The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and the fields. As it turns out, an alternative force law, first proposed in 1908 by Einstein and Laub, exists that is consistent with Maxwell's macroscopic equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material, the Einstein-Laub formulation of electromagnetic force and torque does not invoke hidden entities under such circumstances. Moreover, the total force and the total torque exerted by electromagnetic fields on any given object turn out to be independent of whether force and torque densities are evaluated using the Lorentz law or in accordance with the Einstein-Laub formulas. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions throughout material media. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.
On Lorentz and Einstein-Laub forces in material media
作为讨论的延续（M。Mansuripur，Phys. Rev. Lett. 108，193901（2012）），我们表明，基于物质介质中的洛伦兹力定律的方法，如电磁力的Einstein-Laub表达式，在适当考虑隐藏动量的贡献时，给出了相对论一致的结果。导出了一个与Lorentz和Einstein-Laub方法相容的点状电/磁偶极子的力矩表达式。
Critical study and discrimination of different formulations of electromagnetic force density and consequent stress tensors inside matter
通过对几个例子中作用在物体边界上的电磁力的分析，探讨了不同电磁力密度公式所对应的应力张量与狭义相对论的相容性。电磁力密度的安培-洛伦兹公式在物理上是合理的，因为电场和磁通量密度作用于总电荷和总电流的密度，而不像闵可夫斯基公式完全排除了均匀介质内的有界电荷和有界电流的密度。亚伯拉罕的公式是幻想和缺乏物理意义。乍一看，爱因斯坦-劳布的公式似乎包括了总电荷和总电流的密度，但将有界电荷和有界电流分组为点状偶极子错误地导致隐藏的动量被忽略，因此[Phys. Rev. Lett. 108，193901（2012）]。自然，安培-洛伦兹应力张量符合狭义相对论。闵可夫斯基应力张量也符合狭义相对论。值得注意的是，闵可夫斯基应力张量的数学表达式可能与文献中已知的应力张量形式有很大不同。证明了Einstein-Laub应力张量与狭义相对论不相容，从而反驳了Einstein-Laub力密度。由于电磁场的亚伯拉罕动量密度本质上对应于爱因斯坦-劳布力密度[Phys. Rev. Lett 111，043602（2013）]，我们的反驳也可能揭示关于光的动量的争议。
A New Limit on Signals of Lorentz Violation in Electrodynamics
我们描述了一个实验的结果来测试时空各向异性条款，可能存在的洛伦兹违反。该装置由一对圆柱形超导腔稳定振荡器组成，振荡器工作在TM_{010}模式下，一个轴为东西向，另一个轴垂直。空间各向异性检测通过监测拍频在恒星率及其第一谐波。我们在10^{13}中的一部分没有看到各向异性。这使得一般标准模型扩展中的四个参数线性组合具有可比性的界限，而其他三个参数的界限较弱，<4 x 10^{-9}。
