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Advances in High Energy Physics
Volume 2013 (2013), Article ID 760916, 20 pages
http://dx.doi.org/10.1155/2013/760916
Research Article

Extended Linear and Nonlinear Lorentz Transformations and Superluminality

Department of Sciences, Pima College, West Campus, Tucson, AZ 85709, USA

Received 8 November 2012; Revised 1 March 2013; Accepted 7 March 2013

Academic Editor: S. H. Dong

Copyright © 2013 Dara Faroughy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Two broad scenarios for extended linear Lorentz transformations (ELTs) are modeled in Section 2 for mixing subluminal and superluminal sectors resulting in standard or deformed energy-momentum dispersions. The first scenario is elucidated in the context of four diverse realizations of a continuous function , with and , which is fitted in the ELT. What goes in the making of the ELT in this scenario is not the boost speed , as ascertained by two inertial observers in uniform relative motion (URM), but . The second scenario infers the preexistence of two rest-mass-dependent superluminal speeds whereby the ELTs are finite at the light speed . Particle energies are evaluated in this scenario at for several particles, including the neutrinos, and are auspiciously found to be below the GKZ energy cutoff and in compliance with a host of worldwide ultrahigh energy cosmic ray data. Section 3 presents two broad scenarios involving a number of novel nonlinear LTs (NLTs) featuring small Lorentz invariance violations (LIVs), as well as resurrecting the notion of simultaneity for limited spacetime events as perceived by two observers in URM. These inquiries corroborate that NLTs could be potent tools for investigating LIVs past the customary LTs.