Skip to main content
Springer Nature Link
Log in

On the kinematics of the torsion of space-time

  • Part I. Invited Papers Dedicated To Peter G. Bergmann
  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

On a macroscopic level we take general relativity as the appropriate theory of space-time and gravity. We will argue that, on a more microscopic level, in the Compton wavelength regime of elementary particles, there are good reasons for suspecting the presence of a torsion of space-time. A corresponding gaugetheoretical formalism related to the Poincaré group is reviewed, and the kinematical consequences of the presence of a torsion are worked out. In particular we discuss the operational meaning and the measurability of torsion. The dynamics of torsion is left for a forthcoming article.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Adler, M. Bazin, and M. Schiffer,Introduction to General Relativity (McGraw-Hill, New York, 1965).

    Google Scholar 

  2. R. Aldrovandi and E. Stédile,Int. J. Theor. Phys. 23, 301 (1984).

    Google Scholar 

  3. J. Audretsch,Phys. Rev. D 24, 1470 (1981);25, 605(E) (1982).

    Article  Google Scholar 

  4. P. Baekler,Phys. Lett. B 94, 44 (1980).

    Article  Google Scholar 

  5. P. Baekler,Phys. Lett. B 99, 329 (1981).

    Article  Google Scholar 

  6. P. Baekler,Phys. Lett. A 96, 279 (1983).

    Article  Google Scholar 

  7. G. G. A. Bäuerle and Chr. J. Haneveld,Physica A 121, 541 (1983).

    Google Scholar 

  8. P. G. Bergmann,Introduction to the Theory of Relativity (Prentice-Hall, Englewood Cliffs, New Jersey, 1942; Dover, New York, 1976).

    Google Scholar 

  9. P. G. Bergmann, inEinstein-Centenarium 1979, H.-J. Treder, ed. (Akademie-Verlag, Berlin), p. 62.

  10. P. G. Bergmann and V. DeSabbata, eds.,Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity (Proceedings of the Erice School, May 1979) (Plenum Press, New York, 1980).

    Google Scholar 

  11. F. G. Basombrio,Gen. Relat. Gravit. 12, 109 (1980).

    Article  Google Scholar 

  12. Y. M. Cho,Phys. Rev. D 14, 2521 (1976).

    Article  Google Scholar 

  13. Y. M. Cho,J. Phys. A 11, 2385 (1978).

    Google Scholar 

  14. Y. Choquet-Bruhat, C. DeWitt-Morette, and M. Dillard-Bleick,Analysis, Manifolds and Physics (North-Holland, Amsterdam, 1982), 2nd edn.

    Google Scholar 

  15. R. Debever, ed.,Elie Cartan-Albert Einstein: Letters on absolute parallelism, 1929–1932 (Princeton University Press, Princeton, New Jersey, 1979).

    Google Scholar 

  16. C. Clarke,Elementary General Relativity (E. Arnold, London, 1979).

    Google Scholar 

  17. C. Cognola, R. Soldati, M. Toller, L. Vanzo, and S. Zerbini,Nuovo Cimento B 54, 325 (1979).

    Google Scholar 

  18. R. DeRitis, M. Lavorgna, and C. Stornaiolo,Phys. Lett. A 98, 411 (1983).

    Article  Google Scholar 

  19. W. Drechsler,Ann. Inst. H. Poincaré A 37, 155 (1982).

    Google Scholar 

  20. W. Drechsler,Fortschr. Phys. 32, 449 (1984).

    Google Scholar 

  21. H. P. Dürr,Nuovo Cimento 4, 187 (1971).

    Google Scholar 

  22. H. P. Dürr,Gen. Relat. Gravit. 4, 29 (1973).

    Article  Google Scholar 

  23. R. J. Finkelstein,J. Math. Phys. 1, 440 (1960).

    Article  Google Scholar 

  24. R. J. Finkelstein,Ann. Phys. (N.Y.) 15, 223 (1961).

    Article  Google Scholar 

  25. M. Fukui, ‘Solutions of New General Relativity,” Ph.D. Thesis, University of Osaka. See alsoProg. Theor. Phys. 71, 633 (1984).

    Google Scholar 

  26. H. F. M. Goenner,Found. Phys. 14, 865 (1984).

    Article  Google Scholar 

  27. H. Goenner and F. Müller-Hoissen,Classical and Quantum Gravity 1, 651 (1984).

    Article  Google Scholar 

  28. K. Hayashi and A. Bregman,Ann. Phys. (N.Y.) 75, 562 (1973).

    Article  Google Scholar 

  29. K. Hayashi and T. Shirafuji,Phys. Rev. D 19, 3524 (1979).

    Article  Google Scholar 

  30. K. Hayashi and T. Shirafuji,Prog. Theor. Phys. 64, 866, 883, 1435, 2222 (1980);65, 525, 2079(E) (1981);66, 318, 741(E), 2258 (1981).

