Friday, March 25, 2005

Viscosity vs. entropy density ratio

A reader has asked me to comment on the following article in New Scientist:
The content of this article has something to do with the gauge theory duals of black holes and gases of black holes. At the end, they mention the conjectured production of the "black holes" at RHIC. I have mentioned the article of Horatiu Nastase here and therefore I won't say anything new about this part of the article here.

The beginning of the article describes a rather generic observation - due to people like Buchel, Kovtun, Liu, Son, Starinets - that seems to be a nearly universal law. Let me describe this intriguing insight in the following way:
  • The ratio of shear viscosity to the volume density of entropy seems to be always greater than a fixed constant "1/4.pi" (times hbar over Boltzmann's constant). The inequality is saturated for a large class of strongly coupled interacting quantum field theories - corresponding to a kind of ideal fluids - and one can explain it by the fact that they are the holographic dual of a gas of black holes in some kind of anti de Sitter space.
Two related papers for those who want to know more:

The arguments look convincing to me. I would like to emphasize that such an inequality is not just a consequence of dimensional analysis. Indeed, if we are allowed to use "hbar, c, G_{Newton}", all quantities are effectively dimensionless and may be compared with each other. Does it mean that for any pair of quantities, there is an inequality? No way.

Nevertheless, this inequality is pretty natural. Viscosity is about the lost energy - energy that has been converted to heath, complete chaos. Such a thing may always occur if there are many microstates around. If there are many microstates of "chaos" around, it's reasonable to expect that a lot of energy will be lost - viscosity will be large. But this universal law does not talk about a rough inequality only, it actually defines the precise bound (1/4.pi). It's potentially a very nice universal law and the AdS/CFT correspondence shows its muscles.




Viscosity does not seem to be the most fundamental quantity that theoretical physicists would consider to be the defining observable of the Universe - quite the opposite is true - but it is still interesting enough for similar laws to be studied.