Emergence of Time from Dimensional Reduction in Noncommutative Geometry

TL;DR

This paper proposes a novel dimensional reduction approach in noncommutative field theory that suggests time can emerge from a purely Euclidean space, potentially shedding light on the origin of time in quantum gravity.

Contribution

It introduces a new form of dimensional reduction in noncommutative geometry that allows the emergence of a temporal dimension from Euclidean space.

Findings

Temporal dimension can emerge from Euclidean geometry.

Signature change of spacetime is possible through this mechanism.

Potential implications for understanding the origin of time in quantum gravity.

Abstract

By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean geometry. We suggest that this mechanism may hint at the origin of time in the fundamental theory of quantum gravity.