    Google Scholar 

  31. F. W. Hehl, “Four Lectures on Poincaré Gauge Field Theory,” inCosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity (Proceedings of the Erice School, May 1979), P. G. Bergmann and V. DeSabbata, eds. (Plenum Press, New York, 1980), p. 5.

    Google Scholar 

  32. P. Baekler and F. W. Hehl, inFrom SU(3)to Gravity—Papers in Honour of Yuval Ne'eman, E. Gotsman and G. Tauber, eds. (Cambridge Univ. Press, Cambridge, 1985).

    Google Scholar 

  33. F. W. Hehl, Y. Ne'eman, J. Nitsch, and P. von der Heyde,Phys. Lett. B 78, 102 (1978).

    Article  Google Scholar 

  34. F. W. Hehl, P. von der Heyde, G. D. Kerlick, and J. M. Nester,Rev. Mod. Phys. 48, 393 (1976).

    Article  Google Scholar 

  35. A. Held, ed.,General Relativity and Gravitation. One Hundred Years after the Birth of Albert Einstein, Vol. 1 (Plenum, New York, 1980).

    Google Scholar 

  36. J. D. Hennig. Preprint, University of Clausthal, 1984.

  37. J. Hennig and J. Nitsch,Gen. Relat. Gravit. 13, 947 (1981).

    Article  Google Scholar 

  38. S. Hojman,Phys. Rev. D 18, 2741 (1978).

    Article  Google Scholar 

  39. S. Ikeda,Found. Phys. 13, 629 (1983).

    Article  Google Scholar 

  40. A. Inomata,Phys. Rev. D 18, 3552 (1978).

    Article  Google Scholar 

  41. D. Ivanenko, inRelativity, Quanta, and Cosmology, M. Pantaleo, director, and F. DeFinis, ed., Vol. 1, (Johnson Reprint Corp., New York, 1979), p. 295.

    Google Scholar 

  42. D. Ivanenko and G. Sardanashvily,Phys. Rep. 94, 1 (1983).

    Article  Google Scholar 

  43. E. A. Ivanov and J. Niederle,Phys. Rev. D 25, 976 (1982).

    Article  Google Scholar 

  44. S. Jogia and J. B. Griffiths,Gen. Relat. Gravit. 12, 597 (1980).

    Google Scholar 

  45. M. O. Katanaev,Theor. Mat. Phys. 54, 248 (1983).

    Article  Google Scholar 

  46. G. D. Kerlick, Ph.D. thesis, Princeton University (1975).

  47. G. D. Kerlick,Phys. Rev. D 12, 3004 (1975).

    Article  Google Scholar 

  48. R. Kerner,Ann. Inst. H. Poincaré A 34, 437 (1981).

    Google Scholar 

  49. T. W. B. Kibble,J. Math. Phys. 2, 212 (1961).

    Article  Google Scholar 

  50. H. Kleinert,Gauge Theory of Stresses and Defects, to be published.

  51. W. Kopczyński,Phys. Lett. A 39, 219 (1972).

    Article  Google Scholar 

  52. W. Kopczyński,J. Phys. A 15, 493 (1982).

    Google Scholar 

  53. E. Kreisel,Ann. Phys. (Leipzig) 36, 25 (1979);37, 301 (1980);37, 360 (1980).

    Google Scholar 

  54. E. Kröner, inPhysique de defauts (Les Houches School), R. Balianet al., eds. (North-Holland, Amsterdam, 1981).

    Google Scholar 

  55. H.-J. Lenzen,Nuovo Cimento B 82, 85 (1984).

    Google Scholar 

  56. D.-E. Liebscher, inCosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity (Proceedings of the Erice School, May 1979), P. G. Bergmann and V. DeSabbata, eds. (Plenum Press, New York, 1980), p. 125.

    Google Scholar 

  57. C. P. Luehr and M. Rosenbaum,J. Math. Phys. 21, 1432 (1980);25, 380 (1984).

    Article  Google Scholar 

  58. G. Mack,Fortschr. Phys. 29, 135 (1981).

    Google Scholar 

  59. M. N. Mahanta,Int. J. Theor. Phys. 23, 569 (1984).

    Google Scholar 

  60. J. D. McCrea,J. Phys. A 16, 997 (1983).

    Google Scholar 

  61. J. D. McCrea,Phys. Lett. A 100, 397 (1984).

    Article  Google Scholar 

  62. H. Meyer,Gen. Relativ. Gravit. 14, 531 (1982).

    Article  Google Scholar 

  63. E. W. Mielke, “Über die Hypothesen, welche der Geometrodynamik zugrunde liegen,” Habilitation thesis, University of Kiel (1982).

