# A Review of Searches for Evidence of Tachyons

## Abstract

**:**

## 1. Introduction

## 2. Tachyons as New Particles

## 3. Neutrinos as Tachyons

## 4. Hints from IceCube Data

## 5. Energetically Forbidden $\mathit{\beta}-$Decay

## 6. The Cosmic Ray Spectrum

## 7. A n-p Decay Chain?

## 8. SN 1987A and Its Neutrinos

## 9. The $\mathbf{3}+\mathbf{3}$ Neutrino Model

## 10. The $\mathbf{3}+\mathbf{3}+\mathit{L}\mathit{C}\mathit{R}$ Model

## 11. Evidence for the $\mathbf{3}+\mathbf{3}$ Model

#### 11.1. The ${m}^{2}>0$ Masses in the $3+3$ Model

#### 11.2. The ${m}^{2}<0$ Mass in the $3+3$ Model

## 12. Neutrino Mass Experiments

## 13. The KATRIN Experiment

## 14. $\mathbf{3}+\mathbf{3}$ Model and Cosmology

## 15. Summary and Future Tests

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

- Kreisler, M. Are There Faster-than-Light Particles? A review of the hypotheses about the nature of tachyons and of experimental searches for them. Am. Sci.
**1973**, 61, 201–208. [Google Scholar] - Gillispie, C.C.; Gratton-Guinness, I.; Fox, R. Pierre Simon Laplace, a Life in Exact Science; Princeton University Press: Princetion, NJ, USA, 1999. [Google Scholar]
- Dragan, A.; Ekert, A. Quantum principle of relativity. New J. Phys.
**2020**, 22, 033038. [Google Scholar] [CrossRef] - Bilaniuk, O.M.P.; Deshpande, V.K.; Sudarshan, E.C.G. “Meta” relativity. Am. J. Phys.
**1962**, 30, 718. [Google Scholar] [CrossRef] - Einstein, A. On the electrodynamics of moving bodies. Ann. Phys.
**1905**, 17, 891–921. Available online: https://einsteinpapers.press.princeton.edu/vol2-doc/311 (accessed on 31 May 2022). [CrossRef] - Feinberg, G. Possibility of faster-than-light particles. Phys. Rev.
**1967**, 159, 1089–1105. [Google Scholar] [CrossRef] - Alvager, T.; Kreisler, M.N. Quest for faster-than-light particles. Phys. Rev.
**1968**, 171, 1357. [Google Scholar] [CrossRef] - Davis, M.B.; Kreisler, M.N.; Alväger, T. Search for Faster-Than-Light Particles. Phys. Rev.
**1969**, 183, 1132. [Google Scholar] [CrossRef] - Clay, R.W.; Crouch, P.C. Possible observation of tachyons associated with extensive air showers. Nature
**1974**, 248, 28. [Google Scholar] [CrossRef] - Emery, M.W.; Fenten, A.G.; Fenton, K.B.; Greenhill, J.G.; Humble, J. Search for tachyons preceding cosmic ray extensive air showers. In Proceedings of the 14th International Cosmic Ray Conference, Munich, Germany, 15–29 August 1975; Volume 7, p. 2486. [Google Scholar]
- Fegan, D.J.; OBrien, D.P.; OBrien, S.; Porter, N.A. Results of a Search for Time Structure in the Distribution of Scintillation Counter Events Detected During a 400 μsec Interval Prior to 10
^{15}eV EAS Fronts. In Proceedings of the 14th International Cosmic Ray Conference, Munich, Germany, 15–29 August 1975. [Google Scholar] - Hazen, W.E.; Green, B.R.; Hodson, A.L.; Kass, J.R. A search for precursors to extensive air showers. Nucl. Phys. B
**1975**, 96, 401. [Google Scholar] [CrossRef][Green Version] - Prescott, J.R. Tachyons revisited. In Proceedings of the 14th International Cosmic Ray Conference, Munich, Germany, 15–29 August 1975; Volume 7, p. 2474. [Google Scholar]
- Murthy, P.V.R. Search for tachyons in the cosmic radiation. Nuouo Cim. Lett.
**1971**, 1, YO8. [Google Scholar] [CrossRef] - Smith, G.R.; Standi, S. Search for tachyons preceding cosmic ray extensive air showers of energy >10
^{14}eV. Can. J. Phvs.**1977**, 55, 1280. [Google Scholar] [CrossRef] - Bhat, P.N.; Gopalakrishnan, N.V.; Gupta, S.K.; Tonwar, S.C. Search for tachyons in extensive air showers. J. Phys. G Nucl. Phys.
