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Mathematical way of testing this statement?

  1. Jun 30, 2003 #1

    wolram

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    i dare say i will be jumped on from a great hight for this statment but here goes anyway
    if spacetime has structure as predicted in LQG then anything traveling
    through this structure should have a different speed than in a pure vacuum without gravitational effects, the problem i see is unless one can construct a perfect vacuum without gravitational effects how can it be tested?????
    is there a mathmatical way of testing this statment?
     
    Last edited by a moderator: Feb 5, 2013
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  3. Jun 30, 2003 #2

    marcus

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    Re: LQG

    It seems to me that your questions are often both intuitive and very much on target, or anyway agree with my own notions of what is interesting.

    It sounds like what you are describing is "dispersion relations" which are variations in the speed of light based, e.g., on energy.
    This is actually a place where at least some version of LQG could be shot down.

    There is a short June 2003 paper on this
    "Comments on Challenges for Quantum Gravity"
    Perez and Sudarsky
    arxiv.org/gr-qc/0306113

    In an odd way, one wants a theory to be vulnerable to disproof by experimental evidence, and is always looking for predictions that might be shown false. Because a physical theory that has no chance of being proven false is meaningless! The guts of a theory are in the falsifiable predictions and a model that makes no such predictions is mere mathematical fantasy and thumb-twiddling.

    LQG has in fact recently begun to face observational tests in the area of dispersion relations. Perez Sudarsky have this two-page paper and the first sentence is eerily in line with what you said.

    "There has been recently a great deal of interest in possible modifications of the dispersion relations for ordinary particles that might be the result of quantum gravitational effects."

    They mean to include light, and the first case they consider is photons of light. And "dispersion relations" means a spread in speeds related to energy.

    It is a complicated issue, or so it seems to me, and there is no simple answer. There is a related issue of LQG's "energy-momentum relation". Whatever version of the theory passes the "dispersion relations" test will then meet a test of its energy momentum relation. I have seen hopes expressed that this part of testing could be feasible sometimes within the next 5 years.

    I'll try to find out more about this and post it later.
     
  4. Jun 30, 2003 #3

    marcus

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    planned experimental tests

    Wolram you've raised a really crucial issue. I found a relevant passage about this on pages 17, 18 of a recent paper ("How far are we from a quantum theory of gravity?") by Smolin, posted March 2003.

    It is a nitty-gritty point of disagreement between LQG and string
    http://arxiv.org/hep-th/0303185

    The two theories can be expected to duke it out around the issue of "lorentz", or "poincare" (basically they mean special relativity-type) symmetry at very small scale. String bets are placed on perfect special-rel symmetry down to the smallest scale---LQG bets are on deviating from that perfect flatness or evenness at some point down near Planck scale.

    He gives numbered references to planned experimental tests.
    The equation here is the famed "energy-momentum relation"
    that goes back to Einstein 1905. Energy is E and momentum is p.
    And a couple of miniscule correction terms are stuck in which some people hope turn out to be flat zero and others wouldnt mind if arent quite:


    <<...Loop quantum gravity makes specific predictions ....

    It turns out that this has consequences for the question of whether special relativity, and lorentz invariance, is exactly true in nature, or is only an approximation which holds on scales
    much longer than the Planck scale[28]-[40]. Several recent calculations, done with different methods[36]-[38], yield predictions for modifications to the energy momentum relations for elementary particles. These are of the form,

    E2= p2 + M2+ &alpha; lPl E + &beta; lPl2 E4 + ...

    where predictions have been found for the leading coefficients &alpha;, which generally depend on spin and helicity[36]-[38].

    This is then an area of disagreement with string theory. Further, these modifications appear to be testable with planned experiments[28, 30, 39, 40].

    Hence the different predictions of string theory and loop quantum gravity concerning the fate of lorentz invariance offer a
    possibility of experimentally distinguishing the theories in the near future....>>

    Wolram as you may know or guess, in a perfect special relativity flat Minkowsky world the alpha and beta in the equation up there would be naughts. The suspected corrections are extremely small because, as you can see in the formula, they have the Planck length (lPl) in them. But apparently some people expect they are there and have plans to look for them.

