Moving Charge Distributions in Classical Electromagnetism and the FitzGerald-Lorentz Contraction

Abstract

In [Eur. J. Phys. {\bf 25} (2004) 123-126], Dragan V. Red{\v z}ić is led to the FitzGerald-Lorentz contraction by comparing electromagnetic images of a moving point charge and a moving conducting sphere. We wish to point out that much simpler possibilities intrinsic to electromagnetism already exist from which we may get at the FitzGerald-Lorentz contraction hypothesis. In particular we consider an example going back to Poincaré in [{\it Bulletin des Sciences mathématiques}, 28, (1904) pp. 302-324], in which he considers the problem of two moving, parallel line charges in order to get at length contraction. We develop this model of Poincaré and show that it leads not only to the FitzGerald-Lorentz contraction but also to an elementary derivation of the composition of velocities formula in special relativity for collinear velocities. Red{\v z}ić suggests that, by considering such purely electromagnetic examples, the Maxwellians could have been led to the contraction hypothesis much before the time of the Michelson-Morely experiment, and we agree with him that such elementary results as the ones discussed here could not have escaped their attention. Apparently, it took an extremely sensitive experiment, not intrinsic to electromagnetism, such as was the Michelson-Morley experiment, together with the efforts of persons with authority, like Lorentz and Poincaré, trying to uphold the relativity principle before the radical notion of length contraction could seriously be entertained, and making ripe the way for the genius of Einstein.