Loop quantum gravity and Planck-size black hole entropy

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Loop quantum gravity and Planck-size black hole entropy
http://arxiv.org/abs/gr-qc/0703116
Alejandro Corichi, Jacobo Diaz-Polo, Enrique Fernandez-Borja
Abstract
The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are reviewed. These results are consistent with an asymptotic linear relation (that fixes uniquely a free parameter of the theory) and a logarithmic correction with a coefficient equal to -1/2. The account is tailored as an introduction to the subject for non-experts.
Unfortunately ... this non-expert .... did not see the light.

I did do some research into what is expected to happen at CERN.
I'll just list the links for those who want to persue this line of information.
The fun stuff, my speculations, are in my blog.
------------
http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/EXOTICS/XDim/ExtraDimensions.htm
Extra Dimensions & black holes
https://twiki.cern.ch/twiki/bin/view/Atlas/BlackHoleCSCNoteWikiPage
BlackHoleCSCNoteWikiPage
http://cdsweb.cern.ch/record/681502
Study of Black Holes with the ATLAS detector at the LHC
http://doc.cern.ch//archive/electronic/hep-ph/0411/0411095.pdf
http://arxiv.org/PS_cache/hep-ph/pdf/0205/0205284.pdf [Broken]
p-brane production in Fat brane or Universal extra dimension scenario
http://arxiv.org/PS_cache/hep-ph/pdf/0702/0702187.pdf [Broken]
Black Holes at LHC?
http://arxiv.org/PS_cache/hep-ph/pdf/0702/0702078.pdf [Broken]
Signatures of Spherical Compactification at the LHC
http://arxiv.org/PS_cache/hep-ph/pdf/0502/0502005.pdf [Broken]
Physics Beyond the Standard Model: Exotic Leptons and Black Holes at Future Colliders
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jal
 
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  • #2
marcus
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Loop quantum gravity and Planck-size black hole entropy
http://arxiv.org/abs/gr-qc/0703116
Alejandro Corichi, Jacobo Diaz-Polo, Enrique Fernandez-Borja
...
You have identified an interesting one. I will give some background. Corichi is one of the organizers of this year's main international QG conference---Loops '07----which will be at Mexico's National University (u.n.a.m) in Morelia this summer.

He knows PF and I think sometimes visits and checks the forum out. If he does, it may surprise him to see the title of his paper "LQG and Planck-size BH entropy" on our menu.

Here is an earlier related paper:

http://arxiv.org/gr-qc/0605014 [Broken]
Quantum geometry and microscopic black hole entropy
AlejandroCorichi, Jacobo Díaz-Polo, and Enrique Fernández-Borja
10 pages, 7 figures

"Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that are consistent with a black hole of a given horizon area A0 are computed and the statistical entropy, as a function of the area, is obtained for A0 up to 550 L2P The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to gamma = 0.274, which has been previously obtained analytically. However, a new and unexpected functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation."


Incidental bit of information in case anyone is interested: Corichi et al numerical work, counting BH states, has the effect of helping determine a number called the Barbero-Immirzi parameter. This is a key parameter in Loop QG. There is sure to be some active discussion of the B-I number and BH state-counting at this summer's Loops '07 conference.
Corichi's value for the Barbero-Immirzi parameter is about 0.274, it turns out to be the solution to a certain equation and can be calculated as accurately as one wants, but that is the approximate value.
 
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  • #3
jal
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He knows PF and I think sometimes visits and checks the forum out. If he does, it may surprise him to see the title of his paper "LQG and Planck-size BH entropy" on our menu.


"Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that are consistent with a black hole of a given horizon area A0 are computed and the statistical entropy, as a function of the area, is obtained for A0 up to 550 L2P The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to gamma = 0.274, which has been previously obtained analytically.
However, a new and unexpected functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation."