**1979**, 5, L13. [Google Scholar] [CrossRef] - Marini, A.; Peruzzi, I.; Piccolo, M.; Ronga, F.; Chew, D.M.; Ely, R.P.; Pun, T.P.; Vuillemin, V.; Fries, R.; Gobbi, B.; et al. Experimental limits on quarks, tachyons, and massive particles in cosmic rays. Phys. Rev. D
**1982**, 26, 1777. [Google Scholar] [CrossRef] - Garipov, G.K.; Silaev, A.A. Search for Delayed and Advanced Particles in the Interaction of Ultrahigh-Energy Cosmic Rays with the Earth’s Atmosphere in the Flow of EAS Muons at the MSU EAS Setup. Phys. At. Nucl.
**2020**, 83, 442–452. [Google Scholar] [CrossRef] - Baltay, G.; Feinberg, G.; Yeh, N.; Linsker, R. Search for uncharged faster-than-light particles. Phys. Rev. D
**1970**, 1, 759. [Google Scholar] [CrossRef][Green Version] - Danburg, J.S.; Kalbfleisch, G.R.; Borenstein, S.R.; Strand, R.C.; VanderBurg, V.; Chapman, J.W.; Lys, J. Search for Ionizing Tachyon Pairs From 2.2 GeV/c K
^{−}p Interactions. Phys. Rev. D**1971**, 4, 53. [Google Scholar] [CrossRef] - Danburg, J.S.; Kalbfleish, G.R. Limits on the Rate of Emission of Negative-Energy Tachyons. Phys. Rev. D
**1972**, 5, 1575. [Google Scholar] [CrossRef] - Ljubičic, A.; Pavlović, Ž.; Pisk, K.; Logan, B.A. Further limits on the stability against elastic tachyonic decay. Phys. Rev. D
**1975**, 11, 696. [Google Scholar] [CrossRef] - Bartlett, D.F.; Lahana, M.D. Search for tachyon monopoles. Phys. Rev. D
**1972**, 6, 1817. [Google Scholar] [CrossRef][Green Version] - Bartlett, D.F.; Soo, D.; White, M.G. Search for tachyon monopoles in cosmic rays. Phys. Rev. D
**1978**, 18, 2253. [Google Scholar] [CrossRef] - Fredericks, K.A. Possibility of tachyon monopoles detected in photographic emulsions. J. Condens. Matter Nucl. Sci.
**2015**, 15, 203–230. [Google Scholar] - Perepelitsa, V.P. Tachyon michelson experiment. Phys. Lett.
**1977**, 67B, 471–473. [Google Scholar] [CrossRef] - Rembielinski, J. Tachyons and preferred frames. Int. J. Mod. Phys. A
**1997**, 12, 1677–1709. [Google Scholar] [CrossRef][Green Version] - Radzikowski, M. CPT and Lorentz Symmetry; World Scientific: Singapore, 2010; pp. 224–228. [Google Scholar]
- Perepelitsa, V.P.; Ekelof, T.; Ferrer, A.; French, B.R. A search for anomalous Cherenkov rings. arXiv
**2019**, arXiv:1912.11839. [Google Scholar] - Perepelitsa, V.P.; Ekelof, T.; Ferrer, A.; French, B.R. Physical interpretation of the anomalous Cherenkov rings observed with the DELPHI detector. arXiv
**2020**, arXiv:2001.08576. [Google Scholar] - Cawley, R.G. Neutrino mass bounds. Lett. Nuovo C
**1972**, 3, 523–525. [Google Scholar] [CrossRef] - Chodos, A.; Hauser, A.I.; Kostelecký, V.A. The neutrino as a tachyon. Phys. Lett. B
**1985**, 150B, 6. [Google Scholar] [CrossRef] - Jentschura, U.D.; Wundt, B.J. Localizability of tachyonic particles and neutrinoless double beta decay. Eur. Phys. J. C
**2012**, 72, 1894. [Google Scholar] [CrossRef] - Rembieliński, J.; Caban, P.; Ciborowski, J. Quantum field theory of space-like neutrino. Eur. Phys. J. C
**2021**, 81, 716. [Google Scholar] [CrossRef] - Schwartz, C. Toward a quantum theory of tachyon fields. Int. J. Mod. Phys. A
**2016**, 31, 1650041. [Google Scholar] [CrossRef][Green Version] - Kraus, C. Final results from phase II of the Mainz neutrino mass searchin tritium β−Decay. Eur. Phys. J. C
**2005**, 40, 447–468. [Google Scholar] [CrossRef] - Kostelecký, V.A.; Mewes, M. Neutrinos with Lorentz-violating operators of