Hannay J H
H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK.
J Opt Soc Am A Opt Image Sci Vis. 2009 Oct;26(10):2107-8; discussion 2109-13. doi: 10.1364/JOSAA.26.002107.
The commented paper [J. Opt. Soc. Am. A 25, 543 (2008] denies the truth of a standard general formula of electrodynamics [Eq. (6.52) of Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999)]). The motivation for challenging orthodoxy is that the formula directly disproves the repeated claim of the commented authors that electromagnetic radiation, under some circumstances, can have unusually long range. The formula they challenge is for the magnetic field: B=Integral over all space of (mu0/4pi)[Curl j]/Range. Instead they advocate a (correct) formula for the vector potential: A=Integral over all space of (mu0/4pi)[j]/Range. However, as one might suppose, the former equation follows as a purely mathematical consequence of taking the curl of the latter equation. This is straightforward to make rigorous in the particular circumstances in question (confined smooth current density j). Therefore by their own formula, the standard one of electrodynamics is confirmed, and the disproof of their long range claim stands.
被评论的论文[《美国光学学会志A》25, 543 (2008)]否定了电动力学一个标准通用公式的正确性[杰克逊所著《经典电动力学》第三版（威利出版社，1999年）中的式(6.52)]。挑战正统观念的动机在于，该公式直接反驳了被评论作者反复提出的观点，即在某些情况下电磁辐射可以具有异常长的作用范围。他们所质疑的公式是关于磁场的：(B = \int_{全空间} (\mu_0 / 4\pi) [\nabla\times\vec{j}] / r)。相反，他们主张一个（正确的）关于矢量势的公式：(\vec{A} = \int_{全空间} (\mu_0 / 4\pi) [\vec{j}] / r)。然而，正如人们可能推测的那样，前一个方程是对后一个方程取旋度的纯粹数学结果。在相关的特定情形（受限的光滑电流密度(\vec{j})）下，这很容易严格证明。因此，根据他们自己的公式，电动力学的标准公式得到了证实，他们关于长程的说法被证伪。
