# Relativity 4-ever?

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Basis of Special Relativity

## 3. Golden Shine of the Theory of Relativity

## 4. Why Are We Interested in the Light Speed Barrier?

## 5. Why the Light Speed Barrier?

## 6. For Light Spots, There Is No Light Speed Barrier

## 7. Does Somebody Live to the North of the Himalayas?

## 8. Tachyons

## 9. Tolman’s Antitelephone Paradox

## 10. Can Quantum Theory and Special Relativity Peacefully Coexist?

## 11. Quantum Theory and the Problem of Superluminal Motion

## 12. Frustrated Total Internal Reflection

## 13. There Are No Paradoxes in Physics

## 14. The Idea of Antiparticles

## 15. Stueckelberg—An Unconventional Hero

## 16. Reinterpretation Principle

## 17. Gell-Mann’s Totalitarian Principle

## 18. Classification of Quantons

- 1.
- ${p}^{2}>0$, ${p}^{0}>0$,
- 2.
- ${p}^{2}>0$, ${p}^{0}<0$,
- 3.
- ${p}^{2}=0$, ${p}^{0}>0$,
- 4.
- ${p}^{2}=0$, ${p}^{0}<0$,
- 5.
- ${p}^{\mu}=0$,
- 6.
- ${p}^{2}<0$.

