What are the implications of Ansari's discovery of degeneracy in LQG?

[Danny]

Recently, I read a beautiful paper in which it is proven that ANY surface in LQG contains degeneracy, no matter it being a boundary horizon or whatever else. (http://uk.arxiv.org/abs/gr-qc/0603121) This degeneracy is such that the surface degeneracy is A/4. This is a critial discovery in LQG and can follow up Padmanabhan's idea of associating the lack of information in (http://uk.arxiv.org/abs/gr-qc/0405072) into quantum gravity.

So far, Astekar-Baez-krasnov-Corichi in (http://uk.arxiv.org/abs/gr-qc/9710007) were trying to convince folk that if one treats a horizon as a boundary of space at which the space ends, some independent degrees of freedom appears on the boundary.

What physical condition does force one to think about the horizon as the 2-surface at which the space is terminated? This kind of horizon even if classically work, in quantum space is far away from reality. To me, this picture is not convincing. Ansari raises a physical problem against the ABKC model. He says "In classical general relativity, the spacetime metric extends to the interior of the black hole. Thus there is a need for a quantum description of a black hole spacetime that also includes the interior. To do this, we need to identify the horizon within a state that represents the whole quantum geometry."

"Here, I propose that the horizon can be defined in terms of a partition that splits the manifold into two disjoint sections. In loop quantum gravity an eigenstate of quantum geometry is a spin network state. Therefore,
the horizon will be identified within the part of the spin network that lies in a boundary that separates the two regions."

"One immediate consequence of this definition is that the horizon geometry emerges from the contribution of all states of the near horizon region. By introducing the notion of degeneracy of spin network states, it turns out that the horizon states are degenerate."

If he is right, he has found a critial point in LQG which is extremely useful for the purpose of understanding the meaning of "geometrical Quantization".

What comes right is based on how physically different are ABKC's picture and Ansari's new proposal.

Danny
_________________________________
"I like this universe! Don't you?"
http://uk.arxiv.org/abs/hep-th/0409182

 

[Chronos]

A very interesting discussion, Danny. My read is you get unphysical results when you push the LQG envelope. I think that was the main point. A more subtle point was the futility in trying to apply 'the usual suspects' to any coordinate system. Lorentz invariance appears to break down - albeit, I think, for the wrong reasons.

 

[Danny]

My read is you get unphysical results when you push the LQG envelope. I think that was the main point. A more subtle point was the futility in trying to apply 'the usual suspects' to any coordinate system. Lorentz invariance appears to break down - albeit, I think, for the wrong reasons.

I agree Chronos that Ansari's work is a critical point for LQG, if his work is right, which simply seems to be. Though, it cannot rule out or in LQG. There are some dark points Chronos. I think this is not a physical or unphysical result at all. Let me put this in this way. Lee Smolin in his newest paper (http://uk.arxiv.org/hep-th/0605052) summarizes the emergent aspects of LQG. I think, it is the matter of obseravtion only to judge about the destiny of a theory.

If it is true that any gravitational surface owns the entopy A/4, the experts of LQG must explain if any surface is originally degenerate, there is no way to believe in the ABKC's scenario of the boundary being of a horizon, which may add additional entropy to the original one.

Ashtekar quantizes a classical horizon and calls it a quantum horizon and incorporates to it degress of freedom. Ansari starts off with a quantized surface instead of a classical surface. This reminds me of Hawking-Hertog's new paper (http://uk.arxiv.org/abs/hep-th/0602091) in landscape quantization. They introduce a new method of quantization which "leads to a top down approach to cosmology, in which the histories of the universe depend on the precise question asked."

To me, this method of quantization is important; completely right or completely wrong. It reminds me the Penrose statement in A Complete Guidance of the Laws of the Universe: "We have not understood even the quantization procedure yet. Certainly, a quantum world is more than a quantized classical theory."

Danny
_________________________________
"I like this universe! Don't you?"
http://uk.arxiv.org/abs/hep-th/0409182

 

[marcus]

Danny,
there is an intriguing footnote on page 1 of that Ansari paper which says that

"A different perspective of horizon based on QUANTUM INFORMATION..."
was introduced in http://arxiv.org/gr-qc/0508085
and in http://arxiv.org/gr-qc/0603008

if you happen to know those papers, can you explain briefly what Ansari is talking about?

there is obviously now a split in the QG community about the Immirzi and some people are saying Log(3) and other people are saying transcendental----like 0.274.

an onlooker like myself cannot take sides but can only be glad because difficult to resolve issues sometimes force people to achieve new ideas, and I am hopeful that some new physical understanding will come out of settling the Immirzi.

I am interested in what you might say about this. Does the QUANTUM INFORMATION way to define the horizon offer a possibility of resolving contradictions about the Immirzi? Is there anything simple you can say about it, if you know what Ansari is talking about in this footnote.

thanks in advance for any comment

=================
In case anyone reading this does not know of the split, here is a thread with links to papers by the
Transcendentalists
https://www.physicsforums.com/showthread.php?t=120179
these are people like Ghosh Mitra and Corichi, and one may say also Meissner although he found a different number

on the other hand the Logarithmists are the majority and I guess would include almost anybody you could think of. I am not sure but I guess Ashtekar and Smolin and many others. Maybe Danny can tell us who actually is still a Logarithmist-----at least Ansari but my impression is a big number of others.