arbitrary dimension. Phys. Rev. D
**2012**, 85, 096005. [Google Scholar] [CrossRef][Green Version] - Díaz, J.S.; Kostelecký, V.; Mewes, M. Testing relativity with high-energy astrophysical neutrinos. Phys. Rev. D
**2014**, 89, 043005. [Google Scholar] [CrossRef][Green Version] - Adam, T.; Agafonova, N.; Aleksandrov, A.; Altinok, O.; Alvarez Sanchez, P.; Aoki, S.; Ariga, A.; Ariga, T.; Autiero, D.; Badertscher, A.; et al. OPERA Collaboration, Measurement of the Neutrino Velocity with the OPERA Detector in the CNGS Beam. Available online: https://arxiv.org/vc/arxiv/papers/1109/1109.4897v1.pdf (accessed on 31 May 2022).
- Cohen, A.G.; Glashow, S.L. Pair creation constrains superluminal neutrino propagation. Phys. Rev. Lett.
**2011**, 107, 181803. [Google Scholar] [CrossRef] [PubMed] - Adam, T.; Agafonova, N.; Aleksandrov, A.; Altinok, O.; Alvarez Sanchez, P.; Anokhina, A.; Aoki, S.; Ariga, A.; Ariga, T.; Autiero, D.; et al. OPERA Collaboration, Measurement of the neutrino velocity with the OPERA detector in the CNGS beam. J. High Energy Phys.
**2012**, 2012, 93. Available online: https://link.springer.com/article/10.1007/JHEP10(2012)093 (accessed on 31 May 2022). - The ICARUS Collaboration; Antonello, M.; Baibussinov, B.; Benetti, P.; Boffelli, F.; Calligarich, E.; Canci, N.; Centro, S.; Cesana, A.; Cieslik, K.; et al. Precision measurement of the neutrino velocity with the ICARUS detector in the CNGS beam. J. High Energy Phys.
**2012**, 11, 49. [Google Scholar] - Adamson, P.; Anghel, I.; Ashby, N.; Aurisano, A.; Barr, G.; Bishai, M.; Blake, A.; Castromonte, C.M.; Childress, S.; Christensen, M.; et al. (MINOS Collaboration, NIST, and USNO), Precision measurement of the speed of propagation of neutrinos using the MINOS detectors. Phys. Rev.
**2015**, D92, 052005. [Google Scholar] - Abe, K.; Adam, J.; Aihara, H.; Akiri, T.; Andreopoulos, C.; Aoki, S.; Ariga, A.; Assylbekov, S.; Autiero, D.; Barbi, M.; et al. (T2K Collaboration), Upper bound on neutrino mass based on T2K neutrino timing measurements. Phys. Rev.
**2016**, D93, 012006. [Google Scholar] - Zyla, P.A.; Barnett, R.M.; Beringer, J.; Dahl, O.; Dwyer, D.A.; Groom, D.E.; Lin, C.J.; Lugovsky, K.S.; Pianori, E.; Robinson, D.J.; et al. Particle Data Group, Review of particle physics. Prog. Theor. Exp. Phys.
**2020**, 2020, 083C01. [Google Scholar] - Stecker, F.W.; Scully, S.T. Propagation of superluminal PeV IceCube neutrinos: A high energy spectral cutoff or new constraints on Lorentz invariance violation. Phys. D
**2014**, 90, 043012. [Google Scholar] [CrossRef][Green Version] - Jentschura, U.; Ehrlich, R. Lepton Pair Čerenkov Radiation Emitted by Tachyonic Neutrinos: Lorentz-Covariant Approach and IceCube Data. Adv. High Energy Phys.
**2016**, 2016, 4764981. [Google Scholar] [CrossRef][Green Version] - Stettner, J. For the IceCube Collaboration, Measurement of the diffuse astrophysical muon-neutrino spectrum with ten years of IceCube data. In Proceedings of the 36th International Cosmic Ray Conference (ICRC 2019), Madison, WI, USA, 24 July–1 August 2019. [Google Scholar]
- Liao, J.; Marfatia, D. IceCube’s astrophysical neutrino energy spectrum from CPT violation. Phys. Rev. D
