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

Abstract

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