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

Dear Richard,From the quote below: "it is expected that the 10-dimensional space-time of stringtheory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a6-dimensional space X."This "local product" operation, represented by the 'x' is the act of adding twomanifolds, 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 compactedones are such that any motion (a translational transformation within M^3,1) shifts fromone local 6d manifold to another 6d manifold. The 6d compactified manifolds are Plancksized 6d tori 'glued' (using the math of fiber bundles<http://mathworld.wolfram.com/FiberBundle.html>) to each and every point in the M^3,1space. 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 oftime 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

On 10/26/2012 6:36 PM, Richard Ruquist wrote:The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: "Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, 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 . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world." The 6d space is tiny indeed, said by Yau in his book "The Shape of Inner Space" to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King<stephe...@charter.net> wrote:On 10/26/2012 4:31 PM, Richard Ruquist wrote:Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theoryHi Richard, Could you cut and paste the specific description that answers Brent's question?On Fri, Oct 26, 2012 at 3:01 PM, meekerdb<meeke...@verizon.net> wrote:On 10/26/2012 5:08 AM, Richard Ruquist wrote:No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks.Do you have a reference that describes this 'embedding'? Brent-- Onward! Stephen --You received this message because you are subscribed to the Google Groups "EverythingList" group.To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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