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Quantum Geometry-the Brian Greene quote

  1. Jun 11, 2004 #1


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    Quantum Geometry---the Brian Greene quote

    This is a spin-off from the "Loop Gravity-Rovelli's program" thread
    based on a post by Sol2.

    We were talking about Rovelli's book Quantum Gravity---he recently redid his homepage---and Sol2 posted this, with a quote from Elegant Universe
    and a reference to the notion of quantum geometry:

    what I am hoping people will focus on in this thread is the Brian Greene quote that Sol2 copied in.

    this quote raises a bunch of interesting issues

    The "Rovelli program" thread, where we came from, is serving as a link-basket or surrogate sticky for LQG links. If there is a chance for lengthier discussions IMO we probably should start separate threads like this.
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  2. jcsd
  3. Jun 11, 2004 #2
    Since there were so few papers on this I wonder if many will have a perspective on this issue? I hope so. GR has to lead into QM?

    There is a historical developement here that many do not need to be reminded about, but for a laymen, it was very important to undertand this developement in concert with current technolgical realites. This is a GR generalization and next I hope to demonstrate the other extreme of the Heirarchy problem in terms of Geometrodynamics.

    Membrane Realization?

    http://new.math.uiuc.edu/optiverse/img/rs11-107.jpeg [Broken]

    Bubble eversions

    An Introduction to Geometrodynamics

    The existence of gravitational waves is a prediction of the General Theory of Relativity which is Einstein's explanation of the gravitational interaction (1915). The basic idea is:

    Gravity is no force but an aspect of the geometry of spacetime.

    Space is not an absolute invariant entity, but is influenced by the distribution of mass and energy in the Universe. The basic principle is:

    Matter tells space how to curve, and space tells matter how to move.

    Large masses introduce a strong curvature in spacetime. Light and matter are forced to move according to this metric. Since all the matter is in motion, the geometry of space is constantly changing. Hence Geometrodynamics is a better name for Einstein's theory of gravitation. In order to derive the basic field equation, one has to relate the curvature of space to the mass/energy density:

    G = k T

    http://www.physics.gla.ac.uk/gwg/geodynamics.html [Broken]

    This will not answer the direct comparsion just yet Marcus, but I hope to demonstrate where I think it will lead too. I will back off now and hopefully we can will see a direction (quantum geometry) this forum takes, as well as sci.Physics.strings or even Peter Woit:)

    Is this okay Marcus?
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  4. Jun 11, 2004 #3


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    you betcha! I don't say I'm understanding everything but you put ideas together and I really thought it was good to bring together the Brian Greene quote, as you did, with the mention of the new book QG. I am hoping others can get in here and shed some light.
  5. Jun 11, 2004 #4


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    A propos of the topic "Quantum Geometry", the Cambridge
    University Press published a book on it in 1997.
    the title was Quantum Geometry
    and it was by Jan Ambjorn and others

    I havent looked at the book.
    the approach described in it only bore fruit this year
    in the AJL paper that Baez was discussing recently in TWF
    and on sci.physics.research
  6. Jun 11, 2004 #5
    Just gathering information for consideration

  7. Jun 11, 2004 #6


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    Sol2 that whole webpage is worth reading. By Matt Visser of Washington U., excellent essay! he seems to have spotted the potential in that approach comparatively early (2002)
  8. Jun 11, 2004 #7


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    And the extract shows what I found when I looked up "quantum geometry" in hep-th. Quantum Geometry means the Ashtekar - new variables - LQG project. Quantum Gravity is the name chosen by AJL for their approach. I've really got to internalize more of that AJL paper!
  9. Jun 12, 2004 #8

    Sakharov's induced gravity!

    Great Sol, I have been an admirer of Matt Visser and his perspective papers for sometime. One has to have a arena in which to progress from, there are dimensional frame considerations?..for instance:

    Matter tells space how to curve, and space tells matter how to move.

    The first starting point in this sentence is portraying an allready 'EXISTING' frame of reference, this will lead to a constraining of the models predictions, 3+1 is allready in place!

    Therefore the second part :Space tells matter how to move, will still be part of importance in the 'Geometrodynamics'.

    Matter in its 'allready' existence has ALLREADY been told by SPACE how to move!

    Much better is the fact that the definition 'Flat-Space' (I believe this is the 'Lattice' deemed to be the 'precurser-frame-background' in some new models) has to be assumed to have 'NEVER' told matter to move, because it is Flat, it is Flat as a consequence of it not encountering any curved-matter!

