Spacetime models, fundamental interactions and noncommutative geometry

TL;DR

This paper explores how noncommutative geometry and fundamental interactions influence the modeling of spacetime, emphasizing the role of differential structures and fermions in selecting appropriate spacetime models.

Contribution

It demonstrates that fundamental interactions, within the framework of noncommutative geometry, can determine the spacetime structure among R-compact models, highlighting the importance of fermions.

Findings

R-compact spaces are more appropriate for spacetime modeling

Differential structures significantly constrain possible spacetime models

Fermions are essential in determining the spacetime structure

Abstract

We discuss the problem of determining the spacetime structure. We show that when we are using only topological methods the spacetime can be modelled as an R- or Q-compact space although the R-compact spaces seem to be more appropriate. Demanding the existence of a differential structure substantially narrows the choice of possible models. The determination of the differential structure may be difficult if it is not unique. By using the noncommutative geometry construction of the standard model we show that fundamental interactions determine the spacetime in the class of R-compact spaces. Fermions are essential for the process of determining the spacetime structure.