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 <stephe...@charter.net> 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 <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
>>>
>>> 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_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 <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
>
>
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