126 Chapter 5: pQCD vs. AdS/CFT path, ¯ λ = 1 /ρσ ∼ 1 /α$_{s}$T (in a Debye-screened ultrarelativistic plasma). Just as in the form of loss itself the requirement that τ$_{E}$ < ¯ λ therefore limits the applicability of BH to γ < γ BH c = M$_{Q}$/α$_{s}$T , similar to the AdS/CFT speed limit, Eq. (5.4), but with one less power of T $^{∗}$/M$_{Q}$ . The speed limit Eq. (5.4) was found assuming a constant plasma temper- ature; this is not the case in experiment. Nevertheless, to get a sense of the p$_{T}$ scale where the AdS/CFT approximation could break down, we will plot the momentum cutoffs from Eq. (5.4) for different SYM input parameters with two different assumptions for the mapping of QCD to AdS/CFT parameters, described in detail below. There is still additional ambiguity in the γ$_{c}$ due to the time evolution of the QGP temperature. The smallest γ$_{c}$ corresponds to the largest temperature; we take as the generous lower bound the extreme T ( ⃗ x = ⃗ 0; τ = τ$_{0}$ ), shown as a ‘(’ in the figures. For the largest γ$_{c}$ we use T$_{c}$ , show as a “].” To further emphasize the possibility of corrections in the drag model we gradually fade the curves from the “(” to the “].” Surprisingly the introduction of a thermal plasma in AdS/CFT results in an effective mass smaller than the bare mass; this will result in a reduction of the momentum reach of the drag formalism. Applying Eq. (5.1) to heavy ion collisions requires an additional assump- tion about how to map the QCD temperature and coupling to the gedanken SYM world and its SUGRA dual. The “obvious” first prescription [437] takes g$_{SY M}$ = g$_{s}$ constant, T ∗ = T $^{QCD}$, and N$_{c}$ = 3. However it was suggested in [437] that a more physical “alternative” might be to equate energy densities,