Hi there, I'm new to this but trying like hell to figure the basics of this out, (as I did a while back but failed, then went off and left it.) and was wondering if this is why there's 11 dimensions : 1. Height 2. Width 3. Depth 4. Time Then we move onto the stuff that causes many of us problems, but after reading up for a while I'm hoping (!) that I at least know why there's 11. Are these the extra 7? 5. Kaluza–Klein combination of gravitation and electromagnetism - 5th dimension. 6-10. 5 different string theories that all appear to be correct at the same time, leading to : 11. M-Theory, which says that the 5 string theories are all correct and part of the same thing, which adds 6 dimensions onto the other 5. I'm sure that'll be wrong, but I at least feel closer to working out how it's arrived at....the main confusing thing is : those 5 string theories from 6-10 are all supposed to be detecting 10 dimensions aren't they? So I'm sure I'm wrong, but if any of you could try and break it down like that, but with the correct info I'd be really grateful, because it's driving me half mad. I don't want to fail at grasping the very basics of the idea and then leaving it again either, then going off to learn about other things instead, because I'll only come back at somepoint in the future and get just as wound up again with the whole thing. 2nd post added to make it easier to merge if need be : Nobody? Ok, I just thought about it again a bit and I'm realising that I probably got it wrong with the 5 string theories. (surprise, surprise...) The 5 all say that there's 10 dimensions, but they're not numbers 5-10 like I stupidly thought, they're just 5 theories that add 5 onto the other 5, or 6 onto the 4 of length, width, depth and time. Then M-Theory comes along and says that they're all right, but only when you look at it from this 11th dimension, which as far as I can gather, can view the other 10 from different.....angles so to speak, and is something on a whole other level. Is that closer? But then that leaves me not knowing what the hell the other 5 are after the 4 and 5th that I listed earlier....will have to read up more.
Nobody? Ok, I just thought about it again a bit and I'm realising that I probably got it wrong with the 5 string theories. (surprise, surprise...) The 5 all say that there's 10 dimensions, but they're not numbers 5-10 like I stupidly thought, they're just 5 theories that add 5 onto the other 5, or 6 onto the 4 of length, width, depth and time. Then M-Theory comes along and says that they're all right, but only when you look at it from this 11th dimension, which as far as I can gather, can view the other 10 from different.....angles so to speak, and is something on a whole other level. Is that closer? But then that leaves me not knowing what the hell the other 5 are after the 4 and 5th that I listed earlier....will have to read up more. Also : sorry for making this thread, I've quite clearly got it wrong, so maybe it should be merged with the other one that's on this page. (I just merged these two posts aswell, so this can be deleted, and you can just shift the starter onto the other thread.)
I've been told here that all the extra dimensions of string theory are spatial ones. It is probably not useful to think of time as the fourth dimension. Consider the 'first three': height width depth. Does it matter if you list them as width, height, depth? or any other recombination? It seems there is no preferred order, and trying to list a heirarchy of dimensions is not useful. I hope this helps.
First dimension is time. the Second dimension is Duration. t -> t+1 click click ckick is a frequency? t+1 is the dimension of length. A dot that is on, as time recedes away. To see the two dimension line ( on ((duration)) + time ), You have to add a third dimension. an offset from the straight-on view of the dot + duration in time. Call it x or y, but the offset now gives us a nice two dimensional graph paper clicking away from us at the speed of click click click. ( x,y,t,) To add another dimension we need to add another offset. Easy enough. Two eyes set about z apart. ( x,y,z,t,). Our normal perception. What about including the changes of Yaw, Pitch, Roll, Acceleration, ( all requiring a delta of one or more of the basic four dimensions) and try to put them into the map?
Un-unifyed standard model can be formulated with 7 kaluza klein dimensions, in the same way that electromagnetism can be done with just one KK dimension. Problem is, they need unification and chirality, so the 7 dimensions are not used in most models.
my (effectively undergraduate) understanding is that with E&M as 1 KK dimension, velocity in this extra dimension corresponds to charge density. in the un-unified formulation you mention, do velocities in these extra dimension correspond to hypercharge and colors perhaps? perhaps with 2 related dimensions for the weak force's SU(2) and 3 for the strong's SO(3)? (as a previous class project, I managed to see how KK could encompass e&m, as a current project, I'm trying to see how a yang-mills field could be included.)
there are not 11 dimentions. There are 11 "sets" or "groups" of 11s. HOWEVER, some are Trigonametry based, and some are Calculus based. Some are also certain combinations of Trig and Calculus "11"s, unified with algebra "11"s., The resulting unified math fields, as well as the physically existing structure itself, MUST then "balance" in a "3-D frame of reference" in order for "String Theory" to become "String Fact". I STRESS: AND I MEAN STRESS, everything as I have "explained" so far are nouns. Verbs come later. Summing up: there are only three "measures" to consider so far; Algebra, Calculus, Trig. I STRESS: AND I MEAN STRESS those are also just nouns so far. All string theories, like all advanced mathematics, have a 3-D "heart", or "frame of reference": where the theories begin, and where they are "propossed" to return for unification. "Unification" is ALWAYS a noun, and should never be considered a verb. For this thread, lets state "unification" as "Big U"; the ultimate "goal" or "solution", and stop to recognize a major "brain buster" people get "confused" with. As I read every possible theory I come across, the term: "unify", or the phrase "seeks to unify it all together" create errors in elemetary logic. Both "unifys" are verbs there. When ANY verb is "referenced" or "defined", most people "start it up" too soon. We are just gathering "materials" so far. We'll "start" it later.
