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?
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.
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.
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)?
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 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
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.
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.
Re: A Question About LQG 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.
Quite a while. Since superstringtheory seems to have fallen to the "creative" crowd, I find more real meat over here.
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.
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/