物质内部电磁力密度及其应力张量不同表述的批判性研究与判别
Critical study and discrimination of different formulations of electromagnetic force density and consequent stress tensors inside matter
摘要：
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。
英文摘要：
By examination of the exerted electromagnetic (EM) force on boundary of an object in a few examples, we look into the compatibility of the stress tensors corresponding to different formulae of the EM force density with special relativity. Ampere-Lorentz's formula of the EM force density is physically justifiable in that the electric field and the magnetic flux density act on the densities of the total charges and the total currents, unlike Minkowski's formula which completely excludes the densities of the bounded charges and the bounded currents inside homogeneous media. Abraham's formula is fanciful and devoid of physical meaning. Einstein-Laub's formula seems to include the densities of the total charges and the total currents at first sight, but grouping the bounded charges and the bounded currents into point-like dipoles erroneously results in the hidden momentum being omitted, hence the error in [Phys. Rev. Lett. 108, 193901 (2012)]. Naturally, the Ampere-Lorentz stress tensor accords with special relativity. The Minkowski stress tensor is also consistent with special relativity. It is worth noting that the mathematical expression of the Minkowski stress tensor can be quite different from the well-known form of this stress tensor in the literature. We show that the Einstein-Laub stress tensor is incompatible with special relativity, and therefore we rebut the Einstein-Laub force density. Since the Abraham momentum density of the EM fields is inherently corresponding to the Einstein-Laub force density [Phys. Rev. Lett 111, 043602 (2013)], our rebuttal may also shed light on the controversy over the momentum of light.
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