    There is an curious paper by a string theorist Tom Banks where he says perfect "poincare" invariance cannot be realistic (because space is known to be curved, bumpy, not flat) and he sounds kind of frustrated with string theory because he doesnt see it evolving away from strict poincare invariance. I posted the first few paragraphs of Tom Banks paper recently in another thread. Rigid flat perfection and absolute zero in the energy-momentum relation could be good, could be bad. A cliff-hanger.
     
    Last edited: Jun 30, 2003
  5. Jun 30, 2003 #4

    marcus

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    what he says immediately after that

    Here's a continuation of that, on page 18 of the paper. Hope not posting too much about this, it seems like a central issue:

    <<4. The near term experimental situation

    The most important development of the last few years in quantum gravity is the realization that it is now possible to probe Planck scale physics experimentally. Depending on dynamical assumptions there is now good experimental sensitivity to the &alpha; terms in [the energy-momentum relation] for photons, electrons and protons. Increased sensitivity is expected over the next few years from a number of other experiments so that it is not impossible that even if the leading order E3 terms are absent, it will be possible to put order unity bounds on &beta;, the coefficient of the E4 term.

    However it is crucial to mention that to measure &alpha; and &beta; one has to specify how lorentz invariance is treated in the theory. There are two very different possibilities which must be distinguished.

    • Scenario A) The relativity of inertial frames is broken and there exists a preferred frame. In this case the analysis has to be done in that preferred frame. The most likely assumption is that the preferred frame coincides with the rest frame of the cosmic microwave background. In such theories energy and momentum conservation are assumed to remain linear.

    • Scenario B) The relativity of inertial frames is preserved, but the lorentz transformations are realized non-linearly when acting on the energy and momentum eigenstates of the theory. Such theories are called modified special relativity or doubly special relativity. Examples are given by some forms of non-commutative geometry, for example, &kappa; - Minkowski spacetime[32]. In all such theories energy and momentum conservation become non-linear which, of course, effects the analysis of the experiments. In some, but not all, cases of such theories, the geometry of spacetime becomes non-commutative.

    Among the experiments which either already give sufficient sensitivity to measure &alpha; and &beta;, or are expected to by 2010 are....>>

    He then gives 10 or so instances of near-term observational tests, some of which have already been made. Scenario B seems to survive but scenario A seems (as I would guess) pretty much ruled out.
     
    Last edited: Jun 30, 2003
  6. Jun 30, 2003 #5

    wolram

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    hi MARCUS, from my poit of view string theory is dead, i believe some
    theorists are hanging on to M theory in the hope that it gives a result similar to QLT but from a different perspective
    i was thinking, it is stated that gravity cannot be shielded,as
    QLT deals with plank size loops, it seems to me that it would be imposible to shield against it because it is "everywhere"
    i canot get to the link you gave "page not available"
    iam hopfull that some solid data will soon be forthcomming from QLT
    many thanks wolram
     
  7. Jun 30, 2003 #6

    marcus

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    Thank you for pointing that out. I pasted it in wrong at first and believe it will work now.
     
  8. Jun 30, 2003 #7

    wolram

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    thanks for link MARCUS, its going to take me ages to digest this lot
    there are things in it i do not understand yet but im determined to
    plod through it "wheeler dewitt equation"? think i will print it all
    and read it in comfort
    cheers.....
     
  9. Jun 30, 2003 #8

    marcus

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    I am a bit uneasy about your going to the trouble of printing out
    that long paper. Im in a bind about giving links to papers---there are only a very few whole papers that I would actually RECOMMEND.
    A lot of papers are just too long, with too many formulas.
    Maybe I should try to make a short list of LQG papers that are short and to the point---and somehow mathematically efficient.
    It would not be an easy list to make.

    The worst LQG paper of all, I think, is Thiemann's 286-page "Introduction to Modern Canonical Quantum General Relativity".
    Yet people go on recommending that other people read it.
    Someone named "fando" here at PF was recently advised to go read Thiemann. IMHO Thiemann writes a lot of equations but does not seem as insightful as either Ashtekar or Rovelli. Or Smolin for that matter! So a whole telephone book of Thiemann is an awful thing to contemplate.

