Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quantum geometry includes matter

  1. Jun 24, 2003 #1

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    A short overview of quantum geometry by Ashtekar (2002)
    http://www.arxiv.org/abs/math-ph/0202008

    A recent paper by Perez (2003) points out that quantum geometry, or Loop Quantum Gravity as it is often called, incorporates matter fields in a divergence-free way without the need for the usual renormalizations to remove infinities. As Thiemann discovered, the infinities do not arise essentially because volumes are quantiized.
    See page 4 of Perez
    http://lanl.arxiv.org/abs/gr-qc/0301113
    and the reference to previous work by Thiemann (1997)
    http://arxiv.org/abs/gr-qc/9705019

    The incorporation of fermions by LQG, in particular, has recently proven essential. Corichi confirmed the theory's SU(2) symmetry by invoking (local) fermion number conservation consistent with the Immirzi constant being 1/8.088 See Corichi(2002)

    http://lanl.arxiv.org/abs/gr-qc/0212126

    Quantum Cosmology

    A recent paper by Ashtekar on Loop Quantum Cosmology shows that the time-zero singularity does not arise in the LQG model of the big bang. The model incorporates matter in an essential way and shows that the extreme conditions at time-zero nevertheless remain bounded. See Astekar et al (2002)

    http://www.arxiv.org/abs/gr-qc/0304074
     
    Last edited: Jun 24, 2003
  2. jcsd
  3. Jun 24, 2003 #2

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    The paper is titled "On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry"

    I hope that Alejandro Corichi's paper (link here) may be seminal---may start a larger "thread" of research papers---and am impressed by this quote:

    "The heuristic physical process of conversion of area quanta to matter quanta via the 'emission of an edge' is, of course, very rough. One would like to have a clear picture of this geometry-matter transition."

    In its own way the thinking here could be radical, as was the equivalence of energy and inertia proposed in Einstein's 1905 paper. Corichi's paper---only 3 pages long---suggests that at a BH event horizon matter can convert to area and area to matter. Since we believe that the area of a BH event horizon is proportional to the BH mass, it seems not entirely unnatural to imagine an exchange of matter for area at the horizon.

    I will try if I can to summarize Corichi's main argument in the next post.
     
  4. Jun 24, 2003 #3

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    derivations of the Immirzi parameter

    Corichi assumes the usual SU(2) symmetry for quantum geometry, rejecting the suggestion of Dreyer that the symmetry group is SO(3). Instead, Corichi says that because of the way a BH grows by absorbing material the great majority of the links puncturing its event horizon will be of spin J = 1. This is regardless of how the object originated--he allows for the possibility that it may have begun its existence with "primordial" J = 1/2 punctures. J = 1 is the lowest possible spin with the exception of J = 1/2 which is excluded during the BH's growth by local conservation of fermion number.

    He also uses a standard LQG result that the contribution to the area from a puncture of spin J is 8 pi γ√(J(J + 1)). So that in this case where the vast majority of punctures have J = 1, the typical contribution to the area is 8 pi γ√2.

    Approach 1: A purely classical analysis of the quasinormal vibration modes indicates that a BH gains or loses mass-energy in steps of ln 3/(8 pi M). But the area A = 4 pi (2M)2 = 16 pi M2. So the change in area is 32 pi M ΔM = 32 pi M (ln 3/(8 pi M)) = 4 ln 3.

    We can simply set the typical area associated to one link equal to 4 ln 3 and solve for gamma. Namely,
    8 pi γ√2 = 4 ln 3

    γ = ln 3/(2 pi √2) = 1/8.088.

    Approach 2:

    Let N be the number of punctures. The entropy of the surface is approximately N ln 3. This is the logarithm of 3N, in essence the total dimensionality of the microstates.
    (The Hilbertspace of microstates of the surface corresponding to a puncture with spin label J has dimension 2J + 1, the dominant case being J = 1 and dimension 3.)

    But semiclassical arguments of Bekenstein and Hawking showed the entropy equal to A/4.

    Now from what was said before we have that the area is
    equal to N 8piγ√2, namely the number of punctures times the contribution from a typical one.

    So we can write the entropy as N (8piγ√2)/4
    and also, as was just observed, as N ln 3.

    Setting the two equal we can solve for gamma a second time:
    N (8piγ√2)/4 = N ln 3

    8piγ√2 = 4 ln 3

    γ = 4 ln 3/(2 pi √2) = 1/8.088

    A non-trivial prediction by the theory:

    Corichi makes this point near the end of the paper.

    "Indeed, one could even argue for a stronger result. Namely, one could say that a consistent framework for LQG, incorporating fermions and black holes, requires that jmin = 1 and in fact predicts the QNM frequencies."

