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Loop quantum gravity

  1. May 31, 2003 #1

    jby

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    I don't know if I've come to the right place. I've posted this in the theoretical physics forum and yet to get a reply...

    I recently read this article http://www.sciam.com/article.cfm?ar...F71809EC588EEDF

    and came across this thing called spin network. Anyone with further explanation on this?

    There is also this paragraph in this article on the first page:

    Markopoulou Kalamara approached LQG's extraneous space problem by asking, Why not start with Penrose's spin networks (which are not embedded in any preexisting space), mix in some of the results of LQG, and see what comes out? The result was networks that do not live in space and are not made of matter. Rather their very architecture gives rise to space and matter. In this picture, there are no things, only geometric relationships. Space ceases to be a place where objects such as particles bump and jitter and instead becomes a kaleidoscope of ever changing patterns and processes.

    Giving rise to space and matter? Any explanations?
     
  2. jcsd
  3. May 31, 2003 #2
    You can get the article

    by putting "spin networks" in the search function on the sciam site. Her approach makes a lot of sense. Why should space and matter be brought into a theory separately? They should both come from the same precepts.

    I've long thought that in some deep sense the world is made of mathematical things, and that Physics and Mathematics will one day be completely merged. It may be nothing more than the sum of all logicaly permitted mathematical relationships. Why should it be made of "physical things" that have to be described mathematicaly? That adds an unneccesary layer to the world.
     
  4. May 31, 2003 #3
    Correct. TOE shall explain not only matter but space and time itself. So far all objects we know are just a mathematical outcome of more fundamental entities. But, indeed - why shall space and time be exception?

    It is all math. Physics is just an illusion. Universe seems to be an applied math.
     
  5. Jun 1, 2003 #4

    marcus

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    I downloaded a couple of Fotini Markopolou papers from arXiv
    a while back, so I know journal-type articles by her are readily
    available if you want to see what she actually is talking about.
    One paper was "Holography in a quantum spacetime"
    One paper was "Quantum causal histories".

    As far as I can tell, the title of your thread---"Loop Quantum Gravity"---is one thing and Fotini's thought is something else.
    She makes creative use of ideas which have arisen in LQG without furthering the development of LQG as such. Her work is
    intriguing but I have mixed feelings about it.

    Are you interested in finding out about LQG?
    If not, and just want to follow thru what Fotini talks about,
    why not get her papers---like Quantum Causal Histories
    arXiv:hep-th/9904009
     
  6. Jun 1, 2003 #5

    Eh

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    Specifically, geometry.
     
  7. Jun 1, 2003 #6

    jby

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    yes please marcus or anyone else, can you elaborate more on this LQG stuff? I've read before on this theory but those terminologies make me lose interest in it too fast for me to grasp that theory.
     
  8. Jun 1, 2003 #7

    jby

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    Yes, I do agree with this. However, my idea is that since mathematics stemmed from orderness, it is suffice to say that our world is not chaotic. The universe doesn't understand maths but maths is able to explain the universe because it is consistent and has orderliness imprinted.
    Nevertheless, there's this thing called Godel's Incompleteness Theorem that shows "loopholes"...
     
  9. Jun 1, 2003 #8

    marcus

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    I can only elaborate in steps of very small ideas over the course of several days.

    Our own history includes the gradual invention of mathematical descriptions of space and time which are less and less rigid and absolute.

    Gauss and Riemann helped us to free ourselves from a rigid Euclidean framework (within which Newton happily did great work, so I must no knock Euclidean space!) and to develope
    the "smooth manifold with metric" that GR lives on.

    Gauss actually suspected that the angles of a triangle, if it was big enough, might show up as not exactly 180 degrees and he attempted to measure the angles of a very large triangle.

    This is as quixotic as Galileo and his friend trying to measure the speed of lights by flashing lanterns to each other in the hills around florence.

    We are now in the process of getting rid of the fixed metric and letting the metric be an uncertain quantum dynamic thing, and with it the geometry.

    This is the quest for "Background Independence" that characterizse and drives LQG. To just have a smooth manifold WITHOUT an idea of distance being given and let the metric
    be a quantum mechanical state-----in essence to have a whole hilbert space of metrics the way one has a hilbert space of wavefunctions or quantum states of an electron or whatnot.

    The all important thing, at this point in history, is to be patient with the mathematicians because all really new mathematical inventions are
    ungainly and horrifyingly unfamiliar and even boring.

    I can sketch for you how the effort is going in LQG but in some sense the actual mechanical details and methods are less important than simply the fact that we are trying to peel off one more layer.

