Understanding Entropy in LQG: Evidence from Spin Network Systems

[Spin_Network]

This is a great paper :http://arxiv.org/abs/gr-qc?0505111

I know of 4 actual/specific systems that allready exist that are confirmation of the said paper with respect to spin network?

 

[marcus]

tinkered with spelling, fixed link:

"This is a great paper http://arxiv.org/abs/gr-qc/0505111
I know of 4 actual/specific systems that already exist that are confirmation of the said paper with respect to spin networks."

Entropy and Area in Loop Quantum Gravity
John Swain
7 pages, this essay received an Honourable Mention in the Gravity Research Foundation Essay Competition 2005; accepted for publication by IJMP (Int'l Journal of Mathematical Physics)

"Black hole thermodynamics suggests that the maximum entropy that can be contained in a region of space is proportional to the area enclosing it rather than its volume. I argue that this follows naturally from loop quantum gravity and a result of Kolmogorov and Bardzin' on the the realizability of networks in three dimensions. This represents an alternative to other approaches in which some sort of correlation between field configurations helps limit the degrees of freedom within a region. It also provides an approach to thinking about black hole entropy in terms of states inside rather than on its surface. Intuitively, a spin network complicated enough to imbue a region with volume only let's that volume grow as quickly as the area bounding it."

that is a nice intuition, it could really help someone to understand why entopy acts like that, if spin networks are a good diagram for quantum geometry

and it could help someone to believe in spin networks, if it turned out to give the right result.

thanks for tagging that John Swain paper, maybe I saw it earlier and the coin got stuck in the slot, so you gave it a tap.

 

[Spin_Network]

Thanks marcus, it is refreshing to know that you don't let anything pass by!

I would have placed it elsewhere, it has a relevance to minimum length and a very interesting angle pertaining to Fractal Generation, the recent papers you highlighted:http://arxiv.org/abs/hep-th/0511021

goes well with the J Swain paper?

 

[marcus]

Thanks marcus, it is refreshing to know that you don't let anything pass by!
...

I meant to say that I HAD let it slip by, didnt notice the interest or forgot, the first time. So thanks for spotting it! You like to be in the crow's nest and you are good there, I think.

 

[mccrone]

Swain - "What is being argued here is precisely that this may not be the case when one thinks about spin networks physically. In other words, instead of writing down a spin network in the usual way, thinking of the edges as 1-dimensional and the nodes as 0-dimensional, one should take the physical interpretation seriously and “thicken” the edges so that they have 2-dimensional cross-sections and the nodes so that they are small 3-dimensional balls. The actual sizes are unimportant as long as there is some minimum, which we already know from the quantization of area and volume
in loop quantum gravity."

Hey Spin, is this the bit that excites your interest?

You can also arrive at this same picture using a logic of self-organising, or semiotic, constraint.

Swain makes the correct point, but he has no real "mechanism" for thickening the lines. He can only appeal to a commonsense physicalism to correct the standard Euclidean mathematical imagery.

There are two ways to construct geometry - mechanical construction where you build up from 0D points, or organic/semiotic constraint where you constrain towards the desired dimensionality. So shrink a volume to an asymptote and you get a plane. Do the same to the plane to make a line, and then a line to a point.

A semiotic view of dimensionality would be much richer than this of course. But you can see how it turns Swain's problem on its head. We would start with the assumption that edges are multi-dimensional and have to be constrained - by a context, a "living" system of interpretance - towards a highly constrained 1D existence.

As a matter of (organic) logic, an actual 1D edge would be a mathematical fiction. The commonsense physical view would say that the approach to a 1D limit would be asymptotic. And the scale of the eventual "cut off" would be determined by the properties of the particular system exerting the constraint.

What is not clear to me as yet is whether cramming a volume with circuitry is that good a way of thinking about the situation. Well it is probably correct that stuffing a space full of crisp entropic bits will see a reduction in dimensionality.

Before anything is stuffed into it, the space will be a vagueness - a realm of potential - rather than just an empty space. So to fill it with crisp entropic bits, you are in effect stuffing it with both atoms and void. And if you then just measure the space by the number of entropic atoms you are able to create, then neglect the amount of void needed to frame the atoms. there will indeed seem a drop in the available dimensionality.

Cheers - John McCrone.

 

[Spin_Network]

