How does LQG compare to string field theory?

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  • #1
Eh
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I figured I'd start this forum off with something about the 2 stringy theories of quantum gravity. Both loop quantum gravity and string theory propose that everything is made of 1 dimensional loops, or strings. Both are quantum theories, not classic. This means that strings are not moving around space like an every day object, but instead must be defined in terms of a quantum field. So both LQG and string theory are field theories.

It has been said that when LQG is compared to SFT, the 2 theories are very similar. But there is an important different, because while string field theory is dependent on a background of spacetime, the field itself in LQG defines spacetime. The purpose of this thread is to clarify what exactly this background dependence means. Any takers?
 

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  • #2
I don't know if I'm allowed to say this...I mean, I'm a Mentor here....but honestly, I don't think I believe in String Theory. I mean, I think Dr. Kaku is a genius and I love most of his ideas and the way he writes, etc. I'm just not a huge believer in ST. I will admit that I need to read more of Dr. Kaku's works, though, so I'm not the best to judge.

I'll admit this, too, my roommate is a graduate level physics student and he really doesn't believe in string, so he's always trying to convince me it's wrong. I live with him and I only have Dr. Kaku's books. heh.
 
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  • #3
selfAdjoint
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Well in a background dependent theory the physics happens in spacetime and spacetime is essentially unchanged. In a background free theory, of which GR is the prominant example, spactetime participates in the physics at the local level.
 
  • #4
marcus
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Originally posted by selfAdjoint
Well in a background dependent theory the physics happens in spacetime and spacetime is essentially unchanged. In a background free theory, of which GR is the prominant example, spactetime participates in the physics at the local level.

I think that's a good characterization.
The effort to quantize General Relativity (which means taking a background free approach, because GR itself does not precommit to background geometry) goes back a long ways: maybe the nineteen Forties----among other eminent people, Dirac and John Wheeler worked on the problem.

There is a standard or "Canonical" way to quantize a classical theory which involves transforming elements of the classical theory into operators on a linear space.
In the Sixties the GR variable used was the distance function or "metric" on a smoth manifold. They based their attempts on the metric because that was the most usual way of representing the gravitaitonal field in GR. Since 1986 there has been a change in approach. Most recently the effort to quantize general relativity has used the so-called "New Variables" or "Ashtekar variables"to represent the gravitational field, instead of the metric.

There are several good articles on the web giving the history of the effort to quantize
general relativity. I have to go now but may post some links when I get back, in case anyone's interested in the history.
 
  • #5
marcus
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turns out I dont have to leave immediately and can hang out a while longer.

the history of theories can be a good lens to look at them with the date 1915 is associated with General Relativity and 1926 with Quantum Theory. In both cases there were earlier developments but things came together for the theory in some decisive way at the landmark date.
These two theories have been the pillars of 20th century physics and have
had great predictive successes,

but they seem not to mix easily, people have tried since early times to merge the two
but so far it hasn't been possible, so quantizing general relatitivity is a major
outstanding job and may involve fundamental change at the foundation level
in how the two theories are understood.

There has been a tendency for particle theorists to want to throw out General Relativity because it doesnt fit quantum field theory ("there must be something wrong with the spacetime geometry approach, chuck it, let's explain the force of gravity some other way more like particles")
By contrast, experts in General Relativity, "relativists" as they call themselves, tend to see
their goal more conservatively ("both these theories are successful, let's keep them
and try to understand why it has been so difficult to make them compatible")

A discussion of the history and the issue of background independence can be found
in the book "Quantum Gravity" which is currently available in draft form but which will eventually be published by Cambridge University Press. It is by Carlo Rovelli, a relativist at the University of Marseilles (this fall visiting in Rome) and a historian of science as well as being a relativist (that is, a specialist in GR.)

There is a link to the book at Rovelli's Marseilles website

http://www.cpt.univ-mrs.fr/~rovelli/

An interesting thing about Rovelli's book is that it is not all mathematical.
It has a lot of discussion of the historical development of the theories and efforts to
combine them---and a sharp delineation of the obstacles: different conceptions of space and time. Also discussion of the different meanings that time has in ordinary language and in physical theories. Might sound a bit abstract and dry but personally I didnt find it that.
He knows how to be philosophical and interesting at the same time. Anyway there are these long non-mathematical parts that describe the changes people have gone through thinking about the basic issues.

