Can someone explain to me the 11 dimensions of string theory

[Lightmeow]

I read Brian Greene's book, The Elegant Universe. It said that in String Theory there were 10 dimensions, and in M-Theory there were 11. How can you explain that. I understand almost up to dimension six.

 

And how would you draw or think about a 11 dimensional universe?

 

Thanks,

 

Joshua

[ajb]

And how would you draw or think about a 11 dimensional universe?

You cannot draw 11d space-time nor can you 4-d space-time. What you do is project out some of the dimensions if you need to draw something.

 

In general space-time, classically at least, is a smooth manifold and so admits coordinates much like (x,y,z) on the plane. You can then work with these coordinates using alagbra and calculus. The 11d space-time of M-theory is very similar to standard Minkoswki space-time, just we have more spacial coordinates.

 

In fact you don't always need to use coordinates, but it is the most direct way to work.

[studiot]

 

much like (x,y,z) on the plane.

 

x, y and z

 

 

(Yes I know you can embed a plane, but I think this point needs elucidating to the OP)

 

Edited January 2, 2014 by studiot

[ajb]

x, y and z

Yes, I meant the Eucledian 3-space, sorry for any confusion.

[Lightmeow]

So that being said, could you explain to me how the extra dimensions worked.

 

0 dimensional point in ?

1 dimensional two points connected

2 dimensional lines connected to form a plane

3 dimensional plans rotated to form space?

4 dimensional time?

Then I have no clue

[ajb]

So that being said, could you explain to me how the extra dimensions worked.

I an not really sure what you are asking for here. But think about the 2-d plane first. Every point on that plane requires two numbers to specifiy it, (x,y) say once you have set up some coordinate system. The obvious one here is to pick some point to be zero and set up a rectilinear coordinate system like you did in high school geometry. Note though, you could pick much more complicated coordinate systems, but still you will require exactly two numbers to specify each point.

 

 

You can now do something similar for any number of dimensions. The n dimensional Eucliedian space requires n numbers to specify any point on it, in any chosen coordinate system.

 

Space-time is what we call an n-dimensional smooth manifold, which up to some technicalities means that locally we always have coordinate systems in which every point requires n numbers to specify it. Globally it may look very different to the n dimensional Euclidean space, but locally they look the same.

 

In the case of string theory we have 9 spacial directions and 1 time. For M-theory it is 10 and 1. For standard general relativity it is 4 and 1.

 

You can read more about manifolds on my blog http://blogs.scienceforums.net/ajb/?p=3893

[pears]

So that being said, could you explain to me how the extra dimensions worked.

 

0 dimensional point in ?

1 dimensional two points connected

2 dimensional lines connected to form a plane

3 dimensional plans rotated to form space?

4 dimensional time?

Then I have no clue

 

Is the issue that you're trying to picture them? Don't do that!

[Lightmeow]

Some one told me that if you were a 5th dimensional being, you could go back and forwards in time. If you were a 6th dimensional being, you could go backwards and forwards in time, and go to parallel universes.

 

That is what I meant. I don't know:, here is a link to the idea:

https://blogs.oracle.com/bblfish/entry/the_10_dimensions_of_reality

[studiot]

 

Is the issue that you're trying to picture them? Don't do that!

 

 

 

Excellent point, +1

 

Don't forget that what is meant in technical circles by a 'dimension' is a very different animal from what is meant in general parlance.

[ajb]

That link looks like nonsense. It does not seem to relate to how people work with higher dimensional space-times at all.

[Lightmeow]

Thanks,

I need to check the links of the stuff I am looking at. I still don't understand how there can be more than three spacial dimensions.

 

How do you think scientists could prove string theory if we are on a membrane that was 3 spacial dimensions + 1 time.

[ajb]

How do you think scientists could prove string theory if we are on a membrane that was 3 spacial dimensions + 1 time.

Well gravity is not confined to the branes, remember that D-branes are the places that open strings can start and end and that closed strings are to do with gravity. Closed string can propogate in the bulk. Thus gravity could carry off energy from out brane or indeed supply energy to our brane. This would lead to a seeming violation of the conservation of energy.

 

Another related idea is that the presence of these large extra dimensions lowers the Planck energy. This we might be able to test for via micro black hole production in colliders.

