Physical models from noncommutative causality

TL;DR

This paper reviews noncommutative causality models, revealing their potential to geometrically explain phenomena like fermion trembling motion and constraints on wave packet translations in noncommutative spacetimes.

Contribution

It provides a non-technical overview of noncommutative causal structures in toy models, linking them to physical phenomena and interpretations.

Findings

Geometrical explanation of Zitterbewegung motion

Constraints on translations and energy jumps in Moyal spacetime

Noncommutative causality models offer novel physical insights

Abstract

We introduced few years ago a new notion of causality for noncommutative spacetimes directly related to the Dirac operator and the concept of Lorentzian spectral triple. In this paper, we review in a non-technical way the noncommutative causal structure of many toy models as almost commutative spacetimes and the Moyal-Weyl spacetime. We show that those models present some unexpected physical interpretations as a geometrical explanation of the Zitterbewegung trembling motion of a fermion as well as some geometrical constraints on translations and energy jumps of wave packets on the Moyal spacetime.