JMPJournal of Modern Physics2153-1196Scientific Research Publishing10.4236/jmp.2012.39134JMP-22716ArticlesPhysics&Mathematics On the Extended Lorentz Transformation Model and Its Application to Superluminal Neutrinos alahD. Hamieh1*Department of Physics, Lebanese University, Faculty of Sciences (I), Hadath, Beirut, Lebanon* E-mail:hamiehs@yahoo.fr24092012030910211026June 13, 2012July 25, 2012 August 4, 2012© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

In this paper, we consider the apparent superluminal speed of neutrinos in their travel from CERN to Gran Susso, as measured by the OPERA experiment, within the framework of the Extended Lorentz Transformation Model. The model is based on a natural extension of Lorentz transformation by wick rotation. Scalar and Dirac’s fields are considered and invariance under the new lorentz group is discussed. Moreover, an extension of quantum mechanics to accommodate new particles is considered using the newly proposed Generalized-C quantum mechanics. A two dimensional representation of the new Dirac’s equation is therefore formulated and its solution is calculated.

Natural Asset; Financial Value; Neural Network1. Introduction

Recently, the OPERA collaboration, according to their precision measurement, claims [1] an early arrival time of CNGS (CERN Neutrino beam to Gran Sasso) muon antineutrinos traversing 730 kilometers from CERN to Gran Sasso. This corresponds to . This larger deviation of the neutrino velocity from c is a new result pointing to new physics in the neutrino sector. The CNGS neutrinos have an average energy of 17 GeV with a broad distribution reaching up to several tens of GeV. A separate measurement of neutrinos above and below 20 GeV has revealed no significant energy-dependence of the superluminality in this energy range. The OPERA claim is compatible with earlier results obtained by the MINOS experiment at FERMILAB [2]. This result was recently confirmed in a new investigation by OPERA using a beam with a short-bunch. As we can see from Table 1. To understand the underlying physics, a large number of papers has been published in arXiv that can be categorized into models of geometric solutions in extra dimensions [3], deformed special relativity [4], environmental superluminality [5-7], and explicit Lorentz violation [8], and combinations of these ideas. While most of theories [9-12] are concerned about the Lorentz violation/modification, our main motivation here is the extension of Lorentz transformation using a natural mechanism namely a wick rotation via. As consequence of this transformation, a new dispersion relation is discovered which allows to probe a new velocity domain. The model will be applied to superluminal neutrino to obtain an estimation of neutrino mass. Moreover, as our main concern here is to probe new physics, we have considered the dynamics of superluminal particles not only within the framework of quantum mechanics but also in the generalized quantum mechanics [13].

This paper is organized in the following manner. In the next section, the extended Lorentz transformation Model (ELTM), is presented and its application to neutrino is studied. In Section 3 application of ELTM to field theory is discussed. In Section 4 using the discovered dispersion relation a new Dirac’s equation (DE) within the framework of Generalized-C quantum mechanics (GCQM) is derived. Section 5 summarizes the results of the present investigation and also concluded remarks are given.

2. Modeling Superluminal Particles

The basic idea of the proposed Extended Lorentz Transformation Model (ELTM) is the observation that the Minkowski metric

Table 1. The summary of superluminal neutrinos from OPERA, MINOS.

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