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Maxwell Equations with Accounting of Tensor Properties of Time
Vlokh R., Kvasnyuk O.

Institute of Physical Optics, 23 Dragomanov St., 79005 Lviv, Ukraine

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Keywords: Maxwell equations, time, speed of light, physical vacuum

PACS: 03.50.De, 42.25.Bs, 95.30.Sf
Ukr. J. Phys. Opt. 8 125-137        doi: 10.3116/16091833/8/3/125/2007 
Received: 21.05.2007

The Maxwell equations with accounting for tensors properties of time have been considered. The effects that follow from such consideration are described. These are the appearance of vacuum polarization, anisotropy of electromagnetic wave velocity in vacuum, anisotropy of the vacuum dielectric permittivity, rotation of light polarization plane, as well as the existence of longitudinal components of electromagnetic wave and the rotational (non-potential) component of electric field caused by electric charges.
 

REFERENCES
1. Landau L.D. and Lifshitz E.M. Theoretical physics. Field theory. Moscow: Nauka (1973). 
2. Dirac PAM 1931. Quantised Singularities in the Electromagnetic Field, Proc. London Roy. Soc. A133: 60-72.
3. Munera Hector A and Octavio Guzma, 1997. A Symmetric Formulation of Maxwell Equations. Mod. Phys. Lett. A 12: 2089-2101.
        doi:10.1142/S0217732397002144 http://dx.doi.org/10.1142/S0217732397002144
4. Meyl K, 1990. Potentialwirbel, Indel Verlag, Villingen-Schwenningen Band 1 ISBN 3-9802542-1-6.
5. Meyl K, 1992. Potentialwirbel, Indel Verlag, Villingen-Schwenningen Band 2 ISBN 3-9802542-2-4.
6. Harmuth Henning F, 1986. Corrections of Maxwell equations for signals I. IEEE Transactions of Electromagnetic Compatibility EMC-28: 250-258.
7. Harmuth Henning F, 1986. Corrections of Maxwell equations for signals II. IEEE Transactions of Electromagnetic Compatibility EMC-28: 259-266
8. Harmuth Henning F, 1988. Reply to T.W. Barrett’s Comments on the Harmuth ansatz: Use of a magnetic current density in the calculation of the propagation velocity of signals by amended Maxwell theory, IEEE Transactions of Electromagnetic Compatibility EMC-30: 420-421.
9. Inomata Shiuji, Paradigm of New Science - Principals for the 21st Century, Gijutsu Shuppan Pub. Co. Ltd. Tokyo (1987).
10. Rauscher Elizabeth A, Electromagnetic Phenomena in Complex Geometries and Nonlinear Phenomena, Non-Hertzian Waves and Magnetic Monopoles, Tesla Book Company, Chula Vista CA-91912. (1983).
11. Honig William M, Quaternionic Electromagnetic Wave Equation and a Dual Charge-Filled Space. Lettere al Nuovo Cimento, Ser. 2 19 /4 (28 Maggio 1977) 137-140.
12. De Rujula A, 1995. Effects of virtual monopoles. Nucl. Phys. B435: 257-276.
        doi:10.1016/0550-3213(94)00436-I http://dx.doi.org/10.1016/0550-3213(94)00436-I
13.G. ‘t Hooft, 1974. Magnetic monopoles in unified gauge theories. Nucl. Phys. B79: 276-284.
14. Polyakov AM, 1974. Particle Spectrum in Quantum Field Theory. JETP Lett. 20: 194-195.
15. Craigie NS, Giacomelli G, Nahm W and Shafi Q, Theory and Detection of Magnetic Monopoles in Gauge Theories, World Scientific: Singapore (1986).
16. Lazarides G, Panagiotakopoulos C and Shafi Q, 1987. Magnetic monopoles from superstring models. Phys. Rev. Lett. 58: 1707-1710.
        doi:10.1103/PhysRevLett.58.1707 http://dx.doi.org/10.1103/PhysRevLett.58.1707
17. Bhattacharjee P and Sigl G, 2000. Origin and Propagation of Extremely High Energy Cosmic Rays. Phys. Rept. 327: 109-247.
18. Bertani M, Giacomelli G, Mondardini MR, Pal B, Patrizii L, Predieri F, Serralugaresi P, Sini G, Spurio M, Togo V and Zucchelli S, 1990. Search for magnetic monopoles at the Tevatron collider. Europhys. Lett. 12: 613-616.
