New Quantum Structure of the Space-Time

TL;DR

This paper proposes a quantum space-time framework where coordinates are non-commuting operators, revealing a hyperbolic quantum structure that erases classical horizons and singularities, bridging quantum and classical regimes across mass scales.

Contribution

It introduces a novel quantum space-time model based on non-commuting coordinates, unifying black hole and particle regimes within a discrete hyperbolic structure.

Findings

Quantum space-time has hyperbolic discrete levels of odd numbers.

Classical horizons and singularities are quantum mechanically erased.

Large n levels tend towards classical space-time, low n are quantum.

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)