modes [122–124]. The second order Israel-Stewart formalism was shown to be stable and causal [125–128], but the need to specify 10 independent stress field component initial conditions remains a formidable problem. Much work is underway on modeling, with 2 + 1 D viscous treatments recently published [129, 130]. And there is some hope that with the inclusion of these viscous terms hydrodynamics will finally reproduce the HBT correlation radii as well as the single particle distributions [121]. However fully 3 + 1 D relativistic viscous hydrodynamics models are still unavailable, and will be so for some time. 

Nonetheless a truly quantitative understanding of the size of viscous effects allowed by data in heavy ion collisions is crucial for progress in the field. Teaney [121] estimated that in$_{Rhic}$ collisions the viscosity to entropy density ratio, η/s , often shortened to viscosity to entropy ratio, could be no more than about 0.1. Utilizing elastic channels with perturbative cross sections only, weakly coupled pQCD gives η/s ∼ 1 [131–134]. The most famous and promising result of AdS/CFT is the calculation of η/s = 1 / 4 π in a strongly coupled plasma; for more on the AdS/CFT conjecture see Section 2.3. 

Currently the best bridge between 3+1 D ideal and viscous hydrodynamics comes from parton transport theory [135–137]. For parton cascades including only 2 → 2 processes, the ideal hydrodynamics limit is only approached when using very large elastic cross sections [138]. Nevertheless first comparisons between viscous hydrodynamics calculations and those from the cascade have been made [139]. Recent work by Xu and Greiner [137] has incorporated 