## 19. Tachyons and Instability

## 20. Tachyons and the Light Speed Barrier

## 21. The Frenkel–Kontorova Model

## 22. Frenkel–Kontorova Solitons

## 23. Emergent Relativity

## 24. Supersonic Solitons

## 25. Elvisebrions

## 26. Final Words

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Adam, T.; Agafonova, N.; Aleksandrov, A.; Altinok, O.; Alvarez Sanchez, P.; Anokhina, A.; Aoki, S.; Ariga, A.; Ariga, T.; Autiero, D.; et al. Measurement of the neutrino velocity with the OPERA detector in the CNGS beam. J. High Energy Phys.
**2012**, 10, 093. [Google Scholar] - Chashchina, O.; Silagadze, Z. Breaking the light speed barrier. Acta Phys. Pol. B
**2012**, 43, 1917–1952. [Google Scholar] [CrossRef] - Roberts, T.; Schleif, S. What Is the Experimental Basis of Special Relativity? Available online: http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html (accessed on 5 March 2022).
- Raine, D.J.; Thomas, E.G. An Introduction to the Science of Cosmology; CRC Press: Boca Raton, FL, USA, 2001; p. 55. [Google Scholar] [CrossRef]
- Coleman, S.; Glashow, S.L. Cosmic ray and neutrino tests of special relativity. Phys. Lett. B
**1997**, 405, 249–252. [Google Scholar] [CrossRef] [Green Version] - Pyykkö, P. Relativistic effects in structural chemistry. Chem. Rev.
**1988**, 88, 563–594. [Google Scholar] [CrossRef] - Autschbach, J. Perspective: Relativistic effects. J. Chem. Phys.
**2012**, 136, 150902. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Walker, J. What Gives Gold That Mellow Glow? Available online: https://www.fourmilab.ch/documents/golden_glow/ (accessed on 5 March 2022).
- Ashby, N. Relativity in the Global Positioning System. Living Rev. Relativ.
**2003**, 6, 1. [Google Scholar] [CrossRef] [Green Version] - Ahuja, R.; Blomqvist, A.; Pyykkö, P.; Zaleski-Ejgierd, P. Relativity and the lead-acid battery. Phys. Rev. Lett.
**2011**, 106, 018301. [Google Scholar] [CrossRef] [Green Version] - Blokhintsev, D.I. Basis for special relativity theory provided by experiments in high energy physics. Sov. Phys. Usp.
**1966**, 9, 405–416. [Google Scholar] [CrossRef] - Shukshin, V. The Stubborn Fellow. In Short Stories; Smith, H., Translator; Radouga Publishers: Moscow, Russia, 1990; p. 326. Available online: https://archive.org/details/VassilyShukshinShortStories/page/n325 (accessed on 5 March 2022).
- Einstein, A. On the electrodynamics of moving bodies. Ann. Phys.
**1905**, 17, 891–921. Available online: https://einsteinpapers.press.princeton.edu/vol2-trans/154 (accessed on 5 March 2022). [CrossRef] - Masterypedia. Albert Einstein—A Father of Modern Physics. Available online: https://www.masterypedia.com/2020/08/albert-einstein-biography-in-english.html (accessed on 5 March 2022).
- Bolotovskii, B.M.; Ginzburg, V.L. The Vavilov-Cerenkov effect and the Doppler effect in the motion of sources with superluminal velocity in vacuum. Sov. Phys. Usp.
**1972**, 15, 184–192. [Google Scholar] [CrossRef] - Malykin, G.B.; Romanets, E.A. Superluminal motion (review). Opt. Spectrosc.
**2012**, 112, 920–934. [Google Scholar] [CrossRef] - Bolotovskii, B.M.; Serov, A.V. Radiation of superluminal sources in empty space. Phys.-Uspekhi
**2005**, 48, 903–915. [Google Scholar] [CrossRef] - Budker, G.I.; Shekhtman, I.A.; Ostreiko, G.N.; Nezhevenko, O.A.; Makarov, I.G.; Morozov, S.N.; Karliner, M.M. The Gyrocon—An fficient relativistic high-power VHF generator. Part. Accel.
**1979**, 10, 41–59. [Google Scholar] - Rivlin, L.A. On the transverse type of interaction of an electron beam with a high-frequency field. Proc. Res. Inst. Minist. Radio Ind. USSR
**1956**, 4, 3–15. (In Russian) [Google Scholar] - Kaufman, I.; Oltman, G. Harmonic generation by electron beam pattern motion—The Bermutron. IEEE Trans. Electron Devices
**1965**, 12, 31–39. [Google Scholar] [CrossRef] - Sudarshan, E.C.G. Particles Traveling Faster than Light, C.V. Raman Lecture; University of Texas Report CPT-166; Madras University: Chennai, India, 1972. [Google Scholar]
- Bilaniuk, O.M.P.; Deshpande, V.K.; Sudarshan, E.C.G. “Meta” relativity. Am. J. Phys.
**1962**, 30, 718–723. [Google Scholar] [CrossRef] - Feinberg, G. Possibility of faster-than-light particles. Phys. Rev.
**1967**, 159, 1089–1105. [Google Scholar] [CrossRef] - Connes, A. Advice to the Beginner. The Princeton Companion to Mathematics. 2008, pp. 1005–1007. Available online: http://assets.press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf (accessed on 5 March 2022).
- Alon, N.; Bourgain, J.; Connes, A.; Gromov, M.; Milman, V. (Eds.) Addendum: Discussion at the Dead Sea. In Visions in Mathematics: GAFA 2000 Special Volume. Part II; Birkhäuser: Basel, Switzerland, 2010; pp. 883–884. [Google Scholar] [CrossRef]
- Strum, L. Zur Frage nach der Überlichtgeschwindigkeit in der speziellen Relativitätstheorie. Z. Phys.