Corichi's value for the Barbero-Immirzi parameter is about 0.274, it turns out to be the solution to a certain equation and can be calculated as accurately as one wants, but that is the approximate value.
Barbero-Immirzi parameter is about 0.274 which is 10 times the amount that is obtained from applying the Quantum Minimum Length Structure.
I definetely hopes someone can give me an explanation of such a coincidence.
jal
 
  • #4
jal
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The Barbero-Immirzi parameter, appears to me, to be another way to deal with minimum length.

http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9403/9403008.pdf
Quantum gravity and minimum length
Luis J. Garay
09 May 1995
Abstract
The existence of a fundamental scale, a lower bound to any output of a
position measurement, seems to be a model-independent feature of quantum
gravity. In fact, different approaches to this theory lead to this result. The
key ingredients for the appearance of this minimum length are quantum me-
chanics, special relativity and general relativity. As a consequence, classical
notions such as causality or distance between events cannot be expected to be applicable at this scale. They must be replaced by some other, yet unknown, structure.

you can reduce the coordinate distance between two events as much as you want even though the proper distance between them will not decrease beyond Planck’s length.
Then there is a QMLS.

http://arxiv.org/PS_cache/gr-qc/pdf/0610/0610056.pdf [Broken]
Quantum Mechanics and the Generalized Uncertainty Principle
Jang Young Bang_ and Micheal S. Berger†
01 Dec 2006
VI. SUMMARY AND CONCLUSIONS
We have derived the generalized uncertainty principle from a toy model of discretized space by considering quantum mechanics on a circle where the compacification involves the momentum. This model may be useful in exploring how the ultraviolet limit is approached in more realistic models of discrete spacetime or models of quantum gravity with a fundamental or minimum length. This may result in an improved understanding of the origin of the generalized uncertainty principle in theories of quantum gravity.

http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Agr-qc%2F0304055 [Broken]
Immirzi Ambiguity, Boosts and Conformal Frames for Black
Holes
Luis J Garay and Guillermo A Mena Marug´an
15 April 2003
Abstract
We analyze changes of the Immirzi parameter in loop quantum gravity and
compare their consequences with those of Lorentz boosts and constant conformal transformations in black hole physics.
-----------------
http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703069.pdf [Broken]
High-order gauge-invariant perturbations of a spherical spacetime
David Brizuela, Jos´e M. Mart´ın-Garc´ıa, and Guillermo A. Mena Marug´an
Instituto de Estructura de la Materia, CSIC, Serrano 121-123, 28006 Madrid, Spain
(Dated: March 13, 2007)
We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l = 0, 1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants.

----------------
Already cited in blog
http://arxiv.org/PS_cache/gr-qc/pdf/9710/9710007.pdf [Broken]
Quantum Geometry and Black Hole Entropy
A. Ashtekar, J. Baez, A. Corichi, K. Krasnov

If a single edge punctures a 2-surface transversely, it contributes an area proportional to sq root j(j + 1).
(note: The Barbero-Immirzi parameter)
Smolin [10] was led to introduce gravitational surface states which could be identified with the states of the SU(2) Chern-Simons theory on a surface with punctures.
Second, Rovelli [11], motivated by the work of Krasnov [12], estimated the number of spin-network states which endow a 2-sphere with a given, large area and applied this estimate to black hole horizons.
(note: There would be 6 in a quantum Black Hole)
In the classical theory that we have described, the volume and surface degrees of freedom cannot be separated: all fields on S are determined by fields in the interior of M by continuity.
However, in the quantum theory, the fields describing geometry become discontinuous in certain precise sense [6], and the fields on S are no longer determined by fields in M; in this case there are independent degrees of freedom ‘living’ on the boundary. These surface degrees of freedom are the ones that account for black hole entropy in our approach.

