  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.