    In other words Approach 2 determines what gamma must be based on fermion conservation and the known result about BH entropy. Therefore Approach 1 is not needed as a way of determining gamma and can be turned around into a prediction concerning the Quasinormal Modes of BH vibration. And this is apparently a true predicition, lending credibility to the theory, because the QNM frequencies have been calculated by purely classical means (without any quantum mechanics at all). It means in this case that quantum geometry is looking good in the classical limit.
     
    Last edited: Jun 24, 2003
  5. Jun 24, 2003 #4

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    so THAT'S what you were talking about

    quote:
    --------------------------------------------------------------------------------
    Originally posted by marcus
    The paper is titled "On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry"
    --------------------------------------------------------------------------------



    I alerted you to this paper on 06-10-03 in the "the rotations, SO(3), in Loop Quantum Gravity" thread as follows:


    quote:
    --------------------------------------------------------------------------------
    Originally posted by jeff
    I found a paper yesterday published in january of 2003 in which a by now well-known but inconclusive argument is made that SU(2) can be restored without hurting lubos's result. But for some stupid reason today I can't find it. If you have any time between doing all that typing, see if you can locate it. I think it's important.
    --------------------------------------------------------------------------------

    So that's what you were referring to! It is an interesting paper
    I discovered it in the references of a second Lubos Motl paper, with Andrew Neitzke----"Asymptotic black hole quasinormal frequencies."

    I wish you had included mention of an author's name or part of the title---to use in a keyword search. I'll bet I would have come across the paper much earlier then!

    Thanks for trying to help!




    Report this post to a mentor | IP: Logged
     
  6. Jun 24, 2003 #5

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Your question, Jeff

    You asked:
    It sounds like you're understanding is that the problem of how to include matter in LQG has been solved. Is this so?
    ---------------------------------

    You should know better than that. I am a total skeptic about the current state of quantum geometry

    One should not naively suppose that all the problems have been solved, despite the surprising progress in the past 2 or 3 years.

    Read papers by good people like Ashtekar and Corichi. They qualify their statements and point out what remains to show.
    Corichi is clear in this paper that more needs to be done on the matter problem.
     
  7. Jun 26, 2003 #6

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    Re: Re: Your question, Jeff

    And what would those problems and assumptions be? Currently as I understand it LQG for 4d spacetime is held up by the huge number of possible states that have to be summed. This is a deep problem due to naive assumptions?
     
  8. Jun 27, 2003 #7
    Wich is the problem with decoherence? And what does it has to do with cosmology?. I thought it was just an alternative interpretaton of the wavefunction colapse based in an experimentally oriented aproach.


    Anyway jeff, we clearly differ in the vission we have abouth physycs and mainly about string theory.

    You think it is a deep theory. I think it is a very naive theory wich just uses aproachs that worked in gague theory and try to go with them to realms for where they were not concived.


    The math difficoulties have to do more with internal technicalities that with deeping understanding of anything.

    In fact the most difficoult parts mathematically, if am not wrong, are the perturbative calculations of loops (modulli and all that) and the part related to copactifications (calaby´s orbifolds and all that, wich by the way is the only part of theory i find mathematically beatifull).

    What i readed about d-branes, dualities, and m-theory didn´t result me very hard in the mathemathicall level. In fact my major problem was with the few "heuristic" intepretation.


    And i don´t think LQG is mathemathically easier. It requires a more solid basic in math that string theory. that is it requires a complete formation in math because it uses in every ste full "physician-mathematician" level of rigourosity instead of an "alla Feyman" way of using maths wich is common in the string comunity.

    And what i definitivelly don´t accept is the afirmation about the knowledge of stringy physics aobut QFT. I know a fesw people, and i am getting the impression that it´s number is fastlly increasing, that don´t know almost nothing about gauge theorys. they get a basic course in QFT, (covering lambda phi^4 and a bit of QED) and begin working directlly wiht strings. And thins such borel summability instantons, or confinement are things that read in divulgative books.


    Not to say constructive QFT (wich i must accept i don´t neither know) which i have the impression is bringing as a diferent viewpoint on QFT that the mainstrean interpretation. In particular it seems that they are finding ways to advoid renormalizaton.

    And it is promeoted as an soon experimentally testable theory. If it faills to succed in these it will be left behind, but till them it is the right theory to go with in my viewpoint.


    Anyway i would liike to know which area of string theory you are working. i thought you would answer my question about brane universes but you didn´t.
     
    Last edited: Jun 27, 2003
  9. Jun 27, 2003 #8

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Re: Re: Re: Re: Your question, Jeff

    Excuse me, jeff, but this sounds like your own opinion. Please supply a link to some critique on the web.

    "In order to be a genuine quantum theory of gravity, and not just a quantum theory based on GR - no matter how pretty - a theory must actually produce GR in the low energy limit."

