Locality, Causality and Noncommutative Geometry

TL;DR

This paper investigates how noncommutative geometry alters causality, leading to a modified light wedge, and proposes a new energy condition, with implications for quantum gravity and holography.

Contribution

It demonstrates that noncommutative interactions modify causality from light cone to light wedge and suggests a reformulation of field theory in lower dimensions.

Findings

Nonlocality causes light cone to become light wedge.

Standard energy conditions are violated in noncommutative spacetime.

Dimensional reduction may explain holographic properties of quantum gravity.

Abstract

We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in noncommutative spacetime. On reduction from light cone to light wedge, it looks like the noncommutative dimensions are effectively washed out and suggests a reformulation of noncommutative field theory in terms of lower dimensional degree of freedom. This reduction of dimensions due to noncommutative geometry could play a key role in explaining the holographic property of quantum gravity.