Aharonov--Bohm phase as real-J holonomy Concept DOI: 10.5281/zenodo.20772090 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 This paper reads electromagnetic and gravitational Aharonov--Bohm phases as source-access holonomies. The gauge potential is the real-J dial connection; the observed complex phase is the laboratory projection \(J\mapsto i\). The compact QTT holonomy is \[ W_\gamma^{\mathrm{QTT}} =\exp\!\left\{J\left[ \frac{q}{\hbar c}\int_\gamma A_\mu dx^\mu - \frac{mc^2}{\hbar}\int_\gamma d\tau_{A2} \right]\right\}. \] The finite-edge admissibility gate is \[ \lambda_e^{\mathrm{AB}} =\frac{|\delta S_e^{\mathrm{AB}}|}{\hbar n_e} \le1. \] The standard AB equations are therefore recovered as low-density laboratory shadows of the same source holonomy. Core labels: Σ-AB-REAL-J-HOLONOMY, Σ-A2-GRAVITATIONAL-AB-ENDURANCE, Σ-A6-PHASE-DENSITY-GATE.
Aharonov--Bohm phase as real-J holonomy Concept DOI: 10.5281/zenodo.20772090 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 This paper reads electromagnetic and gravitational Aharonov--Bohm phases as source-access holonomies. The gauge potential is the real-J dial connection; the observed complex phase is the laboratory projection (J\mapsto i). The compact QTT holonomy is [ W_\gamma^{\mathrm{QTT}} =\exp!\left{J\left[ \frac{q}{\hbar c}\int_\gamma A_\mu dx^\mu - \frac{mc^2}{\hbar}\int_\gamma d\tau_{A2} \right]\right}. ] The finite-edge admissibility gate is [ \lambda_e^{\mathrm{AB}} =\frac{|\delta S_e^{\mathrm{AB}}|}{\hbar n_e} \le1. ] The standard AB equations are therefore recovered as low-density laboratory shadows of the same source holonomy. Core labels: Σ-AB-REAL-J-HOLONOMY, Σ-A2-GRAVITATIONAL-AB-ENDURANCE, Σ-A6-PHASE-DENSITY-GATE.
The Aharonov–Bohm (AB) effect demonstrates that a charged particle can acquire an observable phase shift in a region where the local magnetic field identically vanishes provided the configuration space is multiply connected and the electromagnetic connection exhibits non-trivial holonomy. We present a gauge-covariant physico-mathematical framework that systematically disentangles three regimes: (i) the standard ideal AB effect governed by the holonomy of a flat but globally inexact connection on ΩR=R2∖DR with DR={r≤R}; (ii) the path-integral decomposition into homotopy sectors indexed by the winding number, which is constructed on the universal cover; and (iii) non-topological corrections arising from evanescent wave-function penetration when the solenoid is modeled as a finite radial barrier. The ideal AB phase is taken as the reference topological holonomy, while the finite-barrier extension developed here separates the measured phase, under explicit weak-penetration assumptions, as Δφtotal=ΔφABhol+δφfinite+O(Teff2). Here, ΔφABhol=qΦ/ħ is the standard topological holonomy, whereas δφfinite=O(e−2κℓb) is a small dynamical, microphysics-dependent correction controlled by the barrier height, particle energy, and effective forbidden length ℓb. Within Laskin’s fractional quantum mechanics, we use the fractional extension as a diagnostic test: the topological AB phase is independent of the Lévy index α, whereas the finite-barrier correction acquires an anomalous, α-dependent penetration length. The numerical material provides gauge-covariant diagnostics: a Peierls-substituted split-operator scheme, a sector-resolved Monte Carlo path integral benchmarked against the exact Aharonov–Bohm propagator of Gerry and Singh, a WKB/transfer-matrix finite-barrier estimate tracking δφfinite→0, and Berry-phase computations used as consistency checks.