    The Sakharov model has a very interesting dimensional angle on this(I'll dig out my PDFs showing this), now not to put any vague insights into your thread, I will say this only, Newtons-Bucket? :rolleyes:

    Now:Matter tells space how to curve, and space tells matter how to move,

    for instance we can cross into some simplistic avenues for Newtonian Concepts?..watch/read closely :smile:

    Space tells Matter how to un-curve, and Matter tells Space how to move during the encounter/interactions along a defined direction!

    Get it?..Electro-Magnetic-Vacuum

    Gravity in a pre-existing dimension is reduced to E-M-V force :biggrin:

    I have produced some neat extensions to Newtonian Motions and General Relativity Energies, the Newtonian Bucket experiment I have been lead to re-formulate recently has the above consequence, and the total number of Dimensions go no more than 5!

    A good interesting paper here:http://uk.arxiv.org/abs/gr-qc/0406044
    Last edited: Jun 12, 2004
  10. Jun 12, 2004 #9


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    About ten years ago, in 1995, Greene gave some lectures in Les Houches under this title, "quantum geometry". It was clear that there was a nomenclature problem, because by QG he was referring to a very specific topic of string theory.
  11. Jun 12, 2004 #10
    I am tying to get a clear understanding of the basic perceptions of Quantum gravity. This will help greatly I think from what basis we might derive the issues of Quantum geometry?

    Olias:Matter in its 'allready' existence has ALLREADY been told by SPACE how to move!

    This would be a direct connection for sure, and from a dimensional perspective, the gravity field will have been deduced as weak, but there are stronger fields to consider, and why I raised the Heirarchy realtionship to dimensional values.

    I do not understand Newton's bucket to only five dimensions? In context of the bose nova, the jets would say what?

    So on a comsological level the curvaure parameters of the friedman eqaution? Dirac's matrices on a quantum level? Omega and critical density? So the nature of the curvature has to been understood as dynamical in nature. K=O, K>0, K<0, ds2 > 0, ds2 < 0, ds2 = 0.

    G = k T

    So how would this all change if we did not consider the energy value in the hierarchy Scenario, and relate dimension to gravity. I don't know if this made sense:)

    Last edited: Jun 12, 2004
  12. Jun 12, 2004 #11
    Sol from above:Does spacetime geometry make sense near the initial singularity? Deep inside a black hole?

    It does if one links a singularity to the host Galaxy Blackhole? and not a Universal 'Singularity', every Galaxy has a '0', as every Galaxy has a 'Birth-date'.
  13. Jun 12, 2004 #12
    I think we have talked about this before, about the births and deaths of galaxies. Fusion and fission:)

    So through it, there is a geometrical consistancy, like turning something inside out. Do you remember this? Heisenberg's collapsing sphere?

    We are describining diferent "stages" of a consistent view, in regards to those galaxies, in the births and deaths? Why singularities are very difficult if you assume a harmonic vibration, as the basis of this existance?

    You see how this is compatible with the Ekroptic scenario?
    Last edited: Jun 12, 2004
  14. Jun 13, 2004 #13
    Undering the heading of Quantum Gravity I came across some information that I think speaks to the understanding of how we might look at measuring the information released from Gamma Ray Bursts.

    Now what is interesting here is the relationship we had once talked about between Smolin and http://deseretnews.com/photos/1440359.jpg [Broken]. I know that Joao has recieved some very hard criticisms because of the principals of VSL, but what is interesting I will point out shortly.

    So now to the issue here of Quantum Gravity.

    One of the foundation prinicpals that I found in regards to dimension, was a way in which to interpret features in regards to this idea. So we have this graviton as a representative, and what effects do we look for? So the question is, can a graviton slow a passing photon?

    Of course at this point the question about classical discriptions affecting Quantum orientations come to light, and the insistence I have made along these lines of spin orientation. As a laymen then I have to wonder how such a classical discription of General Relativity, can ask us to look in this direction?

    So what is postulated, and it becomes somewhat of a shocker.

    Why the introduction of VSL approaches as an affront as it might seem to respecting physicist's, in relation too, constancy of speed of light, can how we can take this subject seriously?

    Well to set it straight, the idea of photon discription is taken seriously and we will know in the near future of 2006, whether Glast will performs it job?

    Now my interest here is how we might apply some model of quantum geometry to a truly predictable avenue of exploration, and we have seen such experiments spoken to in the nature of LIGO, derived from ideas of the supernova and Kip thorne about those distances? Does anyone see a relationship?

    So in LQG is there a testable hypothesis in regards to what is discrete and in strings, what is continous? I think this question is raised here in the Glast experiment?

    Although I am having difficulting understanding how, if the graviton is raised from the effects of GR, how the heck did Witten made this advance?

    So the insight here in regards to the ideas of continuity and discreteness all of a sudden raise questions about how photon can move over those great distances and not "slight" speed of light constancies?

