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New Quantum Structure of the Space-Time

Abstract : We start from quantum theory (instead of general relativity) to approach quantum gravity within a minimal setting and promote the space-time coordinates to quantum non-commuting operators. Comparison to the harmonic oscillator global phase space is enlighting. 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 dissapear at the quantum level replaced by four Planck scale hyperbolae and a new quantum Planck scale vacuum region emerges. We describe the quantum Rindler and quantum Schwarzshild-Kruskal space-time structures. The horizons and the r=0 singularity are quantum mechanically erased. The four Kruskal regions merge inside a single quantum Planck scale "world". The quantum space-time structure consists of hyperbolic discrete levels of odd numbers (2n + 1) (in Planck units ), n = 0, 1, 2.... . The mass levels are the square root of (2n + 1). Large n 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 covering the whole mass spectrum: from the largest astrophysical objects to the quantum elementary particles passing by the Planck mass. Black holes belong to both branches. (Abridged)
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https://hal-obspm.ccsd.cnrs.fr/obspm-02475877
Contributor : Norma G. Sanchez <>
Submitted on : Wednesday, February 12, 2020 - 12:30:10 PM
Last modification on : Saturday, September 19, 2020 - 4:55:44 AM

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Norma G. Sanchez. New Quantum Structure of the Space-Time. Gravitation and Cosmology, 2019, ⟨10.1134/S0202289319020142⟩. ⟨obspm-02475877⟩

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