**1923**, 20, 36–44. [Google Scholar] [CrossRef] - Malykin, G.B.; Savchuk, V.S.; Romanets, E.A. Lev Yakovlevich Strum and the hypothesis of the existence of tachyons. Phys.-Uspekhi
**2012**, 55, 1134–1139. [Google Scholar] [CrossRef] - Chandler, R. How the Soviet Literary Establishment Censored Vasily Grossman. The New Yorker, 19 June 2019. Available online: https://www.newyorker.com/books/page-turner/how-the-soviet-literary-establishment-censored-vasily-grossman (accessed on 5 March 2022).
- Gordon, A. Etude in white-blue tons. Yegupets
**2007**, 16, 14. Available online: http://judaica.kiev.ua/old/Eg_16/16-14.htm (accessed on 5 March 2022). (In Russian). - Wikimedia Commons. Available online: https://commons.wikimedia.org/wiki/File:Tolman_%26_Einstein.jpg (accessed on 5 March 2022).
- Einstein, A. On the inertia of energy required by the relativity principle. Ann. Phys.
**1907**, 23, 371–384. Available online: https://einsteinpapers.press.princeton.edu/vol2-trans/252 (accessed on 5 March 2022). [CrossRef] [Green Version] - The Nobel Prize. Niels Bohr. Photo Gallery. Available online: https://www.nobelprize.org/images/bohr-einstein-sitting-photo-3463-landscape-medium-gallery-2x.jpg (accessed on 5 March 2022).
- Wilczek, F. Nobel Lecture: Asymptotic freedom: From paradox to paradigm. Rev. Mod. Phys.
**2005**, 77, 857–870. [Google Scholar] [CrossRef] [Green Version] - Butterfield, J. Reconsidering relativistic causality. Int. Stud. Phil. Sci.
**2007**, 21, 295–328. [Google Scholar] [CrossRef] - Hegerfeldt, G.C. Instantaneous spreading and Einstein causality in quantum theory. Ann. Phys.
**1998**, 7, 716–725. [Google Scholar] [CrossRef] - Franson, J.D. Generation of entanglement outside of the light cone. J. Mod. Opt.
**2008**, 55, 2117–2140. [Google Scholar] [CrossRef] - Einstein, A.; Podolsky, B.; Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev.
**1935**, 47, 777–780. [Google Scholar] [CrossRef] [Green Version] - Hartman, T.E. Tunneling of a wave packet. J. Appl. Phys.
**1962**, 33, 3427–3433. [Google Scholar] [CrossRef] - Barton, G.; Scharnhorst, K. QED between parallel mirrors: Light signals faster than c, or amplified by the vacuum. J. Phys. A
**1993**, 26, 2037–2046. [Google Scholar] [CrossRef] - Khriplovich, I.B. Superluminal velocity of photons in a gravitational background. Phys. Lett. B
**1995**, 346, 251–254. [Google Scholar] [CrossRef] [Green Version] - Dolgov, A.D.; Novikov, I.D. Superluminal propagation of light in gravitational field and noncausal signals. Phys. Lett. B
**1998**, 442, 82–89. [Google Scholar] [CrossRef] [Green Version] - Dumont, R.S.; Rivlin, T.; Pollak, E. The relativistic tunneling flight time may be superluminal, but it does not imply superluminal signaling. New J. Phys.
**2020**, 22, 093060. [Google Scholar] [CrossRef] - Liberati, S.; Sonego, S.; Visser, M. Faster than c signals, special relativity, and causality. Ann. Phys.
**2002**, 298, 167–185. [Google Scholar] [CrossRef] [Green Version] - Vörös, Z.; Johnsen, R. A simple demonstration of frustrated total internal reflection. Am. J. Phys.
**2008**, 76, 746–749. [Google Scholar] [CrossRef] - Nimtz, G. On virtual phonons, photons, and electrons. Found. Phys.
**2009**, 39, 1346–1355. [Google Scholar] [CrossRef] [Green Version] - Shvartsburg, A.B. Tunneling of electromagnetic waves: Paradoxes and prospects. Phys.-Uspekhi
**2007**, 50, 37–51. [Google Scholar] [CrossRef] - Nimtz, G. On superluminal tunneling. Prog. Quantum Electron.
**2003**, 27, 417–450. [Google Scholar] [CrossRef] - Winful, H.G. Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox. Phys. Rep.
**2006**, 436, 1–69. [Google Scholar] [CrossRef] - Davidovich, M.V. On the Hartman paradox, electromagnetic wave tunneling, and supraluminal velocities (comment on the paper “Tunneling of electromagnetic waves: Paradoxes and prospects” by A B Shvartsburg). Phys.-Uspekhi
**2009**, 52, 415–418. [Google Scholar] [CrossRef] - Sauter, T. Superluminal signals: An engineer’s perspective. Phys. Lett. A
**2001**, 282, 145–151. [Google Scholar] [CrossRef] - Wikipedia. Günter Nimtz. Available online: https://en.wikipedia.org/wiki/G%C3%BCnter_Nimtz (accessed on 5 March 2022).
- Feynman, R.P.; Leighton, R.B.; Sands, M. The Feynman Lectures on Physics, Vol. II; Addison-Wesley Publishing Company: Boston, MA, USA, 1963; Ch. 17-4; Available online: https://www.feynmanlectures.caltech.edu/II_17.html (accessed on 5 March 2022).
- The Caltech Archives. Richard Feynman Lecturing at Caltech Seminar Day. Available online: https://digital.archives.caltech.edu/islandora/object/image%3A1960 (accessed on 5 March 2022).
- Feynman, R.P. The reason for antiparticles. In Elementary Particles and the Laws of Physics: The 1986 Dirac Memorial Lectures; Cambridge University Press: Cambridge, UK, 1987; pp. 1–60. [Google Scholar]
- Freund, P. A Passion for Discovery; World Scientific: Singapore, 2007. [Google Scholar] [CrossRef]
- Lacki, J.; Ruegg, H.; Wanders, G. (Eds.) E.C.G. Stueckelberg, an Unconventional Figure of Twentieth Century Physics; Birkhäuser: Basel, Switzerland, 2009. [Google Scholar] [CrossRef] [Green Version]