    Just now in the case of Smolin's paper I sort of had to give a reference to it (although it's really too long to ever read thru) because of the clear explanation on pages 17 and 18 of that one issue.

    I dont like to seem to state things on my own say-so! So if I assert something and can give a reference to something on line, I often will----even tho I wouldnt put the entire paper on my short list of goodies.

    Or maybe I would. It is recent (2003) and has a lot of interesting stuff. But 90 pages!!! It seems like he could have condensed it down.

    If this model of spacetime is not shot down by experimental evidence, the writing in it is going to get much more efficient and elegant in the next few years, I believe. This can happen in a new field when people begin to teach courses and get inspired to search for ways to explain things.

    Well, the good thing is you can look at Smolin online and decide for yourself if it is worth printing out.

    Best regards,

    Marcus
     
  10. Jun 30, 2003 #9

    marcus

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    This contains interesting commentary!
     
  11. Jun 30, 2003 #10

    marcus

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    no preferred frame in "Scenario B"

    Wolram, I want to repeat something from my post of 11 AM this morning, and emphasize it because it seems important---the no preferred frame idea, or preserving the "relativity of inertial frames" as he calls it. It seems to be connected with one possible way of handling the nonlinear modification in the energy-momentum relation that comes from microscopic discreteness:

    Your expressing interest in the Smolin paper prompted me to re-read parts of it. I'm finding it better-written and more understandable than before. Earlier maybe I misjudged the paper's merits. Now I'm glad I printed it out.
     
    Last edited: Jun 30, 2003
  12. Jul 1, 2003 #11

    jeff

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    Okay, I think I've discovered the source of your conviction that strings admit only flat backgrounds. Consider the following two (appropriately parsed) quotations from page 1 of tom's paper:

    "Traditional string phenomenology...[asks] for an exact solution of a purported theory of everything, which exhibits exact Poincare symmetry..."

    "There are many...families of Poincare invariant solutions of string theory."

    In both cases, tom is speaking only of the poincare invariant sector of the moduli space of possible backgrounds of string theory. As I've mentioned, the entire moduli space must include general curved spaces. If we make the "formal" identification "TOE = QFT+GR+?", then the above may be viewed as analogous to the way that although traditional particle phenomenology is studied using QFT on flat backgrounds, the gravitational field equations of GR still admit general curved solutions.

    Also, consider - and you may have been aware of this but failed to make the connection - that the LEEFTs of strings are supergravity theories which of course could never arise from a theory whose backgrounds are all flat.

    The balance of the paper reviews how the issues tom raises might be addressed.
     
    Last edited: Jul 1, 2003
  13. Jul 1, 2003 #12

    wolram

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    hi jeff, to answer your last comment, i have to say im not qualified
    to say anything as sutch to any learned person in away that discounts
    there brilliant work, i think i have already said in other posts that" i am just a pleb", the only quality i can assign myself is good intuition, which tells me that string theorists have created a theory that only a few understand in its entirity and seems to me to be detatched from the real world, you may think i am stupid "i do myself somtimes", but to me the theory that will survive will be the one that explians our universe without the complexity of multiple dimentions,
    if people as yourself have patience with people like me it may help to bring science to the masses and encourage better understanding.
    cheers.
     
    Last edited: Jul 1, 2003
  14. Jul 1, 2003 #13

    jeff

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    I fully appreciate your sentiments. I haven't really discussed string theory much because people here are more interested in LQG and I think studying LQG provides good opportunities to learn about all kinds of physics in a very interesting and not too difficult to understand setting.

    As time goes on, I'll introduce people here to various aspects of string theory which I think are also very interesting and as with LQG provide good opportunities to learn some pretty neat physics. Also, you'll come to understand better why most high energy theorists find string theory so compelling.

    I hope to eventually address the half-truths in terms of which both string theory and LQG are portrayed by people like lee smolin.
     
    Last edited: Jul 1, 2003
  15. Jul 1, 2003 #14

    marcus

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    Tom Banks' paper in close agreement w/Smolin p.52

    Banks' critique applies to string theory in general, not merely "traditional"---

    "Balance" of paper (after the quote from page 1) not directed towards suggesting how to repair trouble. Critique still going strong on page 30.

