Why are there exactly 11 dimensions?

[stamba]

Can anyone explaine to me why there is exacly 11 dimensions , why not 13 or 7? I have searched a lot but I have not found it anywhere.

Thanks,
Stamba

 

[PRodQuanta]

look under the "strings, branes, LQG" section of PF. I know I've seen that same question asked.

Paden Roder

 

[Tom McCurdy]

Well i assume than you are talking about M-theory which says there must be 11 dimensions according to the approximate equations worked about by witten when he combined previous 5 theories into one theory

I think you might like to use one of the folliwng resources


http://www.quantumninja.com/toe/StringIntroLecture.mp3



It is about 35 minutes of a lecture I wrote with help from some members here including selfAdjoint

I also have a powerpoint that goes with it
but this lecture was meant to be stand alone if you would like to kind of follow along with the powerpoint
the powerpoint is here

http://www.quantumninja.com/toe/powerpoint.ppt

also a transcript of the speech itself is avaliable here

http://www.quantumninja.com/toe/Speech.doc

If you just want a quick answer just keep reading

http://www-th.phys.rug.nl/~schaar/h...ort/node12.html

Well added dimensions wasn't something completely unique to string theory it actually started with Kaluza Klein theory in 1919 which postulated the existence of an extra spatial dimension that was currled up. You see mathmatically you have a lot more freedom than you do in what you view as reality. For example let's say you calculate the volume of a 4-d object, it would simply be LaTeX graphic is being generated. Reload this page in a moment. So dimensions were added because it allows more freedom mathmatically and allowed the physicsts do do additonal calculations to unify EM with GR. It went from there to 10 dimensions with string theory. The strings needed the extra degrees of freedom to viberate. Since the particular viberation of a string determines what properties it has it needed to be able to viberate in more than just 3 extended dimensions, so again mathmatically they added the dimensions. (here is a good link on history of dimensions in relation to string theory http://www.pbs.org/wgbh/nova/elegant/dimensions.html )

Now if you get why there needs to be extra dimensions (to allow for more freedom for strings) it becomes apparent that the extra dimensions must be in very specific shapes to get particular viberations. This is where the term calabi yau manifold comes from. It is the predicted shape of the curled up dimensions. However there are thousands of calabi yau shapes so they must be limited down further based on how they would create viberations. And I believe currently we need a calabi yau manifold with 3 holes which allows for the extended dimensions we are familar with today.

However the 10 dimensional model of string theory caused a problem for most people becaue it produced 5 different string theories which a man named Ed Witten was able to combine into one theory known as M-theory which basically said the old theories were merely reflections of each other. (Also keep in mind string theory math is approximate at this stage which is why they added a dimension when they learned it needed an extra one)

So they basically came up with the idea for extra dimensions by mathmatically recoginzeing what they could do with extra dimensions in accordance with a particular theory.

if you need more information
one ask me
two go to the string forum
three read the elegant universe

 

[veryyoung]

i believe tom has summed it up rather nicely but really more than 11 dimensions COULD exist although as of now they arent needed and therefore we don't add them. really i would just wait until m theory's full calculations have been done before i said that only 11 can exist.

 

[ШЇSЭЯ]

wow very interesting,,

 

[sifeddin]

So what would you say if there is a theory that can explain ALL the forces of nature as only the consequences of ONE property of VERY LIMITED number of fundamental particles and consistently predicts quantization of electron energy inside an atom, radiation interaction with material, the existence of other particles and their "binding energy", the wiglling of star motion and includes the gravity forces together on equal footage interpreting with few postulates why there is no repultion of masses and there is an static electomagnetic field around our Earth using only three dimensions of the "natural" space and the universal time and give "relativistic-like" conclusions only within "classical-like" mechanics and give all physics the unity it deserves?
I DO NOT mean www.thefinaltheory.com but I mean the Unity Theory of Amr M. Morsi who was one of my students in EM theory at Ain Shams Univ. (where I'm an LA) and then an electronics eng. colleague and finally a personal physics tutor and friend.
However there is another Egyptian Prof. Mohammed-Saladdin ElNashaei (I don't know how his name appears in literature) who I met in Cairo Univ. open lecture and talked about his infinite dimension theory where time is just like anyone of them out of his study of the deterministic chaos. but I did not read anything he wrote (because I cannot spell his english name and my tight time. so if anyone can guide me on his theory my mail is open to receive documents at sifeddinpapers@yahoo.com)
There are still this John Carolle of Camdridge Univ. who claims there are three time dimensions as well asa the three space dimensions that allow to give space-time vortices that explains why there is no isolated magnetic charge.
So how many dimensions do think live in? Would you like to be Mr. Square or Lady Sphere or may be Mr. 4WD!

