Lorentz Transform in Multi-Dimensional Space
Author(s)
I. A. Urusovskii*
ABSTRACT
It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.
It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.
Cite this paper
I. Urusovskii, "Lorentz Transform in Multi-Dimensional Space," Journal of Modern Physics, Vol. 3 No. 11, 2012, pp. 1749-1756. doi: 10.4236/jmp.2012.311217.
I. Urusovskii, "Lorentz Transform in Multi-Dimensional Space," Journal of Modern Physics, Vol. 3 No. 11, 2012, pp. 1749-1756. doi: 10.4236/jmp.2012.311217.
References
[1] F. Klein, “Uber neuere englische Arbeiten zur Gesammelte matematishe Abhandlungen,” Springer, Berlin, 1922. [2] F. Klein, “Vorlezungen über die h?here Geometrie,” Ohne Auftrag in Berlin, Vol. 3, 1926, p. 219. [3] A. A. Margolin, “Principle of Simplicity,” Chemistry and Life, Vol. 9, 1981, p. 79. [4] Yu. B. Rumer, “Investigations on 5-Optics,” Gostekhizdat, Moscow, 1956. [5] I. A. Urusovskii, “Six-Dimensional Treatment of the Relativistic Mechanics and Spin, Metric Gravitational Theory, and the Expanding Universe,” Uspekhi Sovremennoi Radioelectroniki. Zarubezhnaya Radioelectronika, Vol. 3, 1996, p. 3. [6] I. A. Urusovskii, “Six-Dimensional Treatment of the Quark Model of Nucleons,” Uspekhi Sovremennoi Radioelectroniki. Zarubezhnaya Radioelectronika, Vol. 6, 1999, pp. 64-74. [7] I. A. Urusovskii, “Six-Dimensional Treatment of CPT-Symmetry,” Proceedings of International Scientific Meeting Physical Interpretations of Relativity Theory, Moscow, July 4-7, 2005, pp. 318-326. [8] R. O. di Bartini, “Several Relations between Physical Constants,” Doklady Akademii Nauk SSSR, Vol. 163, No. 4, 1965, pp. 861-864. [9] I. A. Gribov, “Dark Matter as Pico-Windows to Physically Equal Multiverse,” 2012. http://www2.hu-berlin.de./leibniz-sozietaet/journal/archive/13_12/01_gribov.pdf [10] J. D. Jackson, “Classical Electrodynamics,” Wiley, New York & London, 1962. [11] I. A. Urusovskii, “Gravity as a Projection of the Cosmological Force,” Proceedings of International Scientific Meeting Physical Interpretations of Relativity Theory, Moscow, 30 June-3 July 2005, pp. 359-367. [12] I. A. Urusovskii, “Gravitational Waves and Papapetrou Metric in the Six-Dimensional Treatment of Gravitation,” Physics of Wave Phenomena, Vol. 18, No. 3, 2010, pp.185-195. doi:10.3103/S1541308X10030064 [13] A. Papapetrou, “Eine Theorie des Gravitationsfeldes mit einer Feldfunrtion,”Zeitschrift fur Physik, Vol. 139, 1954, pp. 518-532. doi:10.1007/BF01374560
[1] F. Klein, “Uber neuere englische Arbeiten zur Gesammelte matematishe Abhandlungen,” Springer, Berlin, 1922. [2] F. Klein, “Vorlezungen über die h?here Geometrie,” Ohne Auftrag in Berlin, Vol. 3, 1926, p. 219. [3] A. A. Margolin, “Principle of Simplicity,” Chemistry and Life, Vol. 9, 1981, p. 79. [4] Yu. B. Rumer, “Investigations on 5-Optics,” Gostekhizdat, Moscow, 1956. [5] I. A. Urusovskii, “Six-Dimensional Treatment of the Relativistic Mechanics and Spin, Metric Gravitational Theory, and the Expanding Universe,” Uspekhi Sovremennoi Radioelectroniki. Zarubezhnaya Radioelectronika, Vol. 3, 1996, p. 3. [6] I. A. Urusovskii, “Six-Dimensional Treatment of the Quark Model of Nucleons,” Uspekhi Sovremennoi Radioelectroniki. Zarubezhnaya Radioelectronika, Vol. 6, 1999, pp. 64-74. [7] I. A. Urusovskii, “Six-Dimensional Treatment of CPT-Symmetry,” Proceedings of International Scientific Meeting Physical Interpretations of Relativity Theory, Moscow, July 4-7, 2005, pp. 318-326. [8] R. O. di Bartini, “Several Relations between Physical Constants,” Doklady Akademii Nauk SSSR, Vol. 163, No. 4, 1965, pp. 861-864. [9] I. A. Gribov, “Dark Matter as Pico-Windows to Physically Equal Multiverse,” 2012. http://www2.hu-berlin.de./leibniz-sozietaet/journal/archive/13_12/01_gribov.pdf [10] J. D. Jackson, “Classical Electrodynamics,” Wiley, New York & London, 1962. [11] I. A. Urusovskii, “Gravity as a Projection of the Cosmological Force,” Proceedings of International Scientific Meeting Physical Interpretations of Relativity Theory, Moscow, 30 June-3 July 2005, pp. 359-367. [12] I. A. Urusovskii, “Gravitational Waves and Papapetrou Metric in the Six-Dimensional Treatment of Gravitation,” Physics of Wave Phenomena, Vol. 18, No. 3, 2010, pp.185-195. doi:10.3103/S1541308X10030064 [13] A. Papapetrou, “Eine Theorie des Gravitationsfeldes mit einer Feldfunrtion,”Zeitschrift fur Physik, Vol. 139, 1954, pp. 518-532. doi:10.1007/BF01374560