    Banks' critique bears out Smolin (e.g. page 52 of March 2003 paper).

    Word "traditional" in second sentence does not apply to the rest---it is for historical perspective, why theory began the way it did. Note that in abstract his argument is not limited to traditional
    but applies to "M theory" another name for general stringery:

    -exerpts from Tom Banks' paper--------
    June 9, 2003

    A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
    T. Banks
    Department of Physics and Institute for Particle Physics
    University of California, Santa Cruz, CA 95064
    and
    Department of Physics and Astronomy, NHETC
    Rutgers University, Piscataway, NJ 08540
    E-mail: banks@scipp.ucsc.edu


    ABSTRACT
    I present a point of view about what M Theory is and how it is related to the real world that departs in certain crucial respects from conventional wisdom. I argue against the possibility of a background independent formulation of the theory,....



    1. Introduction: The Conventional Wisdom

    String theory, although it is a theory of gravity, is a creation of particle physicists. Traditional string phenomenology shows its pedigree by asking for an exact solution of a purported theory of everything, which exhibits exact Poincare symmetry (a symmetry which is clearly only approximate in the real world). This theory is supposed to describe the scattering of particles in the real world, which is thus postulated to be insensitive to the cosmological nature of the universe.

    The basis for this assumption is locality, a property that is evidently only approximately true of string theory at low energy. Super Planckian scattering is dominated by black hole production, and the spectrum and properties of black holes of sufficiently high energy are definitely affected by the global structure of the universe. By continuity, there are effects on low energy physics as well. The only question is how large they are.

    At any rate, a principal defect of this approach is that it already postulates two mathematically consistent solutions of the theory of everything, namely the real, cosmological, world, and the exact Poincare invariant solution. In fact, as is well known, the situation is much worse than that. There are many disconnected continuous families of Poincare invariant solutions of string theory. They have various dimensions, low energy fields, and topologies, but they all share the property of exact SUSY. The program of string phenomenology is to find a SUSY violating, Poincare invariant solution of the theory, which describes low energy scattering in the real world. In [2] I expressed the opinion that no such solution exists.

    ...The theory of the real world has a finite number of states and can be neither Poincare invariant, nor supersymmetric. Since the number of states in the real world is exp(10120), it would not be surprising to find that some of the properties of the real world are well approximated...

    ....[later in the same section, on page 6]...
    The above discussion, and [12] make it clear (to me at least) that the old dream of background independence in string theory is a chimera....

    ----------end of quotes from Tom Banks------
     
  16. Jul 1, 2003 #15

    marcus

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    key quote from Smolin, in line with Banks

    [he is doing a side-by-side comparison of the situations of stringery and loopics and has finished discussing ways LQG could be disproved or fail to achieve a quantum theory of gravity, here he does the parallel thing with string theory]

    ----from Smolin paper page 52---

    I ended the section on loop quantum gravity by indicating how the approach is most likely to fail. Some of the ways that string theory could fail, given present knowledge, include,

    • String theory could fail if there turn out to be no consistent and stable string vacua consistent with all the observed features of our universe including complete super-symmetry breaking, the absence of massless scalar fields and a positive cosmological constant.

    • Conversely, string theory could fail if it turns out that there are so many consistent and stable string vacua consistent with all observations to date that they populate the space of post-standard model physics densely enough that the theory makes no predictions for future experiments.

    • String theory could also fail for theoretical reasons. For example, it may turn out that it lacks both a perturbative defintion, if perturbative finiteness fails past genus two, and a complete non-perturbative definition (if, for example, all attempts to construct non-perturbative regularizations of supersymmetric Yang-Mills and string theories are subject to fermion doubling problems that break supersymmetry.)

    It is also possible that string theory could pass these tests, but one or more of the open conjectures could fail, leading to a different physical picture than is widely believed. For example, we may note that the present evidence is consistent with the following pessimistic conjecture....

    -----end of quote----
     
    Last edited: Jul 1, 2003
  17. Jul 1, 2003 #16

    marcus

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    Re: key quote from Smolin, in line with Banks

    I'm not inclined to take what jeffery says at face value because
    of tendency to misrepresent (eg recent characterization of Banks paper) and use obfuscation ("snow-job" replete with jargon and name-dropping) in the service of cant.

