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Alejandro and the graviton

  1. Aug 3, 2004 #1


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    Alejandro recently submitted a post at SPS which engaged the active attention of Lubos Motl. So much so that unless one has sharp eyes one cannot see Alejandro's original post-----there are so many "moderator notes" inserted by Lubos.

    this means Alejandro's original post probably has some interesting points, so let us reconstruct it here (without the L.M. comment) so we can see the overall tenor of it----after that we can consider what L.M. interjected, and how Alejandro replied and so forth. Here is the reconstructed original:

    ----quote from arivero---
    Some days ago, in another forum, Urs wondered why some of us are very
    positive about the relationship between strings and gauge theory but
    we are not excited about the point of strings "knowing gravity".
    Yep, if one thinks about it, it is surprising that I am not surprised.
    Perhaps it is because string lessons do not derive, as far as I have
    read, Einstein-Hilbert action in some limit.
    Most teachers just show a sort of consistent spin two particle and they
    say "see, the graviton here". Some others note that string is about
    word-sheet actions, thus it contains a constant having the dimensions
    appropiate to measure curvature. But neither spin two nor curvature or
    area are definitive signatures of our gravity. It is possible to formulate
    a curvature theory for other approximations to Einstein gravity, for
    instance for Newtonian gravity.
    Perhaps related to this doubt, note that also Electroweak Theory has a
    non-renormalisable, area-like, constant: fermi constant. But it does
    not have spin two particles by itself.
    And one could devise some ways
    to formulate EW theory, or even electromagnetism, as a worldsheet
    action theory, thus sort of strings.
    But I do not see how a elementary spin two field would be forced by using
    these formulations.

    --------------end quote--------
    I have put numbers as pointers to the "moderator notes", which I will fetch so we can see the general tenor of them as well.
  2. jcsd
  3. Aug 3, 2004 #2


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    Lubos reply interjected

    ----quote from SPS moderator notes---
    [Moderator's note: I thought that Edward Witten experienced the strongest
    intellectual thrill in his life when he learned how string theory
    predicts gravity, and Witten is not the only one. ;-) LM]

    [Moderator's note: Good textbooks and lectures of string theory - e.g.
    chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that
    the background metric must satisfy the correct Einstein equations if
    the worldsheet theory is conformal i.e. consistent. They also explain
    that the same effective action is seen by the scattering of the
    perturbations - namely by the gravitons. This is such a basic feature
    of string theory - and a key motivation to study that I would say
    that someone who has not this calculation does not really know
    what string theory is at the technical level. LM]

    [Moderator's note: One can show the correct mass (zero), correct spin
    (two) and correct interactions of the graviton in string theory.
    Moreover, the correct interactions at low energies are guaranteed by
    the consistency of the theory - general relativity is the only way how
    to define consistent nonzero couplings of massless spin two particles
    in a (special) relativistic theory. Because string theory defined as
    a worldsheet theory can be shown to give a consistent spacetime theory,
    the spacetime theory must automatically contain the right interactions
    at long distances, and explicit calculations show that this is indeed the
    case. LM]

    [Moderator's note: Why should the electroweak theory have spin two
    particles? LM]

    [Moderator's note: Certainly not as anything analogous to string theory as
    we know it. String theory, in the conventional meaning of the word,
    always automatically includes gravity, and it is unique - once the five
    different perturbative versions are unified. The idea that one can make
    a consistent string theory that gives "electroweak theory only" is
    a misunderstanding of basics of string theory. What sort of "new" string
    theory do you have in mind? I think that this is a very popular laymen's
    misunderstanding - they often think that it is possible to modify string
    theory in hundreds of ways and define hundreds of different sibblings of
    string theory. No, string theory - or a theory of quantum gravity -
    is unique. LM]

    [Moderator's note: An elementary spin two field is described by a tensor
    with at least two indices, say . Some of the components of this
    tensor would lead to negative-norm states - namely the mixed time-space
    components. There must be a gauge symmetry that removes these unphysical polarizations and (linearized or nonlinear) general covariance is the only possible gauge symmetry that can remove these states, and still lead to nonzero interactions. Just try to find a different solution, and you
    will see that you fail. LM]

    -----end quote----

    I suppose the first interesting thing one notices is that the moderator notes are somewhat longer than the original post from Alejandro.
    Last edited: Aug 3, 2004
  4. Aug 3, 2004 #3
    But Marcus how would we understand the continuing evolution of theoretical positions for laymen like me, if we did not have Lubos respond to what Arivero writes? Your having a hard time with me as it is, and my thick head sometimes :smile:

    If you noticed, Lubos also took parts of his responses from other posts and repasted them in arivero's post. A sure sign to me, he is drivng the point home :smile:

    I had a addition link by arivero that I showed today as well that might be of interest to you, in terms of parameters, of natural numbers.
  5. Aug 3, 2004 #4


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    the exchange has now continued several more posts and Alejandro says he is convinced by LM and will read Chapter 3 of Green,Schwarz,Witten textbook and also Chapter 3 of Polchinski textbook. thanks to Lubos for the kind and lengthy exposition.

    anyone interested in the whole exchange of posts [and moderator notes]
    can read the full thread in SPS

    the thread is called "not surprised about the graviton?"

    this thread focuses the spotlight on the issue of to what extent and how
    is string theory supposed to "know" about gravity.

