Warped Dimensions-Fridgers Cylinder & Circle Example
Posted: 06.09.2003, 19:50
I moved this from the Unicorn thread so it will have a place of its own. 
Great example Fridger. Yes, that truly would be "warped".
Now, as usual, there are questions
...
Are the sheet (our 4 dimensions) and the circle (warped dimension) physically connected or attached to each other? If so, that would mean our four dimensions should also be warped, which they do not appear to be, at least to us. Or, a better term would be "combined", as half of our universe would be combined with the other half, as the circle was folded into 1/2 it's original size.
Thus, I would assume that our dimensions are *not* attached to the warped dimension.
But, if they are *not* connected, then why would our universe want to wrap itself around the shape of the circle? Or did the circle initially shape itself to the interior of the cylinder (our universe)?
It would also be interesting to find out how we might, or are, interacting with (directly or indirectly) these warped extra dimensions (WEDs). Such as, what kind of measurements can we take (temp, density, composition, etc.?), how would they be, or are they performed, and what are we "expecting" to see / find in these measurements?
Can we currently create WEDs, or only "non-warped" extra dimensions? Or are *all* extra dimensions "warped" by definition?
Are they observable?
If we can create millimeter size extra dimensions, can we create even bigger ones? Or are we simply "coaxing" existing microscopic extra dimensions to become "large", meaning one millimeter, in a specific area we define?
Thank you Fridger!
-Don G.
PS. Does the name James Stadelmann (Physicist) ring any bells, from the years past? He is a somewhat short, German fellow, who used to work at an accelerator in Illinois (operations), back in the 60's or 70's I think.
t00fri wrote:Mathematically the cylinder geometry is said to factorize into the 2d surface sheet and the circle.
But suppose I decide to sew the upper half and the lower half circle together ( i.e. identify it), then mathematicians would call the resulting geometrical object an "orbifold". This horrible thing would be a warped geometry, for example!
Got at least a feeling what this is up to?
Great example Fridger. Yes, that truly would be "warped".
Now, as usual, there are questions
...
Are the sheet (our 4 dimensions) and the circle (warped dimension) physically connected or attached to each other? If so, that would mean our four dimensions should also be warped, which they do not appear to be, at least to us. Or, a better term would be "combined", as half of our universe would be combined with the other half, as the circle was folded into 1/2 it's original size.
Thus, I would assume that our dimensions are *not* attached to the warped dimension.
But, if they are *not* connected, then why would our universe want to wrap itself around the shape of the circle? Or did the circle initially shape itself to the interior of the cylinder (our universe)?
It would also be interesting to find out how we might, or are, interacting with (directly or indirectly) these warped extra dimensions (WEDs). Such as, what kind of measurements can we take (temp, density, composition, etc.?), how would they be, or are they performed, and what are we "expecting" to see / find in these measurements?
Can we currently create WEDs, or only "non-warped" extra dimensions? Or are *all* extra dimensions "warped" by definition?
Are they observable?
If we can create millimeter size extra dimensions, can we create even bigger ones? Or are we simply "coaxing" existing microscopic extra dimensions to become "large", meaning one millimeter, in a specific area we define?
Thank you Fridger!
-Don G.
PS. Does the name James Stadelmann (Physicist) ring any bells, from the years past? He is a somewhat short, German fellow, who used to work at an accelerator in Illinois (operations), back in the 60's or 70's I think.