Exploring Branes: Insights into Gravity and the Universe

[RuroumiKenshin]

I have a question about branes...
#1: Why can't nongravitational fields escape this brane, and gravity can?
I've read that some gravitons, and other particles, actually escape this brane. Where do they go? This implies an "outside" of this universe. Could this universe be a subuniverse?
I also read something about something happening to the brane's surface, making it look like its expanding. Anyone know more about this?

 

[damgo]

There's no outside the universe -- branes usually arise within the context of string/M-theory, where they are just higher-dim analogues of strings. A p-brane is a p-dimensional object (just like a string is a 1-dim object) in the universe, which is 10+1 dimensional in M-theory.

That's as much as I know... can't answer the other q's.

 

[RuroumiKenshin]

Have you heard about the "no boundary" proposal by Stephen Hawking? I don't know if its an official proposal or anything, but I read it in his book "The Universe In a Nutshell". I believe it contradicts the brane theory...but I wouldn't dare try and make an unsubstantiated argument with SH! So if you have, I'd like to work this out properly. If you haven't heard of the proposal, I'd be more than happy to explain it to you.

 

[pelastration]

Subuniverse ... yes I believe so.
But branes theory is postulating that two branes join to create a new universe. Why not close them from start ... and starting with a tube.
That tube penetrates itself creating that way a new dimension (when the membran is unbreakable and infinite stretchable). That membrane will create by this manifolding mechanism: STRINGS. So strings are created by the membrane itself.

Matter and energy are then restructed nothingness.

more: http://www.hollywood.org/cosmology

Why make it difficult when we can do it (and understand it) easy?

 

[Eh]

MajinVegeta,

The no boundary proposal works with 4 dimensions, and doesn't really have anything to do with M theory. The brane models, where the existence of additional branes has been postulated to explain the weakness of gravity, is.

The reason why normal matter and radiation cannot escape the brane, is because the fundamental particles (strings) are attached to it on each end. It's like gluing pieces of string at each end to a sheet of paper. As they wiggle about, they cannot leave the paper. The graviton is said to be a closed loop of string, and is not bound to the brane on either end. Thus, gravity can move freely between branes, while matter and energy cannot.

 

[Loren Booda]

I find the model of discontinuous open strings attached to branes arbitrary and awkward to visualize.

Branes are a manifestation of extradimensions on the macroscopic level, like strings are on the microscopic.

 

[CJames]

But I thought that, at least in most string theories, that all strings were closed? Aren't they? Do you mean like the difference between wound strings and unwound strings? (Strings wound completely around a dimension of spacetime.)

I find the model of discontinuous open strings attached to branes arbitrary and awkward to visualize.

LOL. I find six dimensional surfaces wrapped around infinitesimally thin vibrating loops difficult to visualise.

Branes are a manifestation of extradimensions on the macroscopic level, like strings are on the microscopic.

Heh? My brain hurts. I thought branes existed inside of Calibi-Yau forms, which are very small. Didn't they? I think a few neurons just popped out.

 

[RuroumiKenshin]

What on Earth is a callibi-yau??

Branes are not extrademensions that are visible at a microscopic level. They are actually of a proportional size relative to our brane/universe, 4 demensionally speaking*. Have you heard of the fact that there is hypothetically, a shadowing brane? Hawking corresponds this with dark matter.

 

[CJames]

What on Earth is a callibi-yau??

A Calibi-Yau form is the 10 to 11 dimensional view of the universe that arises when we view it on a small scale. Essentially, they are tiny, folded up dimensions of spacetime. Imagine we thought the universe was 1-dimensional (just to help you visualize this.) Imagine we then discovered that there was in fact a second, circular dimension, so that our universe was actually like the surface of a garden hose. This tiny second circular dimension is present at every point along the "one-dimensional" universe we experience. In the same way, in the real world (supposedly), every point in four-dimensional spacetime is attatched to a very complicated, multidimensional topological form called a Calibi-Yau form or space. The shape of this form affects how strings vibrate, and is thus vital to the laws of physics in our universe.