If I have misunderstood the division over the Immirzi, please correct me and help us get it right! I mean get the division right, not get the Immirzi right

 

[selfAdjoint]

Padmanabhan's takeaway assertion is that every class of observers has a horizon, a two-surface in three-space and every two-surface in three-space can be viewed as the horizon of some class of observers. Ansari's work shows, for the class of closed surfaces, that surfaces behave like horizons in LQG when quantized. This is not at all a defect of LQG, although it may contradict some nonce speculations by well known LQG gurus.

 

[Chronos]

The assumption of closed surfaces is a stretch IMO. Constructing spacetime in this manner leads to paradoxes, again IMO.

 

[marcus]

I can tell you are excited, Chronos.
My kvetching about the Immirzi seems to have been off the mark. But it comes up here and the disagreement on the value is noticeable.

about every closed surface having as much entropy as a BH horizon of the same area it strikes me as just too crazy. Sorry to be superficial but Ansari is a Smolin grad student. Does he have the right to cause such trouble and make turmoil in the family business?

If he is willing, Danny may be able to tell us something we don't suspect that would put this paper of Ansari in a different light. there was an (I think) deeper paper from Perimeter about horizons recently

 

[selfAdjoint]

Well it's not clear what the entropy on an infinite horizon would mean; I think Ansari's whole thesis needs the compactness( finite cover by neighborhoods). This doesn't mean infinite horizons are eliminated from quantization, just that Ansari's methods don't work on them.

 

[marcus]

I have to say, even though nominally off topic, that this paper that Ansari footnotes
http://uk.arxiv.org/abs/gr-qc/0603008
is quite interesting and I wish we could get someone knowledgeable to discuss it with
here is an exerpt from page 23

===quote===
Our goal is to understand the (quantum) metric defined by a spin network state, without referring to any assumed embedding of the spin network in a (background) manifold. We support the basic proposal that a natural notion of distance between two vertices (or more generally two regions) of that spin network is provided by the correlations between the two vertices induced by the algebraic structure of the spin network state. Two parts of the spin network would be close if they are strongly correlated and would get far from each other as the correlations weaken. Our set-up is as follows. We consider two (small) regions, A and B, of the spin network...
A first inspiration is quantum field theory on a fixed background. Considering a (scalar) field phi for example, the correlation <phi(x)phi(y)> between two points x and y in the vacuum state depends (only) on the distance d(x, y) and actually decreases as 1/d(x, y)^2 in the flat four-dimensional Minkowski space-time. Reversing the logic, one could measure the correlation...
===endquote===

the paper tries out doing geometry with only the spin-network state, not embedded in anything. that's interesting

===continued===
...the correlation <phi(x)phi(y)> between the value of a certain field phi at two different space-time points and define the distance in term of that correlation.

Indeed just as the correlations in QFT contain all the information about the theory and describes the dynamics of the matter degrees of freedom, we expect in a quantum gravity theory that the correlations contained in a quantum state to fully describe the geometry of the quantum space-time defined by that state.

Another inspiration is the study of spin systems, in condensed matter physics and quantum information [14, 15, 21]. Such spin systems are very close mathematically and physically to the spin networks of LQG. The key difference is that spin systems are physical systems embedded in a fixed given background metric (usually the flat one) while spin networks are supposed to define that background metric themselves. Looking at spin systems, we notice that the (total) correlation between two spins usually obey a power law with respect to the distance between these two spins. We would like to inverse this relation in the context of LQG: using a similar power law, we could reconstruct the distance between two “points” in term of a well-defined correlation between the corresponding parts of the spin network.

===endquote===

the verb should be either "to invert" or "to reverse" but the idea is clear

 

[hellfire]

To classicaly obtain the entropy of a black hole one has to insert a temperature into the second law of black hole mechanics. Usually this temperature is obtained from the Hawking radiation at infinity of a scalar field. If one assumes that entropy should be entanglement entropy, the degrees of freedom of the scalar field as well as the gravitational field inside the horizon should contribute to trace the total density matrix and further on to obtain the reduced density matrix for the outside of the horizon. This should be used to calculate the von Neumann entropy as entanglement entropy. However, in the approach discussed here only the gravitational degrees of freedom were taken into account. This does not seam consistent to me, or at least it does not seam a trivial step. What am I missing?

 

[Danny]

Marcus: Thanks for inviting me to another thread. I will read it but it seems to be too long! I will write about the quantum information appraoch soon. it is basically a thrid appraoch different from Ansari's and isolated horizon. Thanks for asking.

Self-adjoint: My read is that any single node state is degenerate, no matter if the underlying surface is closed or not. This degeneray is robust and independent of imbedding.

Hellfire: Intersting question! I am not quite sure why Mohammad has chosen this title for his work, while his work is based on defining a new degeneracy.

Does anybody know about other degeneracies that might exist in LQG or any similar theory? I am focusing on the interpretations of different degeneracies and classifying them.

Danny