No one said they were free floating
On Fri, Oct 26, 2012 at 7:55 PM, Stephen P. King <stephe...@charter.net> 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
> "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
> to get a more definitive answer to our questions.
> On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King <stephe...@charter.net>
> On 10/26/2012 4:31 PM, Richard Ruquist wrote:
> Hi Richard,
> Could you cut and paste the specific description that answers Brent's
> 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'?
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