'AdS_5' Geometry Beyond Space-time and 4D Noncommutative Space-time

TL;DR

This paper explores a novel 4D noncommutative space-time modeled as an `AdS_5` geometry, proposing a phase space perspective that extends classical space-time and may inform future quantum gravity theories.

Contribution

It introduces a new geometric framework for quantum space-time using `AdS_5`, integrating noncommutativity and phase space concepts to advance quantum gravity research.

Findings

4D noncommutative space-time resembles part of a phase space.

`AdS_5` geometry models quantum space-time beyond classical notions.

Proposes a foundational approach for quantum gravity with fundamental constants.

Abstract

We discuss a 4D noncommutative space-time as suggested by the version of quantum (deformed) relativity which provides a classical geometry picture as an `AdS_5'. The 4D noncommutative space-time is more like a part of a phase space description, in accordance with the quantum notion -- quantum mechanics talks about only states but not configurations. The `AdS_5' picture also illustrates the classical 4D space-time is to be described as part of a bigger geometry beyond space-time at the quantum level. The radically new picture of quantum 'space-time' is expected to provide the basis for a (still to be formulated) new approach to quantum gravity with fundamental constants (quantum) hbar and Newton's constant G put at a similar level as c, the speed of light.