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New Quantum Structure of Space-Time

Authors
  • Sanchez, Norma G.1
  • 1 Sorbonne Universite UPMC Paris VI, LERMA CNRS UMR 8112 Observatoire de Paris PSL, Research University, 61, Avenue de l’Observatoire, Paris, 75014, France , Paris (France)
Type
Published Article
Journal
Gravitation and Cosmology
Publisher
Pleiades Publishing
Publication Date
Apr 01, 2019
Volume
25
Issue
2
Pages
91–102
Identifiers
DOI: 10.1134/S0202289319020142
Source
Springer Nature
License
Yellow

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 (X2 — T2)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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