Table of Contents
ISRN Mathematical Physics
Volume 2013 (2013), Article ID 156857, 17 pages
http://dx.doi.org/10.1155/2013/156857
Research Article

Unifying the Galilei Relativity and the Special Relativity

1Universidade Federal do Rio de Janeiro, Observatório do Valongo, 20080-090 Rio de Janeiro, RJ, Brazil
2Departamento de Matemática, Universidade Federal de Santa Catarina, 88.040-900 Florianópolis, SC, Brazil

Received 4 April 2013; Accepted 8 May 2013

Academic Editors: G. Cleaver, A. Herrera-Aguilar, D. Singleton, and F. Sugino

Copyright © 2013 Alexandre Lyra and Marcelo Carvalho. 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

We present two models combining some aspects of the Galilei and the Special relativities that lead to a unification of both relativities. This unification is founded on a reinterpretation of the absolute time of the Galilei relativity that is considered as a quantity in its own and not as mere reinterpretation of the time of the Special relativity in the limit of low velocity. In the first model, the Galilei relativity plays a prominent role in the sense that the basic kinematical laws of Special relativity, for example, the Lorentz transformation and the velocity law, follow from the corresponding Galilei transformations for the position and velocity. This first model also provides a new way of conceiving the nature of relativistic spacetime where the Lorentz transformation is induced by the Galilei transformation through an embedding of 3-dimensional Euclidean space into hyperplanes of 4-dimensional Euclidean space. This idea provides the starting point for the development of a second model that leads to a generalization of the Lorentz transformation, which includes, as particular cases, the standard Lorentz transformation and transformations that apply to the case of superluminal frames.