This thread is supposed to be about comparing the effort to quantize GR (loop quantum gravity being part of this effort) with Dr. Kaku's string theory.
My impression is that string theories tend to be extensions of particle theory, and like QFT are based on backgrounds with some fixed geometry. The theories may be "perturbative" in that the background geometry can be perturbed by dynamic fluctuations. But since string theories do not treat geometry in a background free way from the start it is hard to see their relevance to the ongoing program of quantizing general relativity.

So the first kind of comparison to make, I guess, is the one suggested by the previous poster, self Adjoint, which is to say:
how do you compare what the two theories are trying to do as regards the key issues?
where do the theories stand in historical relation to GR and QT (the two main developments in 20th century physics)?
 
  • #6
Kleins Ordering of Geometries

Marcus,

I am ever the student here and your post was very interesting.

Kleins Ordering of Geometries might be a interesting look and the complexities of the maleabiltiy of vison, takes on new form, when we look from euclidean right into the noneulcidean phases of geometries, to finally understand how topology fits.

That we could have define the metric tensors, and found complicated factors, even more so, when the supertensors become more points in which to define that continuity of movement and form? The dynamics played on on those brane states, following geometrical issues of point line plane, to end up with boson productions, are always a interesting quest for understanding in Pierre Ramonds site.


http://www.superstringtheory.com/forum/geomboard/messages4/18.html [Broken]

I have been trying to decipher for a long time and without the physics background it makes it very difficult. But indeed over time I have been able to absorb some things and one of them is the interpretation of dimension and its relevance in how we see information transferred.

Cosmologically, the simplicity of understanding becomes quite complex when we see this representation played out in the quantum mechanics. Continuity of movement becomes really interesting when understanding information transferred in this cosmological sense. Plasma versus solid forms and geometrical consideration.

I look forward to reading your posts in this regard. Paul in superstringtheory board is very knowledgeable, as well as some of the participants on that board.

Sol
 
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  • #7
marcus
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Sol,

Thanks for the kind welcome!

Marcus
 
  • #8
Eh
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Sol, good to see you here. It would be great if we could get a good string theory forum going here, so I hope you'll stick around. If you could somehow convince Dick T. to post here, things would be off to a good start.

No kx21 though.
 
  • #9
selfAdjoint
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Umm, I guess it's time to reveal my secret identity. I am DickT.
 
  • #10
MathematicalPhysicist
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A Question About LQG

because this thread is concerned with lqg i think this is appropiate to ask my question here.
can lqg be implemented in more than the four dimensions which are time and the other 3 spatial dimensions? (i read in an article in hebrew that it can be done), if the answer is yes why can it be done?

thanks in advance for any replies.
 
  • #11
marcus
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Originally posted by loop quantum gravity
because this thread is concerned with lqg i think this is appropiate to ask my question here.
can lqg be implemented in more than the four dimensions which are time and the other 3 spatial dimensions? (i read in an article in hebrew that it can be done), if the answer is yes why can it be done?

thanks in advance for any replies.

Hello LQG, I also have read in several places (but in english!) that it can be done.
This thread is probably mostly for comparison with string field theory so we could
make another thread in "theoretical" forum or "math" forum for it.

the main thing is this. LQG typically starts with a differential manifold Σ representing
space and then builds it's structures representing geometry (like loops and like "connections"
and like "networks") in that continuum Σ
So the same basic procedure is followed to construct the theory whatever the dimension of
the underlying smooth continuum or manifold.
So people often describe LQG and define the basic elements of the theory without ever
specifying the spatial dimension----they just say they are doing it for "a manifold of dimension d" and then this d (which can be 1,2,3,4,5,....whatever) appears in the formulas where
ordinarily would be 3.

