I.P. Popov1

1 Kurgan State University (Kurgan, Russia)

Relevance and formulation of the problem. The number of areas of scientific and practical activity in which it is necessary to take into account relativistic corrections is steadily growing. In many cases, two objects under study move towards each other. This takes place both in relation to astronomical objects and in relation to quantum particles, including colliders - accelerators of charged particles in colliding beams. With counter relativistic motions, the relative velocity does not coincide with the approach velocity. At the same time, taking into account only the relative velocity limits the arsenal of research tools and methods. In contrast to the relative speed, which is determined in accordance with the relativistic formula for adding velocities, the speed of approach of unaccelerated objects is defined as the ratio of the distance between them to the time it takes to overcome it. The aim of this work is to analyze the diversity of the relativistic velocity of approach of objects depending on the choice of inertial reference frames based on the data of the Large Hadron Collider. Results. At the Large Hadron Collider, the speed of protons approaching is almost twice the speed of light in the laboratory reference frame. In frames of reference associated with moving protons, depending on the variants of relativistic transformation of segments of lengths and time intervals, the maximum speed of approach of protons is 1.1·108 с, and the minimum is 1.2 m/s. In accordance with the technique based on the relativistic velocity addition formula, the approach speed in reference systems associated with moving protons is almost equal to the speed of light. In this case, the approach velocity becomes equal to the relative velocity, which should not be considered as a generalization to relativistic mechanics of the classical mechanics rule on the indistinguishability of these velocities. Practical significance. The results obtained may be of interest in assessing the velocities of approach of astronomical objects, including the Earth and asteroids, as well as significantly expand the variability of hypotheses when processing experimental data arrays obtained at elementary particle accelerators, including the Large Hadron Collider.

Popov I.P. Analysis of the variety of relativistic rate of convergence of objects based on the data of the Large Hadron Collider. Nonlinear World. 2023. V. 21. № 1. P. 27-35. DOI: https://doi.org/10.18127/j20700970-202301-04 (In Russian)