    For me, although not party to the discussion at SPS, the abiding question continues to be: if gravity is an effect of the (highly variable) geometry of spacetime----in other words if it is NOT the effect of forces mediated by particles-----then in what sense can a theory with a rigid background geometry model gravity?

    What has repeatedly impressed me, as I listen to discussions like this, is the extent to which the evidence offered for stringy knowledge of gravity resemble Omens or signs of Good Things to Come.

    A graviton, I take it, is not something that a string theorist would impute to nature as something that actually exists----rather it is something that appears in the analysis when a flat approximation is made using Minkowski space or some other artifical convenience.

    It was at one time customary for a Roman official called the Haruspex to consult the entrails of a rabbit and if he found favorable omens then you would go ahead with whatever it was.

    In the String theory case, the Haruspex examines the entrails of Minkowski space and discovers a graviton----this then is a favorable omen.

    -------quote from LM note [2]----------

    ...the background metric must satisfy the correct Einstein equations if
    the worldsheet theory is conformal i.e. consistent. They also explain
    that the same effective action is seen by the scattering of the
    perturbations - namely by the gravitons....

    -----end quote----

    the gravitons, one sees here, are equated with the "perturbations" which are something that occurs in the analysis using a rigid (usually flat) background. One sets up an artificial rigid spacetime framework chosen from a menu, and then one twangs it. The twangs or ripples are the perturbations superimposed on the background. these are the "gravitons".

    If the background were fully dynamic one imagines one would not want or need gravitons.

    At another point the moderator note [2] says "the background metric must satisfy the correct Einstein equations". This prompts me to reflect that
    if the background is flat spacetime---Minkowski space---that is a particular solution of the Einstein equations for the special case when there is no matter or energy in the universe!

    This is certainly a good approximation to Nature wherever there is not much matter or energy around, although I doubt anyone would call it a realistic solution.

    Haelfix had a good post about these quandaries in another thread. i will try to locate a link for it.
    [edit: yes here is the Haelfix post]


    Meanwhile, many thanks to Lubos Motl for such careful and enlightening comments, and cordial thanks as well to Alejandro for giving Lubos the occasion to hold forth!
    Last edited: Aug 3, 2004
  6. Aug 3, 2004 #5


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    Marcus I think the snarky haruspex references are unfair to string physics. Historically they pursued quantized strings for other reasons and did it in the standard way, in terms of flat Minkowski relativity. And lo and behold the graviton, all unlooked for, fell out of their theory, a great new thing. And AFAIK graviton physics cannot be distinguished from GR physics with present day experiments.
  7. Aug 3, 2004 #6


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    It was kind of snarky to mention haruspices wasnt it? :smile: Yes not really fair. And I would guess that you are right. Present-day experiments would not be able to tell real GR physics from graviton physics.

    Perhaps it would only be distinguishable if you actually had a black hole or a big bang in your living room. I suppose it is primarily in those rare cases when you have a highlycurved space that graviton physics doesnt do a good imitation of the real thing, or when geometries change as stars collapse.

    Historically too you I suspect you are right---indeed I suppose that the original string people were brilliant and courageous. The Haruspex image was not historical in nature but came to mind when I imagined a latterday light taking one of us aside in 2004 to interpret the omens for him. "We have examined the graviton and behold it is a Sign we are on the Right Path."
  8. Aug 3, 2004 #7


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    And when it fell out for them, they did take it as such a sign. It had a tremendous effect, converting physicists who were working on other things to stringiness. Likewise the discovery of the superstrings was a blast (Feynmann danced when he heard there was only one superstring theory, but then they discovered the others). And the discovery of the dualities and the glimpses of non-pertubative M-theory have been a sign unto them too, as is Maldacena's discovery of the holographic principle.

    It might be a hit on string physicists that they live from wonder to wonder and become defensive when there hasn't been one for a while. But the critics are always there, and they are only silenced by a new miracle. Nobody hurts more than the string crowd because their string physics is too energetic for today's experiments to test it.
  9. Aug 4, 2004 #8


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    Well, IMHO it should be more readable if s.p.s used the conventional > quotation sign instead of bracketing everything, that is true.

    And yes, I went this morning to the library to get the books, I borrowed the old GSW and glanced Polchiski. I'd say that the real claim is that strings are able to quantise a 26 dim Kaluza-Klein theories or 10 dim supersym ones with very specific matter sources. This is not exactly as to quantise 4dim gravity, but well I think that 26 dim gravity is also non renormalisable, is it?

    Not my theory, but De Vries' one. Interesting anyway.
  10. Aug 4, 2004 #9
    I am not sure of the beauty Lubos or others are seeing, but what is amazing to me, is that this theoretical particle assuming distinctions of quantizing gravitational wavess, could actually inhibit all those hidden dimensions.

