Quote:
Originally Posted by Michael Mooney
Please explain and document (this is a formal request) how seven of the eleven "dimensions" in String/M-theory (after 3-D space and "elapsed time for all movement"... 4-d) are derived and what there referents in the observable cosmos are.
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For a detailed explanation will require more math than I think you are willing to bear
(or I am able demonstrate with proper authority). You might consult a book by Michio
Kaku on M-Theory (though I admit, I have struggled to get past page 30).
I will say the following: the Space(s) as a Subspace of a larger Vector space are treated
together as a Direct Sum when with respect to Dimension as follows
For M an 11-dimensional Vector space can be broken into V a 4-dimensional space and
U a 7-dimensional space. So the larger space can be formed as Direct Sum
M = V + U => 11 = 4 + 7
You can create a vector space when the underlying basis can form a group.
Our 4-dimension space (3 space, 1 time) is Isomorphic to the Quaternion Division Algebra (1, i, j, k).
Equivalently 7-dimensional space is Isomorphic to the Octonion Division if adding 1
dimension (Octonians are of order 8). Octonians along with other order-8 Alternative
Algebras (E8 for instance) are all Isomorphic to Tensors (often used in GR).
So for 11-dimensions (in order to work with Supergravity - which is a Supersymmetric
Gravity representation) for strings (or M-Theory).
BTW one of the variants of String Theory is Heterotic (E8 x E8) String which is the closest
String Theoretic representation of Gravity.
I learned from a book by Roger Penrose that recently Ed Witten has considered adding
one more dimension an to consider using the Group F12 (order 12 group) yielding a
12-dimensional Theory.
Alternately Ed has considered as of 2005-2006 to incorporate Twistor Theory in with
String Theory (M-Theory). Twistors is a representation where the coordinated are
Complexified (each coordinate is complex value instead of Real).
The above does not really do M-Theory justice and would require a whole thread itself and
an actual String Theorist to give the results.
Sad for you is it will require more math than most are willing to stomach (let alone
comprehend). This is the best I could do.
maddog
Moderation Note: Responses concerning math's place in physics were moved to "Discussion of math’s place in physics from a thread on cyclic cosmology" because they are off topic in this thread
