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International Journal of Theoretical Physics

, Volume 31, Issue 4, pp 611–741 | Cite as

The nonsymmetric Kaluza-Klein (Jordan-Thiry) theory in the electromagnetic case

  • M. W. Kalinowski
Article

Abstract

We present the nonsymmetric Kaluza-Klein and Jordan-Thiry theories as interesting propositions of physics in higher dimensions. We consider the five-dimensional (electromagnetic) case. The work is devoted to a five-dimensional unification of the NGT (nonsymmetric theory of gravitation), electromagnetism, and scalar forces in a Jordan-Thiry manner. We find “interference effects” between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric. Our unification, called the nonsymmetric Jordan-Thiry theory, becomes the classical Jordan-Thiry theory if the skew-symmetric part of the metric is zero. It becomes the classical Kaluza-Klein theory if the scalar fieldρ=1 (Kaluza's Ansatz). We also deal with material sources in the nonsymmetric Kaluza-Klein theory for the electromagnetic case. We consider phenomenological sources with a nonzero fermion current, a nonzero electric current, and a nonzero spin density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodetic equations in the theory and the equation of motion for charged test particles. We consider some numerical predictions of the nonsymmetric Kaluza-Klein theory with nonzero (and with zero) material sources. We prove that they do not contradict any experimental data for the solar system and on the surface of a neutron star. We deal also with spin sources in the nonsymmetric Kaluza-Klein theory. We find an exact, static, spherically symmetric solution in the nonsymmetric Kaluza-Klein theory in the electromagnetic case. This solution has the remarkable property of describing “mass without mass” and “charge without charge.” We examine its properties and a physical interpretation. We consider a linear version of the theory, finding the electromagnetic Lagrangian up to the second order of approximation with respect toh μv =g μv n μv . We prove that in the zeroth and first orders of approximation there is no skewonoton interaction. We deal also with the Lagrangian for the scalar field (connected to the “gravitational constant”). We prove that in the zeroth and first orders of approximation the Lagrangian vanishes.

Keywords

Electromagnetic Field Neutron Star Test Particle Density Tensor Linear Version 
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References

