Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Viscosity/Entropy ratio and unitary evolution in quantum gravity

+ 6 like - 0 dislike
890 views

Calculations of the shear viscosity of the quark-gluon plasma (QGP), observed in heavy ions collisions, are performed via the AdS/CFT correspondence [ref1]. One finds that the shear viscosity of the CFT, on the boundary of an AdS spacetime with a black hole in its interior, is equal to the shear viscosity of the fluid theory living on the black hole horizon surface. This quantity in turn can be calculated by considering the cross-section for graviton absorption [ref2] by the horizon in the limit that the frequency $\omega \rightarrow 0$ (low-energy limit).

The end results suggest that the fluid on the horizon (and its dual fluid the QGP) is as close to being a "perfect" fluid as Nature allows. What is found is that the shear viscosity $\eta$ of the horizon is proportional to its surface entropy density $s$. It is conjectured that there is a lower bound:

$$ \frac{\eta}{s} \ge \frac{1}{4\pi} $$

(in natural units) for the viscosity to entropy ratio for any hydrodynamical system.

These results would seem to imply that the evolution of the QGP cannot be given by a unitary theory. Perhaps this is just a naive misinterpretation of the physics on my part. If unitarity in quantum gravity is presumed to be sacrosanct then how does one reconcile the dissipative behavior of the field theory of a QGP and a black hole horizon with the demands of unitarity?


Edit: @Lubos' answer is fairly complete but I would like to see what others have to say. Thus the bounty. Have at it!

This post imported from StackExchange Physics at 2014-04-01 16:24 (UCT), posted by SE-user user346
asked Feb 18, 2011 in Theoretical Physics by Deepak Vaid (1,985 points) [ no revision ]

1 Answer

+ 6 like - 0 dislike

These results would seem to imply that the evolution of the QGP cannot be given by a unitary theory.

Quite on the contrary. Both sides are equivalent so the AdS/CFT is a proof that the black hole dynamics is unitary - because its equivalent to another theory (the CFT) whose dynamics is given by a manifestly and exactly Hermitian Hamiltonian. This also implies that the information is not lost when black holes evaporate.

I am confused by your statement about "sacrosanct unitarity of quantum gravity". If it is sacrosanct, why do you claim it is not true? In reality, even if some people could call it sacrosanct today, the unitarity of quantum gravity is much more nontrivial - and has been much more controversial for decades - than the unitarity of the laws governing quark-gluon plasma. The latter are self-evidently unitary.

The AdS/CFT correspondence became the most well-known method - but not the only method - to resolve the much harder problem of unitarity of quantum gravity. It's the key method that has also convinced Hawking that he was wrong and the information is preserved. And the answer is Yes, any evolution in quantum gravity in an asymptotically AdS (or flat) spacetime is unitary even if it involves the birth and disappearance of black holes.

You may be confused by the term "dissipation". Dissipation doesn't mean that the theory fails to be unitary. Dissipation is a process in which macroscopic forms of energy are converted to the microscopic forms of energy - heat - which allow the entropy to increase. But the full microscopic theory is still unitary; if you measure the degrees of freedom describing the QGP accurately, they will be shown to evolve in a unitary way (even though, the effective theories we use in practice may display some disappearance of the non-uniformities and information).

But in the black hole case, people didn't know any reason (e.g. a description) that would indicate that the information was preserved, even in principle. This changed with the AdS/CFT correspondence, Matrix theory, and others. Since the late 1990s, the status of "dissipation" in quantum gravity has been on par with the status in field theories. At the fundamental level, the evolution is unitary and preserves the information even though approximate, macroscopic effective descriptions of the phenomena fail to see this fact.

This post imported from StackExchange Physics at 2014-04-01 16:24 (UCT), posted by SE-user Luboš Motl
answered Feb 18, 2011 by Luboš Motl (10,278 points) [ no revision ]
@Lubos thanks for your answer. You say that dynamics of the CFT (N=4 SUSY-YM) is "given by a manifestly and exactly Hermitian Hamiltonian." So my question is how does a macroscopic dissipative theory arise from a Hermitian Hamiltonian? Is this analogous to asking how an imperfect classical fluid with irreversible dynamics can arise from the reversible, time-symmetric microscopic laws of motion describing a gas of classical atoms ,the resolution to which is traditionally given by Boltzmann's H-Theorem?

This post imported from StackExchange Physics at 2014-04-01 16:24 (UCT), posted by SE-user user346
Dear space_cadet, dissipative theories - with friction, viscosity, and other irreversible processes that create heat - arise simply because the macroscopic theory doesn't remember the detailed motion of the microscopic constituents, and it replaces it by a statistical description such as the local temperature. Most of the degrees of freedom are then obviously lost.

This post imported from StackExchange Physics at 2014-04-01 16:24 (UCT), posted by SE-user Luboš Motl
Boltzmann's theorem isn't - and hasn't ever been - any resolution to a paradox that existed. It is just a rigorous proof of a statement - the second law of thermodynamics - that was believed as a sacrosanct principle long before most physicists thought that thermal phenomena are due to chaotic motion of atoms. Instead, you seem to be asking about the resolution of a (fringe science) Loschmidt's paradox. Well, the entropy increases - behaves asymmetrically - in a Universe with T-invariant microscopic laws because the logic describing the Universe has an arrow, the logical arrow of time.

This post imported from StackExchange Physics at 2014-04-01 16:24 (UCT), posted by SE-user Luboš Motl
The thermodynamic arrow of time is simply inherited and proved to coincide with the logical arrow of time, and the H-theorem is just the first specific way to prove how this occurs in some quantitative detail. But of course, the H-theorem still has to assume the logical arrow of time - that the past evolves from the future, and not the other way around. No universe with time could exist without a logical arrow of time. The past and future are asymmetric because the past is the "assumptions" and future is its "logical consequences", and assumptions and their implications are not symmetric.

This post imported from StackExchange Physics at 2014-04-01 16:24 (UCT), posted by SE-user Luboš Motl
I wanted to say that in the effective macroscopic theories, the proposition that the "detailed microscopic degrees of freedom are lost" doesn't mean that they're lost in principle. It just means that by the very definition of the effective theory, these degrees of freedom are deliberately thrown away - denied - by the person who uses the effective theory. But this detailed information is needed to reverse the motion. When it's thrown away, the evolution is irreversible - and non-unitary. However, in principle, with all the knowledge, the evolution is unitary and reversible.

This post imported from StackExchange Physics at 2014-04-01 16:24 (UCT), posted by SE-user Luboš Motl
However, in principle, with all the knowledge, the evolution is unitary and reversible, yes, but only observers who can perform global measurements have access to all the knowledge about the system. Any physical observers, such as you and me for instance, can only perform local measurements. The formation of an (apparent) horizon for these observers is a measure of their lack of knowledge about the system. Therefore no (realistic, low-energy) observers can deduce the entire state of the system and the evolution they perceive will therefore appear to be dissipative.

This post imported from StackExchange Physics at 2014-04-01 16:24 (UCT), posted by SE-user user346

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOverf$\varnothing$ow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...