How small could the 4Ds be Out of 11Ds?

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Many books and threads state that the 7 other dimensions are really small. For the 11D model to work, how small could the other 4 (x,y,z,t) theoretically/mathematically be for a stable universe model?
Tardis
 

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tardis said:
Many books and threads state that the 7 other dimensions are really small. For the 11D model to work, how small could the other 4 (x,y,z,t) theoretically/mathematically be for a stable universe model?
Tardis

Well, no smaller than the current radius of the universe, for x, y, and z, and 13.5 billion years, for t. Dimensions of the visible universe, you know.
 
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Is that really true? It seems as if t was 1 year less last year and x,y,z (the observable or known universe) some percent of a light year smaller. So the 4Ds would seem to be possible at a size less than it is today in the 11D model. I was wondering whether there was a mathematical/theoretical limit as to how small one could make x,y,z & t and still have an 11D model that is possible. Is there some size (on the small side) for x,y,z & t at which the 11D model would not be possible?

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tardis said:
Is that really true? It seems as if t was 1 year less last year and x,y,z (the observable or known universe) some percent of a light year smaller. So the 4Ds would seem to be possible at a size less than it is today in the 11D model. I was wondering whether there was a mathematical/theoretical limit as to how small one could make x,y,z & t and still have an 11D model that is possible. Is there some size (on the small side) for x,y,z & t at which the 11D model would not be possible?

T
Then the question is how small could the visibile dimensions be in the big bang. The classical answer is zero - a singularity. But some quantum cosmologies show no singularity, but a minimum around Planck length for the spatial dimensions and Planck time for the time.
 
Don't forget Planck scale represents a maximum energy density, So there is also the question of how hot the Universe could get and be stable. The trajectory for the expanding Universe would be from a hot point to a cold void.

Then on the question of stability, I think this is a good question from a systems point of view. In any self-organising system, you need a certain amount of stuff to make a context. With a quantity of context, new stabilising qualities can emerge. For example, an isolate iron atom is free to point its magnetic field in any direction. But a group of iron atoms would break this symmetry and line-up as a magnetic system.

By analogy, a single Planckian point could not show the system properties of a Universe. You would have to have a certain expanse of spacetime for locations to be stabily distinguished from motions. A singularity does not make physical sense. But neither does the Planck scale, except as a most unstable fluctuation.

These kinds of considerations seem a reason to like approaches such as Linde's who say the Universe starts not at Planck scale but at least a few orders of magnitude larger as a localised cooling in the inflation field. A patch large enough to have both locations and motions. The beginnings of discreteness and continuity as asymptotic bounds.

In this scenario, I think the string dimensions start "large" and contract to Planck scale while the spatial dimensions expand away in the other direction. So you have a divergence from an initial middle ground with strings shrinking to make the smallest grain and the spatial dimensions expanding towards their own global limit.
 
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Thanks to both of you for taking the time to share. This is just what I was looking to find. It provides a several points to continue my reading. Glad to see that there are views on stability - this just seemed like a fertile area for consideration. With little in the general science and physics publications for the general public on this aspect, it is new ground to me. As a newbie, Linde's approach sounds interesting and this sends me back to more reading.
Tardis
 
To avoid any confusion, Linde is not taking a systems approach as such. But he does switch round the usual reductionist story in cosmology so that instead of the universe being a big bang from a planck-scale fluctuation, it is a local random codensation within an infinitely large inflaton field.

Instead of getting something very small out of nothing, Linde is saying something relatively small sprang out of something already incredibly large.

http://www.stanford.edu/~alinde/
 

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