Advertisement

Spacetime with Zero Point Length is Two-Dimensional at the Planck Scale

  • Sumanta ChakrabortyEmail author
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

It is of general belief that any quantum theory of gravity should share a generic feature, namely a quantum of length. The chapter provides a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such that the spacetime naturally acquires a zero-point length, of the order of the Planck length. This prescription leads to several remarkable consequences. In particular, the Euclidean volume becomes two-dimensional as the Planck scale is being approached. This suggests that the physical spacetime becomes essentially 2-dimensional near Planck scale.

References

  1. 1.
    B. DeWitt, Gravity: a universal regulator? Phys. Rev. Lett. 13, 114–118 (1964)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    T. Padmanabhan, Planck length as the lower bound to all physical length scales. Gen. Relativ. Gravit. 17, 215–221 (1985)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    T. Padmanabhan, Physical significance of planck length. Ann. Phys. 165, 38–58 (1985)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    T. Padmanabhan, Duality and zero point length of space-time. Phys. Rev. Lett. 78, 1854–1857 (1997). arXiv:hep-th/9608182 [hep-th]
  5. 5.
    L.J. Garay, Space-time foam as a quantum thermal bath. Phys. Rev. Lett. 80, 2508–2511 (1998). arXiv:gr-qc/9801024 [gr-qc]
  6. 6.
    L.J. Garay, Quantum gravity and minimum length. Int. J. Mod. Phys. A 10, 145–166 (1995). arXiv:gr-qc/9403008 [gr-qc]
  7. 7.
    D. Kothawala, T. Padmanabhan, Entropy density of spacetime as a relic from quantum gravity. Phys. Rev. 90(12), 124060 (2014). arXiv:1405.4967 [gr-qc]
  8. 8.
    G. ’t Hooft, Quantum gravity: a fundamental problem and some radical ideas, in Recent Developments in Gravitation, ed. by M. Levi, S. Deser (Plenum, New York/London, 1978)Google Scholar
  9. 9.
    D. Kothawala, Minimal length and small scale structure of spacetime. Phys. Rev. D 88(10), 104029 (2013). arXiv:1307.5618 [gr-qc]
  10. 10.
    D.J. Stargen, D. Kothawala, Small scale structure of spacetime: the van Vleck determinant and equigeodesic surfaces. Phys. Rev. D 92(2), 024046 (2015). arXiv:1503.03793 [gr-qc]
  11. 11.
    D. Kothawala, T. Padmanabhan, Entropy density of spacetime from the zero point length. Phys. Lett. B 748, 67–69 (2015). arXiv:1408.3963 [gr-qc]
  12. 12.
    S. Chakraborty and T. Padmanabhan, “Under Preparation,” Under Preparation (2016)Google Scholar
  13. 13.
    A. Gray, The volume of a small geodesic ball of a Riemannian manifold. Mich. Math. J 20, 329 (1973)MathSciNetzbMATHGoogle Scholar
  14. 14.
    S. Carlip, R.A. Mosna, J.P.M. Pitelli, Vacuum fluctuations and the small scale structure of spacetime. Phys. Rev. Lett. 107, 021303 (2011). arXiv:1103.5993 [gr-qc]
  15. 15.
    S. Carlip, The small scale structure of spacetime,” in Proceedings, Foundations of Space and Time: Reflections on Quantum Gravity (2009), pp. 69–84. arXiv:1009.1136 [gr-qc], https://inspirehep.net/record/867166/files/arXiv:1009.1136.pdf
  16. 16.
    S. Carlip, Spontaneous dimensional reduction in short-distance quantum gravity? AIP Conf. Proc. 1196, 72 (2009). arXiv:0909.3329 [gr-qc]
  17. 17.
    G. Calcagni, Fractal universe and quantum gravity. Phys. Rev. Lett. 104, 251301 (2010). arXiv:0912.3142 [hep-th]
  18. 18.
    J. Ambjorn, J. Jurkiewicz, R. Loll, Spectral dimension of the universe. Phys. Rev. Lett. 95, 171301 (2005). arXiv:hep-th/0505113 [hep-th]
  19. 19.
    J. Ambjorn, J. Jurkiewicz, R. Loll, Reconstructing the universe. Phys. Rev. D 72, 064014 (2005). arXiv:hep-th/0505154 [hep-th]
  20. 20.
    L. Modesto, Fractal structure of loop quantum gravity. Class. Quantum Gravity 26, 242002 (2009). arXiv:0812.2214 [gr-qc]
  21. 21.
    G. Calcagni, D. Oriti, J. Thurigen, Laplacians on discrete and quantum geometries. Class. Quantum Gravity 30, 125006 (2013). arXiv:1208.0354 [hep-th]
  22. 22.
    G. Calcagni, D. Oriti, J. ThÃŒrigen, Spectral dimension of quantum geometries. Class. Quantum Gravity 31, 135014 (2014). arXiv:1311.3340 [hep-th]
  23. 23.
    V. Husain, S.S. Seahra, E.J. Webster, High energy modifications of blackbody radiation and dimensional reduction. Phys. Rev. D 88(2), 024014 (2013). arXiv:1305.2814 [hep-th]

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsIndian Association for the Cultivation of ScienceJadavpur, KolkataIndia

Personalised recommendations