    More on this as I look at it, and I hope some will respond here. Three Sol responses in a row and I think this thread has run it's course?
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  15. Jun 13, 2004 #14


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    whatever happens with this thread the topic of quantum geometry (and the B.G. quote) is a stubborn enduring topic. it hasnt run its course and it wont go away any time soon, I feel sure.

    also you and Mike2 are both asking what i think are really good questions about gravitons (mike in the other thread)
    simply because i dont answer doesnt mean I dont appreciate the depth of the questions (on the contrary maybe :smile:)

    all I can say will sound very stupid: be patient

    what should a quantum geometry look like?

    (do you think I am going to answer? its a big question!)

    there was that 1997 book "Quantum Geometry" in the Cambridge Monographs in Mathematical Science Series. I havent looked at it. That should have addressed some of the fundamental questions.

    Has a graviton ever been observed? (I think not, correct me if I'm wrong)

    Do we have any reason to suppose that a satisfactory quantum theory of geometry would include gravitons?

    (would it include "volume-ons" and "curve-ons" and "area-ons"
    and "angle-ons"---that was said facetiously, dont give it a second thought---but the elements of geometry concern such things as area and angle and volume)

    So far i only know of gravitons emerging as an approximation to behavior on a fixed background geometry
    You decide on a rigid background geometry and you perturb it with a little ripple and call that a graviton.
    thats because you can separate mentally between the background and the perturbation that twangs across it

    but if there is no fixed background, where is the graviton?

    In a background independent quantum geometry, would there be such things?

    One would certainly expect is that observables corresponding to operators on the hilbertspace of a quantum theory of geometry corresponding to measurements of area, volume etc. would have discrete spectra

    that is the usual thing that happens with quantum theories, there are
    discrete eigenvalues corresponding to discrete outcomes of measurements e.g. discrete energylevels in an atom etc.

    but having geometric observables with discrete spectra does not necessarily mean inventing and "discovering" particles, or does it?

    I dont want to lean either way on this issue. maybe a background independent quantum geometry will have gravitons, maybe not. I personally cannot judge the odds. I am even still asking
    what should a quantum geometry look like?

    maybe i will get that Cambridge Monograph series book on quantum geometry and see what they say. from the library I mean
    1997 is too old to buy.
  16. Jun 13, 2004 #15
    Thank you Marcus.

    I did see Mike2's response.

    You know what's interesting is Arivero's response on fundemental particles, as to how such a standard model might arise from brane scenrios? U(1)*SU(2)*SU(3) and in the understanding of differiential structures, how would this appear in a model's like Greg Egans? It's good to see his animations:) Dirac's belt trick.

    This view has to be consistent from a GR standpoint(geometrcial expression) as well as from a Quantum perspective. Rotations and http://oldsite.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html?

    Moving to the KKtower this becomes a interesting summation to following Klein after Einsteins work. If we united Electromagnetism with gravity then how would spectra be involved? :smile:

    To me then the issue of Calabi Yaus come into the picture because I think they have to complete this rotation mathematically. Someone would have to correct me here. But I think this would signal the unification? :smile: I am speculating here :smile:
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  17. Jun 13, 2004 #16


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    Sol, the U(1) group is just the rotations of a circle (interpeted as the phase changes of EM). SU(2) is the cover of the rotations in three dimensional space, SU(3) transforms the "eightfold way" into itself. I am sure you can find pictures of Gell Mann's eightfold way if you google on it.

    But the key thing about these groups is not what they do in space, but how they define particles. That gets into representations, and it's hard to picture.
  18. Jun 13, 2004 #17
    Sol you quite rightly point out the dirac belt trick?..if I may?

    The existence of the a Graviton is akin to a 720 degree rotational curve, it is interesting that when one reduces the domain, what is a spin 2 particle (graviton) has a different configuration in a 2-D plane (remember Quark-table-confinement?) it turns into a 'double-rotational' static solution :tongue2:

    Spin can only exist due to '3-D freedom', spin translates to rotation in say an E-M-V.

    A 3-D anything that 'spins' or has a 'Spin', cannot execute the same dynamics when confined to the 2-D, there it is Rotation.

    So for instance a particle that some are trying to 'seek' in some models, say the Higgs Particle, will have a static rotational value, because it does not exist in a 3-D domain, in a way it is a 'fixed' reference point, not only that, I would extend this further by stating that its direction of Rotation has two paramiters, when it Rotates one way the solutions are in expansion, and when it Rotates the opposite direction it is collapsing!

    Now for a a 3-D particle that has a actual spin value of say +1, it can be encompassed by a lower dimensional 'particle' that has a Rotational value of 'Expansion', thus the 2-D Rotation will allways surround the 3-D spin.

