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LQG in Higher Dimension?

  1. Feb 16, 2012 #1
    Is it possible for LQG to occur in higher dimension (more than 3+1)? If possible. How?

    If not possible. Do you notice LQG in fixed 4D compared to Strings 10D is pretty boring? Nature doesn't make sense for there to be 4D (3+1T) only when it could create more with no sweat. So this alone may constraint the theories enough to make 4D only LQG unlikely.
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  3. Feb 16, 2012 #2


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    Thomas Thiemann is a quantum relativist who heads a research group at Univ. Erlangen in Germany. Is the author of a rather massive monograph on LQG and many papers. He and two co-authors just wrote 6-8 papers this year about LQG in D > 4 and also what happens if you add supersymmetry (SUSY) to it.

    The results were presented in several talks at the biannual conference in May 2011. I think there is a video of Thiemann's talk at the conference

    If anyone is interested in reading the papers, just ask. I'd be happy to get links. Or just go to arxiv.org and search by authors last name.
    plus further on in thread Atyy gives links to three others.
    Last edited: Feb 16, 2012
  4. Feb 16, 2012 #3


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    Sweat exists. So theories with no sweat are falsified :smile:

    Anyway, string theory cannot do 5,6 dimensions with "no sweat". It has to be 10 (or 11?) dimensional to be consistent.
  5. Feb 16, 2012 #4
    This is the simplest arguments that I read after checking our archives (is the argument sound):

    "Why 10 Dimensions?

    When strings vibrate in space-time, they are described by a mathematical function called the Ramanujan modular function.26 This term appears in the equation:27

    [1-(D - 2)/24]
    where D is the dimensionality of the space in which the strings vibrate. In order to obey special relativity 9and manifest co-variance), this term must equal 0, which forces D to be 26. This is the origin of the 26 dimensions in the original string theory.

    In the more general Ramanujan modular function, which is used in current superstring theories, the twenty-four is replaced by the number eight, making D equal to 10.28

    In other words, the mathematics require space-time to have 10 dimensions in order for the string theory to be self-consistent, but physicists still don’t know why these particular numbers have been selected. "

    So should LQG be in 10 dimensions too?
  6. Feb 16, 2012 #5


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    Another place with a presentation that I could somewhat understand was Baez's talks about his favourite numbers
  7. Feb 16, 2012 #6


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  8. Feb 17, 2012 #7
    Admit it that more than 70 years later.. we are not better off than Einstein's failed Unified Field Theory. Did he really completely ignore the quantum when QFT was finished in the early 1920s. Has anyone actually seen the Einstein Manuscripts on the UFT? Remember when Witten unified the 5 superstrings by proposing another dimension and enclosing them in a hypothetical 11D M-Theory. What if one increases the dimensions in Einstein UFT? Even if you agree it's failed attempt. Have you not actually look at the Einstein manuscript and see what mathematical techniques and steps he used and the conjectures he did? Is there no books that talks about it?
  9. Feb 17, 2012 #8
    If you look here you can see someone still writing papers about Einstein's final theory. But it's very wrong to say
    Einstein was combining relativistic gravity and electromagnetism in various ways. He had vague ideas about explaining quantization with the boundary conditions of his fields, but that went nowhere. So in reality his last theories neither incorporated nor explained quantum mechanics, so they said nothing about particle physics.

    You can look for a unified theory at two levels. First, you can just ask for a single equation that describes the world. If that's what you want, then the standard model is already a unified theory. There is a single "action" containing electromagnetism, weak force, strong force, gravity if you want to include it, and all the quarks and leptons. If you look in this paper on "The New Minimal Standard Model", they start by stating the standard model in just a few lines. They use a highly compressed notation and you should look at the Wikipedia pages on the math of the standard model to understand, but anyway, there's a theory that is "unified" in the sense of putting everything on one equation. (Their "new minimal standard model" adds a few extra details to the 1970s standard model in order to account for dark matter, dark energy, and neutrino masses.)

    Second level, you can look for a theory which explains the details of the standard model. This is what "grand unified theories" in the 1970s were trying to do, and then various "super" theories after that. Many of those theories, e.g. "N=8 supergravity", were considered a realization of Einstein's dream of unification. They were intrinsically defined as quantum theories, but they were trying to get everything from some geometrical principle.