Therefore, (5) implies that the surface states have support only on generalized connections that are everywhere flat except at a finite number of points pi.
It turns out that such generalized connections can be identified with ordinary connections with distributional curvature.
--------------
CERN is concern with validating SUSY (higgs) and her offsprings. Also, a little bit of Randall’s fifth dimension.
https://www.physicsforums.com/showthread.php?t=119294
Therefore, since there is about 2 years left before the first run, what is LQG or any other group doing to make sure that they are ready for when the data comes in?
I think that what is needed is a sound presentation for what I expect will be notice/interpreted …. Black holes and extradimensions.( what I identify as QMLS)
jal
 
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  • #5
jal
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http://en.wikipedia.org/wiki/Schwarzschild_metric
The Schwarzschild solution appears to have singularities at r = 0 and r = rs; some of the metric components blow up at these radii. Since the Schwarzschild metric is only expected to be valid for radii larger than the radius R of the gravitating body, there is no problem as long as R > rs. For ordinary stars and planets this is always the case. For example, the radius of the Sun is approximately 700,000 km, while its Schwarzschild radius is only 3 km.
One might naturally wonder what happens when the radius R becomes less than or equal to the Schwarzschild radius rs. It turns out that the Schwarzschild solution still makes sense in this case, although it has some rather odd properties. The apparent singularity at r = rs is an illusion; it is an example of what is called a coordinate singularity. As the name implies, the singularity arises from a bad choice of coordinates. By choosing another set of suitable coordinates one can show that the metric is well-defined at the Schwarzschild radius.
“The apparent singularity at r = rs is an illusion;”.

At the Schwarzschild radius there exist only x, y, direction. The z direction has been surpressed.
At the Schwarzschild radius you are into "flatland". You have crossed into the second dimension.
Why not admit it?

When you have "something" entering from the z direction it cannot continue in the z direction. The z, direction no longer exist.
You cannot go throught "flatland" and come out of the otherside and continue in the z direction. There is no z direction on the other side of "flatland".
jal
 
  • #6
At the Schwarzschild radius there exist only x, y, direction. The z direction has been surpressed.
At the Schwarzschild radius you are into "flatland". You have crossed into the second dimension.
Why not admit it?
This is a common misconception. Nothing magical happens at the horizon. The metric keeps it's signature, the spacetime dimension stays the same. An observer falling into a large enough black hole wouldn't even know anything was different.
 
  • #7
Chronos
Science Advisor
Gold Member
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jal, you are a trip. Your QIT side is showing - I deeply sympathize. In the end, IMO, the universe will sheepishly admit she is a quantum computer. Lucien Hardy, anyone?

A comment on William Donnelly's observation [which is well presented and cogent] - the real problem with background independence is the backdoor. A more pointed question - signature with respect to what?
 
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  • #8
jal
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:smile: heheh .... What is showing is my interest in Minimum scale. You can get the up todate info that I have been gathering at my blog.
I have not been able to find a paper that applies "spaghettified" to the curvature of space-time at a black hole.
Of course, If you don't support a concept of space quanta that can be affected by gravity, then, you will not be able to se the "spaghetti".
As you approach a black hole, z would be reduced to minimum length and at the Schwarzschild radius there exist only x, y, direction. The z direction has been surpressed.

http://en.wikipedia.org/wiki/Black_hole
Mass bends space-time and creates a gravity field that is capable of accelerating both energy and matter. A black hole contains enough mass in a small enough volume to bend space-time enough to force all matter and energy within a certain distance of the center to move only toward the center. For this reason, even light is trapped by the black hole's gravity.

