UDC 514.774.2

MINUS-COORDINATE TRANSFORMATIONS FOR THE SUPERLUMINAL REGION OF MINKOWSKI SPACETIME Minus-coordinate transformations for the superluminal region of Minkowski spacetime

Published in Journal of Natural Sciences Research · Volume 11, Issue 3 · Pages 9–19 · Rubric: Mathematical sciences
Received: 17.08.2026 Accepted: 17.08.2026 Published: 17.08.2026 Language of publication: ru-RU
Authors
The article proposes new minus-transformations of space and time coordinates for the superluminal region of Minkowski spacetime. According to the methods of their derivation demonstrated by A. Einstein, as well as those generally accepted in the theory of relativity, these transformations are identical in nature to the derivation of Lorentz transformations for the subluminal region of the same spacetime. The transformations form a group and, therefore, conform to the principle of relativity and the principle of the constancy of the speed of light in vacuum, while preserving the invariance of the spacetime interval. Consequently, the transformations and the Special Theory of Relativity are extended to the superluminal region of Minkowski spacetime. The author believes that this may prove useful in the theoretical study of tachyon properties, as well as in the study of quantum entanglement phenomena, in which, as is well known, instantaneous information propagation is assumed.
Special theory of relativity, Lorentz transformations, minus-transformations, principle of relativity, Minkowski, spacetime, tachyon
Text References
Text (PDF)
Read Download

1. Eynshteyn A. Teoriya otnositel'nosti. Izhevsk: NIC «Regulyarnaya i haoticheskaya dinamika». – 2000. – 224 s.

2. Kragh H. Tachyons before tachyons: Lev Strum (1890-1936) and superluminal velocities // The European Physical Journal. – 2025. – Vol. 50, №9. – P. 1-25. DOI: https://doi.org/10.1140/epjh/s13129-025-00103-z

3. Somigliana C. Sulla trasformazione di Lorentz // Rendiconti delle sedute della reale Accademia Nazionale dei Lincei, Classe di scienze fìsiche, matematiche e naturali. – 1922. Ser.5: Vol.31: Fascicolo 10, Seduta del 21 maggio 1922, sem.1. Memorie e Note di Soci 53. – P. 409-414.

4. Terleckiy Ya.P. Princip prichinnosti i vtoroe nachalo termodinamiki // Doklady Akademii Nauk SSSR. – 1960. – T. 133. №2. – S. 329-332.

5. Bilaniuk O.M.R., Deshpande V.K., Sudarshan E.S.G. «Meta» Relativity // American Journal of Physics. – 1962, Vol. 30. №10. – P. 718-723. DOI: https://doi.org/10.1119/1.1941773

6. Jones R.T. Conformal coordinates associated with space-like motions // Journal of the Franklin Institute. – 1963. Vol. 275, №1. – P. 24-45. DOI: https://doi.org/10.1016/0016-0032(63)90616-1

7. Feinberg G. On the Possibility of Faster than Light Particles. Phys. Rev., 1967. Vol.159, P.1089. – (perevod E.I. Volkova i V.P. Shevel'ko). V knige «Eynshteynovskiy sbornik. 1973». – M.: Nauka. – 1974. – S. 134-177. DOI: https://doi.org/10.1103/PhysRev.159.1089

8. Mariwalla K.H. On Tachyon Lorentz Transformation // American Journal of Physics. – 1969. – №37. – P. 1281. DOI: https://doi.org/10.1119/1.1975303

9. Bilaniuk O.M.R., Sudarshan E.S.G. Particles Beyond the Light Barrier, Physics Today, May 1969, Vol.22, №5, P.43-51. – (perevod A.M. Urnova). V knige «Eynshteynovskiy sbornik. 1973». – M.: Nauka. – 1974. – S. 190-214. DOI: https://doi.org/10.1063/1.3035574

10. Parker L. Faster-Than-Light Intertial Frames and Tachyons // Physical Review. – 1969. Vol. 188. – P. 2287-2292. DOI: https://doi.org/10.1103/PhysRev.188.2287

11. Gilson J.G. Through the Light Barrier // The Mathematical Gazette. – 1968. Vol. 52, Issue 380. – P. 162-164. DOI: https://doi.org/10.2307/3612691

12. Rachman A. Dutheil R. On a Lorentz transformation related to the dynamics of tachyons. – I // Lettere Al Nuovo Cimento (1971-1985). – 1973. Vol. 8, №10. – P. 611-617. DOI: https://doi.org/10.1007/BF02891921

13. Recami E., Mignani R. More about Lorentz transformations and tachyons: answer to the comments by Ramachandran, Tagare and Kolaskar. Lettere Nuovo Cimento. – 1972. Vol.4. P. 144-152. DOI: https://doi.org/10.1007/BF02907136

14. Damski B.S. Lorentz Transformations in 1+1 Dimensional Spacetime: Mainly the Superluminal Case // Acta Physica Polonica A. – 2025. Vol. 148. – №1. – P.1-74. DOI: https://doi.org/10.12693/APhysPolA.148.22

15. Dragan A., Debski K., Charzynski S., Turzynski K., Ekert A. Relativity of superluminal observers in 1+3 spacetime ///Classical Quantum Gravity. – 2023. Vol. 20. №2. – P.1-14. DOI: https://doi.org/10.1088/1361-6382/acad60

16. Srivastava V.K., Verma A.K., Vaish G. Generalised transformation relations for superluminal particles in (3+1) dimensional system // Indian Journal of Physic. – 2025. Vol. 99. – P. 1415-1426. DOI: https://doi.org/10.1007/s12648-024-03379-x

17. Srivastava V.K., Verma A.K., Vaish G., Upadhyay S. A review on extended special and general theory of relativity for superluminal particles and their cosmological applications // Zeitschrift fur Naturforschung A: Journal of Physical Sciences. – 2024. Vol. 80. №2. – P. 113-141. DOI: https://doi.org/10.1515/zna-2024-0171

18. Capezzali G. Superluminal Lorentz transformations. Physics Essays. 2021. Vol. 34. №1. P. 44-50. DOI: https://doi.org/10.4006/0836-1398-34.1.44

19. Roldán D., Roldán-Aráuz F.A Transformation Factor for Superluminal Motion That Preserves Symmetrically the Spacetime Intervals // Symmetry. – 2023. Vol. 15(6) – P.1177-1191. DOI: https://doi.org/10.3390/sym15061177

20. Yi-Fang Chang. Developments of Space-Time, Complete Special Relativity, and Superluminal Entangled Communication // Philosophy Study. – 2022. Vol. 12. – №7. P.365-371. DOI: https://doi.org/10.17265/2159-5313/2022.07.001

21. Srivastava V.K., Verma A.K., Vaish G. Generalised transformation relations for (1+1) dimensional motion of superluminal particles // Indian J. Phys. – 2025. Vol. 4. – P. 1415-1426. DOI: https://doi.org/10.1007/s12648-024-03379-x

22. Khadka C.B., Karki B. Theoretical Investigation of Lorentz Transformation of Relativistic Quantities in Two-Dimensional Spacetime Continuum // The Scientific World Journal. – 2025. Vol. 2025. Issue 1. – P.1-5. DOI: https://doi.org/10.1155/tswj/7149569

23. Yi-Fang Chang. Superluminal, contradiction and unification between quantum theory and special relativity // International Journal of Physics and Applications. – 2022. Vol. 4. №1. – P. 17-22. DOI: https://doi.org/10.33545/26647575.2022.v4.i1a.50