  1. 1.
    Kaluza, T., Zum Unitätsproblem der Physik,Sitzgsberichte der Preussiche Akademie der Wissenschaften,192, 966.Google Scholar
  2. 2.
    Klein, O.,Zeitschrift für Physik,37, 895 (1926); Klein, O., On the theory of charged fields, inNew Theories in Physics (Conference Organized in Collaboration with International Union of Physics and the Polish Co-operation Committee, Warsaw, May 30th–June 3rd, 1938), Paris (1939), p. 77.Google Scholar
  3. 3.
    Einstein, A.,The Meaning of Relativity, 5th ed., rev., Methuen, London (1951), Appendix II, p. 127; Jakubowicz, A., and Klekowska, J.,Tensor N.S.,20, 72 (1969); Chung, K. T., and Lee, Y. J.,International Journal of Theoretical Physics,27, 1083 (1988); Chung, K. T., and Hwang, H. J.,International Journal of Theoretical Physics,27, 1105 (1988); Shavokhina, N. S., Nonsymmetric metric in nonlinear field theory, preprint of the JINR, P2-86-685, Dubna (1986).Google Scholar
  4. 4.
    Kaufman, B.,Helvetica Physica Acta Suppl. 1956, 227; Chung, K. T.,Acta Mathematica Hungarica,41(1–2), 47 (1983).Google Scholar
  5. 5.
    Einstein, A., and Kaufman, B.,Annals of Mathematics,59, 230 (1954); Kaufman, B.,Annals of Mathematics,46, 578 (1945).Google Scholar
  6. 6.
    Einstein, A.,Annals of Mathematics,46, 578 (1945); Einstein, A., and Strauss, E. G.,Annals of Mathematics,47, 731 (1946).Google Scholar
  7. 7.
    Kerner, R.,Annales de l'Institut Henri Poincaré,IX, 143 (1968).Google Scholar
  8. 8.
    Cho, Y. M.,Journal of Mathematical Physics,16, 2029 (1975); Cho, Y. M., and Freund, P. G. O.,Physical Review D,12, 1711 (1975).Google Scholar
  9. 9.
    Kopczyski, W., A fibre bundle description of coupled gravitational and gauge fields, inDifferential Geometrical Methods in Mathematical Physics, Springer-Verlag, Berlin (1980), p. 462.Google Scholar
  10. 10.
    Kalinowski, M. W.,International Journal of Theoretical Physics,22, 385 (1983).Google Scholar
  11. 11.
    Thirring, W.,Acta Physica Austriaca Suppl. IX 1972, 256.Google Scholar
  12. 12.
    Kalinowski, M. W.,Acta Physica Austriaca,53, 229 (1981).Google Scholar
  13. 13.
    Kalinowski, M. W.,International Journal of Theoretical Physics,23, 131 (1984).Google Scholar
  14. 14.
    Kalinowski, M. W.,Acta Physica Austriaca,55, 197 (1983).Google Scholar
  15. 15.
    Kalinowski, M. W.,Journal of Physics A (Mathematical and General),15, 2441 (1982).Google Scholar
  16. 16.
    Kalinowski, M. W.,International Journal of Theoretical Physics,20, 563 (1981).Google Scholar
  17. 17.
    Einstein, A.,Annalen der Physik,17, 891 (1905).Google Scholar
  18. 18.
    Kalinowski, M. W.,Journal of Mathematical Physics,24, 1835 (1983).Google Scholar
  19. 19.
    Kalinowski, M. W.,Canadian Journal of Physics,61, 844 (1983).Google Scholar
  20. 20.
    Jordan, P.,Schwerkraft und Weltal, Vieweg, Braunschweig (1955).Google Scholar
  21. 21.
    Thirry, Y.,Étude matématique de equations d'une theorie unitare à quinze variables de champ, Gautiers-Villars (1951).Google Scholar
  22. 22.
    Lichnerowicz, A.,Theorie relativistes de la gravitation et de l'electromagnetisme, Masson, Paris (1955).Google Scholar
  23. 23.
    Kalinowski, M. W.,Journal of Physics A (Mathematical and General),16, 1669 (1983).Google Scholar
  24. 24.
    Kalinowski, M. W.,Nuovo Cimenta,LXXXA, 47 (1984).Google Scholar
  25. 25.
    Kalinowski, M. W.,Journal of Mathematical Physics,25, 1045 (1984).Google Scholar
  26. 26.
    Kalinowski, M. W.,Annals of Physics,148, 241 (1983).Google Scholar
  27. 27.
    Kalinowski, M. W.,Fortschritte der Physik,34, 361 (1986).Google Scholar
  28. 28.
    Kalinowski, M. W., and Mann, R. B.,Classical and Quantum Gravity,1, 157 (1984).Google Scholar
  29. 29.
    Kalinowski, M. W., and Mann, R. B.,Nuovo Cimento,91B, 67 (1986).Google Scholar
  30. 30.
    Kalinowski, M. W., and Kunstatter, G.,Journal of Mathematical Physics,25, 117 (1984).Google Scholar
  31. 31.
    Mann, R. B.,Journal of Mathematical Physics,26, 2308 (1985).Google Scholar
  32. 32.
    Kalinowski, M. W.,International Journal of Theoretical Physics,26, 21 (1987).Google Scholar
  33. 33.
    Kalinowski, M. W.,International Journal of Theoretical Physics,26, 565 (1987).Google Scholar
  34. 34.
