The noncommutative space of light-like worldlines

The noncommutative space of light-like worldlines that is covariant under the (or null-plane) $\kappa$-deformation (3+1) Poincar\'e group fully constructed as quantization corresponding Poisson homogeneous null geodesics. This new geodesics five-dimensional, and turns out to be defined a quadratic algebra can mapped non-central extension direct sum two Heisenberg-Weyl algebras whose parameter just Planck scale $\kappa^{-1}$. Moreover, it shown usual time-like does not allow construction worldlines. Therefore, most natural choice in order model propagation massless particles on quantum Minkowski spacetime seems provided by $\kappa$-deformation.