An object in any very strong gravity field is spaghettified (stretched like spaghetti), because:
• The inverse square law means that there is a stronger gravitational pull on the side of the object nearest the source of the gravity field than on the far side.
• In an extremely strong gravity field, the difference in pull is great enough to stretch the object.
Also, space-time has been spaghettified. Therefore, at the Schwarzschild radius space-time has been reduced to two dimensions. In two dimensions forces cannot be orthogonal.Therefore, the information which was contained in a 3D configuration has been spaghettified. The information has been transformed to two dimensions.
It's all very elementary.
Maybe that's why nobody has written a paper about it.
jal
 
  • #9
A comment on William Donnelly's observation [which is well presented and cogent] - the real problem with background independence is the backdoor. A more pointed question - signature with respect to what?
I was just referring to the usual GR equivalence principle. You put some poor experimenter in a box and toss him into the black hole. As long as he's small enough compared to the black hole he'll keep on doing his experiments (including with clocks, rulers, etc.) and not know the difference until he gets close enough to the singularity.

But is sounds you're alluding to something beyond GR. I'd be interested to hear it.
 
  • #10
jal
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william donnelly
Are you diverting this thread?????
jal
 
  • #11
No, I'm not trying to divert the thread. All I've been doing is answering questions posed in this thread. One was by you, and directed to nobody in particular. The other one was by Chronos and was directed to me.

If you prefer, let me get back to your "spaghetti" idea. Objects near the horizon get stretched like spaghetti by tidal forces. But this does not mean the dimensionality of spacetime changes at the horizon any more than the spacetime dimension changes in an ordinary pasta maker. In fact, for large black holes the effect is undetectably small.

I recommend you look at Leonard Susskind's lecture series on black holes, starting with this one: http://pirsa.org/07030028. It is all very introductory, and talks about "spaghettification" at the horizon and related issues.
 
  • #12
jal
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You are trying to divert this thread.
Do your own thinking.
The light cone does not go smaller than the planck scale.
The Inverse Square Law does not start at less than Planck Scale.
The surface of the black hole cannot be quantizied to less than the Planck Scale.
Read some of the previously quoted papers.
This thread is about minimum length and different approaches that tries to get an understanding of minimum length.
jal
 
  • #13
jal
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Other people have done the reduction to two dimensions by using different approaches.
http://arxiv.org/pdf/gr-qc/0505111
ENTROPY AND AREA IN LOOP QUANTUM GRAVITY
JOHN SWAIN
Department of Physics, Northeastern University, 110 Forsyth Street
Boston, MA 02115
Canada
30 Oct 2005

Conclusion
Here something similar happens in that the microstructure of space is modified in LQG, but now the dimension of space is not reduced by a small amount, but all the way from 3 to 2 as distances become small!
-----------------
http://www.slac.stanford.edu/spires/topcites/2003/eprints/to_gr-qc_alltime.shtml
Top Cited Articles of All Time (2003 edition)
http://www.slac.stanford.edu/spires/topcites/2006/eprints/to_gr-qc_alltime.shtml
Top Cited Articles of All Time (2006 edition)
-----------------
In 2003 .. 455 times, in 2006 .. 659 times
http://arxiv.org/pdf/gr-qc/9310026
DIMENSIONAL REDUCTION in QUANTUM GRAVITY†
G. ’t Hooft
19 Oct 1993
With the request to write a short paper in honor of Abdus Salam I am given the opportunity to contemplate some very deep questions concerning the ultimate unification that may perhaps be achieved when all aspects of quantum theory, particle theory and general relativity are combined. One of these questions is the dimensionality of space and time.
The most direct and obvious physical cut-off does not come from non-renormalizability alone, but from the formation of microscopic black holes as soon as too much energy would be accumulated into too small a region. From a physical point of view it is the black holes that should provide for a natural cut-off all by themselves.
This has been this author’s main subject of research for over a decade. A mathematically consistent formulation of the black hole cut-off turns out to be extremely difficult to find, and in this short note I will explain what may well be the main reason for this difficulty: nature is much more crazy at the Planck scale than even string theorists could have imagined.
Therefore, my approach...
Also, space-time has been spaghettified. Therefore, at the Schwarzschild radius space-time has been reduced to two dimensions. In two dimensions forces cannot be orthogonal.Therefore, the information which was contained in a 3D configuration has been spaghettified. The information has been transformed to two dimensions.
It's all very elementary.
Maybe that's why nobody has written a paper about it.

jal

yes .... this post is being added to my blog
 
  • #14
Hi Jal. Yes, I have read the papers you linked in this thread. The first one is just a review of recent work based on the isolated horizon framework in loop quantum gravity, which I commented on in a different thread.