    Moffat, J. W., Generalized theory of gravitation and its physical consequences, inProceedings of the VII International School of Gravitation and Cosmology. Erice, V. de Sabbata, ed., World Scientific, Singapore (1982), p. 127.Google Scholar
  35. 35.
    Kunstatter, G., Moffat, J. W., and Malzan, J.,Journal of Mathematical Physics,24, 886 (1983).Google Scholar
  36. 36.
    Hilbert, D.,Göttingen Nachrichten,12 (1916).Google Scholar
  37. 37.
    Levi-Civita, T.,Atti R Accademia Nazionale dei Lincei Classe de Scienze Fisichi, Matematiche e Naturali. Memorie,26, 311 (1917); Thiry, Y.,Journal de Mathematiques Pure et Appliquees,30, 275 (1951).Google Scholar
  38. 38.
    Lichnerowicz, A.,Sur certains problems globaux relatifs au systeme des equations d'Einstein, Hermann, Paris (1939).Google Scholar
  39. 39.
    Einstein, A., and Pauli, W.,Annals of Mathematics,44, 131 (1943); Einstein, A.,Revista Universidad Nacional Tucumán,2, 11 (1941).Google Scholar
  40. 40.
    Werder, R.,Physical Review D,25, 2515 (1982); Bartnik, R., and McKinnon, J.,Physical Review Letters,61, 141 (1988).Google Scholar
  41. 41.
    Kunstatter, G.,Journal of Mathematical Physics,25, 2691 (1984).Google Scholar
  42. 42.
    Roseveare, N. T..Mercury's Perihilion: From Le Vertier to Einstein, Clarendon Press, Oxford (1982).Google Scholar
  43. 43.
    Hlavaty, V.,Geometry of Einstein's Unified Field Theory, Nordhoff-Verlag, Groningen (1957); Tonnelat, M. A.,Einstein's Unified Field Theory, Gordon and Breach, New York (1966).Google Scholar
  44. 44.
    Hill, H. A., Bos, R. J., and Goode, P. R.,Physical Review Letters,33, 709 (1983); Hill, H. A.,International Journal of Theoretical Physics,23, 689 (1984); Gough, D. O.,Nature,298, 334 (1982).Google Scholar
  45. 45.
    Moffat, J. W.,Physical Review Letters,50, 709 (1983); Campbell, L., Moffat, J. B.,Astrophysical Journal,275, L77 (1983).Google Scholar
  46. 46.
    Moffat, J. W., The orbit of Icarus as a test of a theory of gravitation, University of Toronto preprint (1982); Campbell, L., McDow, J. C., Moffat, J. W., and Vincent, D.,Nature,305, 508 (1983).Google Scholar
  47. 47.
    Moffat, J. W.,Foundation of Physics,14, 1217 (1984); Moffat, J. W., Test of a theory of gravitation using the data from the binary pulsar 1913+16, University of Toronto Report (1981); Kisher, T. P.,Physical Review D,32, 329 (1985); Will, M. C.,Physical Review Letters,62, 369 (1989).Google Scholar
  48. 48.
    Moffat, J. W., Experimental consequences of the nonsymmetric gravitation theory including the apsidal motion of binaries, Lecture given at the Conference on General Relativity and Relativistic Astrophysics, University of Dalhousie, Halifax, Nova Scotia (1985).Google Scholar
  49. 49.
    McDow, J. C., Testing the nonsymmetric theory of gravitation, Ph.D. thesis, University of Toronto (1983); Hoffman, J. A., Masshal, H. L., and Lewin, W. G. H.,Nature,271, 630 (1978).Google Scholar
  50. 50.
    Bergmann, P. G.,International Journal of Theoretical Physics,1, 52 (1968).Google Scholar
  51. 51.
    Trautman, A.,Reports of Mathematical Physics,1, 29 (1970).Google Scholar
  52. 52.
    Utiyama, R.,Physical Review,101, 1597 (1956).Google Scholar
  53. 53.
    Stacey, F. D., Tuck, G. J., Moore, G. J., Holding, S. C., Goldwin, B. D., and Zhou, R.,Reviews of Modern Physics,59, 157 (1987); Ander, M. E., Goldman, T., Hughs, R. J., and Nieto, M. M.,Physical Review Letters,60, 1225 (1988); Eckhardt, D. H., Jekeli, C., Lazarewicz, A. R., Romaides, A. J., and Sands, R. W.,Physical Review Letters,60, 2567 (1988); Moore, G. I., Stacey, F. D., Tuck, G. J., Goodwin, B. D., Linthorne, N. P., Barton, M. A., Reid, D. M., and Agnew, G. D.,Physical Review D,38, 1023 (1988).Google Scholar
  54. 54.
    Fischbach, E., Sudarsky, D., Szafer, A., Tolmadge, C., and Arnson, S. H.,Physical Review Letters,56, 3 (1985).Google Scholar
  55. 55.
    Thieberg, P.,Physical Review Letters,58, 1066 (1987).Google Scholar
  56. 56.
    Wesson, P. S.,Physics Today,33, 32 (1980).Google Scholar
  57. 57.
    Gillies, G. T., and Ritter, R. C., Experiments on variation of the gravitational constant using precision rotations, inPrecision Measurements and Fundamental Constants II, B. N. Taylor, and W. D. Phillips, eds., National Bureau of Standards (U.S.) Special Publication 617 (1984), p. 629.Google Scholar
  58. 58.
    Rayski, J.,Acta Physica Polonica,XXVIII, 89 (1965).Google Scholar
  59. 59.