I think this is actually not too surprising because LQG is focused on the job of trying
to quantize general relativity and I believe the classical (un-quantum) theory of GR is something that one can do in other dimensionality besides 1+3, so I would expect that
LQG is not very demanding about the dimension and could be done in other dimension
besides 1+3. This year I saw a number of papers doing LQG in dimension 1+2 (one time and 2 space) where several things are simpler and easier-----I think they want to get understanding from the simpler case which they hope then to carry over.

I will go start a LQG thread in "theoretical" forum so as not to mis-use this thread.
 
  • #12
jeff
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Originally posted by Eh
It would be great if we could get a good string theory forum going here

I'm happy to discuss ST, but I think a QFT forum makes alot of sense.
 
  • #13
Eh
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Originally posted by selfAdjoint
Umm, I guess it's time to reveal my secret identity. I am DickT.

Ahh, so everyone is already here. Say, haven't you been posting of PF for a long time?
 
  • #14
selfAdjoint
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Originally posted by Eh
Ahh, so everyone is already here. Say, haven't you been posting of PF for a long time?

Quite a while. Since superstringtheory seems to have fallen to the "creative" crowd, I find more real meat over here.
 
  • #15
paultrr
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Hello Sol, I see everyone has rather moved over here in one way or another.
 
  • #16
pelastration
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He Paul,

good to see you here! Welcome.
For sure we will appreciate your insights!

Dirk
 
  • #17
We Need String People:)

Originally posted by paultrr
Hello Sol, I see everyone has rather moved over here in one way or another.



Hello Paul,

Like Dirk, it is good to see you here.


Sol
 
  • #18
Nereid
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Back in the old forum, it seems Dr S. A. is having a bad week.
 
  • #19
paultrr
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Hello and the Doctor S. A. issue

Hello to all of you and actually Doctor S. A. perhaps has himself in a bit of a fix.
 
  • #20
paultrr
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Folded Brane Models

Since I used a version of the folded-brane model in my own work I did a bit of artwork using the new MAP project data and explored a bit what the other half of the brane should look like. In essence it is simular to a reversed color image of our own. Larger voids and more highly clumped areas of matter. I suspect, following an idea from VSL that as the early universe formed with a slightly displaced from the primal mass event horizon that expanded and was slowly over taken by the expanding mass till the two were equal that that swept out area was responcible for the difference in structure in that part of the brane and our part. Right now its simply a conjecture, but, a conjecture that should apply to any folded brane model. The following link will take you to a short PDF file I did up on this with some explination of all this through an illustration and two images based upon MAP data: http://demoprints.eprints.org/archive/00000602/ [Broken]
 
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  • #21
strubenuff
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In response to the first post, string theory has been updated to "m-theory" and no longer limits the make-up of "things" to one-dimensions strings.
 
  • #22
paultrr
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Both loop quantum gravity and string theory agree on some of the basic issues. They agree that there is a physical scale on which the nature of space and time is very different from that which we observe. This scale is extremely small, far out of the reach of experiments done with even the largest particle accelerators. It may in fact be very much smaller than we have so far probed. It is usually thought to be as much as 20 orders of magnitude different or more. The scale where quantum gravity is necessary to describe space and time is called the Planck scale. Both string theory and loop quantum gravity are theories about what space and time are like on this tiny scale. Generally it has become clear that both are windows and pictures of this realm. One, String Theory, seems to discribe the particles and the forces they generate. One seems to discribe the internal structure of Strings themselves. Together they tend to discribe the branes themselves from 11(or 12) dimensional M-Theory(F-Theory).

As Smolin pointed out in his Three Roads Book, there is a third road troden by those who discarded both relativity and quantum theory as being too flawed and incomplete to be proper starting points. To an extent some of the VSL crowd is part of this third path, even though some of us who hold to VSL concepts clearly accept both String Theory and LQFT. I think personally that the truth is found at the intersection of all three paths. This combined path involves deep, philosophical questions such as, 'What is time?' or, 'How do we describe a universe in which we are participants?', and other strange questions that have always puzzled mankind. It involves coming up with whole new conceptual worlds and mathematical formalisms, some of which those involved in String Theory have encountered.