    As I have shown numerous times now, the Planck Epoch seems very real to me when we can look at the begininning and the end, and can, include this graviton in all it's features?

    Time with 4d space reduced to time 3d space, and we are faced with principals that reveal "electromagnetism"{a gaussian view of hyperdimensional realities} from the unification with gravity. If this is so, then what is in seen in hyperdimensional realites of the graviton?

    Laymen perspective and certainly open to corrections.
  11. Aug 4, 2004 #10
    Yes they are trying to control the chatter and remain pure :smile:

    My post above yours might help, maybe not. But you have to remeber what Baez said in a link supplied by..... and I will supply quote by whom and response.[/quote]

    Yes most certainly.
  12. Aug 4, 2004 #11


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    General relativity is non renomalizable in dimensions greater than two. But string theory has no renormalization to it at all, one of its strong points with physicists. The string graviton does not give GR (with curved space), but it gives physics that looks like GR physics, doing it in flat spacetime with exchange of particles instead of background free in a spacetime whose curvature responds to the matter and energy present.
  13. Aug 4, 2004 #12


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    There is no room for such doubts, my son.

    Another exquisite exchange at SPS:
    Lubos says the background metric must satisfy the correct Einstein equations. then he clarifies that it does not satisfy the Einstein equations, actually, but something that is, one presumes, even more correct and furthermore that there is no room for uncertainty or doubt about this.:smile: I shall burst.

    > > [Moderator's note: Good textbooks and lectures of string theory - e.g.
    > > chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that
    > > the background metric must satisfy the correct Einstein equations if
    > > the worldsheet theory is conformal i.e. consistent.

    Perhaps the language generated some of my doubts. Polchinski, pg. 112.
    just says "The equation b... resembles Einstein's equation". The word
    "resembles" sounds far away from a theorem. It implies that the author is
    being cautious about having gravity there.

    [Moderator's note: Nope. You misunderstood the word "resembles". The
    reason why Polchinski uses the word "resembles" is surely not his
    uncertainty about whether string theory contains gravity. There is no
    room for such an uncertainty and such doubts.
    The verb "resemble"
    means "look like" - in other words, the equations that one derives
    are not exactly the original Einstein's equations, but Einstein's
    equations coupled to matter (dilaton, B-field...) which also can
    acquire various new corrections. String theory also implies
    what sort of matter and corrections appear, and this implication
    is rigorous. The word "resemble" means that the equations are not
    quite the pure and simple laws of GR from 1915. But this disagreement
    does not show a flaw of string theory; on the contrary, it shows
    that the simple laws of GR were not the whole story. LM]

    Hmm. Do you remember where in the books is the limit of small Newton

    [Moderator's note: which limit you exactly want? Linearized gravity?
    In perturbative string theory, GR is obtained in the limit goes
    to zero - in other words, at distances much longer than
    the typical length scale associated with strings. Newton's constant
    is a power of determined by dimensional analysis - times
    . Sending to zero is not enough to reduce string
    theory to pure GR. Even at vanishing string coupling - or, perhaps,
    especially at vanishing string coupling - string theory differs from
    GR or any other theory of pointlike particles. The stringy equations
    of motion - for the background - are derived in Polchinski. The whole
    proof is there and everyone who knows how to take limits can take them.
    I am not sure what you're exactly looking for. But if you want to derive
    the Newtonian limit of GR, the same proof from GR can be used in string
    theory as well, as long as the distances between all objects are much
    longer than where GR is a good approximation of the full
    (string) theory. LM]

    ----end quote----

    Hey Alejandro! You misunderstood the word "resembles"!
    Last edited: Aug 4, 2004
  14. Aug 6, 2004 #13


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    sps thread, remixed for PF

    Before packing, I was sending a further comment to sps. I can not find the content, but here is the draft, just in case you want to follow discussion here in PF too.

    t seems that the claim is that the theory is able to execute a
    consistent quantisation of Kaluza Klein theory when this theory has
    a definite critical dimension and a definite content of matter
    fields. This is seen as a virtue because of the uniqueness: it
    fixes a very specific family of theories, say 26 dim Kaluza Klein
    with the tachions or, better, the 10 dim susy version.

    I am not surprised about having curvatures. It is well known that
    the curvatures in Riemann tensor are essentially a set of two-dimensional
    objects, so it was to be expected that a two dimensional method
    as the string worldsheet were able to catch the Einstein Hilbert

    I was asking for a verification of the quantisation property. In
    the same way that one can get classical electrodinamics from QED, one
    should be able to get the classical Kaluza Klein theory in some
    limit. Also I was asking because sometimes the limit process is not
    the most naive; remember for instance how quantum mechanics
    approaches classical mechanics in the limit of high quantum numbers,
    not really in the h->0.

    Well, I will be on vacation for some days, but I will carry the GSW in the backpack and a candlelight.
  15. Aug 30, 2004 #14


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    Let me remark this:
    IE, only the D=26 bosonic string or the D=11 susy strings do reproduce the correct Einstein equations.
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