Well, I admit that you said that. I said they had a rather crystalline structure. And you repeated my remark. If you think they are free floating, then we are in disagreement. Richard
On Fri, Oct 26, 2012 at 9:21 PM, Stephen P. King <[email protected]> wrote: > Hi Richard, > > OK, then where are we in disagreement? > > > On 10/26/2012 8:05 PM, Richard Ruquist wrote: >> >> 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. > -- 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.
