125 Chapter 5: pQCD vs. AdS/CFT (5.1) cannot be applied. Self consistency within the classical string picture requires a time-like boundary for the string worldsheet [347]. For constant velocity this limits heavy quark “speeds” to γ < γ$_{c}$ , where The work of [343] relaxed the assumptions of infinite quark mass and con- stant velocity. The analytic form of Eq. (5.1) was found to well reproduce the full numerical results (most importantly µ$_{Q}$ remained independent of p$_{T}$ ) but with M$_{Q}$ no longer the bare quark rest mass. All the calculations in this paper were based upon the infinite bare mass approximation of [342, 347] with M$_{Q}$ replaced with realistic quark masses. γ$_{c}$ =$^{(}$1 + 2 M √ λT ∗ ) 2 ≈ 4 M 2 λ ( T $^{∗}$) $_{2}$. (5.4) We note that one may arrive at this same value through a different line of reasoning. Assume that the quark’s constant velocity is maintained by an electric field. The largest electric field sustainable from the Born-Infeld action limits the magnitude of the momentum loss; the critical speed after which the field cannot be strong enough to keep the quark velocity constant is given by Eq. (5.4) [352]. While in the infinitely strongly coupled plasma dual the quasiparticle pic- ture is not applicable, a similar “speed limit” arises for ordinary incoher- ent Bethe-Heitler (BH) radiative energy loss (See Appendix D.1). Landau- Pomeranchuck coherence effects invalidate the linear in E ≈ p$_{T}$ rise of the energy loss when the formation time, τ$_{E}$ ∼ E/M $^{2}$, exceeds the mean free