    Kobayashi, S., and Nomizu, K.,Foundation of Differential Geometry, New York (1963); Kobayashi, S.,Transformation Groups in Differential Geometry, Springer-Verlag, Berlin (1972).Google Scholar
  60. 60.
    Lichnerowicz, A.,Théorié globale des connexions et de group d'holonomie, Cremonese, Rome (1955).Google Scholar
  61. 61.
    Hermann, R.,Yang-Mills, Kaluza-Klein and the Einstein Program, Mathematical Science Press, Brookline, Massachusetts (1978); Coquereaux, R., and Jadczyk, A.,Riemannian Geometry, Fibre Bundle, Kaluza-Klein Theory and All That..., World Scientific, Singapore (1988).Google Scholar
  62. 62.
    Zalewski, K.,Lecture on Rotational Group, PWN, Warsaw (1987) [in Polish]; Barut, A. O., and Raczka, R.,Theory of Group Representations and Applications, PWN, Warsaw (1980).Google Scholar
  63. 63.
    Moffat, J. W.,Physical Review D,19, 3557 (1979).Google Scholar
  64. 64.
    Moffat, J. W.,Physical Review D,23 2870 (1981).Google Scholar
  65. 65.
    Moffat, J. W., Woolgar, E., The Apsidal Motion of the Binary Star in the Nonsymmetric Gravitational Theory, University of Toronto Report (1984); Moffat, J. W., The Orbital motion of DI Hercules As a Test of the Theory of Gravitation, University of Toronto Report (1984).Google Scholar
  66. 66.
    De Groot, S. R., and Suttorp, R. G.,Foundations of Electrodynamics, North-Holland, Amsterdam (1972).Google Scholar
  67. 67.
    Plebański, J.,Nonlinear Electrodynamics, Nordita, Copenhagen (1970).Google Scholar
  68. 68.
    Kalinowski, M. W.,Letters in Mathematical Physics,5, 489 (1981); Kalinowski, M. W.,Acta Physica Austriaca,27, 45 (1958).Google Scholar
  69. 69.
    Kalinowski, M. W.,Zeitschrift für Physik C (Particles and Fields) 33, 76 (1986).Google Scholar
  70. 70.
    Hlavaty, V.,Journal of Rational Mechanics and Analysis,1, 539 (1952);2, 2, 223;4, 247, 654.Google Scholar
  71. 71.
    Wyman, M.,Canadian Journal of Mathematics,1950, 427.Google Scholar
  72. 72.
    Lanczos, C.,The Variational Principles of Mechanics, University of Toronto Press, Toronto (1970).Google Scholar
  73. 73.
    Klotz, A. H.,Macrophysics and Geometry, Cambridge University Press, Cambridge (1983); Klotz, A. H.,Acta Physica Polonica B,19, 533 (1988).Google Scholar
  74. 74.
    Kalinowski, M. W.,Physical Review D,26, 3419 (1982).Google Scholar
  75. 75.
    Kuiper, G. P.,The Sun, University of Chicago Press, Chicago Illinois (1953).Google Scholar
  76. 76.
    Smith, F. G.,Pulsars, Cambridge University Press, Cambridge, New York (1977).Google Scholar
  77. 77.
    Arkuszewski, W., Kopczyński, W., and Ponomaviev, V. N.,Annales de l'Institut Henri Poincaré A,21, 89 (1974).Google Scholar
  78. 78.
    Mann, R. B., Investigations of an alternative theory of gravitation, Ph.D. thesis, University of Toronto, Toronto (1982).Google Scholar
  79. 79.
    Mann, R. B., and Moffat, J. W.,Journal of Physics A,14, 2367 (1981); Corrigenda,Journal of Physics A,15, 1055 (1982).Google Scholar
  80. 80.
    Moffat, J. W.,Physical Review D,19, 3562 (1978).Google Scholar
  81. 81.
    Moffat, J. W., and Boal, D. H.,Physical Review D,11, 1375 (1975).Google Scholar
  82. 82.
    Pant, N. D.,Nuovo Cimento,25B, 175 (1975).Google Scholar
  83. 83.
    Papapetrou, A.,Proceedings of the Royal Irish Academy,52, 96 (1948).Google Scholar
  84. 84.
    Bonnor, W. B.,Proceedings of the Royal Society,210, 427 (1951).Google Scholar
  85. 85.
    Bonnor, W. G.,Proceedings of the Royal Society,209, 353 (1951).Google Scholar
  86. 86.
    Vanstone, J. R.,Canadian Journal of Mathematics,14, 568 (1962).Google Scholar
  87. 87.
    Born, M., and Meld, L.,Proceedings of the Royal Society A,144, 425 (1934).Google Scholar
  88. 88.
    Abraham, M.,Annalen der Physik,10, 105 (1903); Cushing, J. T.,American Journal of Physics,49, 1133 (1981).Google Scholar
  89. 89.
    Campbell, L., and Moffat, J. W., Black Holes in the Nonsymmetric Theory of Gravitation, University of Toronto Report, Toronto (1982).Google Scholar
  90. 90.
    Demianski, M.,Foundations of Physics,16, 187 (1986).Google Scholar
  91. 91.
    Wheeler, J. A.,Physical Review,97, 511 (1955).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • M. W. Kalinowski
    • 1
  1. 1.Institute of Theoritical PhysicsWarsaw UniversityWarsawPoland

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