- Wikipédia. Ernst Stueckelberg. Available online: https://fr.wikipedia.org/wiki/Ernst_Stueckelberg (accessed on 5 March 2022).
- Crease, R.P.; Mann, C.C. The physicist that physics forgot. Sciences
**1985**, 25, 18–23. [Google Scholar] [CrossRef] - Feldman, B. The Nobel Prize: A History of Genius, Controversy, and Prestige; Arcade Publishing: New York, NY, USA, 2000; pp. 193–194. [Google Scholar]
- Matthews, R. Baron, It’s for You. New Scientist, 8 October 1999. Available online: https://www.newscientist.com/article/mg16422075-100-baron-its-for-you/ (accessed on 5 March 2022).
- Recami, E. Classical tachyons and possible applications. Riv. Nuovo Cim.
**1986**, 9, 1–178. [Google Scholar] [CrossRef] - Barashenkov, V.S. Tachyons: Particles moving with velocities greater than the speed of light. Sov. Phys. Usp.
**1975**, 17, 774–782. [Google Scholar] [CrossRef] - Girard, R.; Marchildon, L. Are tachyon causal paradoxes solved? Found. Phys.
**1984**, 14, 535–548. [Google Scholar] [CrossRef] - Bilaniuk, O.-M.; Brown, S.L.; DeWitt, B.; Newcomb, W.A.; Sachs, M.; Sudarshan, E.C.G.; Yoshikawa, S. More about tachyons. Phys. Today
**1969**, 22, 47–52. [Google Scholar] [CrossRef] - White, T.H. The Once and Future King; Ace Books: New York, NY, USA, 1996; p. 121. [Google Scholar]
- Schuster, D.H. A New ambiguous figure: A three-stick clevis. Am. J. Psychol.
**1964**, 77, 673–674. [Google Scholar] [CrossRef] [PubMed] - Lévy-Leblond, J.-M. Towards a proper quantum theory. Hints for a recasting. Dialectica
**1976**, 30, 161–196. Available online: https://www.jstor.org/stable/42970442 (accessed on 5 March 2022). [CrossRef] - Lévy-Leblond, J.-M. Classical apples and quantum potatoes. Eur. J. Phys.
**1981**, 2, 44–47. [Google Scholar] [CrossRef] - Swain, J. Particles, fields, pomerons and beyond. arXiv
**2011**, arXiv:1110.5087. [Google Scholar] - Bekaert, X.; Skvortsov, E.D. Elementary particles with continuous spin. Int. J. Mod. Phys. A
**2017**, 32, 1730019. [Google Scholar] [CrossRef] [Green Version] - Shay, D. Theory of tachyons for arbitrary spin. J. Math. Phys.
**1975**, 16, 1934–1938. [Google Scholar] [CrossRef] - Peskin, M.E.; Schroeder, D.V. An Introduction to Quantum Field Theory; CRC Press: Boca Raton, FL, USA, 2019. [Google Scholar] [CrossRef]
- Teller, P. An Interpretive Introduction to Quantum Field Theory; Princeton University Press: Princeton, NJ, USA, 1994. [Google Scholar]
- Cini, M. How real are quantons? Int. J. Mod. Phys.
**2004**, 18, 565–574. [Google Scholar] [CrossRef] - Bernstein, J. A question of mass. Am. J. Phys.
**2011**, 79, 25–31. [Google Scholar] [CrossRef] - Sen, A. String theory and tachyons. Curr. Sci.
**2001**, 81, 1561–1567. [Google Scholar] - Gibbons, G.W. Thoughts on tachyon cosmology. Class. Quant. Grav.
**2003**, 20, S321–S346. [Google Scholar] [CrossRef] - Braun, O.M.; Kivshar, Y.S. The Frenkel-Kontorova Model: Concepts, Methods, and Applications; Springer: Berlin/Heidelberg, Germany, 2004. [Google Scholar]
- Bers, A.; Fox, R.; Kuper, C.G.; Lipson, S.G. The impossibility of free tachyons. In Relativity and Gravitation; Kuper, C.G., Peres, A., Eds.; Gordon and Breach Science Publishers: New York, NY, USA, 1971; pp. 41–46. [Google Scholar]
- Chase, S.; Baez, J. Do Tachyons Exist? Available online: http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html (accessed on 5 March 2022).
- Aharonov, Y.; Komar, A.; Susskind, L. Superluminal behavior, causality, and instability. Phys. Rev.
**1969**, 182, 1400–1403. [Google Scholar] [CrossRef] - Barone, A.; Esposito, F.; Magee, C.J.; Scott, A.C. Theory and applications of the sine-Gordon equation. Riv. Nuovo Cim.
**1971**, 1, 227–267. [Google Scholar] [CrossRef] - Musienko, A.I.; Manevich, L.I. Classical mechanical analogs of relativistic effects. Phys.-Uspekhi
**2004**, 47, 797–820. [Google Scholar] [CrossRef] - An Optical Illusion. Mouth of Flower by Octavio Ocampo. Available online: https://www.anopticalillusion.com/2015/08/mouth-of-flower-by-octavio-ocampo/ (accessed on 5 March 2022).
- Kosevich, A.M.; Kovalev, A.S. The supersonic motion of a crowdion. The one-dimensional model with nonlinear interaction between the nearest neighbours. Solid State Commun.
**1973**, 12, 763–765. [Google Scholar] [CrossRef] - Patt, B.; Wilczek, F. Higgs-field portal into hidden sectors. arXiv
**2006**, arXiv:hep-ph/0605188. [Google Scholar] - Giudice, G.F.; Raidal, M.; Strumia, A. Lorentz violation from the Higgs portal. Phys. Lett. B
**2010**, 690, 272–279. [Google Scholar] [CrossRef] - Gonzalez-Mestres, L. Properties of a possible class of particles able to travel faster than light. arXiv
**1995**, arXiv:astro-ph/9505117. [Google Scholar] - Geroch, R. Faster than light? arXiv
**2010**, arXiv:1005.1614. [Google Scholar] - Kasner, E.; Newman, J. Mathematics and the Imagination; G. Bell and Sons: London, UK, 1949. [Google Scholar]

