On Fri, Oct 26, 2012 at 6:36 PM, Richard Ruquist <yann...@gmail.com> 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.
"Compactification - Since all of us experience only 3 spatial and 1
temporal dimensions, the 10 and 26 extra-dimensions have to be hidden
under some schemes. One of the two alternatives is to roll them up
into very small size not observable even under a very powerful
microscope. The other one is to consider our existence on a 3 brane
floating in the bulk of ten spatial dimensions. The first alternative
is called compactification. It is more complicated than merely
shrinking the size (of the dimensions). Even in the very simple case
of a (4+1) toy model, compactification to a small circle of radius R
produces particle in the 3-D space with mass = n/R, where n is an
integer. It manifests itself as a scalar particle (spin 0) obeying the
Klein-Gordon equation. Compactification of the 16 extra-dimensions for
the bosonic string, produces the gluon and electroweak gauge fields.
Compactification of the remaining 6 extra-dimensions breaks the
Heterotic string symmetry down to the point where the hadrons and
leptons of more conventional theories are recovered. Viewed from a
distance, the symmetry-broken Heterotic strings look just like
familiar point particles - but without the infinities and anomalies of
the particle approach. In order to maintain conformal invariance
(i.e., the world sheet should remain unchanged by relabeling), these 6
extra-dimensions have to curl up in a particular way - a more
promising one is the Calabi-Yau manifold (see more in
"Compactification") as shown in Figure 12, where each point stands for
a 3-D space.
Figure 12 Calabi-Yau Space "
The keys words are " produces particle in the 3-D space with mass".
The picture of the compact manifolds, somewhat like a crystalline
structure, did not copy over.
More: "Calabi-Yau Manifold - As mentioned in the section of
"Calabi-Yau Manifold for Dummies", all the above-mentioned
requirements are satisfied by the Calabi-Yau manifold as if it is
"made to order" for the occasion. By the way, it also correctly
reproduce the three generations for the fermions, and is itself a
solution of the 6-D field equation in General Relativity (producing
The word embedding appears in this reference: "Another way to compute
g is through "embedding" the Calabi-Yau manifold in a higher
dimensional background space. But so far no one has been able to work
out the coupling constant g or mass for any fermion. Anyway, this is
one example of the attempts to derive fundamental constants in the 3+1
large dimensions from the 6 dimensional compactified space."
Bottomline, I am not satisfied with what I am able to extract from
these references anything to satisfy your criticisms, or even my
concerns. I am afraid that I have been influenced by the "picture" of
the Compact Manifolds as a periodic structure of 6d particles in 3D
> 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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