The people involved in this search include Alain Connes, David Finkelstein, Christopher Isham, Roger Penrose and Raphael Sorkin, Lee Smolin, Steven Hawking, Edward Witten, Fernando Loup, myself, and many here also as well as others. New Scientists a few months ago likened us to the radicals shacking up the very foundation of modern science and indead we are visionary radicals in many way, some of us could be likened to prophet or fool, who prefers that essential uncertainty to the comfort of travelling with a crowd of like-minded seekers. But we've all, I think, been brave enough to challenge the more traditional paths and even had to deal with the criticism of the majority of the Scientific community along the way.

Back in the Middle Ages it took one brillent Monk to shack the very foundations of an establishment and to utter some simple words that had been there all along in the same book that establishment had always upheld as truth, "The Just shall live by faith." Those of us on this quest for a quantum theory of gravity live by a solid faith that Nature itself will provide our answers. So like the Monk of old we plaster our own 95 Thesis upon the doors of the Establishment and seek to shine a light into an area that till now has remained dark. We follow some strange paths, paths that at times defy our common day sence of logic and yet, along the way we have begun to learn somethings that nature has always been trying to show us in little often overlooked ways. But this is a path that has begun to yield way into a land we never thought could exist before, a land one of the founders of this path once called the Quantum Foam.
 
  • #23
meteor
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I've read that the spin network representation replaced the loop representation in LQG. Does it mean that there are no loops in the spin network representation of LQG?
 
  • #24
Paul,


As Smolin pointed out in his Three Roads Book, there is a third road troden by those who discarded both relativity and quantum theory as being too flawed and incomplete to be proper starting points. To an extent some of the VSL crowd is part of this third path, even though some of us who hold to VSL concepts clearly accept both String Theory and LQFT. I think personally that the truth is found at the intersection of all three paths. This combined path involves deep, philosophical questions such as, 'What is time?' or, 'How do we describe a universe in which we are participants?', and other strange questions that have always puzzled mankind. It involves coming up with whole new conceptual worlds and mathematical formalisms, some of which those involved in String Theory have encountered.

Time becomes an important issue in terms of what and how we describe gravity in the continuing develpement of the dynamics of those geometries.

When you move to the Z direction it is already understood that the 2d configuration of the brane enlists the mind to gather length and width(longitudal and transverse understandings as extensions of the photon and the information it carries, along with the graviton, which can leave the brane.

Rotation in having left the brane, is a undertanding of what happens in that Z direction and follows in the undertanding of GR. Time then becomes then becomes the dynamics of movement of the graviton and the photon and there spin orientations.

This logic follows the idea of moon mapping that I have detailed in the other thread as well as elemental consideration in the detection of gravitational variances in those elemental considerations?

http://www.superstringtheory.com/forum/partboard/messages23/102.html [Broken]



Again I am open to corrections.

Sol
 
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  • #25
Nereid
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Why the Moon sol? Why not Mercury (more iron), Venus, or Mars?
 
  • #26
Geometrodynamics

Nereid,

http://www.superstringtheory.com/forum/metaboard/messages18/269.html [Broken]

It is what began for me to make sense of how we would map all globes. I am interested in what the envelope looks like out in space. I am also interested in how we might see the differences in the gravitational fields. I assumed they would be spherical, yet becuase of the elements, this is not so?:)

If we can see what is happening in this way, I believe we have found a new way in which to map possibilties in terms of transportation.

http://www.superstringtheory.com/forum/metaboard/messages18/270.html [Broken]

This is highly speculative of course, yet it is not without some concern that I also see what must be considered in space travel. How could we use the graviton emissions in the bulk, to move accordingly? Along the heavy concentrations of gatherings(?) and we look to the source of the most intense values, energy, and information released from one point in space, our star meausres of distance, is really of dimensional consideration?

You must forgive me, as I am truly a student here. The moon was a starting point, yet the sun holds important factors as well. How would we see the dynamics of the gravitational considerations in this field as well?