    Gen Rel has been done on a manifold-with-metric

    (this itself is a generalization of Euclidean space and time coordinates)

    Now the time has come to erase the metric and venture into unknown waters again.

    this is almost an instinctive drive in the history of mathematics
    (now in this instance it is the drive for "background independence")

    Background independence distinguishes LQG from stringy approaches or "perturbative" that start with a fixed metric and use quantum methods to futz around with it and add on undetermined fuzz. These approaches commit themselves to
    an absolute choice of metric and then "perturb" it with an add-on
    quantum layer. Background independent approaches strip off the metric completely and let it reappear as a purely quantum thing.

    What they have contrived to enable them to do this is quite remarkable and I will probably try to give an overview if nothing else intervenes. this is where the space of "connections" on the manifold (which do parallel transport of vectors) come in and also the "loops" and networks that are used to explore and express the connections and thru them the alternative geometries of the manifold. It sounds like a terrifying bedlam but it is only humans doing what they always do.
     
  10. Jun 2, 2003 #9
    Not nesessary. Math allows both for chaotic solutions (exponential solutions are coomon in math, and they result in catastrophic amplification of small initial changes with time) and for uncertainty (waves are perfect example of a mathematical solution with mathematically entangled properties which results in mutual uncertainty of those entangled quantities).

    Universe does not need to "understand" math. It simply follows it because math is just a logic existing things shall obey. Just by definition of math.

    Incompleteness theorem is not a "loophole" as sometimes laymans feel about it. It simply says that math can create correct structures which can't be proven ONLY from initial postulates. I would not call that "incompleteness" rather than "redunance" of math.
     
    Last edited by a moderator: Jun 2, 2003
  11. Jun 3, 2003 #10

    jby

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    I don't quite understand this phrase. Can you elaborate?

    And one more thing... is quantum physics background independence like GR?
     
  12. Jun 3, 2003 #11

    marcus

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    Rovelli has a fine non-mathematical discussion in his survey of quantum gravity in the web journal LivingReviews

    http://www.livingreviews.org/Articles/Volume1/1998-1rovelli/index.html

    Have a look at:
    3 History of Loop Quantum Gravity, Main Steps

    The first item is about "connections" and the reformulation of GR in terms of connections that was achieved in 1986.

    Loop Quantum gravity seems to have taken off at that point, or begun its journey.

    The connection on a smooth manifold-with-metric is a machine for doing parallel transport of vectors from one point to another along a curve----that is one way of saying what it does, it is much more generally useful than that.

    Imagine a tangent vector at a point on the earth's equator being "parallel transported" up to the north pole. Which way would it point then? This is simple stuff and very intuitive. But mathematicians always need to be very sure what they mean. So they define a definite machine for doing this very intuitive thing.


    Then by a wonderful surprise it turns out that if you have the connection that derived from a metric and know how vectors are transported in every possible case then if you ever forget the metric you can RECOVER it from watching the transport of vectors.
    The connection machine contains the same info in a different form. You can recover the curvature and the distance-idea at least up to a scale adjustment, just from the "connection"

    Maybe that is not so surprising after all.

    Anyway in 1986 Ashtekhar said lets do GR by studying the connection instead of studying the metric.

    Rovelli's review of the history of LQG will make it clearer why that was an important step.


    No, and this does not seem to be a drawback as long as QM just deals with small-scale things on uncurved unexpanding space.

    It seems generally satisfactory to have QM living on Minkowski space which is the ordinary uncurved undynamic 4D space of special relativity.

    The simple answer is No. QM is not background independent. It is not done on a general smooth manifold. It is normally done on very ordinary Euclidean 3D or Minkowsky 4D space. But one must quickly say that there is no harm in this! For such matters as QM deals with, these coordinates are fine and work great!

    The problem is that to quantize the largescale dynamic geometry of spacetime one cant begin by laying out a rigid Minkowski 4D space----that space does not even expand! Nothing interesting is going on there----largescale geometry-wise. It prejudices things by making an early committment to a boring and unrealistic largescale geometry. At least some people have adopted that position and have insisted on making a clean start on a manifold with no prior choice of metric.

    I think Rovelli discusses the need for background independence when one works on largescale geometry (as opposed to microscopic quantum matters). If I find a section reference in his LivingReviews article I will edit it in here.

    Yes this section of the article:
    2.2 What is the problem? The view of a relativist
    talks about background independence in a non-mathematical way.
    I may also find other discussions elsewhere and edit them in as references---unless you find this an adequate reply.
     
    Last edited: Jun 3, 2003
  13. Jun 3, 2003 #12

    jby

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    Grrr this is frustrating
    I can't go to the site you're refering to not even www.livingreviews.org website.
     
  14. Jun 3, 2003 #13

    Eh

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    Why? It's working ok for me.
     
  15. Jun 3, 2003 #14

    jby

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    damn I think my comp is playing tricks on me. I'll have to check the settings. thx.
     
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