**2018**, 97, 041302. [Google Scholar] [CrossRef][Green Version] - Huang, Y.; Ma, B.Q. Lorentz violation from gamma-ray burst neutrinos. Commun. Phys.
**2018**, 1, 62. [Google Scholar] [CrossRef] - Huang, Y.; Li, H.; Ma, B.Q. Consistent Lorentz violation features from near-TeV IceCube neutrinos. Phys. Rev. D
**2019**, 99, 123018. [Google Scholar] [CrossRef][Green Version] - Ellis, J.; Konoplich, R.; Mavromatos, N.E.; Nguyen, L.; Sakharov, A.S.; Sarkisyan-Grinbaum, E.K. Robust constraint on Lorentz violation using Fermi-LAT gamma-ray burst data. Phys. Rev. D
**2019**, 99, 083009. [Google Scholar] [CrossRef][Green Version] - Abe, S.; Asami, S.; Gando, A.; Gando, Y.; Gima, T.; Goto, A.; Hachiya, T.; Hata, K.; Hosokawa, K.; Ichimura, K.; et al. A Search for Correlated Low-energy Electron Antineutrinos in KamLAND with Gamma-Ray Bursts. Ap. J.
**2022**, 927, 69. [Google Scholar] [CrossRef] - Chodos, A.; Kostelecky, V.A.; Potting, R.; Gates, E. Null experiments for neutrino masses. Mod. Phys. Lett. A
**1992**, 7, 467–476. [Google Scholar] [CrossRef] - Greisen, K. End to the cosmic-ray spectrum? Phys. Rev. Lett.
**1966**, 16, 748–750. [Google Scholar] [CrossRef] - Zatsepin, G.T.; Kuz’min, V.A. Upper limit of the spectrum of cosmic rays. J. Exp. Theor. Phys. Lett.
**1966**, 4, 78–80. [Google Scholar] - Ehrlich, R. Implications for the cosmic ray spectrum of a negative electron neutrino mass
^{2}. Phys. Rev. D**1999**, 60, 17302. [Google Scholar] [CrossRef][Green Version] - Ehrlich, R. Is there a 4.5 PeV neutron line in the cosmic ray spectrum? Phys. Rev. D
**1999**, 60, 73005. [Google Scholar] [CrossRef][Green Version] - Ehrlich, R. Six observations consistent with the electron neutrino being a tachyon with mass: m
^{2}= −0.11 ± 0.016 eV^{2}or |m| = 0.33 ± 0.024 eV. Astropart. Phys.**2015**, 66, 11. [Google Scholar] [CrossRef][Green Version] - Abassi, R.U.; Abe, M.; Abu-Zayyad, T.; Allen, M.; Azuma, R.; Barcikowski, E.; Belz, J.W.; Bergman, D.R.; Blake, S.A.; Cady, R. The cosmic ray energy spectrum between 2 PeV and 2 EeV observed with the TALE detector in monocular mode. Ap. J.
**2018**, 865, 74. [Google Scholar] [CrossRef][Green Version] - Kostelecky, V.A. Topics on Quantum Gravity and Beyond; Mansouri, F., Scanio, J.J., Eds.; World Scientific: Singapore, 1993. [Google Scholar]
- Erlykin, A.; Wolfendale, A. The Knee in the Cosmic Ray Spectrum. Available online: https://arxiv.org/abs/0906.3949 (accessed on 31 May 2022).
- Thoudam, S.; Rachen, J.P.; van Vliet, A.; Achterberg, A.; Buitink, S.; Falcke, H.; Hörandel, J.R. Cosmic-ray energy spectrum and composition up to the ankle: The case for a second Galactic component. Astron. Astrophys.
**2016**, 595, A33. [Google Scholar] [CrossRef] - Huzita, H. Neutrino mass speculation on the events of neutrinos from the supernova LMC 1987 A. Mod. Phys. Lett. A
**1987**, 2, 905. [Google Scholar] [CrossRef] - Cowsik, R. Neutrino masses and flavors emitted in the supernova SN1987A. Phys. Rev. D
**1988**, 37, 16851687. [Google Scholar] [CrossRef] - Ehrlich, R. Evidence for two neutrino mass eigenstates from SN 1987A and the possibility of superluminal neutrinos. Astropart. Phys.
**2012**, 35, 625–628. [Google Scholar] [CrossRef][Green Version] - Janka, H.T. Neutrino emission from supernovae. In Handbook of Supernovae (1575–1604); Alsabti, A.W., Murdin, P., Eds.; Springer International Publishing: Cham, Switzerland, 2017. [Google Scholar]
- Loredo, T.J.; Lamb, D.Q. Bayesian analysis of neutrinos observed from supernova SN 1987A. Phys. Rev. D