  64. E. W. Mielke,J. Math. Phys. 25, 663 (1984).

    Article  Google Scholar 

  65. E. W. Mielke,Fortschr. Phys. 32, No. 12 (1984).

  66. E. W. Mielke, to be published.

  67. C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Francisco, 1973).

    Google Scholar 

  68. F. Müller-Hoissen, Ph.D. thesis, University of Göttingen (1983).

  69. F. Müller-Hoissen,Ann. Inst. H. Poincaré A 40, 21 (1984).

    Google Scholar 

  70. F. Müller-Hoissen and J. Nitsch,Phys. Rev. D 28, 718 (1983);Gen. Relativ. Gravit., to be published (1985).

    Article  Google Scholar 

  71. Y. Ne'eman,Lect. Notes Math. (Springer) 676, 189 (1978).

    Google Scholar 

  72. Y. Ne'eman, inGeneral Relativity and Gravitation. One Hundred Years after the Birth of Albert Einstein, Vol. 1, A. Held, ed. (Plenum Press, New York, 1980), p. 309.

    Google Scholar 

  73. Y. Ne'eman, inTo Fulfill a Vision. Jerusalem Einstein Centennial Symposium on Gauge Theories and Unification of Physical Forces, Y. Ne'eman, ed. (Addison-Wesley, Reading, Massachusetts, 1981), p. 99.

    Google Scholar 

  74. J. M. Nester,Phys. Rev. D 16, 2395 (1977).

    Article  Google Scholar 

  75. J. M. Nester, inAn Introduction to Kaluza-Klein Theories, H. C. Lee, ed. (World Scientific, Singapore, to be published, 1984/1985).

    Google Scholar 

  76. W.-T. Ni, inProceedings, 1983 International School and Symposium on Precision Measurement and Gravity Experiment, Taipei, W.-T. Ni, ed. (National Tsing Hua University, Hsinchu, Taiwan, 1983), p. 531.

  77. H. T. Nich and M. L. Yan,Ann. Phys. (N.Y.) 138, 237 (1982).

    Article  Google Scholar 

  78. J. Nitsch, inCosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity (Proceedings of the Erice School, May 1979), P. G. Bergmann and V. DeSabbata, eds. (Plenum Press, New York, 1980), p. 63.

    Google Scholar 

  79. J. Nitsch and F. W. Hehl,Phys. Lett. B 90, 98 (1980).

    Article  Google Scholar 

  80. I. S. Nurgaliev and W. N. Ponomariev,Phys. Lett. B 130, 379 (1983).

    Google Scholar 

  81. R. F. O'Connell,Phys. Rev. D 16, 1247 (1977).

    Article  Google Scholar 

  82. L. O'Raifeartaigh,Rep. Prog. Phys. 42, 159 (1979).

    Article  Google Scholar 

  83. R. Penrose,Found. Phys. 13, 325 (1983).

    Google Scholar 

  84. A. Pérez-Rendón, inProceedings of the International Meeting on Geometry and Physics, M. Modugno, ed. (Pitagora Editrice, Bologna, 1983), p. 185.

    Google Scholar 

  85. R. J. Petti,Gen. Relativ. Gravit. 7, 869 (1976).

    Article  Google Scholar 

  86. F. Pietropaolo and M. Toller,Nuovo Cimento B 77, 129 (1983).

    Google Scholar 

  87. K. A. Pilch,Lett. Math. Phys. 4, 49 (1980).

    Google Scholar 

  88. E. J. Post,Formal Structure of Electromagnetism (North-Holland, Amsterdam, 1962).

    Google Scholar 

  89. D. Rapoport and S. Sternberg,Ann. Phys. (N.Y.) 158, 447 (1984).

    Google Scholar 

  90. J. R. Ray and L. L. Smalley,Phys. Rev. Lett. 49, 1059 (1982).

    Google Scholar 

  91. J. R. Ray and L. L. Smalley,Phys. Rev. D 27, 1383 (1983).

    Google Scholar 

  92. V. I. Rodichev,Soviet Phys. JETP 40, 1169 (1961).

    Google Scholar 

  93. M. Rosenbaum, inRelativity, Cosmology, Topological Mass, and Supergravity (Proceedings of the 4th Silarg-Symposium), C. Aragone, ed. (World Scientific, Singapore, 1983), p. 205.

    Google Scholar 

  94. H. Rumpf,Z. Naturforsch. A 33, 1224 (1978).

    Google Scholar 

  95. H. Rumpf,Gen. Relativ. Gravit. 10, 509, 525, 647 (1979).

    Google Scholar 

  96. H. Rumpf, inCosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity (Proceedings of the Erice School, May 1979), P. G. Bergmann and V. DeSabbata, eds. (Plenum Press, New York, 1980), p. 93.

