On 10/26/2012 8:33 PM, meekerdb wrote:

On 10/26/2012 4:55 PM, Stephen P. King wrote:

Dear Richard,

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` From the quote below: "it is expected that the 10-dimensional
``space-time of string theory is locally the product M4×X of a
``4-dimensional Minkowski space M3,1 with a 6-dimensional space X."
`

` This "local product" operation, represented by the 'x' is the act
``of adding two manifolds, one of 4 dimensions and one of 6 dimensions
``for a total of 10 dimensions, thus this yields a very different
``structure from, for example, a 10d Euclidean manifold.
`` All of the local degrees of freedom are present at every point
``but the compacted ones are such that any motion (a translational
``transformation within M^3,1) shifts from one local 6d manifold to
``another 6d manifold. The 6d compactified manifolds are Planck sized
``6d tori 'glued' (using the math of fiber bundles
``<http://mathworld.wolfram.com/FiberBundle.html>) to each and every
``point in the M^3,1 space. It is not correct to think of the compacted
``manifolds (actually they are tori) as "free floating" in a 3,1
``dimensional (not 4d for technical reasons as the signature of time is
``not the same as the signature of the spatial dimensions) manifold.
``i.e. space-time.
`

`They are manifolds - just some more dimensions that happen to be
``compact. It makes no more sense to talk about them as 'free-floating'
``than to talk about altitude free floating on lat-long; it's another
``'direction', not an object.
`
Brent

I agree!
--
Onward!
Stephen
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