 

[The Undergraduate]

My question is, are these extra dimensions in any particular "order" or would they be of different "classes"? For instance, it seems to me that the dimensions "length", "width", and "height" exist in relation to each other and would therefore be of one "class" of dimensions (spatial). Then we have "time", which seems to be its own kind of dimension. Then we have these "extra" spatial dimensions. Could an object theoretically exist in some dimensions but not others? Could there be a one-dimensional object (using the term "object" loosely) that only exists in, say, time, or one of the unknown dimensions?

 

[VincentS]

"My question is, are these extra dimensions in any particular "order" or would they be of different "classes"? For instance, it seems to me that the dimensions "length", "width", and "height" exist in relation to each other and would therefore be of one "class" of dimensions (spatial). Then we have "time", which seems to be its own kind of dimension. Then we have these "extra" spatial dimensions. Could an object theoretically exist in some dimensions but not others? Could there be a one-dimensional object (using the term "object" loosely) that only exists in, say, time, or one of the unknown dimensions?"

Well acording to the M-Theory, the extra dimensions are claimed to be extremely small, Where every object exists in all the extra dimensions its just to small for us to even notice. These extra dimensions are just curled up into the 3 standed height, length and width ones.

 

[selfAdjoint]

My question is, are these extra dimensions in any particular "order" or would they be of different "classes"? For instance, it seems to me that the dimensions "length", "width", and "height" exist in relation to each other and would therefore be of one "class" of dimensions (spatial). Then we have "time", which seems to be its own kind of dimension. Then we have these "extra" spatial dimensions. Could an object theoretically exist in some dimensions but not others? Could there be a one-dimensional object (using the term "object" loosely) that only exists in, say, time, or one of the unknown dimensions?

The dimensions are in two classes; time, and space. One dimension is time, and all the others are space dimensions. As such they would be interchangeable (as length, width, and height are, really; you can mark those on the edges of a box and then rotate the box any way you want). The thing that breaks the interchangeability symmetry is that seven of the space dimensions are compacted (curled up small). But there isn't any special way to choose which space dimensions become small, it's just a fact of life which are.

 

[Enos]

Ain't 11 dimensions used for the strong & weak forces and electromagnetism to be along the same strenth at one point in time. I'm sure I read something like that somewhere.

 

[selfAdjoint]

Ain't 11 dimensions used for the strong & weak forces and electromagnetism to be along the same strenth at one point in time. I'm sure I read something like that somewhere.

I think that's ten dimensions; supersymmetric GUTs that unify those three forces (without strings) require ten dimensions, and tend to compact them just as string theorists do.

 

[Haelfix]

Why 10 dimensions? Well, 4 usual space/time dimensions and 6 compactified ones. Plus an extra M theory one that is kinda taken to be fuzzy (hard to define a length on it).

So why 10 dimensions? Well it turns out, this number is fixed. You can't deviate from it at all in order for the theory to be consistent. If someone in 10 years says "well we really need 14 dimensions to describe nature', then that something is not string theory. In conformal field theory, much of the mathematics of string theory, quantum anomaly conditions must match precisely and this number outputs 10 dimensions. No more, no less.

 

[Louis Cypher]

mmmmmm?

Hey guys have you ever thought though that m theory and supersymetry are the deluded ravings of mathemeticians who are being driven slowly insane by the wierdness of qm

String theory too could be just an imagined nonsense

Let's maintain some sort of scientific approach to these mathematical sophistries at least until the evidence for them is there

I think we should be wary of claiming that there are any more than 4 dimensions unless we can prove the existence of them we're in danger of dissapearing up our own backsides with this sophistry.

Fantasticaly interesting and clever theories and to be praised and encouraged, but let's not forget that's all they are: theories; actually thinking about it there not even theories there hypothesis since there is no evidence for any of them

I love mathemeticians kinda like ufo nuts with too much spare time and too little scientific experimentation.

Step outside of the envelope people after all the answers in the post

Me just then, A.Smartarse feb 2005

 

[Enos]

I prefer the 4 dimensional universe over the 10 or 11. But we shouldn't cut the strings just yet.