    I claim stringy models dont produce expanding space in ANY limit.
    If you think they do, give a link.
    String models are based on flat Minkowski space---so are unrealistic from the outset, by your own criterion (reproducing essential features of General Relativity.)
    THEY do not reproduce GR, whereas background independent quantum geomety DOES reproduce essential features of GR.

    You seem to be criticising the theoretical development of
    Background Independent Quantum Gravity for being background independent!
    Yet quantizing GR means quantizing geometry (necessitating background independence since it is the very spacetime background that is to be quantized) and this has been a focus of research since the Sixties (Geometrodynamics by JA Wheeler 1962)
    Quantum geometry is a longterm mainstream development in which Ashtekar's approach is only the latest phase.
     
  10. Jun 27, 2003 #9
    I'm not sure what you're saying here. Is it that people are skipping QFT and going directly to strings, because if you are I can tell you that string research requires a deep understanding of QFT.

    Yes, it should. But the thruth is htat the tendence is in the oposite way. For example if you read the prologue of the Polchinsky books it is clearly stated there than they are oriented to people with a weak knowledge of QFT and that they are intended to carry people as quick as possible to the frontier of research withouth requiring an intermediate curse in advanced QFT.


    And certainly many people is getting these way nowadays.

    String theory is pushing pure mathematical research to an extent not equalled by any other scientific theory ever.

    Yes, maths. And Witten is a field medalist. But the TFT are not a rigurous math. Their results need to be confirmated by ulterior investigations using standard math. That´s why i say that string physics is doing maths "alla Feyman".


    By "heuristic" interpretation do you mean you understood the math but not the physics?

    Yes. Or best to say. I missunderstood it the firs time i readed. Later reading of some papers beyond the Kaku bood showed me that my naive physial understanding of the idea couldn´t be correct. i had to reread it and search another sourced to gain a best understanding.

    I´ll read later today the papers you linked and i´ll comment them in the thread about brane universes. Thanks for the info.
     
  11. Jun 27, 2003 #10

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Re: Re: Re: Re: Your question, Jeff

    We have no proof that you are close enough to the physics research community to have any idea of what the "majority view" is. So far you seem something of a loner, not connected with any institution, just developing your own ideas by yourself.

    You should give links to corroborate your statement that your opinion is a "majority view". Something by a qualified mainstream person, reviewing the current state of quantum gravity.

    There was a quantum gravity conference in June 2003, want to know the relative numbers of papers? It's one measure of how mainstream and how live a field is.

    You claim that background indep. quantum gravity is inconsistent with general rel. Give a link. this is way off target. I see plenty of evidence of GR results being matched in the classical limit and refined at planck scale. That is what it's supposed to do and it does it. Can give plenty links to current research papers if you want.
     
  12. Jun 27, 2003 #11

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Re: Re: Re: Re: Re: Re: Your question, Jeff

    That is not true. One of your ideas, which you are constantly airing here, is that there is no room in LQG for matter.
    Here is a quote from your post in the "Quarks in LQG" thread:

    This is unfounded speculation and, in effect, rumor-mongering.
    The literature is amply supplied with LQG papers with gravity coupled with matter.

    It would be very interesting if anyone would do a serious analysis showing "insufficient room".
    I dont just mean innuendo, heckling questions, passing references etc. but some substantive research. Instead of that I see lots of papers with matter fields----often playing key roles.
    No apparent inconsistency with matter as yet!

    YOUR idea, which you like to repeat at PF, is that LQG is going to "hit the wall"----meet with some theoretical obstacle it cant cope with. I wish you would be more specific :wink:

    Or if this is not your private idea, show us a link to some serious substantive mainstream critique indicating that it is encountering fatal contradictions of some kind. This would be news to a lot of people because just now the field is going gangbusters.
     
  13. Jun 27, 2003 #12

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Here's something Jeff posted to Sauron a couple of weeks ago which he must know is misleading (given a paper by Corichi he says he has read). I quote the whole post:
    ******************************

    quote:
    --------------------------------------------------------------------------------
    Originally posted by Sauron
    Jeff, i understand that people eidt it´s messages, but it makes a bit confusing to follow the thread, why not just to indicate your previous mistakes in a new post?
    --------------------------------------------------------------------------------

    Okay, sorry about that.


    quote:
    --------------------------------------------------------------------------------
    Originally posted by Sauron And i still see a self-contradiction in the posts. You say LQG allows particles of spin not minor than 1/2, but that means fermions are allowed, and in other places ou say LQG doesn´t couple to fermionic matter. And your argument says that the absence of SU(2) is forbiding spin 1/2, so ,why are them allowed and only spin 0 particles are not allowed?.
    --------------------------------------------------------------------------------



    The point was simply that lubos's result strengthened a previous result suggesting that the lowest spin particles that can be coupled to gravity in LQG are spin-1 so that the gauge group should be taken as SO(3) rather than SU(2). Since all matter is composed of spin-1/2 particles this would make LQG inconsistent with the existence of matter. If you continue to feel that I'm contradicting myself, quote the contradictory passages and I'll comment on them.

