We solve the relativistic Riemann problem in viscous gluon matter employing a
microscopic parton cascade. We demonstrate the transition from ideal to viscous
shock waves by varying the shear viscosity to entropy density ratio η/s
from zero to infinity. We show that an η/s ratio larger than 0.2 prevents
the development of well-defined shock waves on timescales typical for
ultrarelativistic heavy-ion collisions. Comparisons with viscous hydrodynamic
calculations confirm our findings.Comment: Version as published in PRL 103, 032301 (2009). 4 pages, 4 figure