Swain - "What is being argued here is precisely that this may not be the case when one thinks about spin networks physically. In other words, instead of writing down a spin network in the usual way, thinking of the edges as 1-dimensional and the nodes as 0-dimensional, one should take the physical interpretation seriously and “thicken” the edges so that they have 2-dimensional cross-sections and the nodes so that they are small 3-dimensional balls. The actual sizes are unimportant as long as there is some minimum, which we already know from the quantization of area and volume
in loop quantum gravity."
Hey Spin, is this the bit that excites your interest?
You can also arrive at this same picture using a logic of self-organising, or semiotic, constraint.
Swain makes the correct point, but he has no real "mechanism" for thickening the lines. He can only appeal to a commonsense physicalism to correct the standard Euclidean mathematical imagery.
There are two ways to construct geometry - mechanical construction where you build up from 0D points, or organic/semiotic constraint where you constrain towards the desired dimensionality. So shrink a volume to an asymptote and you get a plane. Do the same to the plane to make a line, and then a line to a point.
A semiotic view of dimensionality would be much richer than this of course. But you can see how it turns Swain's problem on its head. We would start with the assumption that edges are multi-dimensional and have to be constrained - by a context, a "living" system of interpretance - towards a highly constrained 1D existence.
As a matter of (organic) logic, an actual 1D edge would be a mathematical fiction. The commonsense physical view would say that the approach to a 1D limit would be asymptotic. And the scale of the eventual "cut off" would be determined by the properties of the particular system exerting the constraint.
What is not clear to me as yet is whether cramming a volume with circuitry is that good a way of thinking about the situation. Well it is probably correct that stuffing a space full of crisp entropic bits will see a reduction in dimensionality.
Before anything is stuffed into it, the space will be a vagueness - a realm of potential - rather than just an empty space. So to fill it with crisp entropic bits, you are in effect stuffing it with both atoms and void. And if you then just measure the space by the number of entropic atoms you are able to create, then neglect the amount of void needed to frame the atoms. there will indeed seem a drop in the available dimensionality.
Cheers - John McCrone.

Swain - "What is being argued here is precisely that this may not be the case when one thinks about spin networks physically. In other words, instead of writing down a spin network in the usual way, thinking of the edges as 1-dimensional and the nodes as 0-dimensional, one should take the physical interpretation seriously and “thicken” the edges so that they have 2-dimensional cross-sections and the nodes so that they are small 3-dimensional balls. The actual sizes are unimportant as long as there is some minimum, which we already know from the quantization of area and volume
in loop quantum gravity."
Hey Spin, is this the bit that excites your interest?
You can also arrive at this same picture using a logic of self-organising, or semiotic, constraint.
Swain makes the correct point, but he has no real "mechanism" for thickening the lines. He can only appeal to a commonsense physicalism to correct the standard Euclidean mathematical imagery.
There are two ways to construct geometry - mechanical construction where you build up from 0D points, or organic/semiotic constraint where you constrain towards the desired dimensionality. So shrink a volume to an asymptote and you get a plane. Do the same to the plane to make a line, and then a line to a point.
A semiotic view of dimensionality would be much richer than this of course. But you can see how it turns Swain's problem on its head. We would start with the assumption that edges are multi-dimensional and have to be constrained - by a context, a "living" system of interpretance - towards a highly constrained 1D existence.
As a matter of (organic) logic, an actual 1D edge would be a mathematical fiction. The commonsense physical view would say that the approach to a 1D limit would be asymptotic. And the scale of the eventual "cut off" would be determined by the properties of the particular system exerting the constraint.
What is not clear to me as yet is whether cramming a volume with circuitry is that good a way of thinking about the situation. Well it is probably correct that stuffing a space full of crisp entropic bits will see a reduction in dimensionality.
Before anything is stuffed into it, the space will be a vagueness - a realm of potential - rather than just an empty space. So to fill it with crisp entropic bits, you are in effect stuffing it with both atoms and void. And if you then just measure the space by the number of entropic atoms you are able to create, then neglect the amount of void needed to frame the atoms. there will indeed seem a drop in the available dimensionality.
Cheers - John McCrone.

Hi John, you certainly would be correct in your interpretation, especially with regard to Swain Quote.

I have been facinated by a number of recent papers, the J Swain one really caught my attention due to it's insightfull content for Entropic Area's (2-D say) constraining Continuous (3-D say Riemann sphere volume?)..this is something that I have been handwaving about for sometime.

Drawing a bounded area of 3-Dimensionional lattice,(which was quite difficult on ordinary A-4 paper!), I came across an interesting aspect of Geometry I had no prior knowledge of, which really caught my attention, so I had to seek out a number of books to aid my lack of understanding Penrose:Road To Reality, and Karl Sabbagh's:Dr Reimann's Zero's.

I do not have the Mathamatical wizzardry of the average person, but I am learning!

Now what you have so clearly stated in your post, is an independant logical explination of probable cause?..which I do so admire , so let me extrapolate a little, without the breaking of forum guidlines, the PF does not like users to express any independant thinking.

Simplistic Overview:

Take an ordinary 3-D 'VOLUME' of a Hydrogen Atom, it is bounded 'QUASI-SURFACE-AREA' by the Electron with a Dimensionality that is undetermined, but known to exhibit less than 3-D . When the Area is broken from outside, by an ordinary Photon, the inside volume is expanded by a certain amount, caused by the surface area product 'Electron' dimensionally sidestepping the Photon.

The Electron moves and its movement increases the Atomic Volume, from a certain geometric perspective, one can conclude that an area product has allowed the internal constrained volume to slightly increase.

A simple Bossa-Nova experiment in Condensed Matter shows Volume Expansion?

The Proton, Neutron volume difference, also is another specific example.

The Galactic Halo, is been penetrated from all other infalling Light products from outside the Galaxy, this is another Volume expansion example?

The mechinism for dimensional interplay between 3-D and 2-D is all you really need, starting from the Quantum, up to the Edge of the Visible Universe?

The critical constriant is of course important, to allow inside volumes to be 3-D, whilst exhibiting at a intersection of 2-D to 3-D boundary, is almost like an Electron Field propergating 'to' and 'from' a specific Entropic state/