Past and future blurring at fundamental length scale

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.

Essentially, this is the version published in the Phys. Rev. Lett. 105, 211601 (2010). It has 4 pages and contains 2 figures