The New Quantum Structure of the Space-Time

Abstract

We go beyond the classical-quantum duality of the space-time recently discussed and promote the space-time coordinates to quantum non-commuting operators. Comparison to the harmonic oscillator (X, P) variables and 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 due to the relevant [X, T ] conmutator which is always non-zero. 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 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 hyperbolic 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 (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 (√ 2n + 1 ± √ 2n) reflecting the duality of the large and small n behaviours and covering the whole mass spectrum: from the largest astrophysical objects in branch (+) to the quantum elementary particles in branch (passing ng by the Planck mass. Black holes belong to both branches (±). Starting from quantum theory (instead of general relativity) to approach quantum gravity within a minimal setting reveals successful: quantum relativity and quantum space-time structure are described. Further results are reported in another paper. Norma.Sanchez@obspm.fr, https://chalonge-devega.fr/sanchez