Past and future blurring at fundamental length scale

TL;DR

This paper derives $ppa$-deformed Green functions showing causality blurring and light cone smearing at a fundamental length scale, supporting the idea of spacetime fuzziness below this scale.

Contribution

It introduces $ppa$-deformed Green functions and demonstrates causality and light cone smearing at a fundamental length, advancing the understanding of spacetime structure at quantum scales.

Findings

Causality is blurred over a length scale $q$.

Light cone is smeared at the scale $q$.

Supports the concept of fuzzy spacetime regions below $q$.

Abstract

We obtain the $\kappa$-deformed versions of the retarded and advanced Green functions and show that their causality properties are blurred in a time interval of the order of a length parameter $q=1/(2\kappa)$. The functions also indicate a smearing of the light cone. These results favor the interpretation of $q$ as a fundamental length scale below which the concept of a point in spacetime should be substituted by the concept of a fuzzy region of radius $q$, as proposed long ago by Heisenberg.