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.

中文翻译：

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束缚电磁场的传播特性：经典和量子观点

目前的工作受到近期旨在测量束缚电磁 (EM) 场传播速度的实验的推动（Missevitch 等人在 EPL 93:64004, 2011 中；de Sangro 等人在 Eur Phys JC 75:137, 2015 中）这表明在没有 EM 辐射的情况下没有延迟。我们展示了如何将这些发现纳入狭义相对论的数学结构，使我们能够重新考虑经典和量子电动力学的一些选定问题。特别是，我们得出的结论是，如果电磁辐射可以忽略不计，经典系统“粒子加场”的总四动量应该是移动电荷的现态函数。在量子领域，我们分析了最近在量子相位效应研究中提出的动量算符的新定义（Kholmetskii 等人在 Sci. Rep. 8:11937 中，2018）。这意味着束缚电磁场能量和动量也是当前状态函数。与报告的实验一致，这些结论表明有必要进行更精确的实验验证，以额外和独立地确定束缚电磁场的传播特性。还提出了有关该主题的可能实验方案。