Emergence of Time from a Twisted Spectral Triple in Almost-Commutative Geometry

Abstract

This proceeding presents a synthesis of recent results on the emergence of pseudo-Riemannian structures from twisted spectral triples within the almostcommutative framework. It provides a unified algebraic mechanism for addressing the Lorentzian signature problem, demonstrating how the almost-commutative structure underlying the noncommutative Standard Model of particle physics may give rise to Lorentzian spectral triple from a purely Riemannian setting. This notably offers an alternative to Wick rotation, provided by a notion of morphism connecting twisted and pseudo-Riemannian spectral triples.