Description of the Motion of Objects with Sub- and Superluminal Speeds
American Journal of Physics and Applications
Volume 8, Issue 2, March 2020, Pages: 25-28
Received: Apr. 20, 2020; Accepted: May 7, 2020; Published: Jun. 4, 2020
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Janusz Wolny, Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland
Radoslaw Strzalka, Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland
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In this paper a direct derivation of the dynamics of objects moving with relativistic speeds is presented, based on two assumptions: (i) energy and mass of an object in motion are equivalent (mass-energy equivalence, known in special relativity and confirmed in experiments), (ii) an object can be considered as a variable-mass object with mass increasing with velocity (in some interpretations referred to as relativistic mass). In the presented approach the postulate on the constancy of the speed of light is not necessary. Also, the four-dimensional Minkowski spacetime is not used and no assumptions on symmetries are made. Therefore, it applies for sub- and superluminal speeds with the speed of light in a vacuum c being the critical speed, which separates the two interesting regions of speeds. The solution for v<c is fully equivalent to the results of special relativity (including the energy-momentum invariant), but the new possible solution for v>c opens an unknown and unintuitive behavior, which should be subjected to experimental investigation. In the range of superluminal speeds, a solution in which the energy of the material particle decreases as its speed increases is obtained. The critical speed in media other than a vacuum should be replaced to a speed environment-dependent, other than c.
Special Relativity; Equation of Dynamics; Sub- and Superluminal Speeds
To cite this article
Janusz Wolny, Radoslaw Strzalka, Description of the Motion of Objects with Sub- and Superluminal Speeds, American Journal of Physics and Applications. Vol. 8, No. 2, 2020, pp. 25-28. doi: 10.11648/j.ajpa.20200802.12
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Minkowski H. (1907/15). Das Relativitätsprinzip. Ann. Phys. 352, 927-938.
Wolny J., Strzalka R. (2019). Momentum in the dynamics of variable-mass systems: classical and relativistic case. Acta Phys. Pol. A 135, 475-479.
Anderson C. D. (1933). The Positive Electron. Phys. Rev. 43, 491-494.
Aston F. W. (1927). Bakerian Lecture. A New Mass-Spectrograph and the Whole Number Rule. Proc. Roy. Soc. A 115, 487-518.
Rainville S., Thompson J. K., Myers E. G., Brown J. M., Dewey M. S., Kessler Jr. E. G. et al. (2005). A direct test of E=mc2. Nature 438, 1096-1097.
W. Rindler, Essential Relativity: Special, General, and Cosmological, 2nd ed., OUP Oxford, 2006.
R. Resnick, Introduction to Special Relativity, Wiley, 1968.
Okun L. B. (1968). The Concept of Mass. Physics Today 42, 31-36.
Lewis G. N., Tolman R. C. (1909). The Principle of Relativity, and Non-Newtonian Mechanics. Proc. Am. Acad. Arts & Sci. 44, 709-726.
Tolman R. (1912). Non-Newtonian Mechanics. The Mass of a Moving Body. Philos. Mag. 23, 375-380.
R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, chapters 15-1 and 15-8, online access:
Feinberg G., Possibility of Faster-Than-Light Particles, Phys. Rev., 1967, 159, 1089-1105.
Heim B. (1977). Vorschlag eines Weges einer einheitlichen Beschreibung der Elementarteilchen [Recommendation of a Way to a Unified Description of Elementary Particles]. Zeitschrift für Naturforschung 32a, 233-243.
Gonzalez-Diaz P. F. (2000). Warp drive space-time. Phys. Rev. D 62, 044005.
Wang L. J., Kuzmich A., Dogariu A. (2000). Gain-assisted superluminal light propagation. Nature 406, 277-279.
Zhang S., Chen J. F., Liu C., Loy M. M. T., Wong G. K. L., Du S. (2011). Optical Precursor of a Single Photon. Phys. Rev. Lett. 106, 243602.
Chodos A., Kostelecký V. A., Potting R., Gates E. (1992). Null experiments for neutrino masses, Mod. Phys. Lett. A 7, 467-476.
Chang T. (2002). Parity Violation and Neutrino Mass. Nucl. Sci. Tech. 13, 129-133.
Wang Z. Y. (2016). Modern Theory for Electromagnetic Metamaterials. Plasmonics 11, 503-508.
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