19. Fang Z, Nagaosa N, Kei S Takahashi, Asamitsu A, Mathieu R, Ogasawara T, Yamada H, Kawasaki M, Tokura Y and Terakura K, 2003. The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space. Science 302: 92-95.
20. Vlokh R, 2004. Change of optical properties of space under gravitation field. Ukr. J. Phys. Opt. 5: 27-31.
        doi:10.3116/16091833/5/1/27/2004 http://dx.doi.org/10.3116/16091833/5/1/27/2004
21. Nandi KK and Islam A 1995. On the optical-mechanical analogy in general relativity. Amer. J. Phys. 63: 251-256.
        doi:10.1119/1.17934 http://dx.doi.org/10.1119/1.17934
22. Evans J, Nandi KK and Islam A, 1996. The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons. Gen. Rel. Grav. 28: 413-438.
        doi:10.1007/BF02105085 http://dx.doi.org/10.1007/BF02105085
23. Fernando de Felice. 1971. On the gravitational field acting as an optical medium. Gen. Rel. Grav. 2: 347.
        doi:10.1007/BF00758153 http://dx.doi.org/10.1007/BF00758153
24. Puthoff HE, 2002. Polarizable-Vacuum (PV) Approach to General Relativity. Found. Phys. 32: 927-943.
        doi:10.1023/A:1016011413407 http://dx.doi.org/10.1023/A:1016011413407
25. Vlokh R and Kostyrko M, 2005. Estimation of the Birefringence Change in Crystals Induced by Gravitation Field. Ukr. J. Phys. Opt. 6: 125-127.
        doi:10.3116/16091833/6/4/125/2005 http://dx.doi.org/10.3116/16091833/6/4/125/2005
26. Boonserm P, Cattoen C, Faber T, Visser M and Weinfurtner S, 2005. Effective Refractive Index Tensor for Weak-Field Gravity Class. Quant. Grav. 22: 1905.
        doi:10.1088/0264-9381/22/11/001 http://dx.doi.org/10.1088/0264-9381/22/11/001
27. Vlokh R and Kostyrko M, 2006. Comment on “Effective Refractive Index Tensor for Weak-Field Gravity” by P. Boonserm, C. Cattoen, T. Faber, M. Visser and S. Weinfurtner. Ukr. J. Phys. Opt. 7: 147.
        doi:10.3116/16091833/7/3/147/2006 http://dx.doi.org/10.3116/16091833/7/3/147/2006
28.Savchenko AYu and Zel’dovich B Ya, 1994. Birefringence by a smoothly inhomogeneous locally isotropic medium: Three-dimensional case. Phys. Rev. E. 50: 2287-2292.
29.Vlokh R, 1991. Nonlinear medium polarization with account of gradient invariants. Phys. Stat. Sol. (b) 168: K47-K50.
30. Nordtvedt K, 2003. dG/dt measurement and the timing of lunar laser ranging observations. Class. Quant. Grav. 20: L147-L154.
31. Mansouri R, Nasseri F and Khorrami M, 1999. Effective time variation of universe with variable space dimension A 259 194: gr-qc/9905052.
32. Bronnikov KA, Kononogov SA and Melnikov VN, 2006. Brane world corrections to Newton’s law. Gen. Relativ. Gravit. 38: 1215-1232.
33.Will CM, 1971. Relativistic gravity in the Solar system. II. Anisotropy in the Newtonian gravitation constant. Astrophys. J. 169: 141-155.
        doi:10.1086/151125 http://dx.doi.org/10.1086/151125
34. Quinn TJ, Speake CC, Richman SJ, Davis RS and Picard A, 2001. A New Determination of G Using Two Methods. Phys. Rev. Lett. 87: 111101-111105.
        doi:10.1103/PhysRevLett.87.111101 http://dx.doi.org/10.1103/PhysRevLett.87.111101
35. Anderson JD, Laing PA, Lau EL, Liu AS, Nieto MM and Turyshev SG, 1998. Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration. Phys. Rev. Lett. 81: 2858-2861. 
        doi:10.1103/PhysRevLett.81.2858 http://dx.doi.org/10.1103/PhysRevLett.81.2858
36. Fliche HH, Souriau JM and Triay R, 2006. Anisotropic Hubble expansion of large scale structures. Gen. Relativ. Gravit. 38(3): 463-474.
37.Gantmacher F.R. Theory of matrices. Moscow: Nauka (1988). 
38. Einstein A, 1945. Generalisation of the relativistic theory of gravitation. Ann. Math. 46: 578-584. 
        doi:10.2307/1969197 http://dx.doi.org/10.2307/1969197
39. Einstein A and Kaufmann B, 1955. A new form of the general relativistic field equations Ann. Math. 62: 128-138.
        doi:10.2307/2007103 http://dx.doi.org/10.2307/2007103
 

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