Noncommutative Geometry and Structure of Space-Time

TL;DR

This paper reviews how noncommutative geometry provides a framework for understanding the fundamental structure of space-time, explaining the Standard Model's features and suggesting a high-energy unification with Pati-Salam model.

Contribution

It demonstrates that noncommutative geometry uniquely explains the Standard Model's structure and predicts two types of geometric quanta at the Planck scale without additional assumptions.

Findings

Standard Model arises from classification of noncommutative spaces

High-energy unification with Pati-Salam model suggested

Existence of two types of Planck-scale geometric quanta

Abstract

I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the Standard Model and the reasons behind the particular form of gauge fields, Higgs fields and fermions as well as the origin of symmetry breaking. It also points that at high energies the Standard Model is a truncation of Pati-Salam unified model of leptons and quarks. The same conclusions are arrived at uniquely without making any assumptions except for an axiom which is a higher form of Heisenberg commutation relations quantizing the volume of space-time. We establish the existence of two kinds of quanta of geometry in the form of unit spheres of Planck length. We provide answers to many of the questions which are not answered by other approaches, however, more research is needed to answer the remaining challenging questions.