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Article Dans Une Revue Grav.Cosmol. Année : 2019

New Quantum Structure of Space-Time

Résumé

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 (X$^{2}$ — T$^{2}$)$_{n =}$ (2n + 1) (in Planck units ), n = 0,1, 2....(X$_{n}$, T$_{n}$) 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 (—).

Dates et versions

hal-02165519 , version 1 (26-06-2019)

Identifiants

Citer

Norma G. Sanchez. New Quantum Structure of Space-Time. Grav.Cosmol., 2019, 25 (2), pp.91-102. ⟨10.1134/S0202289319020142⟩. ⟨hal-02165519⟩
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