The reason I though branes were microscopic was because I have heard theories of them wrapping around particular segments of a Calibi-Yau form, which to me makes it seem like they must be microscopic. Maybe that assumption was premature.

 

[Mentat]

Originally posted by CJames
But I thought that, at least in most string theories, that all strings were closed? Aren't they?

No, I think there are two (but it may just be one) string theories postulate the existence of "open" strings. However, M-theory unifies them, by showing that both view are just different ways of looking at the same thing (duality).

LOL. I find six dimensional surfaces wrapped around infinitesimally thin vibrating loops difficult to visualise.

As Michio Kaku points out (in his lecture, Journey Through The Tenth Dimension), humans cannot visualize a reality that is consistent of dimensions, other than the four that we are used to. This is because (according to Prof. Kaku) we (humans) have spent our entire existence, mastering our conception of the three spatial dimensions that we normally speak of. Thus, our brains evolved to be very good at concpetualizing three-dimensional spatial reality, but they (our brains) our pretty well useless in conceiving of another spatial dimension. That's why the mathematics is so difficult - no one can ever visualize what it is they are describing.

Heh? My brain hurts. I thought branes existed inside of Calibi-Yau forms, which are very small. Didn't they? I think a few neurons just popped out.

I recommend a hot patch .

Branes do, sort of, exist within Calabi-Yau models. You see, the string is only a [one-dimensional] "string" in three-dimensional (spacial) reality. If you add another spatial dimension, then the string gets "thicker", or - rather - becomes a two-dimensional membrane. At least, I think that's how it works.

 

[pelastration]

Calabi-Yau space:

1. On my website - links: http://hollywood.org/cosmology/links.html (two images)
Or check on google.com (search on images = always very usefull) and you find same two images.

 

[CJames]

Yeah Mentat, I'm pretty sure that's how it works. It's just that I'd never heard branes were macroscopic. And since they can exist inside parts of Calibi-Yau forms I'm really confused.

 

[RuroumiKenshin]

The reason I though branes were microscopic was because I have heard theories of them wrapping around particular segments of a Calibi-Yau form, which to me makes it seem like they must be microscopic. Maybe that assumption was premature.

Branes are not demensions. A brane is a 4D surface, which is further occupied by folded up demensions.

So a callibi-yau(sp?) is basically is the perspective of the 10th and 11th dimensions through a certain form, the Callibi-Yau?

 

[CJames]

Branes are not demensions. A brane is a 4D surface, which is further occupied by folded up demensions.

Well, no branes aren't dimensions, I don't think I said that. But they come in multiple forms. In fact, I think a string is called a 1-brane. (Maybe it's 0-brane, or maybe I'm just way off with that one.) But I know for sure that they come in different dimensions, hence the "p-brane" label.

So a callibi-yau(sp?) is basically is the perspective of the 10th and 11th dimensions through a certain form, the Callibi-Yau?

Okay, the correct spelling is Calabi-Yau, sorry about that. You've got the basic idea down, but I don't think I'm quite explaining it right. In string theory there are 10 dimensions. In m-theory there are 11. So in Calabi-Yau forms are 10 or 11 dimensional, respectively. A Calabi-Yau form is the shape the universe takes on, in multiple dimensions, close to the Planck scale. We don't know the exact shape of our universe's Calabi-Yau form, because there is an infinite set of forms that work with our laws of physics. (But not every Calabi-Yau form we imagine necessarily works with the laws of physics, make sense?)

 

[instanton]

General definition of Calabi-Yau space is: A complex manifold with Ricci-flat Kaehler metric. But, I don't think it's important in this discussion. Importance in string theory is the fact that it is considered as a possible geometry of extra 6 dimension which is supposed to be compactified. It is desirable to have a Ricci flat compact 6 dimension for flat 4 dimensional universe (or Ricci flat 4 dimensional universe.) To have a unbroken N=1 supersymmetry in 4 dimension the compactified dimension also have to be Kaehler.

