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Type: Journal article
Title: Einstein's special relativity beyond the speed of light
Author: Hill, J.
Cox, B.
Citation: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012; 468(2148):4174-4192
Publisher: Royal Soc London
Issue Date: 2012
ISSN: 1364-5021
Statement of
James M. Hill and Barry J. Cox
Abstract: We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving rise to the Einstein special theory of relativity that applies to relative velocities less than the speed of light. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but, most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions. Making use of the dependence on relative velocity of the Lorentz transformation, the paper provides an elementary derivation of the new transformations between inertial frames for relative velocities v in excess of the speed of light c, and further we suggest two possible criteria from which one might infer one set of transformations as physically more likely than the other. If the energy–momentum equations are to be invariant under the new transformations, then the mass and energy are given, respectively, by the formulae m=(P[infinite]/c)[(v/c)²-1]⁻¹⁾² and e=mc² where P[infinite] denotes the limiting momentum for infinite relative velocity. If, however, the requirement of invariance is removed, then we may propose new mass and energy equations, and an example having finite non-zero mass in the limit of infinite relative velocity is given. In this highly controversial topic, our particular purpose is not to enter into the merits of existing theories, but rather to present a succinct and carefully reasoned account of a new aspect of Einstein's theory of special relativity, which properly allows for faster than light motion.
Keywords: special relativity
Lorentz transformation
relativistic mass
Rights: © 2012 The Royal Society
DOI: 10.1098/rspa.2012.0340
Grant ID: ARC
Appears in Collections:Aurora harvest
Mathematical Sciences publications

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