On time irreversibility of universal kinematics

1Grushka, Ya.I
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2016, 7:14-21
https://doi.org/10.15407/dopovidi2016.07.014
Section: Mathematics
Language: Ukrainian
Abstract: 

Using the recently developed mathematical apparatus of the theory of kinematic changeable sets, it is proved that the hypothesis of the existence of material objects and inertial reference systems moving with superluminal velocities does not lead to the violation of the principle of causality, that is, to a possibility of the returning to the own past in general. This result is obtained as the corollary of the abstract theorem on irreversibility, which gives the sufficient condition of time irreversibility for universal kinematic sets.

Keywords: inertial reference system, theory of kinematic changeable sets
References: 
  1. Bilaniuk O.-M. P., Deshpande V. K., Sudarshan E. C. G. Am. J. Phys., 1962, 30, No 10: 718–723. https://doi.org/10.1119/1.1941773
  2. Bilaniuk O.-M. P., Sudarshan E. C. G. Phys. Today, 1969, 22, No 5: 43–51. https://doi.org/10.1063/1.3035574
  3. Ilyashevytch V. I., Medvedev S. Y. Uzhhorod University Scientific Herald. Ser. Phys., 2010, 2010, No 27: 103–111 (in Ukrainian).
  4. Andréka H., Madarász J. X., Németi I., Stannett M., Székely G. Class. Quant. Grav., 2014, 31, No 9: 095005. https://doi.org/10.1088/0264-9381/31/9/095005
  5. Recami E. Riv. Nuovo Cimento, 1986, 9, s. 3, No 6: 1–178.
  6. Hill J. M., Cox B. J. Proc. R. Soc. A, 2012, 468, Iss. 2148: 4174–4192.
  7. Grushka Ya. I. Methods Funct. Anal. Topology, 2013, 20, No 2: 127–145.
  8. Grushka Ya. I. Zbirnyk prats In-ty Matematyky NAN Ukraine, 2015, 12, No 1: 74–118 (in Ukrainian).
  9. Grushka Ya. I. Abstract Coordinate Transforms in Kinematic Changeable Sets and Their Properties, Preprint: arXiv:1504.02685v2, 2015.
  10. Grushka Ya. I. Abstract concept of changeable set, Preprint: arXiv:1207.3751v1, 2012.
  11. Grushka Ya. I. Zbirnyk prats In-ty Matematyky NAN Ukraine, 2015, 12, No 2: 139–204 (in Ukrainian).