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 Yau-Calibi 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?
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.
Is spacetime a dynamical object in String theory? If Hovara gravity is the correct theory of gravity, with its anistopic splitting of space and time, would this falsify string theory?
I think it is fairly well established that string theory includes massless graviton at low energy. Despite a minority of claims otherwise, Feynman has given a lecture in the beginning of the 60's to explain how a massless graviton can only lead consistently to Einstein's gravity. Other people had already made some work in the same vein, possibly with more rigor, but at least from then it became common lore. The full story is that we are still missing a non-perturbative definition of string theory of course. I do not know the answer for sure, but the correct spelling is Hořava gravity.
no...supposedly the shapes of the Calabi-Yau manifolds are what restricts string vibrations and consequently creates the characteristics we observe in the maco world, like mass, spin,etc. So far it's a 10 +1 string world that seems to work. I'm not sure about the "definition" , but exact solutions are definitely missing.
Interesting. Do you know if Feynman's argument is available written down anywhere? Presumably there are various loopholes in the argument, since, e.g., we have tensor-scalar classical theories such as Brans-Dicke gravity. If we knew how to quantize such a theory, I guess we'd get a graviton plus some spin-0 particle. I think there are tensor-scalar theories in which the scalar field is massless (e.g., Brans-Dicke 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 tensor-scalar 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 background-independent theory in the spirit of GR, and it's unknown or controversial whether or not background-independence 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...?)
Hmm...but isn't this just a constraint on the dimensionality, signature, and topology of the space? That's different from assuming a prior *geometry*, i.e., putting in the curvature by hand. I could be wrong, but the impression I get is that string theorists hope that in the low-energy limit, you get a classical field theory that exactly mimics the observable properties of GR, meaning that spacetime acts as a dynamical object. If that didn't happen, wouldn't it mean that string theory was not a candidate for a TOE?
http://arxiv.org/abs/astro-ph/0006423 http://arxiv.org/abs/gr-qc/0409089 http://arxiv.org/abs/0906.0926 BTW, the claim is also made somewhere in MTW.
That's exactly how I read it. Here is what Lee Smolin says in the trouble with Physics,, 2007, pages 119-127.......()...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...."
It is available as a book : "Lectures On Gravitation (Frontiers in Physics)" Richard Feynman, Fernando B. Morinigo, William G. Wagner, David Pines Edited by Brian Hatfield Addison Wesley I did not find such loopholes when I read the book. Others authors have done the same several times in the literature, in particular : "Derivation of gauge invariance and the equivalence principle from Lorentz invariance of the S- matrix" S. Weinberg, Phys. Lett. 9, 357-359 "Photons and gravitons in S-matrix theory : derivation of charge conservation and equality of gravitational and inertial mass" Phys. Rev. 135, B1049-B1056
If there weren't such loopholes, then it would be very exciting, because we could rule out tensor-scalar theories. I don't have convenient access to the Feynman book, but looking at the first reference atyy gave (thanks, atyy!), I see on p. 4 that it assumes Newtonian gravity as its static limit. The static limit of tensor-scalar theories isn't Newtonian gravity, so that seems to be the loophole.
A scalar-tensor 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.
@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 background-independence in string theory, but I think that claim is controversial. On pp. 184-186 of The Trouble with Physics, he has this: If I'm understanding correctly, string theorists are hoping that string theory is background-independent, but just not manifestly background-independent.
How does gravitons interacting according to QFT deal with time dilation as predicted by GR? QFT formalism splits time and space, how does gravitons combine them?
Feynman discusses this in details in his paragraph 5.2 if you want to look it up. Basically, he has the time-time component of the graviton proportional to what becomes the gravitational potential in the Newtonian limit. He then writes up the lagrangian for a scalar field coupling to this graviton and shows that one can compensate for derivative terms by redefining the time as expected from dilatation. 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.
I'm no advocate of ST, but it's true that these terms are used differently by different people. 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 non-observable relations between observables. That's not IMO coherent reasoning and I find it extremely disturbing. /Fredrik
Here's how Wikipedia describes background independence: http://en.wikipedia.org/wiki/String_theory#Background_independence And Smolin seems pretty clear from bottom half of page 186 to 188 and beyond about significant technical problems with string theories....mainly the perturbative nature of calculations....consistent with the Wiki comments above and my prior post.
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 non-perturbative formulation can, will, or even must be background independent should not generate such a controversy.
That's a preferred reference frame that results from a particular geometry. Background independence means there is no preferred geometry built into the theory, which is a completely different thing. See the quote in #13.
I understand, and I think there is an analogous phenomenon in the SM : spontaneous breaking of electroweak or chiral symmetries. The analogy is interesting in that Fermi's theory was superseded once we had the correct constraint of gauge invariance. It does not change the fact that symmetries are not always manifest. I am just saying that background independence may be present in the ultimate formalism, but enforcing the principle while searching for this formalism may prevent us from making progress. Before ghost were introduced, it was for instance unclear how to formulate gauge theories in the path integral rather than the canonical formalism. As Feynman said, for me the difference lies between the babylonian and greek strategies. The babylonians had a web of results which all can be derived one from another. The greeks figured out that it was more efficient to develop mathematics to decide on a set of axioms and derive other results from them (bottom-up). That is fine for mathematicians. But physicists are not mathematicians. The babylonian approach is more suitable because we must always be ready to give up some of our assumptions, and we can not decide in advance which one we must give up. Again I am not saying background independence will go away, I am just saying that it should not cause so much controversy if we are trying to develop a theory without explicit background independence.