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Does string theory merge space and time into spacetime? 
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#1
Aug910, 07:31 PM

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Does string theory merge space and time into spacetime?
GR combines space and time as spacetime, I've heard that in string theory there is 9+1 or 10+1 spatial dimensions, with 3 large, 6 curled, 1 time dimension. Is there a spacetime in string theory? Are YauCalibi manifolds part of this spacetime? How does string theory deal with the different conception of space and time in GR and QM? Is the spacetime in string theory 4D or 11D? 


#2
Aug910, 07:42 PM

P: 2,828

It is special relativity which merges space and time. General relativity makes spacetime into a dynamical object, rather than a stage "onto which" other objects exists.
String theory respects special relativity (as far as anybody knows) so it respects the merging of space and time. 


#3
Aug910, 07:43 PM

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If Hovara gravity is the correct theory of gravity, with its anistopic splitting of space and time, would this falsify string theory? 


#4
Aug910, 07:51 PM

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Does string theory merge space and time into spacetime?
The full story is that we are still missing a nonperturbative definition of string theory of course. 


#5
Aug1010, 07:33 AM

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#6
Aug1010, 11:25 AM

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PF Gold
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Presumably there are various loopholes in the argument, since, e.g., we have tensorscalar classical theories such as BransDicke gravity. If we knew how to quantize such a theory, I guess we'd get a graviton plus some spin0 particle. I think there are tensorscalar theories in which the scalar field is massless (e.g., BransDicke gravity), and others in which it has mass (e.g., http://arxiv.org/abs/1001.1564 ). Does string theory allow the existence of a scalar field that couples to the graviton in anything like the way assumed by tensorscalar theories? There are also purely classical arguments for the uniqueness of GR, but of course they start from certain assumptions, and the existence of viable alternative theories shows that it's not inconceivable to abandon those assumptions. There are lots of theories that obey some form of the equivalence principle, but not the strongest forms. I wonder what the assumptions in Feynman's argument would be if you listed them explicitly. Getting back to the OP's question, the impression I get is that although string theory was clearly designed from the ground up to be consistent with SR, it was not designed from the ground up to be a backgroundindependent theory in the spirit of GR, and it's unknown or controversial whether or not backgroundindependence falls out of string theory. I also get the impression that there is no widely accepted, rigorous definition of the meaning of background independence. (I don't think it's the same thing as coordinate independence, which I believe string theory has...?) 


#7
Aug1010, 11:33 AM

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PF Gold
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#8
Aug1010, 12:35 PM

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http://arxiv.org/abs/grqc/0409089 http://arxiv.org/abs/0906.0926 BTW, the claim is also made somewhere in MTW. 


#9
Aug1010, 12:45 PM

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pages 119127.......()...my added comments in parentheses. ",,,Because string theory is a background dependent theory...by choosing different background geometries we got technically different theories....these (geometric) constraints are part of the description of how strings propagate and interact with each other....the constants that denote the masses of the particles and the strengths of the forces (sounds like he is addressing the standard model here) are being traded for constants that denote the geometry of the extra six dimensions....each of the backgrounds on which a string theory is defined is a solution to Einstein's equations or some generalization of it... the theory that unifies them (a meta theory) MUST NOT LIVE ON ANY SPACETIME BACKGROUND...what is needed to unify them is a single background independent theory...." 


#10
Aug1010, 01:07 PM

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"Lectures On Gravitation (Frontiers in Physics)" Richard Feynman, Fernando B. Morinigo, William G. Wagner, David Pines Edited by Brian Hatfield Addison Wesley "Derivation of gauge invariance and the equivalence principle from Lorentz invariance of the S matrix" S. Weinberg, Phys. Lett. 9, 357359 "Photons and gravitons in Smatrix theory : derivation of charge conservation and equality of gravitational and inertial mass" Phys. Rev. 135, B1049B1056 


#11
Aug1010, 01:17 PM

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#12
Aug1010, 01:34 PM

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A scalartensor theory would not be "minimal" and is not considered in Feynman's book. He tries to get things with as few hypothesis as possible. In any case, the Newtonian limit is an explicit constraint in Feynman's construction.
edit I'm sorry I have not had time to make an explicit list of hypothesis, and/or sketch the construction. The best would be to skim through the forewords. 


