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arXiv:2310.13968

Gauge waves generation and detection in Aharonov-Bohm electrodynamics

Fernando O. Minotti, Giovanni Modanese

Published Oct 21, 2023• 0 citations
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Abstract

The extended Aharonov-Bohm electrodynamics has a simple formal structure and allows to couple the e.m. field also to currents which are not locally conserved, like those resulting from certain non-local effective quantum models of condensed matter. As it often happens in physics and mathematics when one tries to extend the validity of some equations or operations, new perspectives emerge in comparison to Maxwell theory, and some ''exotic'' phenomena are predicted. For the Aharonov-Bohm theory the main new feature is that the potentials $A^μ$ become univocally defined and can be measured with probes in which the ''extra-current'' $I=\partial_μj^μ$ is not zero at some points. As a consequence, it is possible in principle to detect pure gauge-waves with $\mathbf{E}=\mathbf{B}=0$, which would be regarded as non-physical in the Maxwell gauge-invariant theory with local current conservation. We discuss in detail the theoretical aspects of this phenomenon and propose an experimental realization of the detectors. A full treatment of wave propagation in anomalous media with extra-currents and of energy-momentum balance issues is also given.

DOI
10.48550/arxiv.2310.13968

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Gauge waves generation and detection in Aharonov–Bohm electrodynamics

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The extended Aharonov-Bohm electrodynamics has a simple formal structure and allows to couple the e.m. field also to currents which are not locally conserved, like those resulting from certain non-local effective quantum models of condensed matter. As it often happens in physics and mathematics when one tries to extend the validity of some equations or operations, new perspectives emerge in comparison to Maxwell theory, and some ''exotic'' phenomena are predicted. For the Aharonov-Bohm theory the main new feature is that the potentials AμA^μAμ become univocally defined and can be measured with probes in which the ''extra-current'' I=∂μjμI=\partial_μj^μI=∂μ​jμ is not zero at some points. As a consequence, it is possible in principle to detect pure gauge-waves with E=B=0\mathbf{E}=\mathbf{B}=0E=B=0, which would be regarded as non-physical in the Maxwell gauge-invariant theory with local current conservation. We discuss in detail the theoretical aspects of this phenomenon and propose an experimental realization of the detectors. A full treatment of wave propagation in anomalous media with extra-currents and of energy-momentum balance issues is also given.
Abstract The extended Aharonov–Bohm electrodynamics has a simple formal structure and allows to couple the e.m. field also to currents which are not locally conserved, like those resulting from certain non-local effective quantum models of condensed matter. As it often happens in physics and mathematics when one tries to extend the validity of some equations or operations, new perspectives emerge in comparison to Maxwell theory, and some “exotic” phenomena are predicted. For the Aharonov–Bohm theory the main new feature is that the potentials AμA^\mu Aμ A μ become univocally defined and can be measured with probes in which the “extra-current” I=∂μjμI=\partial _\mu j^\mu I=∂μ​jμ I = ∂ μ j μ is not zero at some points. As a consequence, it is possible in principle to detect pure gauge-waves with E=B=0{\textbf{E}}={\textbf{B}}=0E=B=0 E = B = 0 , which would be regarded as non-physical in the Maxwell gauge-invariant theory with local current conservation. We discuss in detail the theoretical aspects of this phenomenon and propose an experimental realization of the detectors. A full treatment of wave propagation in anomalous media with extra-currents and of energy–momentum balance issues is also given.
Abstract Aharonov-Bohm electrodynamics predicts the existence of traveling waves of pure potentials, with zero electromagnetic fields, denoted as gauge waves, or g-waves for short. In general, these waves cannot be shielded by matter since their lack of electromagnetic fields prevents the material from reacting to them. However, a not-locally-conserved electric current present in the material does interact with the potentials in the wave, giving the possibility of its detection. In [1] the basic theoretical description of a detecting circuit was presented, based on a phenomenological theory of materials that can sustain not-locally-conserved electric currents. In the present work we discuss how that circuit can be built in practice, and used for the effective detection of g-waves.
We reconsider some well-known tunneling processes from the point of view of Aharonov-Bohm electrodynamics, a unique extension of Maxwell’s theory which admits charge-current sources that are not locally conserved. In particular we are interested into tunneling phenomena having relatively long range (otherwise the non-Maxwellian effects become irrelevant, especially at high frequency) and involving macroscopic wavefunctions and coherent matter, for which it makes sense to evaluate the classical e.m. field generated by the tunneling particles. For some condensed-matter systems, admitting discontinuities in the probability current is a possible way of formulating phenomenological models. In such cases, the Aharonov-Bohm theory offers a logically consistent approach and allows to derive observable consequences. Typical e.m. signatures of the failure of local conservation are at high frequency the generation of a longitudinal electric radiation field, and at low frequency a small effect of “missing” magnetic field. Possible causes of this failure are instant tunneling and phase slips in superconductors. For macroscopic quantum systems in which the phase-number uncertainty relation ΔNΔφ∼1 applies, the expectation value of the anomalous source I=∂tρ+∇·j has quantum fluctuations, thus becoming a random source of weak non-Maxwellian fields.
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 AμA_\muAμ​, 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 gμνg_{\mu\nu}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.
The gauge invariance of the Aharonov-Bohm (AB) effect with a quantum treatment for the electromagnetic field is demonstrated. We provide an exact solution for the electromagnetic ground energy due to the interaction of the quantum electromagnetic field with the classical charges and currents that act as sources of the potentials in a classical description, in the Lorenz gauge. Then, we use first-order perturbation theory to compute an extra change on the electromagnetic ground energy due to the presence of a quantum charged particle with known wave function in the system. This energy in general depends on the quantum particle path in an interferometer, which results in an AB phase difference between the paths. The gauge invariance of this AB phase difference is then shown for the magnetic, electric, and the recently proposed electrodynamic versions of the AB effect. However, the AB phase difference could depend on the gauge for nonclosed paths, which reinforces the view that it only can be measured in closed paths.
The extended electrodynamic theory introduced by Aharonov and Bohm (after an earlier attempt by Ohmura) and recently developed by Van Vlaenderen and Waser, Hively and Giakos, can be re-written and solved in a simple and effective way in the standard covariant 4D formalism. This displays more clearly some of its features. The theory allows a very interesting consistent generalization of the Maxwell equations. In particular, the generalized field equations are compatible with sources (classical, or more likely of quantum nature) for which the continuity/conservation equation ∂μjμ=0\partial_\mu j^\mu=0∂μ​jμ=0 is not valid everywhere, or is valid only as an average above a certain scale. And yet, remarkably, in the end the observable FμνF^{\mu \nu}Fμν field is still generated by a conserved effective source which we denote as (jν+iν)(j^\nu+i^\nu)(jν+iν), being iνi^\nuiν a suitable non-local function of jνj^\nujν. This implies that any microscopic violation of the charge continuity condition is "censored" at the macroscopic level, although it has real consequences, because it generates a non-Maxwellian component of the field. We consider possible applications of this formalism to condensed-matter systems with macroscopic quantum tunneling. The extended electrodynamics can also be coupled to fractional quantum systems.