    Last edited by jeff on 06-13-2003 at 05:57 AM
    *********************************
    It may "suggest" this to jeff (whose take on things could be unusual) but does not seem to "suggest" it to other people.
    Corichi specifically included the idea that spin-1/2 links could penetrate the BH horizon but argued that because of fermion number conservation they would not be in the majority.
    The whole discussion jeff refers to (including Lubos Motl's paper) concerns BH event horizon area.

    jeff is blowing a few comments by Motl out of proportion. They have not effected the subsequent course of research. The issue was addressed, in any case, by Corichi who is more central to this area of research and whose opinions carry considerably more weight.

    Corichi's paper was referenced in a follow-up one by Motl (that was how I found it in fact).
    I went over it in some detail earlier in this thread. The arXiv number is gr-qc/0212126
     
  14. Jun 27, 2003 #13

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    What kind of link is this? this is to Perez "Spin Foam" models paper, not even to LQG proper! This is not "the most comprehensive review" of anything, contrary to what you say.
     
  15. Jun 27, 2003 #14

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    I doubt you are in line for any academic appointment whatever, with whatever background!

    You strike me as a self-taught loner---a hobbyist to use your term---pretending to speak for a professional research majority to which you do not belong.

    How you got "Spin foams" confused with the main LQG area, I cannot understand. Very different stages of development.
    Shouldnt talk so confidently about stuff you dont understand.
    Yr understanding seems mainly on the verbal level----not physical.
    Noticed this in your denial that a binary system can lose rest mass by gravitational radiation, which went on post after post.
     
  16. Jun 27, 2003 #15

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    jeff you still have not responded to my request that you
    provide links to back up your personal speculations aired here at PF.

    something in "Spin Foams" hardly counts, it is a new field investigating 4D combinatorial models.

    To back up your rather wild innuendo you need a link by some mainstream authoritative figure explaining why standard background-independent quantum gravity (LQG) is "dead on arrival" as you colorfully put it.
     
  17. Jun 27, 2003 #16

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Jeffery you have already "divulged" your identity many times in your posts on Usenet------sci.physics.research

    You wouldnt get in such trouble if you did not have the habit
    of pretending to be an academic.

    You have referred to yourself here at PF as in "high energy research"

    as belonging to the "professional researchers" community

    but these appear to be merely your private fantasies and pretense

    If you really think you are in line for academic appointment as you recently indicated----and should guide research decisions on whether string or loop is more academically respectable or currently has more faculty positions, then good luck
     
    Last edited: Jun 27, 2003
  18. Jun 27, 2003 #17

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    That is simple defensiveness, I am sure you realize. You have made extravagent suggestions of fatal flaws and I have challenged you to provide links-----to critiques by reasonable people.

    You provided one link---it was a canard, a fake answer, not having to do with LQG but with a recent spinoff still in early stages of development.

    Now, because you cannot come up with links to justify your assertions you are thinking up excuses why you shouldnt have to.

    You are aware of my sense that string theories are flawed because they depend on a flat undynamic space time at the very outset.

    Background independent Quantum Gravity, by contrast, is an attempt to quantify general relativity. Many of the recent papers (2002,2003) make liberal use of matter fields. No responsible person claims, as you do, that the theory will prove incapable of accomodating matter!

    Your reasoning about this is, I think you realize, not rigorous and seems to be wishful thinking. It doesnt demonstrate a logical necessity.

    You have not shown that there is any conclusive problem with LQG. But certainly the theory is under development! Every aspect is being worked on and no final answers have been given---which would involve experimental tests.

    The LQG approach to Quantum General Relativity is, it appears, a lot LESS vague about its testable predictions than are Stringy models. LQG is obviously MORE clearly complete and nearer to being testable. It is part of a effort to quantize geometry that has been going on since before 1962 (Wheeler's "Geometrodynamics") and with which flat fixed-background stringy models have nothing to do.

    All active areas of theoretical research are to some extent vague until conclusively tested by observation---and may afterwards be modified and retested. LQG, which doesnt try to explain all the forces and particles in the world but merely to quantize General Relativity (hard enough!, something string-folk avoid!) is LESS vague and LESS apt to be fundamentally flawed and NEARER to being productively testable. But still there is no clearcut answer yes or no to your question----never will be till final experimental tests.

    I think the question is just a defensive ploy because you want an excuse not to back up your statements
     
    Last edited: Jun 27, 2003
  19. Jun 27, 2003 #18

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    I'm getting bored with your bickering.
    Will have to start ignoring your posts till they get a little more sensible
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?