This post Number of Dimentions as nouns, are assumed to be "boundless" at this point. Now NOT each separate physical dimention, they ARE most definately "bounded" as individual "places". That ONLY refers to the MATH, and in no way, states that a dimention can't "expand" There is "always" an "infinity" aspect to the model, per strait line arithematic. We will "nullify" it later. It can be stated as FACT, there are 3 dimentions, and the existance of an "observer" in that frame of reference. "I think, therefore, I am." "And I am somewhere". NOW, we must recognize another possible "roadblock" point. I am NOT stating any "has to be " or "must be there" or even "can't be included at all" concepts as to "observer". Lets cross that "bridge" later. At this point, WE ARE STILL gathering "nouns". When completed, it must "work" with or without "observation". All I have "proven" so far is "where" to begin, keeping with the "it must be real" heart of simple Physics. Basic basics next....
attached are figures taken from greene's fabric of the cosmos and kaku's hyperspace. greene's depicts a calabi-yau manifold at each spacetime point, and kaku's seems to suggest a kaluza-klein-esque combination of forces (he might have been talking about supergravity, I don't remember now). especially in the kaku figure, it seems tempting to continue labeling the rows/columns of the matrix; presumably what he has labeled "einstein" would have headings of time/x/y/z, though I wonder about the others -- I guess he intends the "yang-mills" regions to correspond to the weak force (column headings of isospin & hypercharge perhaps?) and the "quarks-leptons" region to be strong (red/green/blue headings?).
on second reading of the relevant section of the kaku book (pp 144-150), I guess my guesses are a ways off, and it sounds like supergravity has problems anyway. still, I wish I could find some sort of conceptual pegboard to put ideas on as I learn them, a whole that I could relate each new part to. perhaps string theory or LQG could be that pegboard? is it possible to explain to an (effectively) undergraduate how it is thought that each of the forces might fit into these theories? e.g. if the strong force has an SU(3) symmetry, does that suggest that 3 of the "dimensions" of string theory are reserved for this force?
in m theory the extra five dimentions as follow M-theory on circle IIA in 10 dimensions Wrap membrane on circle IIA superstring Shrink membrane to zero size D0-brane Unwrapped membrane D2-brane Wrap fivebrane on circle D4-brane Unwrapped fivebrane NS fivebrane
This is very old, so it has been already answered in modern threads (and there is a guy actually using Pope's lectures!). But the short answer: If the group of symmetry is G you take a subgroup H, the biggest you can, and build G/H, so dimension(G/H)=dim(G)-dim(H). For G=SU(3), the max subgroup is SU(2)xU(1) (just coincidence), and them dim G = 8, dim H= 4, dim G/H=8-4=4. Actually, the quotient is CP^2, the complex projective plane. So 4 of the dimensions of kaluza klein theory are reserved for the SU(3) force.
For our purpuses, with abit of hard work, the two spaces can be identified with each other! just don't listen to mathematicians!! sam
Well, to be honest, we should put some consideration to the case when there are different ways to implement the action of the (sub)group. In this case, I think that there is essentialy only one way to quotient S^5 by U(1). But in the general case we get some parameters in the game, which is interesting.
Sure looks like three spacial dimensions to me. Yes there is that weird space/time mixing that Einstein gave us. But still three spacial dimension. Now there my be several hidden internal degrees of freedom but why do we have to elevate them to spacial dimensions? And how do we feel about hidden degrees of freedom?
By the way, the other thinking that have been emerging during the last years in the understanding of how different $S^4$ is of $CP^2$, or how similar they are. It is about having a kind of Einstein metrics called "self-dual", built by Hitchin in the late nineties.
Hello, Sorry to intrude on the ongoing discussion. Not being a physicist, I have a, hopefully, simple question with regards to the 11 dimensions of M Theory. To preface, I understand that there are various spatial dimensions representing corresponding perpendiculars (not observable beyond 3) passing through an axis point. I understand that the time dimension is a particularly "odd" (inside-out?) perpendicular passing through the axis at the square root of -1 (i). I also understand that the 11th dimension represents the line perpendicular to the surface plane of each of the 2 branes that eventually collide to create the Big Bang. (Correct me if I'm wrong in any of the foregoing, please) NOW MY QUESTION IS: Is this 11th dimensional perpendicular a positive spatial one like the other nine, or is it an imaginary perpendicular (like time), or is it something altogether different? And, if so what?
It is, in your peculiar nomenclature, "positive spatial". IE, the metric in general relativity is (3,1), in string theory is (9,1), in 11D is (10,1), in 26D is (25,1). This number signals the number of positive and negative eigenvalues of a matrix which controls the scalar product of vectors. Were you to "square root" this matrix into some tensor product of vectors, you could put your "imaginary" there.