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)

arXiv comment26 pages, 4 figures, new original material

References in corpus (6)

• Black hole unitarity and antipodal entanglement
• The Quantum Black Hole as a Hydrogen Atom: Microstates Without Strings Attached
• Conceptual unification of elementary particles, black holes, quantum de Sitter and Anti de Sitter string states
• The Classical-Quantum Duality of Nature. New Variables for Quantum Gravity
• Microcanonical model for a gaz of evaporating black holes and strings, scattering amplitudes and mass spectrum
• Semiclassical and Quantum Black Holes and their Evaporation, de Sitter and Anti-de Sitter Regimes, Gravitational and String Phase Transitions

Cited by in corpus (4)

• Soft graviton exchange and the information paradox
• Quantum Discrete Levels of the Universe from the Early Trans-Planckian Vacuum to the Late Dark Energy
• Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase
• Predictive Physics of Inflation and Grand Unification for and from the CMB observations