 

[tardis]

Assuming we accept the 11 dimensional calabi-yau model, does this model REQUIRE that the other three dimensions be very large or is this just a bonus?

Either way, is there a minimum size needed for the 4 large dimensions to make this model work?

 

[lalbatros]

Why three dimensions ?

Would there be any reason why three spatial dimensions is such a good start in physics?
It is well known that 2 dimensions would be quite difficult to live in.
But why are we so happy with 3?

 

[εllipse]

Would there be any reason why three spatial dimensions is such a good start in physics?
It is well known that 2 dimensions would be quite difficult to live in.
But why are we so happy with 3?

We started with three because we only directly experience three. The other spatial dimensions are too small for even the atoms of our bodies to move in and out of. We've only recently discovered more than three because we've only recently started studying things small enough to have some free movement in the other dimensions.

 

[lalbatros]

εllipse,

I totally agree that 3D is a direct experimental evidence.

But, I was wondering if some people had come with temptative explanations / interpretations about the number of 3 'obvious' dimensions.

Of course, if the 11 dimensions are definitively proved, and if -indeed- a bunch of these are microscopic dimension, then it is factual reasons that lead us to 3 dimensions in our daily lifes. By the way, are the reasons for 11 dimensions factual or more fundamental? Does a 11D space have special properties as compared to other spaces?

Finally, let me note that if I had to choose -by myself- an hypothetical dimension for the scene of physics, I would choose the infinite. I have the feeling that this would open a lot of possibilities ...

 

[Fallaciousmiles]

Hey guys have you ever thought though that m theory and supersymetry are the deluded ravings of mathemeticians who are being driven slowly insane by the wierdness of qm

String theory too could be just an imagined nonsense

Let's maintain some sort of scientific approach to these mathematical sophistries at least until the evidence for them is there

I think we should be wary of claiming that there are any more than 4 dimensions unless we can prove the existence of them we're in danger of dissapearing up our own backsides with this sophistry.

Fantasticaly interesting and clever theories and to be praised and encouraged, but let's not forget that's all they are: theories; actually thinking about it there not even theories there hypothesis since there is no evidence for any of them

I love mathemeticians kinda like ufo nuts with too much spare time and too little scientific experimentation.

Step outside of the envelope people after all the answers in the post

Me just then, A.Smartarse feb 2005

Well, from calculations, more specifically, equations they have actually found out that using the curved model of the fifth dimension. The resulting equations would be somewhat similar to those of electromagnetism.

For clarifications, their model of curved dimensions actually only has the fourth dimension large enough to be felt, straight in the face right?
With the speculations that the fifth and above dimensions would be smaller then Planck's constant, thus it being almost impossible to be detected

 

[0zyzzyz0]

I see that this thread has lain dormant for about three years now, but I'm chipping in with my small change on this because it seems to end right about where my thoughts have been wandering lately. If a moderator prefers to turn this into a new thread, that's ok by me.

Fallaciousmiles mentions that there has been speculation that the dimensions beyond the familiar spatial three are somehow smaller than the Planck length. When hearing that these dimensions are curled up (or wound up? -- another speculation of mine) so that they are too small to be detected, I've wondered how small that might be. Specifically, what i am most curious about is whether there has been any serious speculation that anything other dimensionally could be going on at sub-Planck lenths. [Don't throw anything!] Yes... I do appreciate that the Planck length represents a limit beyond which we can't calculate, [Right?] but I've always had difficulty reconciling that with a lot of other thinking cluttering up my mind. I suspect any serious speculation along such lines could only be going on amongst those with greater maths knowledge than i possesses (with my historian/librarian + curiosity background), so i bring my quandary up here.
My thinking along these lines connects with my suspicions that 'existence' must extend by infinite scales of magnitude both towards smaller and larger -- a suspicion i base mostly on the philosophical rationale that either 'all' has ultimately had some sort of beginning ex nihilo [defying our common experience], or there must be an infinite regress of cause and effect [defying nothing in our experience, but challenging our ability to imagine anything as actually infinite].

 

[BigFairy]

turtles all the way up, turtles all the way down lol

 

[Phrak]

There are any connection between D=11
and alfa(Fsc)=137;1+3+7=11?

That depends. What do you get in base 7?

 

[arivero]

This part of the thread stresses an interesting question. If the extra dimensions were Kaluza Klein dimension, whose symmetry generators are gauge bosons, the answer would be an easy one, and to do a good debate about "principia".