 

Another place to look st stringy-physics is in the details of the power spectrum of the CMBR. Fundamental strings may have blow-up in scale due to inflation and maybe these can be seen in the CMBR.

 

I am sure a quick google will give you more suggested tests.

[studiot]

 

Some one told me that if you were a 5th dimensional being, you could go back and forwards in time. If you were a 6th dimensional being, you could go backwards and forwards in time, and go to parallel universes.

 

I agree with ajb your source is spouting nonsense.

 

This again comes from trying to interpret proper scientifically consistent theory in terms of general parlance inexactitude.

 

Consider a matter point at (x₁,y₁,z₁, t₁)

 

It is fundamental in our science and maths that his point cannot also occupy (x₂,y₂,z₂) at t₁

 

That is it cannot be in two places at once.

 

That is it is impossible to travel in space without also travelling in time.

 

That is you cannot travel from (x₁,y₁,z₁, t₁) to (x₂,y₂,z₂, t₁), you can only travel from (x₁,y₁,z₁, t₁) to (x₂,y₂,z₂, t₂) as the transit takes time (t₂ - t₁).

 

 

Populist stories such as by HG Wells have the hero 'travelling' in time, without travelling in space.

 

Incidentally think about what you mean by 'time travel'

Edited January 2, 2014 by studiot

[Alan McDougall]

I read Brian Greene's book, The Elegant Universe. It said that in String Theory there were 10 dimensions, and in M-Theory there were 11. How can you explain that. I understand almost up to dimension six.

 

And how would you draw or think about a 11 dimensional universe?

 

Thanks,

 

Joshua

 

Very few people are brave enough to claim they understand string theory, the father of string theory is a very bright physicist by the name of Edd Wittten, look him up!

 

If you suppose that you could draw or think in 10 spacial dimensions, you should know this is impossible to do. It is even impossible to think in 4 spacial dimensions although a tesserract is thought to be a four -dimensional analogue of a cube

 

 

[BearOfNH]

Populist stories such as by HG Wells have the hero 'traveling' in time, without traveling in space.

 

But the hero does travel in space. The earth is spinning as it orbits the sun while our solar system transits the galaxy, etc. Even for minor Δt, all of Δx,Δy and Δz are gonna be pretty big. How the time-travel machine accounts for that is something I've always wondered.

[michel123456]

 

Is the issue that you're trying to picture them? Don't do that!

IIRC Brian Greene's Elegant Universe, the concept states that from the 11 dimensions, only one is temporal, 3 are the existing spatial ones and the rest are also spatial dimensions curved upon themselves in such a tiny matter that they are not perceptible.

I never understood on which rational basis scientists have ruled out the many times dimensions. It would have been simpler to hide since the only single apparent time dimension of our observable universe is let's say "invisible".

[ajb]

Very few people are brave enough to claim they understand string theory, the father of string theory is a very bright physicist by the name of Edd Wittten, look him up!

Witten is not the farther of string theory, but he is an important contributor.

 

This history goes back to the 1960's as a model for hardons and S-matrix theories. I think it was Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind who discovered the relation of these S-matrix theories with strings in 1969. This was the birth of the bosonic string.

 

Superstrings were constructed in 1970 by Pierre Ramond and John Schwarz + André Neveu in two different ways.

 

Witten in the 1980s as well as the likes of Alvarez-Gaumé, Green and Schwarz discovered the anomaly cancellations in string theory and this really stimulated the idea that string theory could be a consistent theory of quantum gravity rather than a theory of hadrons. This was the first string theory revolution and many papers followed.

 

Witten was also hugely influential in the second string in 1995, in which the role of D-branes and dualities in string theory was really appreciated. This lead to the idea of 11d M-theory. Paul Townsend was also developing things along similar lines to Witten. These two were probably the first to see D-branes as important objects, though they were known about before this. The AdS/CFT correspondence was discovered by Juan Maldacena in 1997 which has been a very important result in this context.

Edited January 5, 2014 by ajb

[Alan McDougall]

Witten is not the farther of string theory, but he is an important contributor.

 

This history goes back to the 1960's as a model for hardons and S-matrix theories. I think it was Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind who discovered the relation of these S-matrix theories with strings in 1969. This was the birth of the bosonic string.

