Fundamental role of the retarded potential in the electrodynamics of superluminal sources: reply to comment

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Neither Eq. (6.52) of Jackson [Classical Electrodynamics, 3rd ed. (Wiley, 1999)], or Hannay's derivation of that dquation in the preceding Comment [J. Opt. Soc. Am. A, ... (2009)], are applicable to a source whose distribution pattern moves faster than light in vacuo with nonzero acceleration. It is assumed in Hannay's derivation that the retarded distribution of the density of any moving source would be smooth and differentiable if its rest-frame distribution is. By working out an explicit example of a rotating superluminal source with a bounded and smooth density profile, we show that this assumption is erroneous. The retarded distribution ... continued below

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Singleton, John; Fasel, Joseph H; Schmidt, Andrea C; Ardavan, Houshang & Ardavan, Arzhang January 1, 2009.

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Neither Eq. (6.52) of Jackson [Classical Electrodynamics, 3rd ed. (Wiley, 1999)], or Hannay's derivation of that dquation in the preceding Comment [J. Opt. Soc. Am. A, ... (2009)], are applicable to a source whose distribution pattern moves faster than light in vacuo with nonzero acceleration. It is assumed in Hannay's derivation that the retarded distribution of the density of any moving source would be smooth and differentiable if its rest-frame distribution is. By working out an explicit example of a rotating superluminal source with a bounded and smooth density profile, we show that this assumption is erroneous. The retarded distribution of a rotating source with a moderate superluminal speed is, in general, spread over three disjoint volumes (differing in shape from each other and from the volume occupied by the source in its rest frame) whose boundaries depend on the spacetime position of the observer. Hannay overlooks the fact that the limits of integration in his expression for the retarded potential (which delineate the boundaries of the retarded distribution of the source) are not differentiable functions of the coordinates of the observer at those points on the source boundary that approach the observer, along the radiation direction, with the speed of light at the retarded time. In the superluminal regime, derivatives of the integral representing the retarded potential are well defined only as generalized functions.

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  • Journal Name: J. Optical Society of America A

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  • Report No.: LA-UR-09-00402
  • Report No.: LA-UR-09-402
  • Grant Number: AC52-06NA25396
  • Office of Scientific & Technical Information Report Number: 956544
  • Archival Resource Key: ark:/67531/metadc931274

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  • January 1, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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Singleton, John; Fasel, Joseph H; Schmidt, Andrea C; Ardavan, Houshang & Ardavan, Arzhang. Fundamental role of the retarded potential in the electrodynamics of superluminal sources: reply to comment, article, January 1, 2009; [New Mexico]. (digital.library.unt.edu/ark:/67531/metadc931274/: accessed July 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.