#13
Aug1010, 01:40 PM

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@Naty1: Thanks for the correction; I was wrong in #7. I know that Smolin has suggested that there may be a fundamentally problematic lack of backgroundindependence in string theory, but I think that claim is controversial. On pp. 184186 of The Trouble with Physics, he has this:



#14
Aug1010, 02:05 PM

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QFT formalism splits time and space, how does gravitons combine them? 


#15
Aug1010, 02:45 PM

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He goes on to discuss how it is merely a consistency check rather an independent prediction, because the result does not really necessitate the full machinery of a theory of gravitation. One can obtain the Doppler shift of photons in (weak) gravitational fields from special relativity plus the Newtonian potential energy. However there is one thing to note at this point in the book. Feynman extends the formula for the time dilatation to a large mass and obtains what we now recognizes as the Schwarzschild radius. He goes on to say that the situation never arises in practice because of the smallness of G. There are many parts in Feynman books which are outdated or even wrong, but those still have a historical value to illustrate Feynman's general approaches and strategies. 


#16
Aug1010, 04:31 PM

P: 2,799

The simplest meaning, is that the "background" refers to a fixed background metric, 4D or whatever dimensionality, where the dynamical metric is supposedly perturbations around this prior. But one can also with background associate to any context, from which an expectation is drawn, and measurements are made. In essence part of defining the observer. In this more general sense, it's not as trivial anymore. It seems to me that it's impossible to make a physical formulation of an expectation without a background  BUT the idea is of course that each background yields different expectations and therefor different actions. These differently acting observers are bound to face interactions that serve to deform the priors. The background independent part would be to try to understand how a web of interacting "priors" eventually emerge a some consistency. As I see it the debate is much to what extent this consistency is to be seen in the form of mathematical structural realism, or wether it's bound to evolve, and that there are only inside views of this evolution. I hold the view that tha latter is the case, and this is why an objective and eternally static representation in closed form of the background indepedendent theory simply isn't physically possible, as it's not inferrable. This is controversial, and I understand that alot of people just doesn't make any sense out of this, but it does make some good sense once if you see that the reason for this impossibility is because we require it to be a result of a scientific inference. This is a loose analogy of my own thinking to B/I problem of ST I make, where I think that even though I'm not a ST fan, some critique against the lack of B/I is a bit simpleminded, and it's somewhat similar to the critique against observer dependent reality, of those that want to restore classical realism and seek loopholes in QM. The same thing, if you require laws of physics to be subject to adbuction (like states are subject to measurement), gives even more strange results than QM. So I think not even structural realism in this popular form makes sense. This is weird, and I know alot of people doesn't make sense out of this. So I think the critique against lack of B/I is deeper than just a question of ST. Note that also LQG has PLENTY of backgrounds in this general sense as well. And in the generalized information theoretic picture, there is no rational ground for differentiating some information (4D metric) from others (dimensionality, symmetries, paramters etc). I expect all information to be constrained to the same inference and mesasurement ideas. Edit: I think it's even important to realize the one very important key to constructing realitivity, is realism, in the sense of objective transformations between the views. It's problematic to carry this same idea over to a MEASUREMENT THEORY, because then our standard are higher, we seek observable structures, we should not seek nonobservable relations between observables. That's not IMO coherent reasoning and I find it extremely disturbing. /Fredrik 


#17
Aug1010, 07:43 PM

P: 5,632

Here's how Wikipedia describes background independence:
http://en.wikipedia.org/wiki/String_...d_independence 


#18
Aug1010, 08:28 PM

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I honestly do not understand why people make such a big deal out of background independence. First, our universe has a preferred background (the CMB for instance). Second, we have no reason to doubt that the theory at low energy gives back Einstein's gravity, which is background independent. Whether an ultimate nonperturbative formulation can, will, or even must be background independent should not generate such a controversy.



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