So I tried to look at dimension, in how we might percieve it in extremes?

http://www.superstringtheory.com/forum/metaboard/messages18/259.html [Broken]

Superfluids, and how we might interpret this dynamical movement when the metric points are somehow considered in dimensional significance? What is time?

It might be all wrong here, I am moving as slow as possible to make sure there are no mistakes. If people do not correct then I am a lose cannon, and could have perpetuated illusions. That's why I always remain open for better minds then mine.

Thanks for asking.

Sol
 
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  • #27
paultrr
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As far as space exploration goes, if you are refering to advanced theoretical types, there are a couple of ways to go when it comes to the usage of gravity.

1.) Warp drives, does not have to be superluminal, but requires a strong gravity field in front, an exotic field at least as far as pressure in the rear, and also a neutralized one around the craft which in effect keeps the craft in a free fall condition.

2.) Wormhole type drives that require a strong gravity field(ie Blackhole state) and exotic energy.

3.) Disjunction or Bias type drives simular to those proposed by Marc Mills original group.

4.) Shut drive that while simular to a wormhole simply uses gravity alone to perform a simular trick on space-time as does the forward portion of a warp drive. To the best of my present knowledge this one has been the least examined and worked out. I've on occasions looked at the idea myself a bit. Does not require exotic energy. But I've yet to see a decent way to keep the craft out of the tidal stress areas, except perhaps to keep the shunt small, use convention drive and allow the shorter travel distances to augment our convention drives. At lower powers the tidal stress appears less.

Problem is all of these require some advances we simply do not have at the present. They each have their good points and their bad points. Two have the common problem of the exotic energy. One suffers a forward navigation problem, the list goes on a bit. But, if we could discover ways from quantum gravity to harness and control gravity some of the problems involved could be engineered around.

I would also like to add one other alternative, untried at present and not at present fully explored and worked out. This other method one could properly term hyperdrive and it involves M-Theory and Brane world concepts about hyperspace and the possibility of getting to points in normal space-time faster by going through Hyperspace. A friend of mine on the outside has been exploring that aspect for a bit by the name of Fernando Loup. Its based upon the more standard brane models that allow gravity to escape off the brane. It has its good points and offers some suggestions on how to actually, using our present tech, test the idea out. Other than that several key ideas related, but under a different title are due to appear over the next few months in a major mainline Journal on gravity. So actually till those appear this one is strickly an up and coming proposal in many ways.
 
  • #28
paultrr
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That one there should read: Shunt Drive not Shut drive. Typo.
 
  • #29
Eh
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M theory does complicate things a little. Would placing the strings on a dynamic background (a brane) mean M theory as a whole is still background dependent?
 
  • #30
paultrr
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M-Theory is generally across the board considered background dependent. You invoke some structures on space-time, etc.
 
  • #31
paultrr
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If one looks at say LQFT as discribing the internal structure of the brane and then higher up Strings then in essence you still have the Strings as background dependent, while LQFT is independent of the background.
 
  • #32
jeff
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Originally posted by paultrr
... the folded-brane model...The following link will take you to a short PDF file I did up on this with some explination of all this through an illustration and two images based upon MAP data: http://demoprints.eprints.org/archive/00000602/ [Broken]

I looked at this and it's one of the most extraordinary displays of crackpottery I've ever seen. There may not have been people at superstringtheory.com that could see this, but there are people here who can, so knock it off: Your posts at best are spam, and spamming violates site guidelines.
 