The Aharonov-Bohm (AB) effect, wherein an electron acquires a phase shift in a field-free region due to electromagnetic potentials, poses a profound challenge to the ontology of quantum mechanics and gauge theories. This paper demonstrates that gauge-invariant explanations, which attribute the phase to measurable quantities, rely on nonlocal and discontinuous mechanism and fail to account for its continuous accumulation along the electron's path—a process evident in the generalized AB effect, where a time-varying magnetic flux induces a phase that builds gradually over time, as predicted by quantum mechanics. Through a new analysis spanning quantum mechanics and quantum electrodynamics, I argue that the electromagnetic potentials Aμ, fixed in the Lorenz gauge, emerge as the fundamental physical reality, offering a local, relativistically consistent account of the phase’s generation. This exclusion of gauge-invariant paradigms reverberates across gauge theories: it redefines the Higgs mechanism, favoring dynamic potentials over static invariants, and extends to general relativity, where gravitational potentials gμν may anchor spacetime’s substantival reality via a gravitational AB effect. By unraveling the AB phase’s continuous generation—locally mediated by potentials—this study not only addresses a long-standing conundrum but also bridges electromagnetic, gravitational, and Yang-Mills frameworks, offering a unified potential-centric perspective with novel implications for physics and philosophy.
Testing whether gravity is quantum or classical remains a cornerstone challenge in fundamental physics. We introduce a practical tabletop experiment to probe gravity's quantum nature via the gravitational Aharonov-Bohm (AB) effect in atom interferometry. Our approach hinges on two pivotal insights: First, unlike electromagnetic AB effects where constant charge ensures gauge-invariant phases for closed paths, semiclassical gravity couples to the particle's total energy, rendering the AB phase gauge-dependent and unobservable when energies differ between paths due to environmental noise or controlled perturbations. Second, in quantum gravity—treating source, particle, and field as quantum—the total phase splits into a gauge-dependent particle contribution and a gauge-invariant source backreaction, yielding precisely half the nominal AB phase as observable. This halved phase discriminates quantum from classical gravity without requiring massive superpositions, aligning with existing technology. Remarkably, Overstreet et al.'s (Science 375, 226 (2022)) data already reveal a nonzero measured AB phase, providing the first experimental evidence for gravitational quantization.
This paper develops a controlled U(1) limit of the Trinity Scalar–Tensor–Observable (STO) gauge package by applying it to the Aharonov–Bohm effect. The goal is not to claim that Trinity is already a completed gauge theory, but to show that a well-controlled gauge phenomenon can be represented inside the Trinity formalism with precise correspondences. In the standard Aharonov–Bohm effect, a charged quantum system acquires a measurable phase shift from the electromagnetic vector potential even in a region where the local field strength vanishes. This makes the effect an important test case for the Trinity gauge package, because it distinguishes between local curvature records and global holonomy records. The paper identifies the electromagnetic U(1) potential as an Abelian sector of the Trinity awareness/selector connection A_mu^T, treats the scalar clock phi as the invariant ordering background, and shows that the standard Aharonov–Bohm phase Delta theta_AB = q Phi_B / hbar is recovered as selector holonomy in the controlled U(1) limit. The central contribution is the claim that local curvature observables of the form O(x) = C(F_mu nu^T, phi)(x) are not sufficient for all gauge phenomena. Aharonov–Bohm physics requires loop-dependent holonomy observables O_Gamma = C_Gamma(A_mu^T, phi), which are then coarse-grained into measurable detector records such as shifted interference fringes. In Trinity terms, the observed fringe displacement is interpreted as a stabilized record of scalar-clock evolution under nontrivial selector transport. The paper extends the STO gauge package by distinguishing two classes of observable records: local curvature records and global holonomy records. This result brings the Trinity/STO formalism closer to the mathematical structure of gauge theory while preserving the distinctive Trinity interpretation that observable space and time arise as projection faces of deeper scalar-clock order.
Abstract: This work develops a unified and gauge-invariant framework in which quantum interference is described as a measurement of relative holonomy between two coherent evolutions in a combined configuration space X = M × Λ. Both the Aharonov–Bohm (Abelian) and Wilczek–Zee (non-Abelian) effects appear as limits of a single Wilson-loop observable. A block connection is introduced on the direct-sum bundle E = H ⊕ (T X ⊗ ℂ), with structure group U(n) × O(p,q), thereby unifying Berry parallel transport and Levi-Civita geometry within one connection. The formalism ensures gauge and diffeomorphism covariance, analytic well-posedness under back-reaction, and establishes conditions for reconstructing the spacetime metric from holonomy data. The resulting theory provides a mathematically consistent and experimentally testable synthesis of geometric phase, interference, and spacetime connection. Potential physical implementations include mesoscopic rings, cold-atom systems, and superconducting circuits. Keywords: geometric phase; holonomy; Aharonov–Bohm effect; Berry phase; Wilczek–Zee connection; differential geometry; quantum interference; gauge theory.
Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.