ("Magnetic CT Scan") . Official DOI: https://doi.org/10.5281/zenodo.15936280 A Professionally Printed Edition is also available on Amazon: MAGNETIC ORBITALS
First publication: 15 July 2025 This research introduces an experimental methodology capable of revealing geometrical structures corresponding to spherical harmonics within macroscopic magnetic fields , making visible field configurations that have never before been experimentally observed in the real world. Atomic orbitals represent some of the most recognizable geometrical structures emerging from quantum mechanics. They arise as solutions of the Schrödinger equation for the hydrogen atom and are mathematically described by spherical harmonics . In modern physics these structures are traditionally interpreted as probability distributions associated with the quantum state of the electron, rather than as spatial geometries directly observable at the macroscopic scale. In this work, a three-dimensional experimental visualization of structures isomorphic to atomic orbitals is presented for the first time. These structures are obtained through the detection and spatial mapping of magnetic field configurations using Hall-effect sensors. The experimental method employs a bipolar Hall sensor operating in dynamic scanning mode while maintaining a constant angular orientation relative to the magnetic source. This measurement configuration introduces a different observational framework compared to conventional representations of magnetic fields derived directly from Maxwell’s equations. When the magnetic field is explored by explicitly considering dipole-dipole interactions and by maintaining a fixed sensor orientation during spatial scanning , the measurements correspond to local projections of the magnetic field along a constant angular direction. The spatial reconstruction of these projections reveals three-dimensional field structures that exhibit a remarkable correspondence with the spherical harmonic geometries associated with the atomic orbitals of the hydrogen atom . These configurations do not normally appear in standard visualizations of magnetic fields, such as field lines or equipotential surfaces, because their emergence requires a measurement approach capable of highlighting the angular components of dipolar interactions. From this observation derives the title of the research. The structures observed in this work coincide with forms historically associated exclusively with the quantum solutions of the Schrödinger equation for the hydrogen atom. However, in this context they emerge as measurable geometric configurations of a macroscopic magnetic field , suggesting the existence of a structural relationship between these two physical descriptions. The research has also been deliberately structured to provide interpretations consistent with both classical mechanics and quantum mechanics , offering the reader multiple theoretical perspectives. By using the classical geometry of magnetic fields as an interpretative framework, several concepts typically associated with quantum mechanics acquire an unexpectedly intuitive and geometrically rational representation. This approach allows the exploration of possible structural connections between the probabilistic formalism of quantum mechanics and geometric patterns emerging from observable macroscopic physical fields , offering an alternative interpretative perspective on the relationship between classical physics and quantum phenomena. The work also includes a fully replicable experimental methodology for generating and visualizing these structures by scanning one or more permanent magnets using Hall sensors, effectively providing a procedure comparable to a form of three-dimensional magnetic tomography ("Magnetic CT Scan") . Official DOI: https://doi.org/10.5281/zenodo.15936280 A Professionally Printed Edition is also available on Amazon: MAGNETIC ORBITALS
Abstract:The quantum measurement problemthe fundamental conict between the deterministic, unitary evolution described by the Schrödinger equation and the stochastic, irreversible outcomes observed in experimentshas remained unresolved since the inception of quantum mechanics nearly a century ago. Here we demonstrate that the Chrono-Singularity Unication (CSU) framework provides a complete, rst-principles resolution of all ve components of the measurement problem with zero adjustable parameters. From a minimal informational substrate ΨI characterized by three internally-calibrated constants (α = ln 2, β = ln 2, w = −1), we derive: (i) the Born rule P = |ψ| 2 as a mathematical necessity via the GNS construction and spectral theorem; (ii) the emergence of the preferred (position) basis through Dobrushin concentration bounds on redundant environmental records; (iii) single denite outcomes from the sampled-history ontology without dynamical collapse; (iv) full compatibility with special relativity through topological linking that preserves no-signaling while permitting Bell-inequality violation; and (v) unique, falsi- able experimental predictions including a mass-dependent gravitational decoherence oor testable in near-future molecular interferometry experiments. Significance:This framework provides the exact geometric scaling required to resolve the Hubble tension and derives the Diósi-Penrose gravitational decoherence floor (τ=ℏ/ΔEG) strictly as a low-energy macroscopic limit. This paper serves as the theoretical foundation for a fully deterministic, parameter-free unification of quantum mechanics and general relativity.