For M theory compactification we need 7 dimensional manifold, which Calabi-Yau isn't. (Being complex manifold C-Y is always even dimensional.) Currently popular choice is a 7 dimensional class of manifold called singular G_2 manifold. It is a special class of manifold with holonomy belong to G_2. Anyway, it is (roughly) often a product of some singular manifold with other regular one.

Instanton

 

[drag]

Greetings !

Originally posted by CJames
Okay, the correct spelling is Calabi-Yau, sorry about that. You've got the basic idea down, but I don't think I'm quite explaining it right. In string theory there are 10 dimensions. In m-theory there are 11. So in Calabi-Yau forms are 10 or 11 dimensional, respectively. A Calabi-Yau form is the shape the universe takes on, in multiple dimensions, close to the Planck scale. We don't know the exact shape of our universe's Calabi-Yau form, because there is an infinite set of forms that work with our laws of physics. (But not every Calabi-Yau form we imagine necessarily works with the laws of physics, make sense?)

I assume you're drawing that "extensive" info from
the one main source I also remmember it from...
(A good book btw.)

Anyway, if memory serves me right then prof. Greene
says that M theory which deals with 11 dimensions
is added another dimension not to the Calabi-Yau
forms but the strings themselves that become two
dimensional. Also, I believe he said that there are
phousands of possible Calabi-Yaus to choose from that
can explain the physics in our Universe - not an
infinite amount. (I hope my memory is good... )

Live long and prosper.

 

[CJames]

I assume you're drawing that "extensive" info from
the one main source I also remmember it from...

Anyway, if memory serves me right then prof. Greene
says that M theory which deals with 11 dimensions
is added another dimension not to the Calabi-Yau
forms but the strings themselves that become two
dimensional.

Well, according to instanton, who I think is correct, the extra dimension is added to the Calabi-Yau form...but as he pointed out it is no loner called a Calabi-Yau form, just confusing matters more. I think you may be right about that also adding a dimension to the string, although I'm not positive.

Also, I believe he said that there are
phousands of possible Calabi-Yaus to choose from that
can explain the physics in our Universe - not an
infinite amount.

There is a finite set of general topological forms that potentially work with respect to our laws of physics, but an infinite amount of variations on each general topological form. Which is why string theorists hope to mathematically derive a C-Y form rather than just build one.

 

[damgo]

instanton -- I've seen a CY manifold defined as complex manifold with holonomy group in SU(n). I assume this is equivalent? What exactly is Ricci-flat; does that just mean the Ricci scalar vanishes everywhere?

 

[instanton]

Yes, you got it.

It was Calabi who conjectured (and proved by Yau later) that Kaeler manifold with SU(n) holonomy admit a metric that is Ricci-flat, which means, as you said, vanishing Ricci scalar everywhere.

Instanton

 

[RuroumiKenshin]

What is a SU(n) holomony?

 

[instanton]

It's a bit technical and I am not sure it is an appropriate topic to discuss in detail here. Roughly, it goes like this.
For a bundle with a structure group G, a natural connection is a one form which takes a value on the Lie algebra of G. Consider a closed loop on the base manifold. Holonomy is piecewise integral of the connection one form along the loop. What it mean in nut-shell is that it indicates how much your vector "rotate" after you parallelly transform along the loop using the connection compatible with the structure group. It is relate to curvature of the space with respect to connection. Usual metric compatible connection defines SO(n) holonomy - it really is a rotation on tangent space after you loop around.

Instanton

 

[instanton]

Originally posted by instanton
[B <snip>
Ricci-flat, which means, as you said, vanishing Ricci scalar everywhere.

Instanton [/B]

Oops, not Ricci scalar, but Ricci tensor, R_a_b = 0.

Instanton