    The physicist who now most resembles the later Einstein is Gerard 't Hooft, who did more than anyone else to make the standard model possible (and who got a Nobel Prize for it), and who worked on quantum gravity, and who is now trying to explain quantum mechanics in terms of a deeper theory. Then maybe in second place is Roger Penrose, who also has deviant ideas about explaining quantum mechanics, and whose twistor theory really has entered the physics mainstream now. There's also a lot of free-floating mathematical invention going on in non-string quantum gravity, various ideas about quantum information networks, and so on. And on the "fringe of the fringe", there are quite a few people who could have been mainstream physicists, but instead spent their life developing some other framework of concepts. You can find quite a few of those people on vixra.org (hidden among a lot of papers that are much less interesting).

    So there's heaps of stuff happening, and of course the "mainstream" itself is quite relevant too. :-) The real progress will emerge from some subset of all this.
  10. Feb 17, 2012 #9
    Where did those people writing papers about Einstein's final theory see the einstein UFT manuscripts? Have you seen them yourself? Why are they not published in a book? It's still kept hidden in a vault?

    Isn't this we haven't united Electroweak and Strong force yet. The proton doesn't decay. What perflexed me is how do they plan to unite them under String theory when they were still not convensionally

    Do you consider some papers at arxiv as crackpottery? How do you define the term crackpottery and know how to judge whether a paper is one or not?
  11. Feb 17, 2012 #10
    Einstein kept publishing research papers in the usual journals, up to the end of his life. It's all just slight modifications of his 1915 theory of gravity, general relativity.
    In the weaker sense of unification - combined in the same theory - we have unified electroweak and strong. The stronger sense that is usually intended by gauge unification is that the symmetry groups for these two forces are subgroups of a larger symmetry which is broken at low energies.

    The failure to observe proton decay was the first real problem for these "grand unified theories", but they get around it by making the new force particles that would cause proton decay extremely heavy. Just as the Higgs mechanism makes the W and Z massive, it can also be used to make these "X and Y" particles supermassive.

    I think there are two main reasons why GUTs are still at the center of beyond-standard-model particle physics. First, the embeddings of the standard model group into the bigger symmetry groups can explain some of the details of the standard model. Second, the strength of the forces changes with energy ("running of coupling constants") and they converge roughly on the same value at very high energies. At very high energies the full symmetry should be restored and all the force particles should couple with the same strength, so this is consistent with the idea of unification. (Also, the convergence is even better if you assume supersymmetry as well as grand unification, so this is a standard reason for believing in supersymmetry. But the improved convergence is due to just a few of the many new particles introduced by supersymmetry - possibly you only need the "higgsinos" to obtain it - so I think it's rather weak evidence for supersymmetry; all you really need are some additional higgsino-like particles, which doesn't require SUSY.)

    Another reason would be that GUTs arise naturally within string theory. So it could be that the mainstream has been on the right track ever since the 1970s, and all it has to do is keep going a little further, and we'll hit upon the model that explains everything.
    There would surely be a few crackpot papers at arxiv. But we could distinguish between professional and unprofessional crackpottery. "Unprofessional crackpottery" is when someone who doesn't even know the basics of the subject they want to write about, then goes and says crazy things. "Professional crackpottery" is when people who are technically competent in the subject, say the crazy things. This is an example: this is a group of renowned cosmologists, who can't find a way to sensibly define probability in an infinite universe, who therefore propose that time will end a few billion years from now, for no other reason except to make their definition of probability work.

    We could talk for a long time about the various different flavors of error, bad judgment, madness, etc, which can show up when people tackle problems like this. People can get confused, they can make bad philosophical choices which lead to dumb interpretations of what their research implies, they can be seduced by a combination of ideas and waste ten years on it. Most of the supposed intellectual sins of crackpots are just evil twins of intellectual virtues.

    But outright crackpottery is not usually the problem in the arxiv. If a paper is bad, it will be because the author is careless, the result is true but unimportant, the hypothesis being developed is unlikely, etc. People also complain, not that papers are bad, but that they are written about fashionable topics. Also that people write papers for careerist reasons - to increase their publication count, to increase their number of citations, and all this will help them to get grants, because grants are partly decided on the basis of how many papers people have written and how many citations they got... So the complaint here is of an avalanche of careerist mediocrity. But mediocrity is also part of the process. Occasionally there is a new idea that opens up a whole new field of possibilities, much too big for one person or even for ten people to explore. It's actually helpful to have dozens or hundreds of researchers scouring the new landscape, it means that the new topic gets covered and understood.

