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

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 at the macroscopic scale. Atomic orbitals are well-known geometrical structures arising as solutions of the Schrödinger equation for the hydrogen atom, mathematically described by spherical harmonics. In modern physics, these structures are interpreted as probability distributions, rather than observable spatial geometries. In this work, a three-dimensional experimental visualization of structures isomorphic to atomic orbitals is presented for the first time through spatial mapping of magnetic field configurations using Hall-effect sensors. The method employs a bipolar Hall sensor operating in dynamic scanning mode, maintaining a constant angular orientation relative to the magnetic source. Instead of directly representing the magnetic field through Maxwell’s equations, the system records local projections of the magnetic field along a fixed angular direction. The spatial reconstruction of these projections reveals three-dimensional geometries that closely correspond to spherical harmonic structures associated with hydrogen atomic orbitals. These configurations do not appear in conventional representations such as field lines or equipotential surfaces, as their emergence requires a measurement framework sensitive to the angular components of dipole–dipole interactions. The observed structures coincide with forms historically associated exclusively with quantum solutions of the Schrödinger equation, yet here they emerge as measurable geometric configurations of a macroscopic magnetic field, suggesting a possible structural relationship between classical and quantum descriptions. The research is deliberately presented in a way that remains compatible with both classical and quantum mechanics, offering a more intuitive geometric interpretation of concepts typically confined to quantum formalism. Overall, this work explores structural connections between the probabilistic framework of quantum mechanics and geometric patterns arising in observable macroscopic fields, providing an alternative perspective on the relationship between classical physics and quantum phenomena. The study also delivers a fully replicable experimental methodology for generating and visualizing these structures by scanning permanent magnets with Hall sensors, effectively implementing a form of three-dimensional magnetic tomography: a “Magnetic CT Scan”. A Professionally Printed Edition is also available on Amazon: MAGNETIC ORBITALS