Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Knot wormholes in geometrodynamics?

  • Research Articles
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

The familiar wormhole model of geometrodynamics is extended to allow for knotted embeddings of the initial hypersurface. It is shown that topology change is not only a means to modify the connectivity of the space, but also the knot invariants of its embedding. In a probabilistic framework the process of “wormhole scattering” can be expressed by creation and annihilation operators acting on the wave function of quantum geometrodynamics. Implications concerning Wheeler's exciton model of elementary particles, thef-gravity approach to hadronic matter, and interrelations with Jehle's flux quantization program are discussed.

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. Bing, R. H. (1965). InTopology Seminar, Wisconsin, eds. Bing, R. H., and Bean, R. J. (Princeton University Press, Princeton, N.J.), p. 89.

    Google Scholar 

  2. Bing, R. H., and Martin, J. M. (1971).Trans. Am. Math. Soc.,155, 217.

    Google Scholar 

  3. Brill, D. (1972). InMagic without Magic: John Archibald Wheeler, ed. Klauder, J. R. (W. H. Freeman and Co., San Francisco), p. 309.

    Google Scholar 

  4. Christodoulou, D. (1975).Nuovo Cimento,26B, 335.

    Google Scholar 

  5. Conway, J. H. (1970). InComputational Problems in Abstract Algebra, ed. Leech, J. (Pergamon Press, New York), p. 329.

    Google Scholar 

  6. Crowell, R. H., and Fox, R. H. (1963).Introduction to Knot Theory. (Ginn and Co., Boston).

    Google Scholar 

  7. DeWitt, B. S. (1970). InRelativity, eds. Carmeli, M., Fickler, S. I., and Witten, L. (Plenum Press, New York), p. 359.

    Google Scholar 

  8. Feynman, R. P. (1972).Statistical Mechanics. (W. A. Benjamin, New York).

    Google Scholar 

  9. Finkelstein, D., and Rubinstein, J. (1968).J. Math. Phys.,9, 1762.

    Google Scholar 

  10. Fischer, A. E. (1970). InRelativity, eds. Carmeli, M., Fickler, S. I., and Witten, L. (Plenum Press, New York), p. 303.

    Google Scholar 

  11. Fox, R. H. (1962). InTopology of 3-Manifolds, ed. Fort, M. K., Jr. (Prentice-Hall, Englewood Cliffs, N.J.), p. 120.

    Google Scholar 

  12. Fuller, R. W., and Wheeler, J. A. (1962).Phys. Rev.,128, 919.

    Google Scholar 

  13. Gannon, D. (1975).J. Math. Phys.,16, 2364.

    Google Scholar 

  14. Geroch, R. P. (1966).J. Math. Phys.,36, 147.

    Google Scholar 

  15. Geroch, R. (1968).Ann. Phys. (N.Y.),48, 526.

    Google Scholar 

  16. Gluck, H. (1961).Bull. Am. Math. Soc,67, 586.

    Google Scholar 

  17. Gluck, H. (1965).Ann. Math.,81, 195.

    Google Scholar 

  18. Goldsmith, D. L. (1975). InKnots, Groups and 3-Manifolds, Papers Dedicated to the Memory of R. H. Fox, ed. Neuwirth, L. P. (Princeton Univ. Press, Princeton, N.J.), p. 3.

    Google Scholar 

  19. Gowdy, R. H. (1974).Ann. Phys. N.Y.,83, 203.

    Google Scholar 

  20. Graves, J. C. and Brill, D. R. (1960).Phys. Rev.,120, 1507.

    Google Scholar 

  21. Graves, J. C. (1971).The Conceptual Foundation of Contemporary Relativity Theory. (MIT Press, Cambridge).

    Google Scholar 

  22. Greub, W., Halperin, S., and Vanstone, R. (1972).Connections, Curvature, and Cohomology, Vol. I. (Academic Press, New York).

    Google Scholar 

  23. Greub, W., and Petry, H.-R. (1975).J. Math. Phys.,16, 1347.

    Google Scholar 

  24. Grünbaum, A. (1973).J. Phil.,70, 775.

    Google Scholar 

  25. Hu, S.-T. (1959).Homotopy Theory. (Academic Press, New York).

    Google Scholar 

  26. Jehle, H. (1915).Phys. Rev. D,11, 2147.

    Google Scholar 

  27. Kanitscheider, B. (1971).Geometrie und Wirklichkeit, Erfahrung und Denken Band 36. (Duncker & Humblot, Berlin).

    Google Scholar 

  28. Kauffman, L. H. (1974).Michigan Math. J.,21, 33.

    Google Scholar 

  29. Kiehn, R. M. (1975).Nuovo Cimento Lett.,12, 300.

    Google Scholar 

  30. Komorowski, J. (1973). In: The Greek Mathematical Society C. Carathéodory Symposium, p. 318.

  31. Lindquist, R. W., and Wheeler, J. A. (1957).Rev. Mod. Phys.,29, 432.

    Google Scholar 

  32. Mielke, E. W. (1974).Bull. Am. Phys. Soc,19, 508.

    Google Scholar 

  33. Milnor, J. (1962).Am. J. Math.,84, 1.

    Google Scholar 

  34. Milnor, J. (1963).L'Enseignment Mathématique,9, 198.

    Google Scholar 

  35. Milnor, J. (1964).Fundam. Math.,54, 335.

    Google Scholar 

  36. Misner, C. W. (1960).Phys. Rev.,118, 1110.

    Google Scholar 

  37. Misner, C. W. (1963).Ann. Phys. (N. Y.),24, 102.

    Google Scholar 

  38. Misner, C. W., and Wheeler, J. A. (1957).Ann. Phys. (N.Y.),2, 525, reprinted in Wheeler, J. A. (1962).Geometrodynamics. (Academic Press, New York).