    Google Scholar 

  97. H. Rund,Found. Phys. 11, 809 (1981).

    Google Scholar 

  98. G. Sardanashvily,Ann. Phys. (Leipzig) 41, 23 (1984).

    Google Scholar 

  99. J. A. Schouten,Ricci Calculus (Springer, Berlin, 1954), 2nd edn.

    Google Scholar 

  100. M. A. Schweizer, inCosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity (Proceedings of the Erice School, May 1979), P. G. Bergmann and V. DeSabbata, eds. (Plenum Press, New York, 1980), p. 117.

    Google Scholar 

  101. M. A. Schweizer, Ph.D. thesis, University of Zürich (1980).

  102. M. Schweizer and N. Straumann,Phys. Lett. A 71, 493 (1979).

    Article  Google Scholar 

  103. M. A. Schweizer, N. Straumann, and A. Wipf,Gen. Relativ. Gravit. 12, 951 (1980).

    Article  Google Scholar 

  104. D. W. Sciama, inRecent Developments of General Relativity (Festschrift for Infeld) (Pergamon, Oxford, 1962), p. 415.

    Google Scholar 

  105. M. Seitz,Ann. Phys. (Leipzig), to be published (1984/1985).

  106. R. U. Sexl and H. K. Urbantke,Gravitation und Kosmologie (Bibliographissches Institut, Mannheim, 1983), 2nd edn.

    Google Scholar 

  107. L. L. Smalley,Phys. Rev. D 21, 328 (1980).

    Google Scholar 

  108. M. Soffel, B. Müller, and W. Greiner,Phys. Rep. 85, 51 (1982).

    Google Scholar 

  109. J.-L. Staudenmann, S. A. Werner, R. Colella, and A. W. Overhauser,Phys. Rev. A 21, 1419 (1980).

    Google Scholar 

  110. K. S. Stelle and P. C. West,J. Phys. A 12, 205 (1979).

    Google Scholar 

  111. S. Sternberg,Ann. Phys. (N.Y.), to be published (1985).

  112. W. Szczyrba,Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity (Proceedings of the Erice School, May 1979), P. G. Bergmann and V. DeSabbata, eds. (Plenum Press, New York, 1980), p. 105.

    Google Scholar 

  113. W. Szczyrba,Phys. Rev. D 25, 2548 (1982).

    Google Scholar 

  114. W. Thirring,Lect. Notes Phys. (Springer) 116, 272 (1980).

    Google Scholar 

  115. M. Toller,J. Math. Phys. 24, 613 (1983).

    Google Scholar 

  116. A. Trautman,Symp. Math. 12, 139 (1973).

    Google Scholar 

  117. A. Trautman,Nature (Phys. Sci.) 242, 7 (1973).

    Google Scholar 

  118. A. Trautman, inGeneral Relativity and Gravitation. One Hundred Years after the Birth of Albert Einstein, Vol. 1, A. Held, ed. (Plenum Press, New York, 1980), p. 287.

    Google Scholar 

  119. H.-J. Treder,Ann. Phys. (Leipzig) 20, 194 (1967).

    Google Scholar 

  120. H.-J. Treder,Ann. Phys. (Leipzig) 28, 238 (1972).

    Google Scholar 

  121. H.-J. Treder, private communication (1984).

  122. A. A. Tseytlin,Phys. Rev. D 26, 3327 (1982).

    Google Scholar 

  123. R. Utiyama,Phys. Rev. 101, 1597 (1956).

    Article  Google Scholar 

  124. R. Utiyama,Prog. Theor. Phys. 64, 2207 (1980).

    Google Scholar 

  125. P. von der Heyde,Phys. Lett. A 58, 141 (1976).

    Google Scholar 

  126. P. von der Heyde,Z. Naturforsch. A 31, 1725 (1976).

    Google Scholar 

  127. R. P. Wallner,Gen. Relativ. Gravit. 12, 719 (1980).

    Article  Google Scholar 

  128. R. P. Wallner,Acta Phys. Austr. 54, 165 (1982).

    Google Scholar 

  129. R. P. Wallner, Ph.D. thesis, University of Vienna (1982).

  130. P. B. Yasskin, Ph.D. thesis, University of Maryland (1979).

  131. P. B. Yasskin and W. R. Stoeger,Phys. Rev. D 21, 2081 (1980).

    Google Scholar 

Download references

Author information

Author notes

  1. Friedrich W. Hehl

    Present address: Institute of Theoretical Physics, University of Cologne, D-5000, Cologne 41, West Germany

Authors and Affiliations

  1. Department of Physics, University of California, 90024, Los Angeles, California

    Friedrich W. Hehl

Authors
  1. Friedrich W. Hehl
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hehl, F.W. On the kinematics of the torsion of space-time. Found Phys 15, 451–471 (1985). https://doi.org/10.1007/BF01889281

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01889281

Keywords

Search

Navigation