Calabi-Yau Manifolds

woodchip · Post by **woodchip** » Sat Sep 05, 2009 8:48 am

Nope, not anything involving the ethical treatment of engines or carburetors so gear heads need not read on.

In a attempt to keep my aging brain from ossifying completely, I've started to read up on the why and how of the universe. So one of the things that intrigues me are Calabi-Yau Manifold (c-ym from here on).

As I understand it so far, c-ym's contain as many as 6 more dimensions beyond our standard 3 + 1 (time) dimensions. My first question would be, does a c-ym have the extra 6 along with the four we know about or would our known 4 dimensions be excluded?

Next thing I am unclear on is some researchers state a c-ym exists everywhere in visible space as infinitely small specks, yet others say our universe sits on a 3 dimensional brane which in turn fits inside a c-ym. So which is true? Or are both true?

Lastly, for now, does anyone have any concept of how the additional 6 dimensions may be defined? Pressure, potential energy?

Will Robinson · Post by **Will Robinson** » Sat Sep 05, 2009 11:27 am

Not sure but if you find all the socks that went into my clothes drier but never came out let me know....

BlueFlames · Post by **BlueFlames** » Sat Sep 05, 2009 2:11 pm

Can't help much on this subject, but....

Lastly, for now, does anyone have any concept of how the additional 6 dimensions may be defined? Pressure, potential energy?

You can't really try to think of additional spacial dimensions (beyond length, width, and depth) as other physical quantities. There isn't any way for us to perceive those extra spacial dimensions, so it's incredibly difficult to try to describe what they are. You can try to imagine how a nine/ten-dimensional object can interact with a three-dimensional universe, though.

Imagine existing in a two-dimensional plane. You can see and move up, down, forward, and back (and along the diagonals in between). Length and width are familiar concepts, but depth doesn't exist. Three-dimensional objects, in the universe around you, are typically beyond perception, unless they interact with the plane on which you exist, and even then, you won't be able to see them as three-dimensional objects. Consider a basketball, being thrown through your plane of existance: Initially, there won't be anything to see, while the ball is en route. When it makes first contact, it will appear as a point, that will expand into a circle, and continue to grow. Once the ball is halfway through, the circle will begin to contract, until finally, it vanishes.

When investigating objects that exist in more than three spacial dimensions, that's the kind of interaction that is sought: something that is briefly perceived and then vanishes, not because its mass or energy have ceased to exist, but because it has moved outside of the spacial dimensions in which the observer exists.

Anyway, enjoy the String Theory. I got out of studying Physics, while that was still way above my head.

Spidey · Post by **Spidey** » Sat Sep 05, 2009 2:27 pm

Two dimensions are impossible.
Three dimensions are an illusion.
The entire universe and every object in it consist of infinite dimensions.

Insurrectionist · Post by **Insurrectionist** » Sat Sep 05, 2009 2:43 pm

Still it's only a theory. It will remain a theory until proved other wise. One answer is that they're rolled up into such a small shape that they're unobservable by humans.

Tunnelcat · Post by **Tunnelcat** » Sat Sep 05, 2009 2:50 pm

OUCH! My brain, my brain! Stack overflow!

http://bccp.lbl.gov/dimensions.html

Foil · Post by **Foil** » Sat Sep 05, 2009 2:58 pm

Sounds like woodchip's been reading about string theory (for which Calabi-Yau manifolds are sometimes used). Topologically interesting stuff, although I don't think much of string theory in general.

To answer woody's questions, though:

woodchip wrote:does a c-ym have the extra 6 along with the four we know about or would our known 4 dimensions be excluded?

Generally speaking, C-Ym manifold is a class of manifold, so it could potentially be any number of dimensions.

I'll assume you're asking about the specific application to string theory, though. In that case, from what I can tell, the idea is that our physical observable space is included.

woodchip wrote:Next thing I am unclear on is some researchers state a c-ym exists everywhere in visible space as infinitely small specks, yet others say our universe sits on a 3 dimensional brane which in turn fits inside a c-ym. So which is true? Or are both true?

My understanding (again, it's been a while for me) is that they're saying both. One, that all ten dimensions (four we know, plus six 'unseen'/'compact') can be modeled by a C-Ym. Two, that the six extra dimensions are satisfied by a C-Ym structure.

woodchip wrote:Lastly, for now, does anyone have any concept of how the additional 6 dimensions may be defined? Pressure, potential energy?