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  • #33
paultrr
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If you would bother to go to http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v411/n6841/full/411986a0_r.html for a starting point one of the proposed folded brane models, something I did not propose is based on the idea our exotic energy actually comes from the otherside of the brane as this Nature article points out. In essence the idea through gravity crossing the brane becomes reversed on our side. The original article which was a published one was done by others. To quote Nature itself, "One entertaining version of brane-world theory offers an unusual explanation for 'dark matter', the Universe's 'missing' mass that can be detected by its gravitational influence, yet seems to emit no radiation. Arkani-Hamed, Dvali, Dimopoulos and Nemanja Kaloper, also at Stanford, have proposed that our brane Universe could be folded back on itself (see diagram, right), so that stars at huge distances from us along the brane could be less than a millimetre away along a higher dimension6. Their light would not yet have reached us because it has to travel all the way around the folded brane, but their gravity could take the short cut. " The reference here is Arkani-Hamed, N., Dimopoulos, S., Kaloper, N. & Dvali, G. J. High Energy Phys. [online] <http://jhep.sissa.it/archive/papers/jhep122000010/jhep122000010.pdf> (2000). If the other side has mass causing some of this effect, and this is just theory, then any map of this side would be reversed differently on the other side which does have some implications as far as cosmology goes. As far as posting that map on the other string forum since it is down that was never done. So I might suggest checking out what some of the published proposed brane models actually suggest first before you attack something and who actually proposed those models in the first place since I did not original propose that specific model. I believe if you run a check under those names given in that Nature article you can locate the original articles they all did themselves and also you can find other suggestions by other theorists on that specific model. All I did, and that is stated in that article was to suggest if their idea holds true then the CMB image here is a reverse of the other side, thus the simple color flipped image I used. In fact, my own article discribed that as the reason I chose that method.

Now I believe that taking an already proposed theory and making the suggestion that we could use our CMB plot to get an idea of what the other side of the brane appears like does not constitute Spam in the least. If that was the case then any time any one in research was to suggest an idea based upon a proposed theory that would be spam also.

Now I believe I have shown the folded brane model is a published theory at present. I believe I have also shown were that idea of things getting reversed a bit across the brane comes from which is itself published an public domain. That tends to imply the suggest is not without founded merit and you're own suggestion that those extra dimensions in F-theory are not real dimensions considering some F=Theory based articles do consider them such makes that statement a bit false itself. Also given that at present any dimensions outside of the known four remain theoretical and unproven tends to bring up the issue weither any of these dimensions actually exist. A lot of us believe they do. But not everyone does. As it stands, using you're own quote back at you that would tend to bring into question weither or not you're own stance,or mine, or anyone else who subscribes to M-Theory in general is actually physical. Now should we also consider posting of ideas related to that as spam since both are based upon already published and established models.
 
  • #34
jeff
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Originally posted by paultrr
So I might suggest checking out what some of the published proposed brane models actually suggest first before you attack something and who actually proposed those models in the first place since I did not original propose that specific model.

It's your idea's that are crackpottery, not theirs.

Originally posted by paultrr
you're own suggestion that those extra dimensions in F-theory are not real dimensions considering some F=Theory based articles do consider them such makes that statement a bit false itself.

What I said was...

Originally posted by jeff
As I said, in the case of F-theory, the two extra dimensions aren't dimensions in the usual sense: There's no limit in which they decompactify to become normal spacetime dimensions. Although there are some applications of F-theory in which it is convenient to view one of the two extra dimensions as an additional "time" dimension, we do not view the F-torus as possessing a defacto extra time dimension. In fact, we're not sure what the ultimate significance of the F-torus or the rest of F-theory is.

Originally posted by jeff
The 10-dimensional IIB string theory allows two equivalent descriptions; one in which ordinary strings are very heavy while D-strings (1-dimensional D-branes) are very light, and one in which the opposite holds. This duality has a geometric interpretation in terms of two additional toroidal dimensions. But these appear not to be actual dimensions in the sense that the extra dimension in M-theory is. Although aspects of F-theory are known to originate in M-theory and have been useful tools in framing some 10-dimensional problems in terms of 12-dimensional geometries, it's ultimate meaning is unclear.
 
  • #35


Originally posted by jeff
I looked at this and it's one of the most extraordinary displays of crackpottery I've ever seen.

Originally posted by jeff
It's your idea's that are crackpottery, not theirs.

This basically speaks for itself. However much we try to topologically glue things together in string theory there will allways be cracks in the pot ie. there will allways be new fields (porous media) beneath topological structures (potters clay) once the theory dries up; it's mathematical and particle smashing resources). It all depends on what kind of topical glue we use to fix the laws/habits of nature.
 

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