Article: Jin, CR; Lazar, M; (2015) “A Note on Lorentz-like Transformations and Superluminal Motion”, Zamm-Zeitschrift Fur Angewandte Mathematic Und Mechanik, 95 (7):690-694
Abstract: In this extended note a critical discussion of an extension of the Lorentz transformations for velocities faster than the speed of light given recently by Hill and Cox [1] is provided. The presented approach reveals the connection between faster-than-light speeds and the issue of isotropy of space. It is shown if the relative speed between the two inertial frames v is greater than the speed of light, the condition of isotropy of space cannot be retained. It further specifies the respective transformations applying to -<v<-c and c<v<+infinity. It is proved that such Lorentz-like transformations are improper transformations since the Jacobian is negative. As a consequence, the wave operator, the light-cone and the volume element are not invariant under such Lorentz-like transformations. Also it is shown that such Lorentz-like transformations are not new and already known in the literature. (C) 2014 WILEY-VCH Veriag GmbH & Co. KGaA, Weinheim
Funding Acknowledgement: Deutsche Forschungsgemeinschaft [La1974/2-1, La1974/2-2, La1974/3-1]
Funding Text: L. gratefully acknowledges the grants obtained from the Deutsche Forschungsgemeinschaft (Grant Nos. La1974/2-1, La1974/2-2, La1974/3-1). The authors acknowledge the useful remarks and suggestions of the reviewers.