From what I recall of string theory, those extra dimensions are only defined mathematically; they don't have any common physical analogs

That's one of the big issues I have with string theory; it's well-defined mathematical stuff, very interesting... but there's very little real evidence for it.

Tunnelcat · Post by **Tunnelcat** » Sat Sep 05, 2009 3:26 pm

That's the rub. How can we as humans, who only see things in 3 dimensions, even prove to ourselves that multiple dimensions exist when we can only see the universe from our limited frame of reference? Like you said Foil, it can be done mathematically, but not in any way we can see, sense, experience or measure physically.

Duper · Post by **Duper** » Sat Sep 05, 2009 3:39 pm

the same can be said of atoms....

Tunnelcat · Post by **Tunnelcat** » Sat Sep 05, 2009 3:57 pm

We can almost see atoms with electron microscopes.

Duper · Post by **Duper** » Sat Sep 05, 2009 4:25 pm

but atoms were theorized for centuries. In fact millenniums. It's only been recently that's we've had that ability.

You start somewhere.

Will Robinson · Post by **Will Robinson** » Sat Sep 05, 2009 5:56 pm

BlueFlames wrote:...
Imagine existing in a two-dimensional plane.... ...Consider a basketball, being thrown through your plane of existance: Initially, there won't be anything to see, while the ball is en route. When it makes first contact, it will appear as a point, that will expand into a circle, and continue to grow. Once the ball is halfway through, the circle will begin to contract, until finally, it vanishes.....

Wouldn't the ball appear first as a point and then as an ever growing line and then as an ever shrinking line until it became a point again and ultimately disappeared since you never get to see the circular profile from anywhere within your plane of existence?
No, wait...that is wrong.
Actually it seems like it would be invisible to you since there is no depth "dimension" from which to see a cross section of it as it passes through and you can't move off your plane to see it from any angle that shows it from the approach or departure.

My brain hurts from trying to figure this out....
I think two dimensions can only exist for someone living in three or more dimensions. Nothing can exist in two dimensions.

Spidey · Post by **Spidey** » Sat Sep 05, 2009 6:33 pm

Exactly, 2 dimensions are impossible, even when you try to use your imagination, you can see the problem.

Woody, I would have to say that all the dimensions would have to be defined the same as the other three IE: spatial dimensions. You would simply IMHO just give them names. Height, width, depth, splarg, shnitt & blaggg.

Once you realize that there are more than 3 dimensions, and I have heard scientists talk about all kinds of numbers, 6, 9...23,

you are on your way to getting to the truth.

AlphaDoG · Post by **AlphaDoG** » Sat Sep 05, 2009 6:49 pm

There are exactly 29 dimensions of love. (according to eHarmony)

woodchip · Post by **woodchip** » Sun Sep 06, 2009 1:16 pm

Well if time is considered a dimension, would not motion (speed) be a dimension as speed affects time?

If a warp drive engine were ever developed would not the drive place you in another dimension when activated?

TigerRaptor · Post by **TigerRaptor** » Sun Sep 06, 2009 1:21 pm

AlphaDoG wrote:There are exactly 29 dimensions of love. (according to eHarmony)

One of them is through the stomach.

Grendel · Post by **Grendel** » Sun Sep 06, 2009 5:34 pm

woodchip wrote:Well if time is considered a dimension, would not motion (speed) be a dimension as speed affects time?

No, motion is a 3D transition in through the 4th dimension (time), effectively an object in 4D space-time.

woodchip wrote:If a warp drive engine were ever developed would not the drive place you in another dimension when activated?

Not really, it would place you in a finite space-time region.

woodchip · Post by **woodchip** » Sat Sep 12, 2009 6:12 am

Well, going to throw a wrinkle in here. Seem a researchers is postulating that some people can \"see\" time just as some people see letters in color. The condition is known as Synaesthete:

\"a condition caused by an unusually high number of connections between two areas of the brain's sensory cortex, making two senses inseparable. \"

http://news.bbc.co.uk/2/hi/science/nature/8248589.stm

So the question is raised (at least in my fertile mind), that if one can mix the senses manually...say through gene manipulation or drugs...can we start experiencing those different manifolds? Were the old acid heads tripping out on LSD experiencing something more than just hallucinations?

Calabi-Yau Manifolds

Calabi-Yau Manifolds

Re:

Re:

Re: