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Propagation Properties of Bound Electromagnetic Field: Classical and Quantum Viewpoints

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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.

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Notes

  1. As is pointed out in Ref. [38], other models of inertial reference frames are also possible, where the operations of measurement obey the requirements of definiteness, reversibility and transitivity. At the same time, as is also shown in [38], all such possible models are equivalent to Einstein’s model of inertial reference frame defined here.

  2. We can add that Eq. (20) can be also derived via the general procedure by Hilbert (see, e.g., [40]), when the Lagrangian density for the system “charged particles and their EM field” is taken in the form [13]

    \(L = - \frac{1}{16\pi }F_{\mu \nu } F^{\mu \nu } - \frac{1}{c}A_{\mu } j^{\mu }\),(i).

    instead of the standard choice for the Lagrangian density, containing only the “field part” (i.e., the first term on rhs of Eq. (i)). However, as soon as the bound EM field component is involved, we have to realize that it cannot exist without its source charges. Therefore, in the general case, where we deal with both bound and radiative EM fields, only the sum of two terms of Eq. (i) (where the second terms stands for the “particles part”) has the physical meaning.

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Acknowledgment

The authors thank an anonymous reviewer for useful comments and recommendations, which were helpful for the improvement of the paper.

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Authors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    A. L. Kholmetskii

  2. Institute for Nuclear Problems, Belarusian State University, Minsk, Belarus

    O. V. Missevitch

  3. Istanbul Okan University, Akfirat, Istanbul, Turkey

    T. Yarman

  4. Complutense University, Madrid, Spain

    R. Smirnov-Rueda

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  1. A. L. Kholmetskii
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  2. O. V. Missevitch
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  3. T. Yarman
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  4. R. Smirnov-Rueda
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Correspondence to A. L. Kholmetskii.

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Kholmetskii, A.L., Missevitch, O.V., Yarman, T. et al. Propagation Properties of Bound Electromagnetic Field: Classical and Quantum Viewpoints. Found Phys 50, 1686–1722 (2020). https://doi.org/10.1007/s10701-020-00396-8

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