    Also seems to understand things mostly on a superficial verbal level, as e.g. an English Lit/creative writing major might (if mimicking how he thinks real physicists sound). Impressive verbal intelligence. But no right to claim authority or to (as just now with wolram) play the bully----"do you really know enough to express an opinion, little man". A real physicist would not talk like that, only a phony pretending to be one. In my modest opinion anyway.

    But that said, even tho string theory seems to be a dead horse (as wolram indicated) and not very interesting, it DOES seem interesting how closely Smolin March 2003 and Banks June 2003 papers agree on the main string troubles

    A combination of no realistic theories and too many theories.

    A key thing is a realistic theory must break supersymmetry (SUSY) at the everyday level because the real world does not exhibit supersymmetry. Both writers are concerned that the string groundstate (vacuum = basic ground state-----the model of plain "empty" space) seems unrealistic in this respect.

    Another is that real nature has no massless scalar fields. Both writers appear concerned that string theories (there always seem to be a bunch of them) predict these, etc.

    Another thing Banks is concerned with is the absence of a background independent non-perturbative theory (he says such a hoped-for thing is a "chimera"). the theories are based on
    a perfectly flat conventional spacetime ("minkowski" space, with
    "poincare" symmetry, what namedroppers we all are and I mean all not just stringers) which is then "perturbed" to put some realistic bumps in it. This "perturbative" approach worries Banks
    and he is also worried by the dependence on perfect poincare symmetry which he says is not a feature of nature. He seems bothered by this way of starting off even if you put some bumps in later---rightly or wrongly he sees it as an unrealistic foundation.
    Not something to be glossed over. The essential conservatism
    (like Ptolemy, add more epicycles and force the old model to work) of that approach as opposed to trying for a fundamentally new model of space and time.

    I will try to link up the two papers. Must say that Banks paper does shed light on what Smolin is talking about. Both know string from inside----Smolin's published string papers as well as LQG.

     
    Last edited: Jul 1, 2003
  18. Jul 1, 2003 #17

    jeff

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    Re: Tom Banks' paper in close agreement w/Smolin p.52

    You dropped the key word:

    "Traditional...phenomenology..."

    A theory and it's associated phenomenology are related but separate things. When you say phenomenology you're talking about the space of solutions to the equations of the theory, not the equations themselves. Some solutions will be poincare invariant and those are the ones we traditionally use since it's only in those cases that spin and mass are globally defined. But the rest of the solutions - in this case of string theories - are curved.

    Just pick up a book on strings and have a look.
     
    Last edited: Jul 1, 2003
  19. Jul 1, 2003 #18

    marcus

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    My point is that you gave a distorted gloss of Banks paper in your post just now, with the emphasis on traditional which you added. Unreliable. Wastes time.

     
  20. Jul 1, 2003 #19

    jeff

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    I didn't mean to distort or waste time, but do you see my point? Why is it that you're polite with everyone else, but with me you insist on being rude always reading the worst of intentions into my posts? I could have easily said that you're distorting things too, but I don't believe that you are, you're just posting what you believe to be true, which is fine with me. Why can't my posts be fine with you in this way?
     
    Last edited: Jul 1, 2003
  21. Jul 1, 2003 #20

    jeff

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    Okay, I think I've found the origin of your remarks about strings, time-dependent backgrounds and cosmology.

    On page 48 of smolin's "How far are we from the quantum theory of gravity?" we find the following remark:

    "So far no string theory background is known which is time dependent, as is our universe."

    In theories like LQG which are based on a (3+1)-dimensional canonical decomposition of spacetime, we have the idea of a spatial hypersurface whose evolution is parametrized by a time coordinate. As you know, cosmological models are typically framed in terms of this sort of noncovariant picture. In string theory however, although moduli space runs over generally curved spacetimes, there is no generally accepted way of making this sort of decomposition so string cosmology cannot be studied in the traditional way.

    Again, just pick up a book on string theory and you'll find it filled to the brim with curved spacetime.
     
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