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.

snail feedback (6) :

Lubos:

I thought you were going to comment on it. Where is your comment?

The correlation between viscosity and density is correlated should not come as a surprise to any one with a little bit solid training in physics. Remember the dimensional analysis I meantioned? That's a powerful tool.

In quantum mechanics, the ACTION is quantized. In GUITAR theory, the quantum entropy is quantized. There is one to one correlation between action and quantum entropy. i.e., the number of actions is always equal to the number of entropy, give or take a small numerical factor.

Viscosity is defined as force per unit area, per unit velocity gradient. Hence:

Viscosity = Force *
1/(length^2) *
length/velocity
= Force * time / length^2
= (force*length) *
time /length^3
= energy * time / volume
= action / volume

Action is quantize according to quantum mechanics:
Action = Q_action * hbar

The Q_action is the action quantum number, same as the quantum number for quantum information:
Q_action = Q_entropy

Therefore:
Viscosity = Q_entropy * hbar / volue
= Entropy_density * hbar

As for the boltzmann constant. It is purely an un-necessary constant due to our selection of unit of temperature. So it doesn't need to occur.

So this is a trivial discovery that simply says quantum of information equals to quantum of action. No big deal. And it is absurd to connect this trivial result to 10-D blackholes.

Quantoken

Lubos:

I thought you were going to comment on it. Where is your comment?

The correlation between viscosity and density is correlated should not come as a surprise to any one with a little bit solid training in physics. Remember the dimensional analysis I meantioned? That's a powerful tool.

In quantum mechanics, the ACTION is quantized. In GUITAR theory, the quantum entropy is quantized. There is one to one correlation between action and quantum entropy. i.e., the number of actions is always equal to the number of entropy, give or take a small numerical factor.

Viscosity is defined as force per unit area, per unit velocity gradient. Hence:

Viscosity = Force *
1/(length^2) *
length/velocity
= Force * time / length^2
= (force*length) *
time /length^3
= energy * time / volume
= action / volume

Action is quantize according to quantum mechanics:
Action = Q_action * hbar

The Q_action is the action quantum number, same as the quantum number for quantum information:
Q_action = Q_entropy

Therefore:
Viscosity = Q_entropy * hbar / volue
= Entropy_density * hbar

As for the boltzmann constant. It is purely an un-necessary constant due to our selection of unit of temperature. So it doesn't need to occur.

So this is a trivial discovery that simply says quantum of information equals to quantum of action. No big deal. And it is absurd to connect this trivial result to 10-D blackholes.

Quantoken

Lubos:

I thought you were going to comment on it. Where is your comment?

The correlation between viscosity and density is correlated should not come as a surprise to any one with a little bit solid training in physics. Remember the dimensional analysis I meantioned? That's a powerful tool.

In quantum mechanics, the ACTION is quantized. In GUITAR theory, the quantum entropy is quantized. There is one to one correlation between action and quantum entropy. i.e., the number of actions is always equal to the number of entropy, give or take a small numerical factor.

Viscosity is defined as force per unit area, per unit velocity gradient. Hence:

Viscosity = Force *
1/(length^2) *
length/velocity
= Force * time / length^2
= (force*length) *
time /length^3
= energy * time / volume
= action / volume

Action is quantize according to quantum mechanics:
Action = Q_action * hbar

The Q_action is the action quantum number, same as the quantum number for quantum information:
Q_action = Q_entropy

Therefore:
Viscosity = Q_entropy * hbar / volue
= Entropy_density * hbar

As for the boltzmann constant. It is purely an un-necessary constant due to our selection of unit of temperature. So it doesn't need to occur.

So this is a trivial discovery that simply says quantum of information equals to quantum of action. No big deal. And it is absurd to connect this trivial result to 10-D blackholes.

Quantoken

The findings of RHIC have been compared to the finding of America and I tend to agree.

When the first findings suggesting collective effects in conflict with quark-gluon plasma picture came around 2002, I developed a model for them as a fractally scaled down variant of TGD (Topological GeometroDynamics) inspired cosmology. (Not so) big crunch followed by (not so) big bang. The fact that the gravitational mass per comoving volume approaches zero at the initial moment indeed allows this.

The alternative view is as a collapse of hadronic blackhole followed by evaporation with Planck length replaced by hadronic length scale. The idea is that color magnetic flux tubes behaving like strings and give rise to strong gravity.

In spirit of stringy thinking hadronic blackhole is a higly folded color magnetic flux tube in Hagedorn temperature, which then transforms to quark gluon plasma via a phase transition period, which correspond to critical cosmology with flat 3-space (analogous to inflationary period). Single parameter (its duration) characterizes this period and corresponds to Hagedorn temperature. The prediction for the transition temperature from hadronic string tension is consistent with freeze-out temperature for 4-dimensional mesonic strings.

The liquid like character I see as a direct evidence for what I call conformal confinement. TGD predicts that conformal weights of particles are in generic case complex and closely related to the non-trivial zeros of Riemann Zeta. For physical states the net conformal weight vanishes. In color glass condensate, and perhaps also for valence quarks, the weights are non-vanishing so that the system behaves like a single particle and the outcome is macroscopic quantum phase.

For more details and for the relation to the idea about dark matter as macroscopically quantum coherent phase see the mini articles Evidence for Many-Sheeted Space-time in RHIC?! and More about black hole like objects in RHIC at my blog and references therein.

Matti Pitkanen

Lubos said:
"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."

First, you are not allowed to use hbar, C, G. You are allowed to use hbar, C, and one another thing, but not G. G contains a scaling factor that's correlated to the size of our universe, so G is too small.

Any time you calculate anything that contains a G, you either get something many orders of magnitude too large, or many orders of magnitude too small. Isn't it true you have the cosmological constant problem and things like that?

Use somehting more natural, like a unit mass M0, where Me = alpha*M0.

If you use hbar, C, M0, every quantity boils down to dimensionless quantities. I believe in a TOE theory, you can boil all the constants down to only ONE free parameter left. Then all the dimensionless quantities that represent physics constant can be grouped into two batches.

One batch A, those that do NOT depend on the sole free parameter. All of them can be described as a trivial numerical constant of order one, which can be derived from the TOE.

Another batch B, those that DO depend on the sole free parameter. All of those can be described as a trivial numerical constant, multiplied by a function of that free parameter.

Clearly there is always a numerical relationship, if you pick any two variables from group A. But if you pick up anything from group B, then there is no simple numerical relationship except for one where the free parameter is involved.

In the discussed case of viscosity and entropy density. They both belong to group A. BTW the sole free parameter is the big alpha. I have shown that you can derive G, the scale of the universe, CMB temperature, and a bunch of other things, very precisely, from nothing but alpha.

Also I believe in the viscosity and entropy density case, the true relationship is an equality, not an in-equality. The author failed to count all the entropy that needs to be counted, for example, in evaluating the viscosity of water.

There are very strong interactions between water molecules, such interaction makes the water viscosity several hundred times bigger than otherwise. Clearly such inter-molecular interactions contribute both to the viscosity, and to the entropy density as well. If you count that part of entropy in, you will find the final relationship is an exact equality for all possible fluids, although I do not know the exact porportion constant.

Quantoken