Stepping outside the neighborhood of $T_c$ at LHC

"As you are well aware, many in the RHIC community are interested in the LHC heavy-ion program, but have several questions: What can we learn at the LHC that is qualitatively new? Are collisions at LHC similar to RHIC ones, just with a somewhat hotter/denser initial state? If not, why not? These questions are asked in good faith, and this talk is an opportunity to answer them directly to much of the RHIC community." With these words, the organizers of Quark Matter 2009 in Knoxville invited me to discuss the physics opportunities for heavy ion collisions at the LHC without recalling the standard arguments, which are mainly based on the extended kinematic reach of the machine. In response, I emphasize here that lattice QCD indicates characteristic qualitative differences between thermal physics in the neighborhood of the critical temperature (T_c < T < 400 - 500 MeV) and thermal physics at higher temperatures (T > 400-500 MeV), for which the relevant energy densities will be solely attainable at the LHC.