  The deformation of the relativistic dispersion relation caused by
noncommutative (NC) Quantum Mechanics (QM) is studied using the extended
phase-space formalism. The introduction of the additional commutation relations
induces Lorentz invariance violation. It is shown that this deformation does
not affect the propagation speed of free massless particles. From the
deformation of the dispersion relation for massless particles, gamma ray burst
data is used to establish an upper bound on the noncommutative parameter,
$\eta$, namely $\sqrt{\eta} \lesssim 10^{-12} \,\mathrm{eV/c}$. Additionally, a
putative metric structure for the noncommutative phase-space is discussed.
