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Loop quantum gravity and Planck-size black hole entropy

  1. Mar 23, 2007 #1


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    Loop quantum gravity and Planck-size black hole entropy
    Alejandro Corichi, Jacobo Diaz-Polo, Enrique Fernandez-Borja
    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.
    Extra Dimensions & black holes
    Study of Black Holes with the ATLAS detector at the LHC
    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
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Mar 23, 2007 #2


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    Dearly Missed

    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.
    Last edited by a moderator: May 2, 2017
  4. Mar 24, 2007 #3


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    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.
  5. Mar 25, 2007 #4


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    The Barbero-Immirzi parameter, appears to me, to be another way to deal with minimum length.

    Quantum gravity and minimum length
    Luis J. Garay
    09 May 1995
    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

    http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Agr-qc%2F0304055 [Broken]
    Immirzi Ambiguity, Boosts and Conformal Frames for Black
    Luis J Garay and Guillermo A Mena Marug´an
    15 April 2003
    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)

    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

    CERN is concern with validating SUSY (higgs) and her offsprings. Also, a little bit of Randall’s fifth dimension.
    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)
    Last edited by a moderator: May 2, 2017
  6. Apr 2, 2007 #5


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    “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".
  7. Apr 2, 2007 #6
    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.
  8. Apr 3, 2007 #7


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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?
    Last edited: Apr 3, 2007
  9. Apr 3, 2007 #8


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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.

    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.
  10. Apr 3, 2007 #9
    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.
  11. Apr 3, 2007 #10


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    william donnelly
    Are you diverting this thread?????
  12. Apr 3, 2007 #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.
  13. Apr 3, 2007 #12


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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.
  14. Apr 3, 2007 #13


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    Other people have done the reduction to two dimensions by using different approaches.
    Department of Physics, Northeastern University, 110 Forsyth Street
    Boston, MA 02115
    30 Oct 2005

    Top Cited Articles of All Time (2003 edition)
    Top Cited Articles of All Time (2006 edition)
    In 2003 .. 455 times, in 2006 .. 659 times
    G. ’t Hooft
    19 Oct 1993
    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.


    yes .... this post is being added to my blog
  15. Apr 4, 2007 #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.
  16. Apr 4, 2007 #15


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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.
  17. Apr 7, 2007 #16


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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
    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.
    Quantum Geometry and its Implications for Black Holes∗
    Martin Bojowald
    28 July 2006
    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
    Therefore, Schwarzschild radius z=0 and that at the horizon you have only 2d. No orthogonal spins (right angle).
    On the counting of black hole states in loop quantum gravity
    Sergei Alexandrov_
    11 Aug 2004
    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.
    Quantum Isolated Horizons: The Planck Scale Regime
    Alejandro Corichi
    Last edited by a moderator: May 2, 2017
  18. Apr 8, 2007 #17


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    I have just added the following to my blog.


    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.
  19. Apr 10, 2007 #18


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    Another entry for my blog
    http://www.gravity.psu.edu/research/articles/solvaynet.pdf [Broken]
    Abhay Ashtekar
    March 6, 2006
    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.
    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.

    Lattice refining loop quantum cosmology, anisotropic models and stability
    Martin Bojowald∗
    09 April 2007
    Last edited by a moderator: May 2, 2017
  20. Apr 13, 2007 #19


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    All approaches are about symmetry and minimum length.

    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??).

    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.

    Attached Files:

    Last edited by a moderator: May 2, 2017
  21. Apr 14, 2007 #20


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    Thanks to Marcus, bring out this reference, I now have a better understanding of the Immirzi parameter.
    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
    The Immirzi parameter in quantum general relativity
    Carlo Rovelli
    22 May 1997
    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.
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