The role of the anomalous moment in the geometric algebra of proton topological mass generation suggests that the anomaly is not an intrinsic property of the free space proton, but rather a topological effect of applying the electromagnetic bias field required to define the eigenstates probed by the magnetic moment measurement. Quantum interpretations strive to explain emergence of the world we observe from formal quantum theory. This variant on the canonical measurement problem is examined in the larger context of quantum interpretations. A more detailed presentation of this content may be found here: https://www.youtube.com/watch?v=uyM4cZgSprI
The role of the anomalous moment in the geometric algebra of proton topological mass generation suggests that the anomaly is not an intrinsic property of the free space proton, but rather a topological effect of applying the electromagnetic bias field required to define the eigenstates probed by the magnetic moment measurement. Quantum interpretations strive to explain emergence of the world we observe from formal quantum theory. This variant on the canonical measurement problem is examined in the larger context of quantum interpretations. A more detailed presentation of this content may be found here: https://www.youtube.com/watch?v=uyM4cZgSprI
A century’s proliferation of Quantum Interpretations has been driven by an incomplete understanding of the measurement problem, by an incomplete understanding of the unobservable wavefunction and its unobservable interactions. Yet it remains that the observer effect - observing a phenomenon necessarily changes that phenomenon - is at the historical foundation of quantum mechanics. The semantic confusion, that wavefunction interactions are unobservable yet the observer effect is irrefutable, can be resolved by considering the difference between simple passive measurement and active transfer function measurement. In the first, one registers whatever lump of energy lands upon a sensor, and there is no observer effect. In the second, one excites the system of interest and measures the response, and there is an observer effect. Magnetic moment measurements are transfer function measurements. To measure an amplitude one must align the spin, applying a magnetic field to separate the energy eigenstates, and excite the system to measure their difference. A paper presented to Spin 2016 suggests that the measured anomaly is not an intrinsic property of the fermionic proton, but rather an observer effect. In our presentation to Spin 2018 we propose to extend the Spin 2016 interpretation to the neutron anomalous moment.
Quantum Interpretations seek to explain observables from formal theory. Impedances govern the flow of energy, are helpful in such attempts. An earlier note documented first efforts to resolve the interpretational ambiguities and contentions from the practical perspective of our model-based approach. In the interim, discovery of the deep connections between the impedance model and geometric Clifford algebra has shed new light on the measurement problem and its manifestations, which we revisit here.
Abstract Topological and geometrical effects appear in the solution of the Schrödinger equation due to special geometrical forms of the interaction, or due to interactions which do not result from conservative forces acting on the system (see Section 1.2). A conscientious reader may point out that all these effects could be entirely explained using the Schrödinger equation only. But the geometrical phase formalism is useful because it sometimes plays a role in fundamental quantum phenomena and it shows that additional phase factors exist which are easily overlooked, making the interpretation of measured effects more mysterious than necessary. Thus, our understand-ing of quantum mechanics has deepened since the existence of geometrical phases was explicitly revealed (Shapere and Wilczek 1989). This happened due to the seminal works of Pancharatnam (1956), Berry (1984), Anandan (1992), and Bhandari (1997). It also shows that a wavefunction often carries much more information than is usually extracted in a standard experiment. A typical example is the assumption of adiabaticity, where the magnetic moment of the neutron produces (inside a slowly varying magnetic field) a dynamical phase shift proportional to the path integral ∫ B ds, but when the direction of the field varies slowly an additional, i.e. geometrical, phase also appears. The back reaction of a quantum measurement can also be described as a kind of an induced topological phase (Aharonov et al. 1998).
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
The quantum geometric tensor - the Berry curvature together with the quantum metric - now underlies a long list of observables, from the anomalous Hall effect to the superfluid weight of a flat band. We ask which of these observables actually require quantum mechanics. To answer this question, we study a purely classical system: a point particle carrying a classical magnetic moment ℓ that precesses in a momentum-dependent magnetic field B(p). Within Hamiltonian classical mechanics, the component of ℓ along the field reproduces the Berry-curvature phenomena, while its precessing transverse component reproduces the quantum-metric phenomena. The particle acquires a position spread whose second moment is the metric, an orbital magnetic moment, and - most strikingly - an inertial mass generated by a position-dependent force, and with it a nonzero Drude weight in a system that is nominally dispersionless.
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