11 Dimensions in M-Theory

Factual Questions
1

I believe the current M-Theory has that each point of spacetime is composed of 11 dimensions (1 of time, 10 of space). In our experience of the 4 dimensions (1 of time, 3 of space) we can move in one dimension (e.g. a line), two dimensions (e.g. a circle) or 3 dimensions (e.g. a Dali watch ;)). This is complete freedom of movement in these 3 dimensions. The other 6 dimensions are thought to be a Calabi-Yau* manifold at each point in 3D spacetime.

Can a point in 11-dimensional space move in Calabi-Yau space while moving in our 3D space? Would you have to rotate out of Calabi-Yau space, move in 3D, then rotate back into Calabi-Yau space?

E.g. (t[sub]0[/sub],0,0,0,[sub]0,0,0,0,0,0[/sub]) to (t[sub]1[/sub],1,2,3,[sub]0,0,0,0,0,0[/sub]) we experience as a single transition. Would (t[sub]0[/sub],0,0,0,[sub]0,0,0,0,0,0[/sub]) to (t[sub]1[/sub],1,2,3,[sub]0,0,4,5,6,0[/sub]) also be a single transition, or would it require rotating to (t[sub]0[/sub],0,0,0,[sub]0,0,0,0,0,0[/sub]), moving to (t[sub]1[/sub],1,2,3,[sub]0,0,0,0,0,0[/sub]), and then rotating to (t[sub]1[/sub],1,2,3,[sub]0,0,4,5,6,0[/sub])?

Since there is nothing special about (t[sub]n[/sub],x,y,z,[sub]0,0,0,0,0,0[/sub]) with all zeroes, it seems that you should have freedom of movement in any combination of spatial dimensions. Is this correct?

[sub]* Note that my knowledge of Calabi-Yau manifolds extends just far enough to spell it correctly.[/sub]

2

There’s no reason you couldn’t move in that way. In fact, that’s kind of essential to the model, since the whole point is that the various kinds of particles arise from strings oscillating in those various directions. So what we call a moving electron, for instance, would be a piece of string oscillating in whatever dimensions an electron oscillates in, while simultaneously moving in the dimensions we perceive.

3

So each string can oscillate at 1/2,1,2,etc of it’s natural frequency in each dimension and each oscillation is independent of the other?

We perceive no limit to our three dimensions. Are each of the other six similarly limitless or constrained to something (e.g. The Plank length)?

4

The current hypothesis is that the other dimensions are “curled up” so that they’re very small. Imagine a sheet of paper rolled in a tight tube. It’s technically 2-dimensional, but from a distance it looks like a line.

5

Since a dimension has no thickness, an unimaginably huge expanse can be curled up small. We see 14 billion light years of 3D space. Could the other curled up dimensions be 14 billion light years each in size? Or some extent that wraps back around to itself (if it does wrap around to itself) in more than a few Plank lengths?

6

By “curled up small”, folks mean that the distance you travel along that dimension before you get back to your starting point is small. There’s no meaningful way to define “curled up into a tight space”, since that means that you’re assuming that space is inside space.

And even in the conventional, curled-up-small interpretation, there’s still a heck of a lot of room larger than the Planck scale that hasn’t yet been ruled out by experiment. Plus, there are other models where some or all of the extra dimensions are large, and which propose other mechanisms by which we would remain unable to easily detect them.

7

This seems to imply that the different Calabi-Yau dimensions may have different properties. Are there specific properties that are theoretically the same or different? Size, speed of light, conservation of (angular) momentum or energy?

Have any of the fundamental properties (charge, spin, mass, etc) been theoretically assigned to one or more dimensions?

Is the graviton the only suspected closed string and one that travels between dimensions while other particles and forces are closed strings on a brane?

8

Is each open string, vibrating in the 11 dimensions, anchored to n-of-11 dimensions on one end and m-of-11 (or the same n-of-11) on the other end? This would suggest that some strings could be anchored and vibrate in dimensions other than our familiar three. Might this account for dark energy and dark matter?