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Gravitation and Cosmology

, Volume 25, Issue 2, pp 91–102 | Cite as

New Quantum Structure of Space-Time

  • Norma G. SanchezEmail author
Article
  • 13 Downloads

Abstract

Starting from quantum theory (instead of general relativity) to approach quantum gravity within a minimal setting allows us here to describe the quantum space-time structure and the quantum light cone. From the classical-quantum duality and quantum harmonic oscillator (X, P) variables in global phase space, we promote the space-time coordinates to quantum noncommuting operators. The phase space instanton (X, P = iT) describes the hyperbolic quantum space-time structure and generates the quantum light cone. The classical Minkowski space-time null generators X = ±T disappear at the quantum level due to the relevant quantum [X, T] commutator which is always nonzero. A new quantum Planck scale vacuum region emerges. We describe the quantum Rindler and quantum Schwarzschild-Kruskal space-time structures. The horizons and the r = 0 space-time singularity are quantum mechanically erased. The four Kruskal regions merge inside a single quantum Planck scale “world.” The quantum space-time structure consists of hyper bolic discrete levels of odd numbers (X2T2)n = (2n + 1) (in Planck units ), n = 0,1, 2....(Xn, Tn) and the mass levels being v(2n + 1). A coherent picture emerges: large n levels are semiclassical tending towards a classical continuum space-time. Low n are quantum, the lowest mode (n = 0) being the Planck scale. Two dual (±) branches are present in the local variables (v2n + 1 ± v2n) reflecting the duality of the large and small n behaviors and covering the whole mass spectrum from the largest astrophysical objects in branch (+) to quantum elementary particles in branch (—) passing by the Planck mass. Black holes belong to both branches (+) and (—).

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Notes

Acknowledgments

The author thanks G. ’t Hooft for interesting and stimulating communications on several occasions, M. Ramon Medrano for useful discussions and en-couredgement and F. Sevre for help with the figures.

References

  1. 1.
    N. G. Sanchez, “The classical-quantum duality of nature including gravity,” Int. J. Mod. Phys. D 28, 1950055 (2019).MathSciNetCrossRefGoogle Scholar
  2. 2.
    N. G. Sanchez, Int. J. Mod. Phys. A 19, 4173 (2004).CrossRefGoogle Scholar
  3. 3.
    N. Sanchez, “Semiclassical quantum gravity in two and four dimensions,” in Gravitation in Astro physics (Cargese 1986, NATO ASI Series B156) Eds. B. Carter and J. B. Hartle (Plenum Press, N.Y., 1987); pp. 371–381.CrossRefGoogle Scholar
  4. 4.
    N. Sanchez and B. F. Whiting, Nucl. Phys. B 283, 605 (1987).CrossRefGoogle Scholar
  5. 5.
    G. W. Gibbons, Nucl. Phys. B 271, 497 (1986).CrossRefGoogle Scholar
  6. 6.
    N. Sanchez, Nucl. Phys B 294, 1111 (1987).CrossRefGoogle Scholar
  7. 7.
    G. Domenech, M. L. Levinas, and N. Sanchez, Int. J. Mod. Phys. A 3, 2567 (1988).CrossRefGoogle Scholar
  8. 8.
    G. ’t Hooft, Found. Phys. 49 +++(9), 1185 (2016).CrossRefGoogle Scholar
  9. 9.
    G. ’t Hooft, arXiv: 1605.05119.Google Scholar
  10. 10.
    M. Ramon Medrano and N. Sanchez, Phys. Rev. D 61, 084030 (2000).MathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Ramon Medrano and N. Sanchez, Int. J. Mod. Phys. A 22, 6089 (2007) and references therein.CrossRefGoogle Scholar
  12. 12.
    D. J. Cirilo-Lombardo and N. G. Sanchez, Int. J. Mod. Phys. A 23, 975 (2008).CrossRefGoogle Scholar
  13. 13.
    N. G. Sanchez, in preparation.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.LERMA CNRS UMR 8112 Observatoire de Paris PSL, Research UniversitySorbonne Universite UPMC Paris VIParisFrance

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