 

Superstrings were constructed in 1970 by Pierre Ramond and John Schwarz + André Neveu in two different ways.

 

Witten in the 1980s as well as the likes of Alvarez-Gaumé, Green and Schwarz discovered the anomaly cancellations in string theory and this really stimulated the idea that string theory could be a consistent theory of quantum gravity rather than a theory of hadrons. This was the first string theory revolution and many papers followed.

 

Witten was also hugely influential in the second string in 1995, in which the role of D-branes and dualities in string theory was really appreciated. This lead to the idea of 11d M-theory. Paul Townsend was also developing things along similar lines to Witten. These two were probably the first to see D-branes as important objects, though they were known about before this. The AdS/CFT correspondence was discovered by Juan Maldacena in 1997 which has been a very important result in this context.

 

 

I stand corrected

[Schneibster]

(Answering the Thread Topic Query)

 

Yes. In simple terms:

 

The first four are spacetime. Up-down, left-right, closer-farther, past-future. These are the degrees of freedom of gravity, and the definition of it as a force.

 

The next one adds electromagnetism, as a single degree of freedom at every point in spacetime.

 

The next two add the weak nuclear force, which has not only a +W and a -W current, like electricity, but also adds, with its second dimension, a "neutral current," which has a charge that is neither + nor -. Physicists call the particle that carries this charge a Z or Z₀.

 

The next three add the color force, which is the underlying force of which the strong nuclear force is a remainder force among nucleons, just as van der Waals forces are remainder forces of the electromagnetic forces among atoms and molecules generated by the charged nuclei and the charged electron clouds.

 

There are ten: 1+2+3+4. And you will find that the math works, too. In modern physics, "symmetries" underlie our knowledge of the forces, and these symmtries have mathematical names that denote a) their type and b) their dimensionality. They are referred to as "symmetry groups" because frequently there are many different examples both from math and from science. These symmetry groups, then, are U(1), which is the symmetry of electromagnetism, and which is combined for reasons we can discuss later with SU(2), which is the symmetry of the weak force. And, of course, SU(3), which is the color force.

 

You will note I have left out gravity. Physicists have not yet found a symmetry group that works for gravity.

 

And last, there is the eleventh dimension. When the Second String revolution happened, it was because Witten used the eleventh dimension to unite all the string theories; they all turned out to be different branches of a single underlying theory called "M-theory." And this in turn brought in gravity; because we only had five "string theories;" but the math Witten found when he added the eleventh dimension made it clear that the most advanced non-string theory of the time, called "supergravity," was in fact the "sixth string theory." So that's where the eleventh dimension comes in.

 

Now, this means that we have seven dimensions that all exist at every point in spacetime, but that are all so small we never notice them and can't directly measure them.

 

And the key is, the exact shape of each of these dimensions controls a different aspect of a different force. You know, not only that one's a little bigger or this one's a little flattened, but their relations to each other, this angle and that, and are they right circular or elliptical or parabolic or hyperbolic, as well as their relations in all these ways to the four "big" dimensions of spacetime.

 

String physicists call these little twisted-up balls of dimensions "Calabi-Yau spaces." And one of the questions is, how many of them are there? When you figure this out you come out with about 10³⁰⁰ possible Calabi-Yau spaces of seven dimensions, each representing different laws of physics.

 

And that's what the eleven dimensions are.

[ajb]

The first four are spacetime. Up-down, left-right, closer-farther, past-future. These are the degrees of freedom of gravity, and the definition of it as a force.

 

The next one adds electromagnetism, as a single degree of freedom at every point in spacetime.

 

The next two add the weak nuclear force, which has not only a +W and a -W current, like electricity, but also adds, with its second dimension, a "neutral current," which has a charge that is neither + nor -. Physicists call the particle that carries this charge a Z or Z₀.

 

The next three add the color force, which is the underlying force of which the strong nuclear force is a remainder force among nucleons, just as van der Waals forces are remainder forces of the electromagnetic forces among atoms and molecules generated by the charged nuclei and the charged electron clouds.

 

There are ten: 1+2+3+4.

I don't understand how the fields of the standard model directly place constraints on the consistent dimension of string theory.

