  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.