**Figure 2.**Albert Einstein posing for a portrait painting. Taken from [14].

**Figure 3.**Richard Tolman with Einstein at California Institute of Technology in 1932. Taken from [30].

**Figure 4.**Niels Bohr and Albert Einstein in 1925. Taken from [32].

**Figure 5.**Günter Nimtz in the Physics laboratory of the University of Koblenz, 2008. Taken from [51].

**Figure 6.**Richard Feynman lecturing at Caltech Seminar Day, 1978. Taken from [53].

**Figure 7.**Ernst Carl Gerlach Stueckelberg in 1934 at London International Conference on Physics. Taken from [57].

**Figure 12.**Visualization of the Lorentzian contraction of the width of the Frenkel–Kontorova kink (see the text for explanation).

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

© 2022 by the authors. 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**

Chashchina, O.; Silagadze, Z.
Relativity 4-ever? *Physics* **2022**, *4*, 421-439.
https://doi.org/10.3390/physics4020028

**AMA Style**

Chashchina O, Silagadze Z.
Relativity 4-ever? *Physics*. 2022; 4(2):421-439.
https://doi.org/10.3390/physics4020028

**Chicago/Turabian Style**

Chashchina, Olga, and Zurab Silagadze.
2022. "Relativity 4-ever?" *Physics* 4, no. 2: 421-439.
https://doi.org/10.3390/physics4020028