    Suppose we consider a model that is fashionable right now, the "G2-MSSM". This is M-theory compactified on a manifold with "G2 holonomy", so as to produce the "minimal supersymmetric standard model". By now, there would be a dozen or two dozen papers on this topic. But before this topic could even be developed, someone had to think of studying M-theory on G2 manifolds. And before that they had to come up with M-theory, and before that they had to come up with string theory and then unify it. While on the other side, they had to invent supersymmetry and then apply it to the standard model.

    So from the mid-1970s standard model, even just to get to the possibility of thinking about the G2-MSSM, three or four big leaps of theory had to occur. In each case, there was a new idea, and then hundreds of people went over the subject for a decade, and then by the time that was done, and only then, it was now possible for someone to see the next step. I'm not saying the G2-MSSM is necessarily the apex of physics history; there are many "summits" that people have climbed towards, but only one of them will break through the clouds to see the truth. I'm just trying to convey how there can be thousands of papers written over several decades, 99% of them promoting ideas that are wrong, and yet the overall process still might get us to the right answer.
  12. Feb 17, 2012 #11


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    Eternal inflation predicts that time will end
    Raphael Bousso, Ben Freivogel, Stefan Leichenauer, Vladimir Rosenhaus
    (Submitted on 23 Sep 2010)
    Present treatments of eternal inflation regulate infinities by imposing a geometric cutoff. We point out that some matter systems reach the cutoff in finite time. This implies a nonzero probability for a novel type of catastrophe. According to the most successful measure proposals, our galaxy is likely to encounter the cutoff within the next 5 billion years.
    Comments: 22 pages, 1 figure
    "We're stuck between a rock and a hard place," says Bousso. "If you don't like the cut-off, then you have no way of making predictions and deciding what's probable in eternal inflation."

    This could simply indicate something wrong with assuming eternal inflation.

    I would say if there is a problem it is with the "eternal inflation" idea. Straining to make empirical science out of it. Better and simpler to avoid eternal inflation altogether, the way that Cai and Easson do. Let the RG (renormalization group) take care of inflation and let the Higgs field take care of fluctuations. You don't need an inflaton field (exotic thing anyway!) so you aren't plagued by it forever coming back to life.
    Google "easson inflation higgs" and get:
    Higgs Boson in RG running Inflationary Cosmology
    Yi-Fu Cai, Damien A. Easson
    (Submitted on 6 Feb 2012)
    An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
    5 pages

    Mitchell I like your post a lot! but I wouldn't call Bousso a "renowned cosmologist" in the usual straight sense of cosmologist. He's string and at best a stringymultiversy cosm'ist. Straight cosmologists would be like George Smoot, Adam Riess, Saul Perlmutter (Cosmo Nobels) or Charley Lineweaver, Simon White, Ned Wright, David Spergel, Michael Turner,...
    I think maybe Bousso deserves some credit for showing us another possible ridiculousness of "eternal inflation". The poet William Blake said "If a fool persists in his folly he will become wise." Humanity learns by following its wrong ideas out to their conclusions.

    Stefan Leichenauer, Vladimir Rosenhaus are not renowned anything, each has about 5-7 papers on arxiv. Beginners. Ben Freivogel is, I believe, a visitor attached to Bousso's group at Berkeley. He has 20 some papers on arxiv going back to 2002. I'd call him (guessing) an advanced postdoc. He focusses on stringymultiversy stuff, branes, eternal inflation etc. Again not mainstream cosmology.

    Just a quibble but let's call them renowned string multiversers. Less apt to unfairly undermine the cred of real cosmologists (hard at work checking model against a steady river of data from observatories on ground and in space).
    Last edited: Feb 17, 2012
  13. Feb 18, 2012 #12
    Hmm... Loop Quantum Gravity at higher dimension is still somewhat boring. Can they also occur inside Branes? According to Smolin, Branes can exist independent of String Theory. The idea of Branes are very and more interesting. It says that just 1mm distance from you may lie another Brane and another 3D world just like ours. Now how would LQG model this branes thing. What segregate certain LQG spin networks/foam to certain branes separate from others? Paper references needed. Thanks.
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