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.

#### Linked References

- M. Longo, “Tests of relativity from SN1987a,”
*Physical Review D*, vol. 36, no. 10, pp. 3276–3277, 1987. View at Google Scholar - The OPERA Collaboration, T. Adam, N. Agafonova, A. Aleksandrov et al., “Measurement of the neutrino velocity with the OPERA detector in the CNGS beam,” http://arxiv.org/abs/1109.4897v1. In press.
- The OPERA Collaboration, T. Adam, N. Agafonova, A. Aleksandrov et al., “Measurement of the neutrino velocity with the OPERA detector in the CNGS beam,” http://arxiv.org/abs/1109.4897. In press.
- The OPERA Collaboration, T. Adam, N. Agafonova, A. Aleksandrov et al., “Measurement of the neutrino velocity with the OPERA detector in the CNGS beam using the 2012 dedicated data,” http://arxiv.org/abs/1212.1276. In press.
- The MINOS Collaboration, P. Adamson, C. Backhouse, G. Barr et al., “Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam,” http://arxiv.org/abs/0706.0437. In press.
- MINOS collaboration, P. Adamson, D. S. Ayres, G. Barr et al., “Search for Lorentz invariance and CPT violation with muon antineutrinos in the MINOS Near Detector,” http://arxiv.org/abs/1201.2631. In press.
- ICARUS Collaboration, M. Antonello, P. Aprili, B. Baibussinov et al., “A search for the analogue to Cherenkov radiation by high energy neutrinos at superluminal speeds in ICARUS,” http://arxiv.org/abs/1110.3763. In press.
- M. Antonello, P. Aprili, B. Baibussinov et al., “Measurement of the neutrino velocity with the ICARUS detector at the CNGS beam,” http://arxiv.org/abs/1203.3433. In press.
- K. Peacock, “Would superluminal influences violate the principle of relativity?” http://arxiv.org/abs/1301.0307. In press.
- J. Hill and B. Cox, “Einstein's special relativity beyond the speed of light,”
*Proceedings of the Royal Society A*, vol. 468, no. 2148, pp. 4174–4192, 2012. View at Publisher · View at Google Scholar - G. Ghirardi and R. Romano, “On a proposal of superluminal communication,” http://arxiv.org/abs/1205.1416. In press.
- K. Fujii, “Superluminal group velocity of neutrinos: review, development and problems,” http://arxiv.org/abs/1203.6425. In press.
- I. Oda, “Subluminal OPERA neutrinos,” http://arxiv.org/abs/1112.5793. In press.
- G. Ter-Kazarian, “Extended Lorentz code of a superluminal particle,” http://arxiv.org/abs/1202.0469. In press.
- Z.-Y. Wang, C.-D. Xiong, and B. He, “Superluminal propagation of evanescent modes as a quantum effect,” http://arxiv.org/abs/0712.0347. In press.
- A. Y. Li, “Relativistic theory of superluminal particles,” http://arxiv.org/abs/1110.0969. In press.
- V. Gupta, “A modification of the relativistic energy-momentum relation,” http://arxiv.org/abs/1204.4478. In press.
- J. Schechter and M. N. Shahid, “Neutrinos with velocities greater than
*c*?” http://arxiv.org/abs/1201.4374. In press. - H. Behera and G. Mukhopadhyay, “On the invariance of the speed of light,” http://arxiv.org/abs/1111.6516. In press.
- G. Guo and X. -G. He, “Dispersion relations explaining OPERA data from deformed lorentz transformation,” http://arxiv.org/abs/1111.6330. In press.
- M. E. Perel'man, “Uncertainty relations describing the short-term violations of Lorentz invariance: superluminal phenomena, particles transformations,” http://arxiv.org/abs/quant-ph/0510123. In press.
- L. Gonzalez-Mestres, “Lorentz invariance and superluminal particles,” http://arxiv.org/abs/physics/9703020. In press.
- G. Amelino-Camelia, G. Gubitosi, N. Loret, F. Mercati, G. Rosati, and P. Lipari, “OPERA-reassessing data on the energy dependence of the speed of neutrinos,” http://arxiv.org/abs/1109.5172. In press.
- G. Amelino-Camelia, “Phenomenology of philosophy of science: OPERA data,” http://arxiv.org/abs/1206.3554. In press.
- G. Y. Bogoslovsky, “Dynamic rearrangement of vacuum and the phase transitions in the geometric structure of space-time,” http://arxiv.org/abs/1201.2521. In press.
- D. Faroughy,
*Finite Special Relativity and Definite Upper Limits For the Velocities, Masses and the Energies of Massive Particles*, San Jose State University, SJSU, San Jose, Calif, USA, 1985. - Inspire/Spires Records and D. Faroughy,
*Mass & Quantum Dependent Chiral Lorentz Transformations and a New Theory of Ether*, University of Lavern, Lavern, Calif, USA, 1988. - D. Faroughy, “Several action and action deformation proposals in f(R) variable G modified gravities and a brief expose on variable G ontology,” http://arxiv.org/abs/0712.0450. In press.
- S. R. Coleman and S. L. Glashow, “High-energy tests of Lorentz invariance,”
*Physical Review D*, vol. 59, no. 11, p. 116008, 1999. View at Publisher · View at Google Scholar - A. G. Cohen and S. L. Glashow, “New constraints on neutrino velocities,” http://arxiv.org/abs/1109.6562. In press.
- F. Bezrukov and H. M. Lee, “Model dependence of the bremsstrahlung effects from the superluminal neutrino at OPERA,” http://arxiv.org/abs/1112.1299. In press.
- U. D. Jentschura and B. J. Wundt, “An infinitesimally superluminal neutrino is left-handed, conserves Lepton number and solves the autobahn paradox (Illustrative Discussion),” http://arxiv.org/abs/1206.6342. In press.
- P. Abreu, M. Aglietta, E.J. Ahn et al., “Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter,”
*Astroparticle Physics*, vol. 34, no. 5, pp. 314–326, 2010. View at Publisher · View at Google Scholar - A. V. Glushkov, “On the anisotropy of ${E}_{0}\ge 5.5$ eV cosmic rays according to data of the Pierre Auger collaboration,” http://arxiv.org/abs/1202.4520. In press.
- S. A. Thomas, F. B. Abdalla, and O. Lahav, “Upper bound of 0.28 eV on neutrino masses from the largest photometric Redshift survey,”
*Physical Review Letters*, vol. 105, no. 3, p. 031301, 2010. View at Publisher · View at Google Scholar - The Pierre Auger Collaboration, P. Abreu, M. Aglietta, and M. Ahlers, “A search for ultra-high energy neutrinos in highly inclined events at the Pierre Auger Observatory,” http://arxiv.org/abs/1202.1493. In press.
- M. Dresden and A. Albano, “Nonlinear space-time transformations related to the Lorentz group,”
*Proceedings of the National Academy of Sciences of the United States of America*, vol. 58, no. 3, pp. 916–922, 1967. View at Publisher · View at Google Scholar - A. Lyra and M. Carvalho, “A geometrical setting for constructing nonlinear Lorentz transformations of the Albano-Dresden type,”
*Physics Research International*, vol. 2011, Article ID 302164, 9 pages, 2011. View at Publisher · View at Google Scholar