**2002**, 65, 063002. [Google Scholar] [CrossRef][Green Version] - Aguilar, A.; Auerbach, L.B.; Burman, R.L.; Caldwell, D.O.; Church, E.D.; Cochran, A.K.; Donahue, J.B.; Fazely, A.; Garvey, G.T.; Gunasingha, R.M.; et al. LSND Collaboration, Evidence for neutrino oscillations from the observation of anti-neutrino (electron) appearance in a anti-neutrino (muon) beam. Phys. Rev. D
**2001**, 64, 112007. [Google Scholar] [CrossRef][Green Version] - Aguilar-Arevalo, A.A.; Brown, B.C.; Bugel, L.; Cheng, G.; Conrad, J.M.; Cooper, R.L.; Dharmapalan, R.; Diaz, A.; Djurcic, Z.; Finley, D.A.; et al. MiniBooNE Collaboration, Significant excess of electronlike events in the MiniBooNE short-baseline neutrino experiment. Phys. Rev. Lett.
**2018**, 121, 221801. [Google Scholar] [CrossRef][Green Version] - Kopp, J.; Machado, P.A.N.; Maltoni, M.; Schwetz, T. Sterile neutrino oscillations: The global picture. J. High Energy Phys.
**2013**, 2013, 50. [Google Scholar] [CrossRef][Green Version] - Maltoni, M.; Schwetz, T. Sterile neutrino oscillations after first MiniBooNE results. Phys. Rev. D
**2007**, 76, 093005. [Google Scholar] [CrossRef][Green Version] - Ehrlich, R. Tachyonic neutrinos and the neutrino masses. Astropart. Phys.
**2013**, 41, 1–6. [Google Scholar] [CrossRef][Green Version] - Chodos, A. Light Cone Reflection and the Spectrum of Neutrinos. arXiv
**2012**, arXiv:1206.5974. [Google Scholar] - Ehrlich, R. Review of the Empirical Evidence for Superluminal Particles and the 3 + 33 + 3 Model of the Neutrino Masses. Adv. Astron.
**2019**, 2019, 2820492. [Google Scholar] [CrossRef][Green Version] - Chan, M.H.; Ehrlich, R. Sterile neutrino fits to dark matter mass profiles in the Milky Way and in galaxy clusters. Astrophys. Space Sci.
**2014**, 349, 407. [Google Scholar] [CrossRef][Green Version] - Mohapatra, R.N.; Sciama, D.W. Diffuse ionization in the Milky Way and sterile neutrinos. arXiv
**1998**, arXiv:9811446v2. [Google Scholar] - Sciama, D.W. Modern Cosmology and the Dark Matter Problem; Cambridge University Press: Cambridge, UK, 1993. [Google Scholar]
- Phan, V.H.N.; Morlino, G.; Gabici, S. What causes the ionization rates observed in diffuse molecular clouds? The role of cosmic ray protons and electrons. Mon. Not. R. Astron. Soc.
**2018**, 480, 5167–5174. [Google Scholar] [CrossRef][Green Version] - Adamson, P.; Anghel, I.; Aurisano, A.; Barr, G.; Bishai, M.; Blake, A.; Bock, G.J.; Bogert, D.; Cao, S.V.; Carroll, T.J.; et al. (MINOS+ Collaboration), Search for sterile neutrinos in MINOS and MINOS+ using a two-detector fit. Phys. Rev. Lett.
**2019**, 122, 091803. [Google Scholar] [CrossRef][Green Version] - Denton, P. Sterile Neutrino Searches with MicroBooNE: Electron Neutrino Disappearance. arXiv
**2021**, arXiv:2111.05793. [Google Scholar] - Caban, P.; Rembieliński, J.; Smoliński, K.A.; Walczak, Z. Oscillations Do Not Distinguish Between Massive and Tachyonic Neutrinos. Found. Phys. Lett.
**2006**, 19, 619–623. [Google Scholar] - Giani, S. Experimental evidence of superluminal velocities in astrophysics and proposed experiments. AIP Conf. Proc.
**1999**, 458, 881. [Google Scholar] - Ehrlich, R. The Mont Blanc neutrinos from SN 1987A: Could they have been monochromatic (8 MeV) tachyons with m
^{2}= −0.38 keV^{2}? Astropart. Phys.**2018**, 99, 21–29. [Google Scholar] [CrossRef] - Krasznahorkay, A.J.; Csatlós, M.; Csige, L.; Gácsi, Z.; Gulyás, J.; Hunyadi, M.; Kuti, I.; Nyakó, B.M.; Stuhl, L.; Timár, J.; et al. Observation of Anomalous Internal Pair Creation in
^{8}Be: A Possible Indication of a Light, Neutral Boson. Phys. Rev. Lett.**2016**, 116, 042501. [Google Scholar] [CrossRef] [PubMed][Green Version] - Krasznahorkay, A.J.; Csatlós, M.; Csige, L.; Gulyás, J.; Hunyadi, M.; Ketel, T.J.; Krasznahorkay, A.; Kuti, I.; Nagy, Á.; Nyakó, B.M.; et al. New results on the
