How does Calabi-Yau space blend into ordinary 3-space?

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How does Calabi-Yau space "blend" into ordinary 3-space?

Hi there,

I'm wondering about the following:

Assume that string theory is more or less correct and that particular 6-dimensional Calabi-Yau manifold(s) are in fact extra dimensions of spacetime.

Do physicists / mathematicians already understand how this compact space "blends" into the long/extended 3-space that we observe?

I'm not really talking about compactification (or am I?) but more wondering if we are treating the 6-space and 3-space separately or if they influence one another mathematically (a blending of sorts).

My view is that there must be some sort of "blending" since an electron (a presumed string) indeed propagates through 3-space.

Does anyone have any relevant thoughts / sources they wish to share?

Thanks
 

Answers and Replies

  • #2
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Hi there,

Do physicists / mathematicians already understand how this compact space "blends" into the long/extended 3-space that we observe?

There is no such thing as blending. Analogously the dimension "height" (with coordinate "z", say) does not "blend" into the two orthogonal dimensions with coordinates "x" and "y".
 
  • #3
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So all 9 dimensions are orthogonal to each other?

Thank you for your reply.
 
  • #4
415
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So all 9 dimensions are orthogonal to each other?

Loosely speaking, yes, that's what "dimension" means.

I spare you a more precise definition that is needed when spaces are curved.
 
  • #6
dpa
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This is a helpful illustration

I don't like the way that specific model, there!:confused:
or the calabi-yau manifold itself, more precisely, as representing higher dimensional manifold!
:confused:
Because, you see, any point on that manifold can be located by three coordinates, sufficiently.

And is not number of coordinates needed to accurately locate an point/event, or whatever you call it in more than 4 higher dimensional manifold, more precise than number of perpendicular axes?

So, is not it 3-dimensional. and how come it be more than three dimensional! Merely because of the distortions and so on?

I dont know much and please clarify me if i am wrong!:blushing:
 
  • #7
545
3


I don't like the way that specific model, there!:confused:
or the calabi-yau manifold itself, more precisely, as representing higher dimensional manifold!
:confused:
Because, you see, any point on that manifold can be located by three coordinates, sufficiently.

And is not number of coordinates needed to accurately locate an point/event, or whatever you call it in more than 4 higher dimensional manifold, more precise than number of perpendicular axes?

So, is not it 3-dimensional. and how come it be more than three dimensional! Merely because of the distortions and so on?

I dont know much and please clarify me if i am wrong!:blushing:

Because the illustration is not how Calabi-Yau manifolds really look like... it is merely an illustration of 3D projection of a higher dimensional object.
 
  • #8
bapowell
Science Advisor
Insights Author
2,243
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I don't like the way that specific model, there!:confused:
or the calabi-yau manifold itself, more precisely, as representing higher dimensional manifold!
:confused:
Because, you see, any point on that manifold can be located by three coordinates, sufficiently.

And is not number of coordinates needed to accurately locate an point/event, or whatever you call it in more than 4 higher dimensional manifold, more precise than number of perpendicular axes?

So, is not it 3-dimensional. and how come it be more than three dimensional! Merely because of the distortions and so on?

I dont know much and please clarify me if i am wrong!:blushing:
Yeah, it's because we can't draw pictures in 10 dimensions. You'll have to make do, and get used to looking at, lower dimensional analogs of higher dimensional spaces. For example, in this illustration, the 2D grid is meant to represent our 3D space. The Calabi-Yau is given a 3D perspective in this illustration, making it the analog of a 4D space. Of course, this fails miserably to convey the full 10 dimensions of the true space; this illustration is merely meant to show you how the compactified extra dimensions are situated relative to the three large dimensions that we know and love.
 

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