But this paper isn't saying the same thing you are saying - that space becomes 2-dimensional at the Schwarzschild radius. The presence of a minimum length is quite a different idea from the idea of dimensional reduction, though each is an interesting idea in its own right.
 
  • #15
jal
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william donnelly
Thank you.
As you have probably gathered, heheh, I'm kinda hoping that the "math kids" will be able to get a "breakthrough" and that it might be as G. ’t Hooft has speculated, by understanding minimum length and quantum black holes.
jal
 
  • #16
jal
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I have been checking the people and their papers for Loops '07 conference.
Here is what I found with my comments.
slide presentation
http://relativity.phys.lsu.edu/ilqgs/pullin032707.pdf
Spherically symmetric space-times in loop quantum gravity
Jorge Pullin
Full paper
http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703135v1.pdf [Broken]
Loop quantization of spherically symmetric midi-superspaces
Miguel Campiglia1, Rodolfo Gambini1, Jorge Pullin2
------------------
He is looking for something that is not there.
Will not admit that space-time has been spaghettified. Therefore, at the Schwarzschild radius z=0 and that at the horizon you have only 2d.
-----------
http://arxiv.org/PS_cache/gr-qc/pdf/0607/0607130v1.pdf
Quantum Geometry and its Implications for Black Holes∗
Martin Bojowald
28 July 2006
The whole spectrum of flux operators is then discrete implying, since fluxes encode spatial geometry, discrete spatial quantum geometry. This translates to discrete spectra also of more familiar spatial geometric expressions such as area or volume.
p. 7 Thus, the system provides an interesting consistency check of the general scheme by determining which boundary, the singularity or the horizon, is removed upon quantization. The horizon boundary should not be removed because at this place our minisuperspace approximation breaks down. Indeed it is just the classically singular boundary which is removed by including the sign of pc in the analysis, providing a non-trivial test of the singularity removal mechanism of loop quantum cosmology.
… Instead, matter will be able to leave the black hole region, defined by the presence of trapped surfaces and a horizon H [46, 47, 48, 49], after the evaporation process restoring all correlations.
The trapped surfaces and a horizon H is the last chance … this is the region where z = the quantum minimum length

Note for newbies: spin
http://en.wikipedia.org/wiki/Spin_(physics)
There is one irreducible representation of SU(2) for each dimension.
For example, spin 1/2 particles transform under rotations according to a 2-dimensional representation, which is generated by Pauli matrices:
Therefore, Schwarzschild radius z=0 and that at the horizon you have only 2d. No orthogonal spins (right angle).
-------------------
http://arxiv.org/PS_cache/gr-qc/pdf/0408/0408033v1.pdf
On the counting of black hole states in loop quantum gravity
Sergei Alexandrov_
11 Aug 2004
Abstract
We argue that counting black hole states in loop quantum gravity one should take
into account only states with the minimal spin at the horizon.
p. 3 On the other hand, it is known that approaching the equilibrium the black hole looses all its “hairs” and, if there is no angular momentum, it becomes spherically symmetric. Thus, all non-homogeneity of the horizon geometry should disappear. In terms of loop quantum gravity this means that the interaction changes the punctures on the horizon in such a way that their distribution becomes homogeneous, given by a single spin value.

Whether one can introduce an internal space with the property (8) will be investigated elsewhere.
Is there something on the other side of the 2d, the horizon, the Schwarzschild radius?
The present math approaches cannot tell.
Since I suspect that the minimum length is at 10^- 18 and that the smallest black hole will be 24 units, CERN will be able to produce mini black holes for us to study.
---------------
From the ILQGS series http://relativity.phys.lsu.edu/ilqgs/
I found these slides (Tuesday November 7th ) which are easier to understand than the paper which started this thread.
http://relativity.phys.lsu.edu/ilqgs/corichi111406.pdf
Quantum Isolated Horizons: The Planck Scale Regime
Alejandro Corichi
------------
jal
 
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  • #17
jal
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I have just added the following to my blog.

http://online.kitp.ucsb.edu/online/singular_m07/ashtekar/

Jan 12, 2007
Quantum Physics Beyond Classical Singularities: Cosmological Models
Prof. Abhay Ashtekar, Penn State & KITP

look at slide # 18 & 19

“a” max approx. 23 planck length
universes with “a” max. aprox. 25 planck length already semiclasical.

Now go read my blog.
From a Quantum Minimum Length Structure approach, I have arrives at “our universe”, having 24 units.

We use to have a “Big Bang” with inflation and expansion … now we have a “Bounce” with expansion.
However, if you do a realistic/semiclasical stop at 24 units you get the approach that I have been advocating which includes a new mechanism for explaining expansion.
Jal
 
  • #18
jal
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Another entry for my blog
http://www.gravity.psu.edu/research/articles/solvaynet.pdf [Broken]
QUANTUM NATURE OF THE BIG BANG IN LOOP QUANTUM COSMOLOGY
Abhay Ashtekar
March 6, 2006
p. 3 …. Riemannian geometry is now quantized: there are well-defined operators corresponding to, say, lengths, areas and volumes, and all their eigenvalues are discrete.
A new representation of the algebra generated by holonomies and triads becomes available.1 We have new quantum mechanics [9].

In loop quantum gravity, the standard Hamiltonian constraint is expressed in terms of the triads E and the curvature F of A. F can be expressed as a limit of the holonomy around a loop divided by the area enclosed by the loop, as the area shrinks to zero. Since there is no operator corresponding to A itself, in the quantum theory the limit does not exist. This is also a ramification of quantum geometry since area is quantized. Thus the quantum nature of geometry suggests that to obtain the quantum Hamiltonian constraint in quantum cosmology, one should shrink the loop only till it has the minimum non-zero eigenvalue of area.
This is where I differ in order to preserve the quantum minimum length.
The loop should only be shrunk to the minimum area that can be enclosed by units of the minimum length. As a result there is a minimum length structure which is enclosing a singularity which I have labeled a void.
the size of the step being dictated by the first non-zero area eigenvalue |i.e., the `area gap'| in quantum geometry. Qualitative differences from the Wheeler-DeWitt theory emerge precisely near the Big Bang singularity. In effect, gravity becomes repulsive near the singularity and there is a quantum bounce.
However, in my approach, there is no bounce. There is just the 2d structure.
--------------
If you have not done so read the following paper.
Standard Theory SU(3)xSU(2)xU(1).…. String …. Have not done it.
Martin Bojowald is the first to address the Inverse Square Law.

http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.1137v1.pdf
Lattice refining loop quantum cosmology, anisotropic models and stability
Martin Bojowald∗
09 April 2007
 
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  • #19
jal
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All approaches are about symmetry and minimum length.

http://arxiv.org/PS_cache/hep-th/pdf/9301/9301028v2.pdf
Knot Theory and Quantum Gravity in Loop Space: A Primer ∗
Jorge Pullin
09 Jan 1992
p. 8 In summary, tetrads have all the information needed to reconstruct the metric of spacetime but there are extra degrees of freedom in them, and this will have a reflection in the canonical formalism.
p. 38 … It is a remarkable fact that there is a connection between General Relativity and Knot Theory at a dynamical level.
-------------

http://arxiv.org/PS_cache/gr-qc/pdf/9504/9504036v1.pdf [Broken]
Spin Networks in Nonperturbative Quantum Gravity
John C. Baez
April 15, 1995

p.14 To apply these results to gauge theory on Rn one must then investigate not only the ‘continuum limit’ in which the lattice spacing goes to zero, but also the ‘large-volume limit’.

If you apply the QMLS then the lattice spacing cannot go to zero.

p. 23 … the Hamiltonian constraint poses serious problems even in the new variables formalism, so called ‘ultraviolet problems’, which might be due to falsely extrapolating our picture of spacetime as a manifold to arbitrarily small length scales.

Therefore, the QMLS solves the problem.

p. 25 … general relativity is all about a metric on spacetime, while gauge
theories are all about a connection on some bundle over spacetime.

p.28 … where a connection on a Riemannian manifold having self-dual curvature 2-form is automatically a solution of the Yang-Mills equation, called an ‘instanton’ [29]. When M is compact, the space of instantons modulo gauge transformations is finite-dimensional.

Would not the QMLS, 24 units, be the smallest allowed?
p.29 … The two basic fields in the Plebanski formalism are a complex-valued
soldering form, that is, 1-form on M with values in CT , and a self-dual Lorentz connection A+, that is, a connection on P+.

When self dual is mentioned, I see the double tetra. (see image)
p.30 … the configuration space of general relativity is no longer the space of all metrics on S. Instead, it is the space A+ of all connections on P+ restricted to S, or more precisely, to some fixed spacelike slice St ⊂ M. As in the metric formulation,
one can separate the equations of motion into evolutionary equations and constraints.

As a result, I see, (look at the image), (with void in the center), created by 12 instantons dancing around the void (knotting??).
http://www.geocities.com/j_jall/3dspace.gif

p. 31 In the self-dual formalism, no conditions on ˜E need hold for it to come from a complex soldering form e.

Would not the minimum length be a condition?

p. 37 … However, Rovelli and Smolin [46] have considered the area of a surface and the volume of a region in S, which are technically simpler, and obtained explicit formulas for their quantum versions as operators on L2(A/G), in terms of the spin network basis. These operators turn out to have discrete spectrum: certain multiples of Planck length squared for the area operator, and certain multiples of the Planck length cubed for the volume operator.

Ahhhh! Here it comes!!! The QMLS?

p. 37 …. Moreover, this prediction of discreteness of area and volume at the Planck scale is absurdly hard to test with present technology!

Since this has been written, others have said that with scaling to 10^-18 CERN would be able to detect this discreteness of area and volume. (the QMLS).
As a result the devil can be pushed to the dynamics to produce some broken symmetry.
So, now you can go and enjoy my blog.
 

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  • #20
jal
549
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Thanks to Marcus, bring out this reference, I now have a better understanding of the Immirzi parameter.
http://arxiv.org/PS_cache/gr-qc/pdf/9806/9806079v1.pdf
Loop quantum gravity and quanta of space: a primer
Carlo Rovelli, Peush Upadhya
Physics Department, University of Pittsburgh, Pittsburgh PA 15260, USA
(May 19, 2006)
19 june 1998
-----------
http://arxiv.org/PS_cache/gr-qc/pdf/9705/9705059v1.pdf
The Immirzi parameter in quantum general relativity
Carlo Rovelli
22 May 1997
Recently, Immirzi has pointed out that the overall scale of these spectra is not determined by the theory [3]. More precisely, Immirzi has considered a certain scale transformation introduced by Barbero [4], and noticed that if we quantize the theory starting from scaled elementary variables, we end up with different spectra for the same geometrical quantities.

Similarly, there are two length scales in quantum gravity: the Planck constant lP = p¯hG/c3 and the quantum of area A0 = 8√3πιl2 P .
Unless some non yet understood requirement fixes the value of the Immirzi parameter, these two length scales are independent.
If the Carlo Rovelli's of this world can take the time to show me why/how I'm wrong .... I will correct my blog.
Otherwise readers will assume that it makes a relationship with quantum black holes.
jal
 
  • #21
jal
549
0
I can only attribute the silence of this forum to the fact that the “seekers” have been correlating information.
On SCALING AND DIMENSIONAL REDUCTION -“Quantum Gravidynamics”
fixed point = minimum length = void created by the structure of double tetra
I find this approach to be a doorway into the dynamics.
http://relativity.livingreviews.org/Articles/lrr-2006-5/ [Broken]
"The Asymptotic Safety Scenario in Quantum Gravity"
by
Max Niedermaier and Martin Reuter
05 Oct 2006
You can start by reading
1.4 Relation to other approaches
Ref. pdf http://ru.arxiv.org/PS_cache/gr-qc/pdf/0610/0610018v1.pdf
---------------------
In case you have not read it yet.
http://arxiv.org/PS_cache/hep-th/pdf/0511/0511021v1.pdf
A Minimal Length from the Cutoff Modes in Asymptotically Safe Quantum Gravity
Martin Reuter and Jan-Markus Schwindt
02 Nov 2005
------------------


Definitions:
Q-TIPS: A cotton swab on a stick. A senior with white hair. A person whose hade ingrown hair that came back out white after hitting calcification of the brain.
Zits: Are what happen when the oil glands in your skin get clogged and pus is what comes out when you pop them. Someone who is young who thinks that he is the first to have discovered the “answer”.
KY: A jelly that is water soluble, fragrance free, alcohol-free, Non-greasy. A person who thinks that he has the “answer” and thinks that he has “made it.”
SEEKER: Someone making a search or inquiry. Someone not standing in the shadow of the elephant.
(BTW, the elephant could be a 2d making a 3d shadow.)
----------------
This will go in my blog under dynamics.
jal
 
Last edited by a moderator:
  • #22
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Black hole entropy quantization????

Hi,

What is your opinion about the new papper about black hole entropy quantization?

It's surprising for me...

What is the physical meaning of this????
 
  • #23
jal
549
0
Entro
What is your opinion about the new papper about black hole entropy quantization?
It's surprising for me...
What is the physical meaning of this????
I'm not sure of which paper you are refering to.
However ...
Calculations for black holes have eliminated the presence of electrical and magnetic fields. It’s a good thing since it agrees with the observations of the astronomers. The astronomers have not found a concentration of electrical or magnetic activities that would be accompanied by the location of black holes.
Electrical and magnetic fields are at 90 degrees (orthogonal). I have not read anything that would suggest that can it be anything but at 90 degrees.
You cannot get 90 degrees to a 2d surface unless you are in 3d.
Therefore, the event horizon of a black hole is 2d and agrees with observations and calculations. (There is a paper here for someone to write, on what is the topological relationship of the tetras and the electrical and magnetic fields; 60 degrees and 90 degrees.)
jal
 
  • #24
2
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Thanks jal, but I was asking about the gr-qc/0609122.

In this article Corichi, Diaz-Polo and Fernandez-Borja say that black hole entropy show a new not expected behaviour, some kind of ladder...

Thanks
 
  • #25
jal
549
0
Thanks jal, but I was asking about the gr-qc/0609122.
In this article Corichi, Diaz-Polo and Fernandez-Borja say that black hole entropy show a new not expected behaviour, some kind of ladder...
Thanks
http://arxiv.org/PS_cache/gr-qc/pdf/0609/0609122v2.pdf
Black hole entropy quantization
Alejandro Corichi, Jacobo D´ıaz-Polo, and Enrique Fern´andez-Borja
Updated 01 May 2007
....some kind of ladder...
Here we shall show that loop quantum gravity, in which area is not quantized in equidistant steps can nevertheless be consistent with Bekenstein’s equidistant entropy proposal in a subtle way.
It's interesting that another simpler approach would also demonstrate that a black hole would be stable only in "non equal steps".
How many units of minimum length/area would you need to add to a sphere to get another larger sphere?
jal
 

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