I still believe such is the case, and that there is some reason forbidding the symmetry of W and Z "translations" (or rotations) to get a massless mode, the next available being then of the order of the mass of the top (and probably the "size" of such dimension).
Remember that 7 extra dimensions is the quantity you need to fit independent actions of SU(3) times SU(2) time U(1): a product of three manifolds of respective dimensions 4, 2 and 1.

My question is, are these extra dimensions in any particular "order" or would they be of different "classes"? For instance, it seems to me that the dimensions "length", "width", and "height" exist in relation to each other and would therefore be of one "class" of dimensions (spatial). Then we have "time", which seems to be its own kind of dimension. Then we have these "extra" spatial dimensions. Could an object theoretically exist in some dimensions but not others? Could there be a one-dimensional object (using the term "object" loosely) that only exists in, say, time, or one of the unknown dimensions?

 

[Freezeezy]

That depends. What do you get in base 7?

I don't care about 7.For me interesting base 2.
11 to binary is 1011. This is reminding my Metasymmetry idea.
https://www.physicsforums.com/showthread.php?t=220894

I read this... Are you on the "Hippy-Lettuce"?

To be honest you need to now find three intelligent ideas in that bong-ridden head of yours to balance out that one very bad one... oh wait... 3:1... Nevermind... You are just making very vague comparisions to try and explain a very complex universe. The numbers 1, 2, 3, 5, 7, 11, ect are all very common, universally-associated numbers. This is likely due to them being prime numbers... but you didn't know that, right?

The real answer is that the 7 other dimensions are, yet again, just another tiny measument of the universe. Too small for us to accurately observe so we don't know the implecations other than those on paper. Interesting?

The real interesting thing is that none of you (Other than Arivero and OzyzzyzO, thanks for your contributions) seem to sound like you haven't done any research...


HERE:
http://www.sukidog.com/jpierre/strings/

Read all of this... then post again. Thanks.

 

[arivero]

The real interesting thing is that none of you (Other than Arivero and OzyzzyzO, thanks for your contributions) seem to sound like you haven't done any research...


HERE:
http://www.sukidog.com/jpierre/strings/

Read all of this... then post again. Thanks.

Yep, and while it is OT, and I guess it has been threaded in the general subforums a 1000nd of times, I keep wondering why people can be at the same time interested and uninterested in a topic. (as I say, it is OT... please link to other subforum thread if answering this ;-)

 

[gorgos]

Can anyone explaine to me why there is exacly 11 dimensions , why not 13 or 7? I have searched a lot but I have not found it anywhere.

Thanks,
Stamba

To my opinion best answer you can read on
http://arxiv.org/abs/hep-th/0205309

 

[humanino]

To my opinion best answer you can read on
http://arxiv.org/abs/hep-th/0205309

Very interesting paper. Townsend is certainly a major figure in this business. However, as pleasant as this paper is, I find it technical for the level of the discussion here, so can you please point us exactly where is the question addressed ?

I tend to think that

Note that fixing the position in {\cal M}_{8-k} yields a supermembrane in a Minkowski spacetime of dimension D = 4, 5 or 7, according to whether k = 1, 2 or 4, respectively; as it happens, these are precisely the other dimensions for which the supermembrane action is classically consistent, so the existence of these lower-dimensional supermembrane actions is explained by the existence of the 11-dimensional supermembrane.

for instance, will confuse anybody who does not already know how to calculate the numbers 26 or 10.

 

[robheus]

Would there be any reason why three spatial dimensions is such a good start in physics?
It is well known that 2 dimensions would be quite difficult to live in.
But why are we so happy with 3?

Stable planetary orbits and atoms exist only in 3d.
And a curiosity is also that knots only exist in 3d space.

 

[arivero]

Stable planetary orbits and atoms exist only in 3d.
And a curiosity is also that knots only exist in 3d space.

I think that the point about knots is a low-dimensional effect, as the existence of regular n-poligons. But the one on stability and properties of 1/r^n interactions is a good point, and one wonders why it is not exploited in actual theories.

 

[Demystifier]

That depends. What do you get in base 7?

But the base is not arbitrary. The base is the number of dimensions of perturbative superstring theory = 10. The number of physical degrees of freedom is 10-2=8, which gives
2 X 8 + 10 = 26, which is the number of dimensions of bosonic string theory.
Everything fits.