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

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 are among 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 typically interpreted as probability distributions of the electron rather than as spatial geometries 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 by means of 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. Unlike conventional magnetic field representations derived directly from Maxwell’s equations, this measurement approach records local projections of the magnetic field along a fixed angular direction. The spatial reconstruction of these projections reveals three-dimensional structures showing a remarkable correspondence with the spherical harmonic geometries associated with hydrogen atomic orbitals. These configurations do not appear in standard visualizations such as field lines or equipotential surfaces because their emergence requires a measurement framework capable of highlighting the angular components of dipole-dipole interactions. The structures observed coincide with forms historically associated exclusively with the quantum solutions of the Schrödinger equation for the hydrogen atom. Here, however, 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 is intentionally presented through interpretations compatible with both classical and quantum mechanics, allowing several concepts typically associated with quantum theory to acquire a more intuitive geometric representation through the classical geometry of magnetic fields. This approach explores possible structural connections between the probabilistic formalism of quantum mechanics and geometric patterns emerging from observable macroscopic fields, offering an alternative perspective on the relationship between classical physics and quantum phenomena. The work also provides a fully replicable experimental methodology for generating and visualizing these structures by scanning one or more permanent magnets with Hall sensors, effectively implementing a form of three-dimensional magnetic tomography ("Magnetic CT Scan"). A professionally printed edition is also available on Amazon: MAGNETIC ORBITALS