^{8}Be anomaly. J. Phys. Conf. Ser.**2018**, 1056, 012028. [Google Scholar] [CrossRef][Green Version] - Hirata, K.S.; Kajita, T.; Kifune, T.; Kihara, K.; Nakahata, M.; Nakamura, K.; Ohara, S.; Oyama, Y.; Sato, N.; Takita, M.; et al. Kamiokande collaboration, Observation of
^{8}B solar neutrinos in the Kamiokande-II detector. Phys. Rev. Lett.**1989**, 63, 1. [Google Scholar] [CrossRef][Green Version] - Ehrlich, R. The KATRIN neutrino mass results: An alternative interpretation. arXiv
**2021**, arXiv:2106.00681v4. [Google Scholar] - Bodine, L.I.; Parno, D.S.; Robertson, R.G.H. Assessment of molecular effects on neutrino mass measurements from tritium β-Decay. Phys. Rev. C
**2015**, 91, 035505. [Google Scholar] [CrossRef][Green Version] - Aker, M.; Altenmüller, K.; Arenz, M.; Babutzka, M.; Barrett, J.; Bauer, S.; Beck, M.; Beglarian, A.; Behrens, J.; Bergmann, T.; et al. KATRIN Collaboration, Improved Upper Limit on the Neutrino Mass from a Direct Kinematic Method by KATRIN. Phys. Rev. Lett.
**2019**, 123, 221802. [Google Scholar] [CrossRef][Green Version] - Aker, M.; Beglarian, A.; Behrens, J.; Berlev, A.; Besserer, U.; Bieringer, B.; Block, F.; Bornschein, B.; Bornschein, L.; Böttcher, M.; et al. KATRIN Collaboration, Direct neutrino-mass measurement with sub-electronvolt sensitivity. Nat. Phys.
**2022**, 2022, 18. [Google Scholar] - Valentino, E.D.; Gariazzo, S.; Mena, O. Most constraining cosmological neutrino mass bounds. Phys. Rev. D
**2021**, 104, 083504. [Google Scholar] [CrossRef] - Chudaykin, A.; Gorbunov, D.; Nedelko, N. Exploring ΛCDM extensions with SPT-3G and Planck data: 4σ evidence for neutrino masses, full resolution of the Hubble crisis by dark energy with phantom crossing, and all that. arXiv
**2022**, arXiv:2203.03666. [Google Scholar] - Stecker, F.W. Neutrino Physics and Astrophysics, Stecker. In Encyclopedia of Cosmology II; Fazio, G.G., Ed.; World Scientific Publishing Company: Singapore, 2022. [Google Scholar]
- Jentschura, U.D.; Wundt, B.J. From Generalized Dirac Equations to a Candidate for Dark Energy. ISRN High Energy Phys.
**2013**, 2013, 374612. [Google Scholar] [CrossRef][Green Version] - Davies, P.C.W.; Moss, I.G. Cosmological bounds on tachyonic neutrinos. Astropart. Phys.
**2012**, 35, 609–684. [Google Scholar] [CrossRef][Green Version] - Schwartz, C. Tachyon dynamics—For neutrinos? Int. J. Mod. Phys. A
**2018**, 33, 1850056. [Google Scholar] [CrossRef][Green Version] - Ade, P.A.R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Bartolo, N.; et al. Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys.
**2016**, 594, A13. [Google Scholar] - Tang, Y. More is different: Reconciling eV sterile neutrinos with cosmological mass bounds. Phys. Lett. B
**2015**, 750, 201–208. [Google Scholar] [CrossRef][Green Version] - Ashtari Esfahani, A.; Böser, S.; Buzinsky, N.; Claessens, C.; de Viveiros, L.; Doe, P.J.; Doeleman, S.; Fertl, M.; Formaggio, J.A.; Gödel, M.; et al. Letter of Interest Secondary Physics Potential of the Project 8 Experiment. In Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021); Available online: https://www.snowmass21.org/docs/files/summaries/NF/SNOWMASS21-NF5_NF2_Project8_Secondary_Physics-171.pdf (accessed on 31 May 2022).
- Ehrlich, R. Hunt for the Faster than Light Tachyon, and Finding Three Unicorns and a Herd of Elephants; CRC Press and Taylor & Francis Group: Oxfordshire, UK, 2022. [Google Scholar]