1. Popov I.P. Gruppovaja skorost' volnovogo paketa, obrazovannogo dvumja svobodnymi identichnymi chasticami s raznymi nereljativistskimi skorostjami. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika. 2015. № 3(35). S. 69–72 (In Russian).
2. Drjomin I.M. Fizika na Bol'shom adronnom kollajdere. Uspehi fizicheskih nauk. 2009. T. 179. № 6. S.571–579 (In Russian).
3. Camattari R., Bandiera L., Bagli E., Mazzolari A., Sytov A., Guidi V., Romagnoni M., Haaga S., Kabukcuoglu M., Danilewsky A., Hänschke D., Baumbach T., Bode S., Bellucci V., Cavoto G. X-ray characterization of self-standing bent si crystal plates
   for Large Hadron Collider beam extraction. Journal of Applied Crystallography. 2020. V. 53. № 2. P. 486-493.
   DOI: 10.1107/S1600576720002800
4. Bally B., Bender M., Giacalone G., Somà V. Evidence of the triaxial structure of XE 129 at the Large Hadron Collider. Physical Review Letters. 2022. V. 128. № 8. P. 082301. DOI: 10.1103/PhysRevLett.128.082301.
5. Bredov M.M., Rumjancev V.V., Toptygin I.N. Klassicheskaja jelektrodinamika. M.: Nauka. Glav. Red. fiz-mat. lit. 1985. 400 s. (In Russian).
6. Cannoni M. Lorentz invariant relative velocity and relativistic binary collisions. International Journal of Modern Physics A. 2017. V. 32. № 2-3. P. 1730002. DOI: 10.1142/S0217751X17300022 (In Russian).
7. Sekerin V.I. Podchinenie dvizhenija jelektromagnitnogo izluchenija (sveta) klassicheskomu zakonu slozhenija skorostej. Inzhenernaja fizika. 2015. № 5. S. 46-48 (In Russian).
8. Semikov S.A. Ob jeksperimental'noj proverke ballisticheskoj teorii sveta. Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo. 2013. № 4-1. S. 56-63 (In Russian).
9. Veklenko B.A. Jenergija, informacija i zapredel'nye skorosti v kvantovoj jelektrodinamike. Svetotehnika. 2020. № 2. S. 6771 (In Russian).
10. Kuznecov A.M., Romanov A.A. Metodika obrabotki kollizij radiotehnicheskih signalov AIS na bortu kosmicheskogo apparata. Nelinejnyj mir. 2015. T. 13. № 4. S. 35–42 (In Russian).
11. Semikov S.A. Priroda jeffekta Barra i anomal'nyh jekscentrisitetov jekzoplanet. Nelinejnyj mir. 2016. T. 14. № 2. S. 3–37 (In Russian).
12. Sazanov A.A. Reljativistskaja popravka k zakonu gravitacii N'jutona. Nelinejnyj mir. 2011. T. 9. № 3. S. 168-183 (In Russian).
13. Podosenov S.A., Dzhjejkov Foukzon, Potapov A.A. Zadacha Bella i issledovanie jelektronnyh sgustkov v linejnyh kollajderah. Nelinejnyj mir. 2009. T. 7. № 8. S. 612–621 (In Russian).
14. Sazanov A.A. Obshhaja prichina jeffektov Jejnshtejna i Doplera. Nelinejnyj mir. 2011. T. 9. № 4. S. 255-270 (In Russian).
15. Fiaschi J., Giuli F., Hautmann F., Moretti S. Enhancing the Large Hadron Collider sensitivity to charged and neutral broad resonances of new gauge sectors. Journal of High Energy Physics. 2022. V. 2022. № 2. Р. 16. DOI: 10.1007/JHEP02(2022)179.
16. Stakia A., Held A., Dorigo T., de Castro P., Strong G.C., Banelli G., Liew S.P., Weiler A., Bortoletto D., Tosciri C., Casa A., Kotkowski G., Menardi G., Scarpa B., Delaere C., Giammanco A., Maltoni F., Saggio A., Vischia P., Donini J., et al. Advances in multi-variate analysis methods for new physics searches at the Large Hadron Collider. Reviews in Physics. 2021. V. 7. P. 100063. DOI: 10.1016/j.revip.2021.100063.
17. Lechner A., Bélanger P., Efthymiopoulos I., Grob L., Lindstrom B., Schmidt R., Wollmann D. Dust-induced beam losses in the cryogenic arcs of the Cern Large Hadron Collider. Physical Review Accelerators and Beams. 2022. V. 25. № 4. P. 041001. DOI: 10.1103/PhysRevAccelBeams.25.041001.
18. Dahbi S.-E., Choma J., Mokgatitswane G., Ruan X., Lieberman B., Mellado B., Celik T. Machine learning approach for the search of resonances with topological features at the Large Hadron Collider. International Journal of Modern Physics A. 2022. V. 37. № 3. P. 21502419. DOI: 10.1142/S0217751X21502419.
19. Bai W., Reno M.H., Diwan M., Garzelli M.V., Jeong Y.S. Far-forward neutrinos at the Large Hadron Collider. Journal of High Energy Physics. 2020. V. 2020. № 6. P. 32. DOI: 10.1007/JHEP06(2020)032.
20. Gorzawski A., Abramov A., Bruce R., Fuster-Martinez N., Krasny M., Molson J., Redaelli S., Schaumann M. Collimation of partially stripped ions in the Cern Large Hadron Collider. Physical Review Accelerators and Beams. 2020. V. 23. № 10.
    P. e101002. DOI: 10.1103/PhysRevAccelBeams.23.101002.
21. Philipp D., Hackmann E., Lämmerzahl C., Müller J. Relativistic geoid: gravity potential and relativistic effects. Physical Review D. 2020. V. 101. № 6. P. 064032. DOI: 10.1103/PhysRevD.101.064032.
22. Martín-Martínez E., Rodriguez-Lopez P. Relativistic quantum optics: the relativistic invariance of the light-matter interaction models. Physical Review D. 2018. V. 97. № 10. P. 105026. DOI: 10.1103/PhysRevD.97.105026.
23. Fukue J. Radiatively driven relativistic spherical winds under relativistic radiative transfer. Monthly Notices of the Royal Astronomical Society. 2018. V. 476. № 2. P. 1840-1848. DOI: 10.1093/MNRAS/STY358.
24. Anantua R., Tchekhovskoy A., Blandford R. Multiwavelength observations of relativistic jets from general relativistic magnetohydrodynamic simulations. Galaxies. 2018. V. 6. № 1. P. 31. DOI: 10.3390/galaxies6010031.