    Google Scholar 

  39. Misner, C. W., Thome, K. S., and Wheeler, J. A. (1973).Gravitation. (A. W. Freeman and Co., San Francisco) (quoted as MTW).

    Google Scholar 

  40. Patton, C. M., and Wheeler, J. A. (1975). InQuantum Gravity, eds. Isham, C. J., Penrose, R., and Sciama, D. W. (Oxford University Press, London), p. 538.

    Google Scholar 

  41. Penrose, R. (1975). InQuantum Gravity, eds. Isham, C. J., Penrose, R., and Sciama, D. W. (Oxford University Press, London), p. 268.

    Google Scholar 

  42. Price, P. B., Shirk, E. K., Osborne, W. Z., and Pinsky, L. S. (1975).Phys. Rev. Lett.,35, 487.

    Google Scholar 

  43. Regge, T., and Teitelboim, C. (1974).Ann. Phys. N. Y.,88, 286.

    Google Scholar 

  44. Reidemeister, K. (1932).Knotentheorie, in Ergebnisse der Mathematik, Vol. 1. (Chelsea Publishing Company, New York).

    Google Scholar 

  45. Sakharov, A. D. (1972). “The Topological Structure of Elementary Charges and CPT-Symmetry,” in “Problems of Theoretical Physics, A Memorial Volume to Igor E. Tamm.” (“NAUKA”, Moscow, 1972), p. 243.

    Google Scholar 

  46. Salam, A. (1975). InQuantum Gravity, eds. Isham, C. J., Penrose, R., and Sciama, D. W. (Oxford University Press, London), p. 500.

    Google Scholar 

  47. Schubert, H. (1956).Math. Z.,65, 133.

    Google Scholar 

  48. Seifert, H., and Threlfall, W. (1934).Lehrbuch der Topology. (Chelsea Publishing Company, New York).

    Google Scholar 

  49. Strazhev, V. I., and Tomil'chik, L. M. (1973).Sov. J. Part. Nucl.,4, 78.

    Google Scholar 

  50. Stachel, J. (1974). inBoston Studies in the Philosophy of Science, Volume XX, Schaffner, K. F., and Cohen, R. S., eds. (D. Reidel Publishing Company, Dordrecht-Holland), p. 31.

    Google Scholar 

  51. Sumners, D. W. (1971).Comm. Math. Helv.,46, 240.

    Google Scholar 

  52. Sumners, D. W. (1972).Proc. Cambridge Phil. Soc.,71, 1.

    Google Scholar 

  53. Waldhausen, F. (1968).Topology,7, 195.

    Google Scholar 

  54. Westenholz, C. (1971).Ann. Inst. Henri Poincaré,XV, 182.

    Google Scholar 

  55. Wheeler, J. (1962). InLogic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress, eds. Nagel, E., Suppes, P., and Tarski, A. (Stanford University Press, Stanford, Calif.), p. 361.

    Google Scholar 

  56. Wheeler, J. A. (1968).Einsteins Vision, (Springer-Verlag, Berlin) contained in part inBattelle Rencontres: 1967 Lectures in Mathematics and Physics, DeWitt, C, and Wheeler, J. A., eds. (W. A. Benjamin, New York).

    Google Scholar 

  57. Wheeler, J. A. (1970a). InAnalytic Methods in Mathematical Physics, eds. Gilbert, R.P., and Newton, R. (Gordon and Breach, New York), p. 335.

    Google Scholar 

  58. Wheeler, J. A. (1970b). InRelativity, eds. Carmeli, M., Fickler, S. I., and Witten, L. (Plenum Press, New York), p. 31.

    Google Scholar 

  59. Wheeler, J. A. (1973). InThe Physicist's Conception of Nature, ed. Mehra, J., (D. Reidel Publishing Company, Dordrecht-Holland), p. 202.

    Google Scholar 

  60. Whiston, G. S. (1973).Int. J. Theor. Phys.,3, 99.

    Google Scholar 

  61. Whiston, G. S. (1975).Int. J. Theor. Phys.,12, 225.

    Google Scholar 

  62. Yanagawa, T. (1969).Osaka J. Math.,6, 447.

    Google Scholar 

  63. Yanagawa, T. (1970).Osaka J. Math.,7, 165.

    Google Scholar 

  64. Yodzis, P. (1973).Gen. Rel. Grav.,4, 299.

    Google Scholar 

Download references

Author information

Author notes

  1. Eckehard W. Mielke

    Present address: Mathematical Institute, University of Oxford, 24-29 St. Giles, OX1 3LB, Oxford, England

Authors and Affiliations

  1. Joseph Henry Laboratories, Princeton University, 08540, Princeton, New Jersey

    Eckehard W. Mielke

Authors
  1. Eckehard W. Mielke
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work supported by a grant of the Studienstiftung des deutschen Volkes and in part by National Science Foundation grant No. GP 30799 X to Princeton University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mielke, E.W. Knot wormholes in geometrodynamics?. Gen Relat Gravit 8, 175–196 (1977). https://doi.org/10.1007/BF00763546

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00763546

Keywords

Search

Navigation