**Figure 1.**Plot of missing mass, that is the mass of X for the reaction ${K}^{-}+p\to {\mathsf{\Lambda}}^{0}+X$.

**Figure 2.**Plot of ${E}^{3}J\equiv {E}^{3}dF/dE$ for the cosmic ray spectrum using data from the four indicated experiments showing the locations of the two knees, the ankle, and the GZK cut-off.

**Figure 3.**Plot of $1/{E}^{2}$ versus neutrino arrival time t for 25 neutrinos from SN 1987A providing evidence for two masses, based on the clustering of neutrino events near two straight lines.

**Figure 4.**

**The 3 + 3 model.**${m}^{2}$ values in eV${}^{2}$ for the three active–sterile doublets in the model and their splittings, $d{m}^{2}$. The choice of ${m}_{3}$ was made so that the three doublets have a common fractional splitting, $d{m}^{2}/{m}^{2}.$ The plot is not to scale.

**Figure 5.**

**The 3 + 3 + LCR model.**Three active–sterile pairs having the indicated ${m}^{2}$ values under the assumptions of LCR symmetry and the $d{m}^{2}$ values observed in neutrino oscillation data (including $d{m}_{sbl}^{2}).$ It is further assumed that oscillations are predominantly between states having the same $\left|m\right|.$ Whether the active or sterile states have ${m}^{2}>0$ is unspecified. The plot is not to scale.

**Figure 6.**Predicted percentage deviations from the single mass $m=0$ integrated spectrum for the $3+3$ model, for three choices of the contribution from the ${m}_{1}=4$ eV mass. The choice of $94\%$ results in the smallest departure from the single mass spectrum, namely <0.8% at all energies.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ehrlich, R.
A Review of Searches for Evidence of Tachyons. *Symmetry* **2022**, *14*, 1198.
https://doi.org/10.3390/sym14061198

**AMA Style**

Ehrlich R.
A Review of Searches for Evidence of Tachyons. *Symmetry*. 2022; 14(6):1198.
https://doi.org/10.3390/sym14061198

**Chicago/Turabian Style**

Ehrlich, Robert.
2022. "A Review of Searches for Evidence of Tachyons" *Symmetry* 14, no. 6: 1198.
https://doi.org/10.3390/sym14061198