Astrophysical Limit on the Deformation of the Poincare Group

The deformed Poincar\'{e} group contains a characteristic mass, $\kappa$. At energies exceeding $\kappa$, deviations from the special theory of relativity become significant. However, small deviations from ordinary relativistic kinematics are observable even at energies substantially lower than $\kappa$. The observation of distant events producing ultra high energy (UHE) particles leads to a lower limit on $\kappa$. From an analysis of the UHE data on the burst in the binary system HER X1 in 1986, we deduce $\kappa > 1.3 10^{12}$~GeV.