Propagation Properties of Bound Electromagnetic Field: Classical and Quantum Viewpoints
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Propagation Properties of Bound Electromagnetic Field: Classical and Quantum Viewpoints A. L. Kholmetskii1 · O. V. Missevitch2 · T. Yarman3 · R. Smirnov‑Rueda4 Received: 4 May 2020 / Accepted: 16 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The present work is motivated by recent experiments aimed to measure the propagation velocity of bound electromagnetic (EM) field (Missevitch, et al. in EPL 93:64004, 2011; de Sangro et al. in Eur Phys J C 75:137, 2015) that reveal no retardation in the absence of EM radiation. We show how these findings can be incorporated into the mathematical structure of special relativity theory that allows us to reconsider some selected problems of classical and quantum electrodynamics. In particular, we come to the conclusion that the total four-momentum for a classical system “particles plus fields” ought to be a present state function of moving charges if EM radiation is negligible. In quantum domain, we analyze novel definition of the momentum operator recently suggested in the study of quantum phase effects (Kholmetskii et al. in Sci. Rep. 8:11937, 2018). It implies that bound EM field energy and momentum are to be present state functions, too. Being in agreement with reported experiments, these conclusions suggest the necessity to carry out more precise experimental verifications for additional and independent determination of propagation properties of bound EM fields. A scheme of a possible experiment on this subject is also proposed. Keywords Classical electrodynamics · Bound electromagnetic field · Special relativity · Quantum electrodynamics · Quantum phases
1 Introduction During last decades, a number of experimental results had been presented (see [1–8] and references therein), putting in manifest a superluminal behavior of an electromagnetic (EM) field observed under appropriate conditions. It is worth noting that in some situations the superluminality may be understood as an apparent effect when the resultant signal is formed by a superposition of elementary * A. L. Kholmetskii [email protected] Extended author information available on the last page of the article
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EM waves propagating with the light velocity c (see, e.g., [6]). In order to avoid this ambiguity at a quantitative level, especially convincing results have been reported recently in experiments dealing with bound (velocity-dependent) magnetic field [3, 4, 7] and bound electric field [8], where any possibility of apparent superluminal behavior can be discarded (Sect. 2). The experimental approach realized in [4, 7] shows that pulses of bound magnetic field generated by electrically small loop antenna turn out to be highly superluminal in the near zone (where the intensity of bound EM fields exceeds the intensity of EM radiation), whereas outside it the propagation rate tends to the velocity of light c. With respect to EM radiation (acceleration-dependent component) it was confirmed that its propagation veloc
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