No one said they were free floating On Fri, Oct 26, 2012 at 7:55 PM, Stephen P. King <[email protected]> wrote: > Dear Richard, > > 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) 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. > > 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 <[email protected]> > 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_theory > > Hi Richard, > > Could you cut and paste the specific description that answers Brent's > question? > > > On Fri, Oct 26, 2012 at 3:01 PM, meekerdb <[email protected]> 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 > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en.
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