    My model is correct up to a certain value :rolleyes:

    If one has a spinning top with two strands wrapped around it in opposite directions, one can pull both strings away from the top to reveal the direction of which way it spins.

    So let me ask you to think about this, which way does a top spin if so?..hint think Parity Conservation :smile:
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  19. Jun 14, 2004 #18
    I will use this picture for reference.

    A string can only vibrate in one direction in a dimensional sense. It can compress and stretch, and in this consideration, what is the photon as a wave,that the photon has been reconfigured, and considered as a longitudal wave?

    Now if the string includes this longitudal wave capability, what is two dimensional that we now consider, the traverse application of gravitational waves? So we have now set up our thinking, not only geometrically, and I leave out the direct connections[geometrical correlations] in life of what others might see intuitively, and what they I hope wil share in the vision share of.

    When these two waves are joined in the three dimensional world the tranverse waves can now rotate( what are our neutron stars doing). In a higher dimensional understanding we have seen where this correlation had followed the strick logic and consequences, to have understood not only the pendulum, but also the neutron stars orbit, to have come to a culmination of what is seen with the help of kaluza in that the model up top is now given forward for interpretation.

    What I recognize is how we must find a consistent method on these degrees of freedom. I have another link I wanted to place here in these consideration and to speak to the way you are thinking.

    http://www.sciencenews.org/articles/20000909/a3744_3415.JPG [Broken]

    A mirror universe" is predicted to exist if parity and/or time reversal are unbroken symmetries of nature [1,2]. The idea is that for each ordinary particle, such as the photon, electron, proton and neutron, there is a corresponding mirror particle, of exactly the same mass as the ordinary particle. The parity symmetry interchanges the ordinary particles with the mirror particles so that the properties of the mirror particles completely mirror those of the ordinary particles. For example the mirror proton and mirror electron are stable and interact with the mirror photon in the same way in which the ordinary proton and electron interacts with the ordinary photons. The mirror particles are not produced in Laboratory experiments just because they couple very weakly to the ordinary particles.

    In the modern language of gauge theories, the mirror particles are all singlets under the standard G _ SU(3) SU(2)L U(1)Y gauge interactions. Instead the mirror particles interact with a set of mirror gauge particles, so that the gauge symmetry of the theory is doubled, i.e. G G (the ordinary particles are, of course, singlets under the mirror gauge symmetry) [2]. Parity is conserved because the mirror particles experience V +A (i.e. right handed) mirror weak interactions while the ordinary particles experience the usual V _ A (i.e. left-handed) weak interactions. Ordinary and mirror particles interact with each other predominately by gravity only. At the present time there is some experimental evidence that mirror matter exists coming from cosmology [3] as well as from the neutrino physics anomalies [4].

    It was realized some time ago by Glashow [5] that the orthopositronium system provides one sensitive way to search for the mirror universe. The idea is that small kinetic mixing of the ordinary and mirror photons may exist which would mix ordinary and mirror ortho positronium, leading to maximal ortho positronium - mirror orthopositronium oscillations.

    http://arxiv.org/PS_cache/hep-ph/pdf/0003/0003278.pdf [Broken]

    To get to the graviton we had to move through GR and its consistancy, and then enter the quatum realm for consideration.

    One of the foundation prinicpals that I found in regards to dimension, was a way in which to interpret features in regards to this idea. So we have this graviton as a representative, and what effects do we look for? So the question is, can a graviton slow a passing photon?

    Of course at this point the question about classical discriptions affecting Quantum orientations come to light, and the insistence I have made along these lines of spin orientation. As a laymen then I have to wonder how such a classical discription of General Relativity, can ask us to look in this direction?
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  20. Jun 14, 2004 #19


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    This is not physically correct. A string can vibrate in the transverse directions, that's 24 for bosonic strings and 8 for superstrings (subtracting the dimension along the string and the time dimension).
  21. Jun 14, 2004 #20
    Woud it have been better to say the string is a one dimenisonal entity?


    The correlation to U(1) charcteristics as a circle (boson considerations)

    "Point and line," are entangled here? I am trying to remain geometrically consistsent. IN a flat world, eucildean. Yet the energy determinations move to hyperdimensional realities?

    There is a metric field to consider in any quark to quark measure? This energy determination depends on the string's length? :smile:

    It does not logically make sense to me that a string's length cannot remain consistent geometrically, if you do not transfer the thinking to a energy value? Why the Radius of U(1) becomes a determination of a point?

    But then lets look at a point on the brane? In supersymmetry how shall we express this point?

    ---------.---------http://wc0.worldcrossing.com/WebX?14@72.ABPtcShRb6u.2@.1dde5d80/4 [Broken]

    What will a Gamma ray blast tell us? Can some photons act short and long?
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