On the Extended Lorentz Transformation Model and Its Application to Superluminal Neutrinos


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.

Share and Cite:

S. Hamieh, "On the Extended Lorentz Transformation Model and Its Application to Superluminal Neutrinos," Journal of Modern Physics, Vol. 3 No. 9, 2012, pp. 1021-1026. doi: 10.4236/jmp.2012.39134.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] T. Adam, et al., “Measurement of the Neutrino Velocity with the OPERA Detector in the CNGS Beam,” arXiv: 1109.4897, 2011.
[2] P. Adamson, et al., “Measurement of Neutrino Velocity with the MINOS Detectors and NuMI Neutrino Beam,” Physical Review D, Vol. 76, No. 7, 2007, Article ID: 072005. doi:10.1103/PhysRevD.76.072005
[3] S. S. Gubser, “Superluminal Neutrinos and Extra Dimensions,” Physics Letters B, Vol. 705, No. 3, 2011, p. 279. doi:10.1016/j.physletb.2011.10.028
[4] G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman and L. Smolin, “OPERA Neutrinos and Deformed Special Relativity,” arXiv:1110.0521, 2011.
[5] G. Dvali and A. Vikman, “Price for Environmental Neutrino-Superluminality,” arXiv:1109.5685, 2011.
[6] A. Kehagias, “Relativistic Superluminal Neutrinos,” arXiv: 1109.6312, 2011.
[7] I. Oda and H. Taira, “Superluminal Neutrinos from Gauge Field,” arXiv:1110.0931, 2011.
[8] J. Alexandre, J. Ellis and N. E. Mavromatos, “On the Possibility of Superluminal Neutrino Propagation,” arXiv: 1109.6296, 2011.
[9] B. Alles, “Relativity Accommodates Superluminal Mean Velocities,” arXiv:1111.0805, 2011.
[10] L. Iorio, “Environmental Fifth-Force Hypothesis for the OPERA Superluminal Neutrino Phenomenology: Con- straints from Orbital Motions around the Earth,” arXiv: 1109.6249, 2011.
[11] E. Saridakis, “Superluminal Neutrinos in Horava-Lifshitz gravity,” arXiv:1110.0697, 2011.
[12] J. S. Diaz and V. A. Kostelecky, “Three-Parameter Lorentz-Violating Texture for Neutrino Mixing,” Physics Letters B, Vol. 700, No. 5, 2011, p. 25. doi:10.1016/j.physletb.2011.04.049
[13] S. Hamieh and H. Abbas, “Two Dimensional Representation of the Dirac Equation in Non Associative Algebra,” arXiv:1104.3416, 2011.
[14] S. Adler, “Quaternion Quantum Mechanics and Quantum Fields,” Oxford University Press, New York, 1995.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.