 

The closest I can think of are the Chan–Paton factors, but this is to do with the charges rather than the dimensions.

 

Please can you explain this properly?

[Schneibster]

I don't understand how the fields of the standard model directly place constraints on the consistent dimension of string theory.

 

The closest I can think of are the Chan–Paton factors, but this is to do with the charges rather than the dimensions.

 

Please can you explain this properly?

 

Do you know the Kaluza-Klein theory of electromagnetism? It postulates one additional, small dimension, added to GR. You can derive Maxwell's Equations from it, in exactly the same manner you derive Einstein's Field Equations in four dimensions.

 

There's the first of the seven dimensions of the Calabi-Yau space that defines our universe's particular string theory.

 

That's the "1" in "U(1)," which is the unitary symmetry group of dimension one, which is the symmetry group of the electromagnetic force.

 

This is pretty basic; it's in The Elegant Universe, IIRC. Have you read it? On Edit: Hmmm, maybe it's in The Cosmic Landscape.

 

And of course I don't mean to indicate that this most obvious idea is actually a mathematically correct description; a lot of really smart people looked at it and if it were that easy physics would be, heh, finished. (Snicker, this strikes me the same as the ISP commercial where the computer announces to the dude he has "finished the Internet.") OTOH, add in supersymmetry and it starts to look kinda like supergravity, which is the sixth theory in M-theory. K-theory is having quite a strong look at Kaluza-Klein theory, actually, just at the moment. Hot topic.

 

The naïve theories have all been tried long ago; my goal is rather to help the folks who perhaps can't handle all the math understand. Your contributions in clarifying places I was unclear are appreciated and will be.

 

The reason the naïve theories fail is simply the energy scales, as Kaku 1993 says on page 6. The relatively modest value of α_em at ~1/137 governs the EM interaction and makes it tractable to a relatively naïve quantum theory. Unfortunately, none of the other forces is so convenient; α_color at ~14 is totally immune to renormalization; and G_newton has dimensionful components and is immune to renormalization as well, though for a different reason. G_weak is the only one in a range and of a character to support investigation, and has turned out to be a weird sort of mix with EM.

 

Here's a brief note on supergravity which is the sixth theory of M-theory: http://en.wikipedia.org/wiki/Supergravity#N_.3D_8_Supergravity_in_4_Dimensions at the end you will find the comment:

 

N=8 Supergravity is the most symmetric quantum field theory which involves gravity and a finite number of fields. It can be found from a dimensional reduction of 11D supergravity by making the size of 7 of the dimensions go to zero.

Does this sound anything like my seven dimensions of a Calabi-Yau space to you? Do you think that's a coincidence? I don't.

 

Also, please can you explain what you think a Calabi-Yau space is if it doesn't have dimensions?

 

Witten did actually know what he was doing including supergravity.

Edited February 21, 2014 by Schneibster

[Sensei]

On Edit: Hmmm, maybe it's in The Cosmic Landscape.

 

 

The Cosmic Landscape by Susskind is about multiverses as answer why some constant have value as we know.

[Schneibster]

 

The Cosmic Landscape by Susskind is about multiverses as answer why some constant have value as we know.

 

He's got a really good overview of physics and physical cosmology before he gets to the multiverse stuff. You really want to pay attention. If you want to be a professional physicist, it won't help you, but if you just want to be an amateur and have a clue WTF they're talking about, you'll find it helpful, I hope.

[Sensei]

Professional physicists would concentrate on finding the real answer why constant have value such as Compton frequency. Mathematic analysis supported by indispensable experiments.

Propagation of idea of multi universes, parallel universes, bubbling universes (different regions of same universe with different physical constants) is not possible to be experimentally confirmed.

So it's not even a science, when you can't make an experiment verifying your theory and you just have to believe..

 

[Schneibster]

Sensei, your argument is as good against string physics. Did you intend it to be?

 

Not to mention, have you heard of the Hercules-Corona Borealis Great Wall? It looks like the Great Edge of the Great Bubble to me. And have you heard about the latest one, that they found with GRBs? It's ten times bigger still, and ten times farther away.

 

The universe is huge bubbles of emptiness surrounded by a minor froth of mass that makes galaxy clusters.

Edited February 21, 2014 by Schneibster